TSTP Solution File: SWV838-1 by iProverMo---2.5-0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : SWV838-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n022.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 19:22:25 EDT 2022
% Result : Unsatisfiable 153.61s 153.85s
% Output : CNFRefutation 153.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 491
% Syntax : Number of formulae : 3620 ( 669 unt; 0 def)
% Number of atoms : 9198 (1771 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 10661 (5083 ~;5578 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 28 ( 26 usr; 1 prp; 0-9 aty)
% Number of functors : 64 ( 64 usr; 13 con; 0-6 aty)
% Number of variables : 13137 (1032 sgn5157 !; 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,
! [X19,X20,X21,X22,X23,X24,X25,X26,X3] :
( c_Complete__Lattice_Ocomplete__lattice(X25,X26,c_COMBC(X21,X3,X3,tc_bool),c_COMBC(X22,X3,X3,tc_bool),X20,X23,X19,X24,X3)
| ~ c_Complete__Lattice_Ocomplete__lattice(X26,X25,X21,X22,X23,X20,X24,X19,X3) ),
file('<stdin>',cls_complete__lattice_Odual__complete__lattice_0) ).
fof(c_0_1,axiom,
! [X19,X20,X21,X22,X23,X38,X24,X25,X39,X26,X5,X6,X3] :
( hBOOL(hAPP(hAPP(X21,c_Complete__Lattice_Ocomplete__lattice_OINFI(X26,X5,X39,X3,X6)),hAPP(X39,X38)))
| ~ hBOOL(c_in(X38,X5,X6))
| ~ c_Complete__Lattice_Ocomplete__lattice(X26,X25,X21,X22,X23,X20,X24,X19,X3) ),
file('<stdin>',cls_complete__lattice_OINF__leI_0) ).
fof(c_0_2,axiom,
! [X19,X20,X21,X22,X23,X38,X24,X25,X39,X26,X5,X6,X3] :
( hBOOL(hAPP(hAPP(X21,hAPP(X39,X38)),c_Complete__Lattice_Ocomplete__lattice_OSUPR(X25,X5,X39,X3,X6)))
| ~ hBOOL(c_in(X38,X5,X6))
| ~ c_Complete__Lattice_Ocomplete__lattice(X26,X25,X21,X22,X23,X20,X24,X19,X3) ),
file('<stdin>',cls_complete__lattice_Ole__SUPI_0) ).
fof(c_0_3,axiom,
! [X19,X20,X21,X22,X23,X24,X25,X39,X26,X5,X6,X3] :
( c_Complete__Lattice_Ocomplete__lattice_OINFI(X26,X5,c_COMBK(X39,X3,X6),X3,X6) = X39
| X5 = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool))
| ~ c_Complete__Lattice_Ocomplete__lattice(X26,X25,X21,X22,X23,X20,X24,X19,X3) ),
file('<stdin>',cls_complete__lattice_OINF__const_0) ).
fof(c_0_4,axiom,
! [X19,X20,X21,X22,X23,X24,X25,X39,X26,X5,X6,X3] :
( c_Complete__Lattice_Ocomplete__lattice_OSUPR(X25,X5,c_COMBK(X39,X3,X6),X3,X6) = X39
| X5 = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool))
| ~ c_Complete__Lattice_Ocomplete__lattice(X26,X25,X21,X22,X23,X20,X24,X19,X3) ),
file('<stdin>',cls_complete__lattice_OSUP__const_0) ).
fof(c_0_5,axiom,
! [X19,X20,X21,X22,X23,X24,X16,X8,X25,X26,X3] :
( hAPP(X25,c_Set_Oinsert(X8,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)) = hAPP(hAPP(X20,X8),X16)
| ~ c_Complete__Lattice_Ocomplete__lattice(X26,X25,X21,X22,X23,X20,X24,X19,X3) ),
file('<stdin>',cls_complete__lattice_OSup__binary_0) ).
fof(c_0_6,axiom,
! [X19,X20,X21,X22,X23,X24,X16,X8,X25,X26,X3] :
( hAPP(X26,c_Set_Oinsert(X8,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)) = hAPP(hAPP(X23,X8),X16)
| ~ c_Complete__Lattice_Ocomplete__lattice(X26,X25,X21,X22,X23,X20,X24,X19,X3) ),
file('<stdin>',cls_complete__lattice_OInf__binary_0) ).
fof(c_0_7,axiom,
! [X2,X19,X20,X21,X22,X23,X24,X25,X26,X5,X3] :
( hBOOL(hAPP(hAPP(X21,hAPP(X26,X5)),X2))
| ~ hBOOL(c_in(X2,X5,X3))
| ~ c_Complete__Lattice_Ocomplete__lattice(X26,X25,X21,X22,X23,X20,X24,X19,X3) ),
file('<stdin>',cls_complete__lattice_OInf__lower_0) ).
fof(c_0_8,axiom,
! [X2,X19,X20,X21,X22,X23,X24,X25,X26,X5,X3] :
( hBOOL(hAPP(hAPP(X21,X2),hAPP(X25,X5)))
| ~ hBOOL(c_in(X2,X5,X3))
| ~ c_Complete__Lattice_Ocomplete__lattice(X26,X25,X21,X22,X23,X20,X24,X19,X3) ),
file('<stdin>',cls_complete__lattice_OSup__upper_0) ).
fof(c_0_9,axiom,
! [X19,X20,X21,X22,X23,X24,X8,X25,X26,X3] :
( hAPP(X25,c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)) = X8
| ~ c_Complete__Lattice_Ocomplete__lattice(X26,X25,X21,X22,X23,X20,X24,X19,X3) ),
file('<stdin>',cls_complete__lattice_OSup__singleton_0) ).
fof(c_0_10,axiom,
! [X19,X20,X21,X22,X23,X24,X8,X25,X26,X3] :
( hAPP(X26,c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)) = X8
| ~ c_Complete__Lattice_Ocomplete__lattice(X26,X25,X21,X22,X23,X20,X24,X19,X3) ),
file('<stdin>',cls_complete__lattice_OInf__singleton_0) ).
fof(c_0_11,axiom,
! [X19,X20,X21,X22,X23,X24,X8,X25,X26,X5,X3] :
( hAPP(X25,c_Set_Oinsert(X8,X5,X3)) = hAPP(hAPP(X20,X8),hAPP(X25,X5))
| ~ c_Complete__Lattice_Ocomplete__lattice(X26,X25,X21,X22,X23,X20,X24,X19,X3) ),
file('<stdin>',cls_complete__lattice_OSup__insert_0) ).
fof(c_0_12,axiom,
! [X19,X20,X21,X22,X23,X24,X8,X25,X26,X5,X3] :
( hAPP(X26,c_Set_Oinsert(X8,X5,X3)) = hAPP(hAPP(X23,X8),hAPP(X26,X5))
| ~ c_Complete__Lattice_Ocomplete__lattice(X26,X25,X21,X22,X23,X20,X24,X19,X3) ),
file('<stdin>',cls_complete__lattice_OInf__insert_0) ).
fof(c_0_13,axiom,
! [X19,X20,X21,X22,X23,X24,X25,X26,X3] :
( hAPP(X25,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))) = X24
| ~ c_Complete__Lattice_Ocomplete__lattice(X26,X25,X21,X22,X23,X20,X24,X19,X3) ),
file('<stdin>',cls_complete__lattice_OSup__empty_0) ).
fof(c_0_14,axiom,
! [X19,X20,X21,X22,X23,X24,X25,X26,X3] :
( hAPP(X26,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))) = X19
| ~ c_Complete__Lattice_Ocomplete__lattice(X26,X25,X21,X22,X23,X20,X24,X19,X3) ),
file('<stdin>',cls_complete__lattice_OInf__empty_0) ).
fof(c_0_15,axiom,
! [X43,X2,X15,X28,X29,X32] :
( c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X15,X28,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X28,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X32,X29,X28,X15)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X32,X29,X28,X15,X2,X43)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,X15,X43,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
file('<stdin>',cls_conseq_2) ).
fof(c_0_16,axiom,
! [X43,X2,X15,X28,X29,X32] :
( c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X15,X28,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X28,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X32,X29,X28,X15)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X32,X29,X28,X15,X2,X43)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,X15,X43,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
file('<stdin>',cls_hoare__derivs_Ointros_I6_J_2) ).
fof(c_0_17,axiom,
! [X15,X28,X29,X32] :
( c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X15,X28,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(hAPP(c_COMBC(c_fequal(tc_Com_Ostate),tc_Com_Ostate,tc_Com_Ostate,tc_bool),v_sko__Hoare__Mirabelle__Xescape__2(X32,X29,X28,X15)),tc_fun(tc_Com_Ostate,tc_bool),t_a),X15,c_COMBK(hAPP(X28,v_sko__Hoare__Mirabelle__Xescape__1(X32,X29,X28,X15)),tc_fun(tc_Com_Ostate,tc_bool),t_a),t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
file('<stdin>',cls_escape_1) ).
fof(c_0_18,axiom,
! [X43,X2,X15,X50,X28,X29,X32] :
( c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X15,X28,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X43,X50),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X32,X29,X28,X15,X2,X43)))
| ~ hBOOL(hAPP(hAPP(X2,X50),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X32,X29,X28,X15)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,X15,X43,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
file('<stdin>',cls_hoare__derivs_Ointros_I6_J_1) ).
fof(c_0_19,axiom,
! [X43,X2,X15,X50,X28,X29,X32] :
( c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X15,X28,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X43,X50),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X32,X29,X28,X15,X2,X43)))
| ~ hBOOL(hAPP(hAPP(X2,X50),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X32,X29,X28,X15)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,X15,X43,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
file('<stdin>',cls_conseq_1) ).
fof(c_0_20,axiom,
! [X7,X1,X2,X4,X5,X6,X3] :
( c_Nitpick_Ofold__graph_H(X4,X7,X5,hAPP(hAPP(X4,X2),X1),X3,X6)
| ~ c_Nitpick_Ofold__graph_H(X4,X7,c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X1,X3,X6)
| ~ hBOOL(c_in(X2,X5,X3)) ),
file('<stdin>',cls_fold__graph_H_Ointros_I2_J_0) ).
fof(c_0_21,axiom,
! [X7,X1,X2,X4,X5,X6,X3] :
( c_Finite__Set_Ofold__graph(X4,X7,X5,hAPP(hAPP(X4,X2),X1),X3,X6)
| ~ hBOOL(c_in(X2,X5,X3))
| ~ c_Finite__Set_Ofold__graph(X4,X7,c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X1,X3,X6) ),
file('<stdin>',cls_Diff1__fold__graph_0) ).
fof(c_0_22,axiom,
! [X7,X1,X2,X4,X5,X6,X3] :
( c_Finite__Set_Ofold__graph(X4,X7,c_Set_Oinsert(X2,X5,X3),hAPP(hAPP(X4,X2),X1),X3,X6)
| ~ c_Finite__Set_Ofold__graph(X4,X7,X5,X1,X3,X6)
| hBOOL(c_in(X2,X5,X3)) ),
file('<stdin>',cls_fold__graph_OinsertI_0) ).
fof(c_0_23,axiom,
! [X4,X9,X5,X6,X3] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(c_Set_Oimage(X4,X5,X6,X3),c_Set_Oimage(X4,X9,X6,X3),tc_fun(X3,tc_bool))),c_Set_Oimage(X4,c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X6,tc_bool)),X6,X3))),
file('<stdin>',cls_image__diff__subset_0) ).
fof(c_0_24,axiom,
! [X2,X4,X8,X5,X3] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X4,c_Set_Oinsert(X8,X5,X3),X3),X2))
| hBOOL(c_in(X8,X5,X3))
| ~ c_Finite__Set_Ofold__graph(X4,X8,X5,X2,X3,X3) ),
file('<stdin>',cls_fold1Set_Ointros_0) ).
fof(c_0_25,axiom,
! [X7,X2,X4,X6,X3] :
( X2 = X7
| ~ c_Finite__Set_Ofold__graph(X4,X7,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X2,X3,X6) ),
file('<stdin>',cls_empty__fold__graphE_0) ).
fof(c_0_26,axiom,
! [X7,X2,X4,X5,X6,X3] :
( c_Finite__Set_Ofinite(X5,X3)
| ~ c_Finite__Set_Ofold__graph(X4,X7,X5,X2,X3,X6) ),
file('<stdin>',cls_fold__graph__imp__finite_0) ).
fof(c_0_27,axiom,
! [X15,X51,X28,X52,X29,X32] :
( c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X15,X28,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X28,v_sko__Hoare__Mirabelle__Xconseq12__1(X29,X52,X28,X51)),v_sko__Hoare__Mirabelle__Xconseq12__3(X29,X52,X28,X51)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X52,X15,X51,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
file('<stdin>',cls_conseq12_2) ).
fof(c_0_28,axiom,
! [X15,X51,X28,X52,X29,X32] :
( c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X15,X28,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X29,v_sko__Hoare__Mirabelle__Xconseq12__1(X29,X52,X28,X51)),v_sko__Hoare__Mirabelle__Xconseq12__2(X29,X52,X28,X51)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X52,X15,X51,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
file('<stdin>',cls_conseq12_0) ).
fof(c_0_29,axiom,
! [X7,X4,X6,X3] : c_Nitpick_Ofold__graph_H(X4,X7,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X7,X3,X6),
file('<stdin>',cls_fold__graph_H_Ointros_I1_J_0) ).
fof(c_0_30,axiom,
! [X7,X4,X6,X3] : c_Finite__Set_Ofold__graph(X4,X7,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X7,X3,X6),
file('<stdin>',cls_fold__graph_OemptyI_0) ).
fof(c_0_31,axiom,
! [X15,X50,X51,X28,X52,X29,X32] :
( c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X15,X28,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X51,X50),v_sko__Hoare__Mirabelle__Xconseq12__3(X29,X52,X28,X51)))
| ~ hBOOL(hAPP(hAPP(X52,X50),v_sko__Hoare__Mirabelle__Xconseq12__2(X29,X52,X28,X51)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X52,X15,X51,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
file('<stdin>',cls_conseq12_1) ).
fof(c_0_32,axiom,
! [X18,X15,X27,X28,X29,X32,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OSemi(X15,X18),X27,X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X28,X18,X27,X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X15,X28,X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3) ),
file('<stdin>',cls_Comp_0) ).
fof(c_0_33,axiom,
! [X2,X9,X5,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),c_Set_Oinsert(X2,X9,X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool))),X9)) ),
file('<stdin>',cls_subset__insert__iff_4) ).
fof(c_0_34,axiom,
! [X2,X9,X5,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),c_Set_Oinsert(X2,X9,X3)))
| ~ hBOOL(c_in(X2,X5,X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool))),X9)) ),
file('<stdin>',cls_subset__insert__iff_3) ).
fof(c_0_35,axiom,
! [X2,X9,X5,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),c_Set_Oinsert(X2,X9,X3)))
| ~ hBOOL(c_in(X2,X5,X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool))),X9)) ),
file('<stdin>',cls_diff__single__insert_0) ).
fof(c_0_36,axiom,
! [X2,X49,X9,X5,X6,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),hAPP(X5,X2)),X9))
| ~ hBOOL(c_in(X2,X49,X6))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X49,X5,X6,tc_fun(X3,tc_bool))),X9)) ),
file('<stdin>',cls_UN__subset__iff_0) ).
fof(c_0_37,axiom,
! [X15,X28,X29,X32] :
( c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X15,X28,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X29,v_sko__Hoare__Mirabelle__Xescape__1(X32,X29,X28,X15)),v_sko__Hoare__Mirabelle__Xescape__2(X32,X29,X28,X15))) ),
file('<stdin>',cls_escape_0) ).
fof(c_0_38,axiom,
! [X15,X28,X29,X32] :
( c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X15,X28,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X29,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X32,X29,X28,X15)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X32,X29,X28,X15))) ),
file('<stdin>',cls_conseq_0) ).
fof(c_0_39,axiom,
! [X15,X28,X29,X32] :
( c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X15,X28,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X29,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X32,X29,X28,X15)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X32,X29,X28,X15))) ),
file('<stdin>',cls_hoare__derivs_Ointros_I6_J_0) ).
fof(c_0_40,axiom,
! [X2,X4,X9,X5,X6,X3] :
( hBOOL(c_in(hAPP(X4,X2),X9,X3))
| ~ hBOOL(c_in(X2,X5,X6))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_Set_Oimage(X4,X5,X6,X3)),X9)) ),
file('<stdin>',cls_image__subset__iff_0) ).
fof(c_0_41,axiom,
! [X4,X9,X5,X6,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X6,tc_bool)),c_Set_Oimage(X4,X5,X3,X6)),c_Set_Oimage(X4,X9,X3,X6)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9)) ),
file('<stdin>',cls_image__mono_0) ).
fof(c_0_42,axiom,
! [X2,X4,X5,X6,X3] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X6,tc_bool)),X2),X5))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_Set_Oimage(X4,X2,X6,X3)),c_Set_Oimage(X4,X5,X6,X3))) ),
file('<stdin>',cls_subset__image__iff_2) ).
fof(c_0_43,axiom,
! [X15,X51,X28,X29,X32] :
( c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X15,X28,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X28,v_sko__Hoare__Mirabelle__Xconseq2__1(X28,X51)),v_sko__Hoare__Mirabelle__Xconseq2__2(X28,X51)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X15,X51,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
file('<stdin>',cls_conseq2_1) ).
fof(c_0_44,axiom,
! [X15,X28,X52,X29,X32] :
( c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X15,X28,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X52,v_sko__Hoare__Mirabelle__Xconseq1__1(X29,X52)),v_sko__Hoare__Mirabelle__Xconseq1__2(X29,X52)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X52,X15,X28,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
file('<stdin>',cls_conseq1_1) ).
fof(c_0_45,axiom,
! [X2,X9,X5,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool))),X9))
| ~ hBOOL(c_in(X2,X5,X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),c_Set_Oinsert(X2,X9,X3))) ),
file('<stdin>',cls_subset__insert__iff_0) ).
fof(c_0_46,axiom,
! [X15,X28,X52,X29,X32] :
( c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X15,X28,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X29,v_sko__Hoare__Mirabelle__Xconseq1__1(X29,X52)),v_sko__Hoare__Mirabelle__Xconseq1__2(X29,X52)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X52,X15,X28,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
file('<stdin>',cls_conseq1_0) ).
fof(c_0_47,axiom,
! [X15,X51,X28,X29,X32] :
( c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X15,X28,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X51,v_sko__Hoare__Mirabelle__Xconseq2__1(X28,X51)),v_sko__Hoare__Mirabelle__Xconseq2__2(X28,X51)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X15,X51,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
file('<stdin>',cls_conseq2_0) ).
fof(c_0_48,axiom,
! [X8,X9,X3] : c_Set_Oinsert(X8,X9,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X3),X3,X3,tc_bool),X8),X3),X9,tc_fun(X3,tc_bool)),
file('<stdin>',cls_insert__def_0) ).
fof(c_0_49,axiom,
! [X42,X11,X9,X5,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool))),c_HOL_Ominus__class_Ominus(X11,X42,tc_fun(X3,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X42),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X11)) ),
file('<stdin>',cls_Diff__mono_0) ).
fof(c_0_50,axiom,
! [X42,X11,X9,X5,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(X11,X42,tc_fun(X3,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X42))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X11)) ),
file('<stdin>',cls_Un__mono_0) ).
fof(c_0_51,axiom,
! [X4,X9,X5,X6,X3] :
( c_Finite__Set_Ofinite(X9,X6)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X6,tc_bool)),X9),c_Set_Oimage(X4,X5,X3,X6)))
| ~ c_Finite__Set_Ofinite(X5,X3) ),
file('<stdin>',cls_finite__surj_0) ).
fof(c_0_52,axiom,
! [X11,X9,X5,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),c_Lattices_Oupper__semilattice__class_Osup(X9,X11,tc_fun(X3,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool))),X11)) ),
file('<stdin>',cls_Diff__subset__conv_0) ).
fof(c_0_53,axiom,
! [X4,X9,X5,X6,X3] :
( ~ class_OrderedGroup_Oab__group__add(X6)
| c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),X3,X6) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X4,X5,X3,X6),c_Finite__Set_Osetsum(X4,X9,X3,X6),X6)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X5))
| ~ c_Finite__Set_Ofinite(X5,X3) ),
file('<stdin>',cls_setsum__diff_0) ).
fof(c_0_54,axiom,
! [X11,X9,X5,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool))),X11))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),c_Lattices_Oupper__semilattice__class_Osup(X9,X11,tc_fun(X3,tc_bool)))) ),
file('<stdin>',cls_Diff__subset__conv_1) ).
fof(c_0_55,axiom,
! [X11,X9,X5,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool))),X11))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X11))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X11)) ),
file('<stdin>',cls_Un__least_0) ).
fof(c_0_56,axiom,
! [X11,X9,X5,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool))),X11))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X11))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X11)) ),
file('<stdin>',cls_Un__subset__iff_2) ).
fof(c_0_57,axiom,
! [X2,X9,X5,X3] :
( c_HOL_Oord__class_Oless(X5,c_Set_Oinsert(X2,X9,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X9,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X5,X9,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_psubset__insert__iff_9) ).
fof(c_0_58,axiom,
! [X2,X9,X5,X3] :
( c_HOL_Oord__class_Oless(X5,c_Set_Oinsert(X2,X9,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X9,tc_fun(X3,tc_bool))
| hBOOL(c_in(X2,X9,X3)) ),
file('<stdin>',cls_psubset__insert__iff_5) ).
fof(c_0_59,axiom,
! [X18,X15,X16,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X16),X18))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X16))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X8,X16,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X15,X18,X3))) ),
file('<stdin>',cls_atLeastatMost__subset__iff_1) ).
fof(c_0_60,axiom,
! [X18,X15,X16,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X15),X8))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X16))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X8,X16,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X15,X18,X3))) ),
file('<stdin>',cls_atLeastatMost__subset__iff_0) ).
fof(c_0_61,axiom,
! [X4,X16,X8,X3] :
( X8 = X16
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X4,c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),X16)) ),
file('<stdin>',cls_fold1Set__sing_0) ).
fof(c_0_62,axiom,
! [X11,X9,X5,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X11))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool))),X11)) ),
file('<stdin>',cls_Un__subset__iff_0) ).
fof(c_0_63,axiom,
! [X11,X9,X5,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X11))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool))),X11)) ),
file('<stdin>',cls_Un__subset__iff_1) ).
fof(c_0_64,axiom,
! [X18,X15,X16,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X15),X8))
| hBOOL(hAPP(hAPP(c_lessequals(X3),X16),X8))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X8,X16,X3)),c_SetInterval_Oord__class_OatLeastLessThan(X15,X18,X3))) ),
file('<stdin>',cls_atLeastLessThan__subset__iff_0) ).
fof(c_0_65,axiom,
! [X18,X15,X16,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X16),X18))
| hBOOL(hAPP(hAPP(c_lessequals(X3),X16),X8))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X8,X16,X3)),c_SetInterval_Oord__class_OatLeastLessThan(X15,X18,X3))) ),
file('<stdin>',cls_atLeastLessThan__subset__iff_1) ).
fof(c_0_66,axiom,
! [X8,X9,X5,X6,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X6,tc_bool)),hAPP(X9,X8)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X9,X3,tc_fun(X6,tc_bool))))
| ~ hBOOL(c_in(X8,X5,X3)) ),
file('<stdin>',cls_UN__upper_0) ).
fof(c_0_67,axiom,
! [X2,X16,X9,X5,X6,X3] :
( hBOOL(c_in(X16,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X9,X6,tc_fun(X3,tc_bool)),X3))
| ~ hBOOL(c_in(X16,hAPP(X9,X2),X3))
| ~ hBOOL(c_in(X2,X5,X6)) ),
file('<stdin>',cls_UN__iff_2) ).
fof(c_0_68,axiom,
! [X16,X8,X9,X5,X6,X3] :
( hBOOL(c_in(X16,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X9,X3,tc_fun(X6,tc_bool)),X6))
| ~ hBOOL(c_in(X16,hAPP(X9,X8),X6))
| ~ hBOOL(c_in(X8,X5,X3)) ),
file('<stdin>',cls_UN__I_0) ).
fof(c_0_69,axiom,
! [X4,X8,X5,X6,X3] :
( ~ class_OrderedGroup_Oab__group__add(X6)
| c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3,X6) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X4,X5,X3,X6),hAPP(X4,X8),X6)
| ~ hBOOL(c_in(X8,X5,X3))
| ~ c_Finite__Set_Ofinite(X5,X3) ),
file('<stdin>',cls_setsum__diff1_0) ).
fof(c_0_70,axiom,
! [X4,X8,X5,X6,X3] :
( ~ class_Ring__and__Field_Oring(X6)
| c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3,X6) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X4,X5,X3,X6),hAPP(X4,X8),X6)
| ~ hBOOL(c_in(X8,X5,X3))
| ~ c_Finite__Set_Ofinite(X5,X3) ),
file('<stdin>',cls_setsum__diff1__ring_0) ).
fof(c_0_71,axiom,
! [X39,X9,X5,X6,X3] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X6,tc_bool)),X39,X6,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X39,X6,tc_fun(X3,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,X39,X6,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
file('<stdin>',cls_UN__Un_0) ).
fof(c_0_72,axiom,
! [X2,X9,X5,X3] :
( c_HOL_Oord__class_Oless(X5,c_Set_Oinsert(X2,X9,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X2,X5,X3))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X9,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X5,X9,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_psubset__insert__iff_8) ).
fof(c_0_73,axiom,
! [X2,X9,X5,X3] :
( c_HOL_Oord__class_Oless(X5,c_Set_Oinsert(X2,X9,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X2,X5,X3))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X9,tc_fun(X3,tc_bool))
| hBOOL(c_in(X2,X9,X3)) ),
file('<stdin>',cls_psubset__insert__iff_4) ).
fof(c_0_74,axiom,
! [X4,X9,X5,X6,X3] : c_Set_Oimage(X4,c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X6,tc_bool)),X6,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(X4,X5,X6,X3),c_Set_Oimage(X4,X9,X6,X3),tc_fun(X3,tc_bool)),
file('<stdin>',cls_image__Un_0) ).
fof(c_0_75,axiom,
! [X9,X5,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_HOL_Ouminus__class_Ouminus(X5,tc_fun(X3,tc_bool))),c_HOL_Ouminus__class_Ouminus(X9,tc_fun(X3,tc_bool)))) ),
file('<stdin>',cls_Compl__subset__Compl__iff_0) ).
fof(c_0_76,axiom,
! [X2,X9,X5,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_Set_Oinsert(X2,X5,X3)),X9)) ),
file('<stdin>',cls_insert__subset_1) ).
fof(c_0_77,axiom,
! [X2,X16,X9,X5,X6,X3] :
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X9,X3,tc_fun(X6,tc_bool)),X16))
| ~ hBOOL(hAPP(hAPP(X9,X2),X16))
| ~ hBOOL(c_in(X2,X5,X3)) ),
file('<stdin>',cls_SUP1__iff_2) ).
fof(c_0_78,axiom,
! [X16,X8,X9,X5,X6,X3] :
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X9,X3,tc_fun(X6,tc_bool)),X16))
| ~ hBOOL(hAPP(hAPP(X9,X8),X16))
| ~ hBOOL(c_in(X8,X5,X3)) ),
file('<stdin>',cls_SUP1__I_0) ).
fof(c_0_79,axiom,
! [X8,X42,X11,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_Set_Oinsert(X8,X11,X3)),c_Set_Oinsert(X8,X42,X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X11),X42)) ),
file('<stdin>',cls_insert__mono_0) ).
fof(c_0_80,axiom,
! [X38,X39,X5,X6,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X6)
| hBOOL(hAPP(hAPP(c_lessequals(X6),hAPP(X39,X38)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X39,X3,X6)))
| ~ hBOOL(c_in(X38,X5,X3)) ),
file('<stdin>',cls_le__SUPI_0) ).
fof(c_0_81,axiom,
! [X2,X9,X5,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_Set_Oinsert(X2,X5,X3)),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9))
| ~ hBOOL(c_in(X2,X9,X3)) ),
file('<stdin>',cls_insert__subset_2) ).
fof(c_0_82,axiom,
! [X2,X3] : hBOOL(hAPP(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3))),
file('<stdin>',cls_Nitpick_OEx1__def_2) ).
fof(c_0_83,axiom,
! [X2,X4,X5,X17,X3] :
( ~ hBOOL(c_in(X2,X5,X17))
| hBOOL(c_in(hAPP(X4,X2),c_Set_Oimage(X4,X5,X17,X3),X3)) ),
file('<stdin>',cls_rev__image__eqI_0) ).
fof(c_0_84,axiom,
! [X2,X4,X5,X6,X3] :
( ~ hBOOL(c_in(X2,X5,X6))
| hBOOL(c_in(hAPP(X4,X2),c_Set_Oimage(X4,X5,X6,X3),X3)) ),
file('<stdin>',cls_image__iff_2) ).
fof(c_0_85,axiom,
! [X2,X4,X5,X6,X3] :
( hBOOL(c_in(hAPP(X4,X2),c_Set_Oimage(X4,X5,X6,X3),X3))
| ~ hBOOL(c_in(X2,X5,X6)) ),
file('<stdin>',cls_image__eqI_0) ).
fof(c_0_86,axiom,
! [X2,X4,X5,X6,X3] :
( hBOOL(c_in(hAPP(X4,X2),c_Set_Oimage(X4,X5,X3,X6),X6))
| ~ hBOOL(c_in(X2,X5,X3)) ),
file('<stdin>',cls_imageI_0) ).
fof(c_0_87,axiom,
! [X29,X32,X3] : c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OSKIP,X29,X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3),
file('<stdin>',cls_hoare__derivs_OSkip_0) ).
fof(c_0_88,axiom,
! [X18,X15,X16,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X8,X16,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X15,X18,X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X16),X18))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X15),X8)) ),
file('<stdin>',cls_atLeastatMost__subset__iff_3) ).
fof(c_0_89,axiom,
! [X2,X5,X3] :
( X5 = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| X5 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3))) ),
file('<stdin>',cls_subset__singletonD_0) ).
fof(c_0_90,axiom,
! [X2,X9,X5,X3] :
( hBOOL(c_in(X2,X9,X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_Set_Oinsert(X2,X5,X3)),X9)) ),
file('<stdin>',cls_insert__subset_0) ).
fof(c_0_91,axiom,
! [X2,X9,X5,X3] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X9,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X2,X5,X3))
| hBOOL(c_in(X2,X9,X3))
| ~ c_HOL_Oord__class_Oless(X5,c_Set_Oinsert(X2,X9,X3),tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_psubset__insert__iff_1) ).
fof(c_0_92,axiom,
! [X4,X8,X5,X6,X3] :
( ~ class_OrderedGroup_Oab__group__add(X6)
| c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3,X6) = c_Finite__Set_Osetsum(X4,X5,X3,X6)
| hBOOL(c_in(X8,X5,X3))
| ~ c_Finite__Set_Ofinite(X5,X3) ),
file('<stdin>',cls_setsum__diff1_1) ).
fof(c_0_93,axiom,
! [X11,X9,X5,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X11))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X11))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9)) ),
file('<stdin>',cls_subset__trans_0) ).
fof(c_0_94,axiom,
! [X2,X9,X5,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),c_Set_Oinsert(X2,X9,X3)))
| hBOOL(c_in(X2,X5,X3)) ),
file('<stdin>',cls_subset__insert_0) ).
fof(c_0_95,axiom,
! [X2,X9,X5,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9))
| hBOOL(c_in(X2,X5,X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),c_Set_Oinsert(X2,X9,X3))) ),
file('<stdin>',cls_subset__insert__iff_1) ).
fof(c_0_96,axiom,
! [X4,X8,X5,X3] :
( c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3,tc_nat) = c_Finite__Set_Osetsum(X4,X5,X3,tc_nat)
| hBOOL(c_in(X8,X5,X3)) ),
file('<stdin>',cls_setsum__diff1__nat_1) ).
fof(c_0_97,axiom,
! [X9,X5,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_HOL_Ouminus__class_Ouminus(X9,tc_fun(X3,tc_bool))),c_HOL_Ouminus__class_Ouminus(X5,tc_fun(X3,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9)) ),
file('<stdin>',cls_Compl__anti__mono_0) ).
fof(c_0_98,axiom,
! [X9,X5,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_HOL_Ouminus__class_Ouminus(X5,tc_fun(X3,tc_bool))),c_HOL_Ouminus__class_Ouminus(X9,tc_fun(X3,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X5)) ),
file('<stdin>',cls_Compl__subset__Compl__iff_1) ).
fof(c_0_99,axiom,
! [X8,X3] : c_Collect(hAPP(c_COMBC(c_fequal(X3),X3,X3,tc_bool),X8),X3) = c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),
file('<stdin>',cls_singleton__conv_0) ).
fof(c_0_100,axiom,
! [X11,X9,X5,X3] :
( c_HOL_Ominus__class_Ominus(X9,c_HOL_Ominus__class_Ominus(X11,X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X5
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X11))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9)) ),
file('<stdin>',cls_double__diff_0) ).
fof(c_0_101,axiom,
! [X2,X9,X5,X6,X3] :
( c_Finite__Set_Ofinite(hAPP(X9,X2),X6)
| ~ hBOOL(c_in(X2,X5,X3))
| ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X9,X3,tc_fun(X6,tc_bool)),X6)
| ~ c_Finite__Set_Ofinite(X5,X3) ),
file('<stdin>',cls_finite__UN_0) ).
fof(c_0_102,axiom,
! [X31,X49,X5,X6,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(X5,X31),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X49,X5,X3,tc_fun(X6,tc_bool)),tc_fun(X6,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X49,X5,X3,tc_fun(X6,tc_bool))
| ~ hBOOL(c_in(X31,X49,X3)) ),
file('<stdin>',cls_UN__absorb_0) ).
fof(c_0_103,axiom,
! [X2,X4,X3] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(X4,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),X2)),
file('<stdin>',cls_fold1Set__sing_1) ).
fof(c_0_104,axiom,
! [X2,X9,X5,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),c_Set_Oinsert(X2,X9,X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9))
| hBOOL(c_in(X2,X5,X3)) ),
file('<stdin>',cls_subset__insert_1) ).
fof(c_0_105,axiom,
! [X2,X9,X5,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),c_Set_Oinsert(X2,X9,X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9))
| hBOOL(c_in(X2,X5,X3)) ),
file('<stdin>',cls_subset__insert__iff_2) ).
fof(c_0_106,axiom,
! [X27,X28,X29,X30,X6,X3] : hAPP(hAPP(c_COMBC(X29,X6,X30,X3),X28),X27) = hAPP(hAPP(X29,X27),X28),
file('<stdin>',cls_COMBC__def_0) ).
fof(c_0_107,axiom,
! [X8,X3] : c_The(hAPP(c_COMBC(c_fequal(X3),X3,X3,tc_bool),X8),X3) = X8,
file('<stdin>',cls_the__eq__trivial_0) ).
fof(c_0_108,axiom,
! [X18,X15,X16,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X8,X16,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X15,X18,X3)))
| hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X16)) ),
file('<stdin>',cls_atLeastatMost__subset__iff_2) ).
fof(c_0_109,axiom,
! [X8,X9,X5,X6,X3] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oinsert(X8,X5,X6),X9,X6,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(X9,X8),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X9,X6,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
file('<stdin>',cls_UN__insert_0) ).
fof(c_0_110,axiom,
! [X2,X4,X5,X6,X3] :
( c_Set_Oinsert(hAPP(X4,X2),c_Set_Oimage(X4,X5,X3,X6),X6) = c_Set_Oimage(X4,X5,X3,X6)
| ~ hBOOL(c_in(X2,X5,X3)) ),
file('<stdin>',cls_insert__image_0) ).
fof(c_0_111,axiom,
! [X16,X9,X5,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),c_Set_Oinsert(X16,X9,X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9)) ),
file('<stdin>',cls_subset__insertI2_0) ).
fof(c_0_112,axiom,
! [X2,X16,X8,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_Lattices_Oupper__semilattice__class_Osup(X8,X16,X3)),X2)) ),
file('<stdin>',cls_le__supE_0) ).
fof(c_0_113,axiom,
! [X2,X16,X8,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X16),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_Lattices_Oupper__semilattice__class_Osup(X8,X16,X3)),X2)) ),
file('<stdin>',cls_le__supE_1) ).
fof(c_0_114,axiom,
! [X7,X1,X2,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X7))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3)),X7)) ),
file('<stdin>',cls_le__sup__iff_0) ).
fof(c_0_115,axiom,
! [X7,X1,X2,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X7))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3)),X7)) ),
file('<stdin>',cls_le__sup__iff_1) ).
fof(c_0_116,axiom,
! [X1,X2,X3] :
( X1 = c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)
| ~ hBOOL(hAPP(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X1)) ),
file('<stdin>',cls_Nitpick_OEx1__def_3) ).
fof(c_0_117,axiom,
! [X4,X8,X9,X6,X3] : c_Set_Oimage(X4,c_Set_Oinsert(X8,X9,X6),X6,X3) = c_Set_Oinsert(hAPP(X4,X8),c_Set_Oimage(X4,X9,X6,X3),X3),
file('<stdin>',cls_image__insert_0) ).
fof(c_0_118,axiom,
! [X9,X5,X3] :
( X5 = X9
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9)) ),
file('<stdin>',cls_equalityI_0) ).
fof(c_0_119,axiom,
! [X9,X5,X3] :
( X5 = X9
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9)) ),
file('<stdin>',cls_set__eq__subset_2) ).
fof(c_0_120,axiom,
! [X9,X5,X3] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool))),X5)),
file('<stdin>',cls_Diff__subset_0) ).
fof(c_0_121,axiom,
! [X10,X4,X6,X3] :
( ~ class_HOL_Oord(X6)
| c_HOL_Oord__class_Oless(X4,X10,tc_fun(X3,X6))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,X6)),X10),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,X6)),X4),X10)) ),
file('<stdin>',cls_less__fun__def_2) ).
fof(c_0_122,axiom,
! [X18,X15,X16,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X8,X16,X3),c_SetInterval_Oord__class_OatLeastAtMost(X15,X18,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X15),X18))
| ~ c_HOL_Oord__class_Oless(X15,X8,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X16),X18))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X15),X8)) ),
file('<stdin>',cls_atLeastatMost__psubset__iff_5) ).
fof(c_0_123,axiom,
! [X18,X15,X16,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X8,X16,X3),c_SetInterval_Oord__class_OatLeastAtMost(X15,X18,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X15),X18))
| ~ c_HOL_Oord__class_Oless(X16,X18,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X16),X18))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X15),X8)) ),
file('<stdin>',cls_atLeastatMost__psubset__iff_6) ).
fof(c_0_124,axiom,
! [X15,X9,X5,X3] :
( hBOOL(c_in(X15,X9,X3))
| hBOOL(c_in(X15,X5,X3))
| ~ hBOOL(c_in(X15,c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),X3)) ),
file('<stdin>',cls_UnE_0) ).
fof(c_0_125,axiom,
! [X2,X16,X8,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_Lattices_Oupper__semilattice__class_Osup(X8,X16,X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X16),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X2)) ),
file('<stdin>',cls_le__supI_0) ).
fof(c_0_126,axiom,
! [X7,X1,X2,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3)),X7))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X7))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X7)) ),
file('<stdin>',cls_le__sup__iff_2) ).
fof(c_0_127,axiom,
! [X7,X1,X2,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_Lattices_Oupper__semilattice__class_Osup(X1,X7,X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X7),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2)) ),
file('<stdin>',cls_sup__least_0) ).
fof(c_0_128,axiom,
! [X2,X9,X5,X3] :
( c_HOL_Oord__class_Oless(X5,c_Set_Oinsert(X2,X9,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9))
| hBOOL(c_in(X2,X5,X3))
| ~ c_HOL_Oord__class_Oless(X5,X9,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_psubset__insert__iff_7) ).
fof(c_0_129,axiom,
! [X2,X9,X5,X3] :
( c_HOL_Oord__class_Oless(X5,c_Set_Oinsert(X2,X9,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9))
| hBOOL(c_in(X2,X5,X3))
| hBOOL(c_in(X2,X9,X3)) ),
file('<stdin>',cls_psubset__insert__iff_3) ).
fof(c_0_130,axiom,
! [X3] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)))),
file('<stdin>',cls_subset__Compl__self__eq_1) ).
fof(c_0_131,axiom,
! [X16,X8,X3] :
( X16 = X8
| ~ hBOOL(c_in(X16,c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)) ),
file('<stdin>',cls_singletonE_0) ).
fof(c_0_132,axiom,
! [X18,X15,X16,X8,X3] :
( c_Set_Oinsert(X8,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X15,c_Set_Oinsert(X18,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)
| X8 = X18
| X8 = X15 ),
file('<stdin>',cls_doubleton__eq__iff_0) ).
fof(c_0_133,axiom,
! [X18,X15,X16,X8,X3] :
( c_Set_Oinsert(X8,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X15,c_Set_Oinsert(X18,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)
| X16 = X15
| X8 = X15 ),
file('<stdin>',cls_doubleton__eq__iff_1) ).
fof(c_0_134,axiom,
! [X18,X15,X16,X8,X3] :
( c_Set_Oinsert(X8,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X15,c_Set_Oinsert(X18,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)
| X8 = X18
| X16 = X18 ),
file('<stdin>',cls_doubleton__eq__iff_2) ).
fof(c_0_135,axiom,
! [X18,X15,X16,X8,X3] :
( c_Set_Oinsert(X8,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X15,c_Set_Oinsert(X18,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)
| X16 = X15
| X16 = X18 ),
file('<stdin>',cls_doubleton__eq__iff_3) ).
fof(c_0_136,axiom,
! [X8,X9,X5,X3] : c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X8,X9,X3),tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X9,tc_fun(X3,tc_bool)),
file('<stdin>',cls_Diff__insert2_0) ).
fof(c_0_137,axiom,
! [X15,X9,X5,X3] :
( ~ hBOOL(c_in(X15,X9,X3))
| ~ hBOOL(c_in(X15,c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),X3)) ),
file('<stdin>',cls_DiffE_1) ).
fof(c_0_138,axiom,
! [X8,X5,X3] :
( c_Set_Oinsert(X8,c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3) = X5
| ~ hBOOL(c_in(X8,X5,X3)) ),
file('<stdin>',cls_insert__Diff_0) ).
fof(c_0_139,axiom,
! [X8,X9,X6,X3] : c_Set_Oinsert(X8,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)),X9,X6,tc_fun(X3,tc_bool)),X3) = c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),
file('<stdin>',cls_UN__extend__simps_I1_J_0) ).
fof(c_0_140,axiom,
! [X2,X9,X5,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9))
| hBOOL(c_in(X2,X5,X3))
| hBOOL(c_in(X2,X9,X3))
| ~ c_HOL_Oord__class_Oless(X5,c_Set_Oinsert(X2,X9,X3),tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_psubset__insert__iff_2) ).
fof(c_0_141,axiom,
! [X56,X57,X58,X59,X60,X61,X3] :
( c_Hoare__Mirabelle_Otriple_Otriple(X59,X61,X57,X3) != c_Hoare__Mirabelle_Otriple_Otriple(X58,X60,X56,X3)
| X59 = X58 ),
file('<stdin>',cls_triple_Oinject_0) ).
fof(c_0_142,axiom,
! [X56,X57,X58,X59,X60,X61,X3] :
( c_Hoare__Mirabelle_Otriple_Otriple(X59,X61,X57,X3) != c_Hoare__Mirabelle_Otriple_Otriple(X58,X60,X56,X3)
| X61 = X60 ),
file('<stdin>',cls_triple_Oinject_1) ).
fof(c_0_143,axiom,
! [X56,X57,X58,X59,X60,X61,X3] :
( c_Hoare__Mirabelle_Otriple_Otriple(X59,X61,X57,X3) != c_Hoare__Mirabelle_Otriple_Otriple(X58,X60,X56,X3)
| X57 = X56 ),
file('<stdin>',cls_triple_Oinject_2) ).
fof(c_0_144,axiom,
! [X40,X39,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_Finite__Set_Olinorder__class_OMax(X39,X3)),c_Finite__Set_Olinorder__class_OMax(X40,X3)))
| ~ c_Finite__Set_Ofinite(X40,X3)
| X39 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X39),X40)) ),
file('<stdin>',cls_Max__mono_0) ).
fof(c_0_145,axiom,
! [X40,X39,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_Finite__Set_Olinorder__class_OMin(X40,X3)),c_Finite__Set_Olinorder__class_OMin(X39,X3)))
| ~ c_Finite__Set_Ofinite(X40,X3)
| X39 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X39),X40)) ),
file('<stdin>',cls_Min__antimono_0) ).
fof(c_0_146,axiom,
! [X53,X41,X32,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(X41,X53,tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X32,X53,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(X41,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3) ),
file('<stdin>',cls_hoare__derivs_Oinsert_0) ).
fof(c_0_147,axiom,
! [X15,X9,X5,X3] :
( hBOOL(c_in(X15,X5,X3))
| ~ hBOOL(c_in(X15,c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),X3)) ),
file('<stdin>',cls_DiffE_0) ).
fof(c_0_148,axiom,
! [X8,X9,X5,X3] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X8,X9,X3),tc_fun(X3,tc_bool)),X3) ),
file('<stdin>',cls_finite__Diff__insert_0) ).
fof(c_0_149,axiom,
! [X2,X10,X4,X6,X3] :
( ~ class_HOL_Oord(X6)
| hBOOL(hAPP(hAPP(c_lessequals(X6),hAPP(X4,X2)),hAPP(X10,X2)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,X6)),X4),X10)) ),
file('<stdin>',cls_le__funD_0) ).
fof(c_0_150,axiom,
! [X54,X53,X32,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X32,X53,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),X53),X54))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X32,X54,X3) ),
file('<stdin>',cls_weaken_0) ).
fof(c_0_151,axiom,
! [X18,X15,X16,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X16,X18,X3)
| c_HOL_Oord__class_Oless(X15,X8,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X16))
| ~ c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X8,X16,X3),c_SetInterval_Oord__class_OatLeastAtMost(X15,X18,X3),tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_atLeastatMost__psubset__iff_2) ).
fof(c_0_152,axiom,
! [X2,X9,X5,X3] :
( hBOOL(c_in(X2,X9,X3))
| ~ hBOOL(c_in(X2,X5,X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9)) ),
file('<stdin>',cls_set__mp_0) ).
fof(c_0_153,axiom,
! [X15,X9,X5,X3] :
( hBOOL(c_in(X15,X9,X3))
| ~ hBOOL(c_in(X15,X5,X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9)) ),
file('<stdin>',cls_subsetD_0) ).
fof(c_0_154,axiom,
! [X2,X9,X5,X3] :
( hBOOL(c_in(X2,X9,X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9))
| ~ hBOOL(c_in(X2,X5,X3)) ),
file('<stdin>',cls_set__rev__mp_0) ).
fof(c_0_155,axiom,
! [X41,X9,X5,X3] :
( hBOOL(c_in(X41,X9,X3))
| ~ hBOOL(c_in(X41,X5,X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9)) ),
file('<stdin>',cls_subset__iff_0) ).
fof(c_0_156,axiom,
! [X18,X15,X16,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X15),X8))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X16))
| ~ c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X8,X16,X3),c_SetInterval_Oord__class_OatLeastAtMost(X15,X18,X3),tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_atLeastatMost__psubset__iff_0) ).
fof(c_0_157,axiom,
! [X18,X15,X16,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X16),X18))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X16))
| ~ c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X8,X16,X3),c_SetInterval_Oord__class_OatLeastAtMost(X15,X18,X3),tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_atLeastatMost__psubset__iff_1) ).
fof(c_0_158,axiom,
! [X9,X5,X6,X3] : c_Lattices_Oupper__semilattice__class_Osup(X5,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)),X9,X6,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X5,
file('<stdin>',cls_UN__extend__simps_I3_J_0) ).
fof(c_0_159,axiom,
! [X9,X5,X6,X3] : c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)),X5,X6,tc_fun(X3,tc_bool)),X9,tc_fun(X3,tc_bool)) = X9,
file('<stdin>',cls_UN__extend__simps_I2_J_0) ).
fof(c_0_160,axiom,
! [X9,X5,X6,X3] : c_HOL_Ominus__class_Ominus(X5,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)),X9,X6,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X5,
file('<stdin>',cls_INT__extend__simps_I4_J_0) ).
fof(c_0_161,axiom,
! [X2,X4,X3] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X2)),
file('<stdin>',cls_empty__fold1SetE_0) ).
fof(c_0_162,axiom,
! [X5,X3] :
( X5 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),c_HOL_Ouminus__class_Ouminus(X5,tc_fun(X3,tc_bool)))) ),
file('<stdin>',cls_subset__Compl__self__eq_0) ).
fof(c_0_163,axiom,
! [X15,X9,X5,X3] :
( hBOOL(c_in(X15,c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),X3))
| hBOOL(c_in(X15,X9,X3))
| ~ hBOOL(c_in(X15,X5,X3)) ),
file('<stdin>',cls_Diff__iff_2) ).
fof(c_0_164,axiom,
! [X15,X9,X5,X3] :
( hBOOL(c_in(X15,c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),X3))
| hBOOL(c_in(X15,X9,X3))
| ~ hBOOL(c_in(X15,X5,X3)) ),
file('<stdin>',cls_DiffI_0) ).
fof(c_0_165,axiom,
! [X12,X13,X14,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(X14,X13,X3),c_SetInterval_Oord__class_OatLeastLessThan(X13,X12,X3),tc_fun(X3,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X14,X12,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X13),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X13)) ),
file('<stdin>',cls_ivl__disj__un_I17_J_0) ).
fof(c_0_166,axiom,
! [X12,X13,X14,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OgreaterThanAtMost(X14,X13,X3),c_SetInterval_Oord__class_OgreaterThanAtMost(X13,X12,X3),tc_fun(X3,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X14,X12,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X13),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X13)) ),
file('<stdin>',cls_ivl__disj__un_I20_J_0) ).
fof(c_0_167,axiom,
! [X12,X13,X14,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastAtMost(X14,X13,X3),c_SetInterval_Oord__class_OgreaterThanAtMost(X13,X12,X3),tc_fun(X3,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X14,X12,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X13),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X13)) ),
file('<stdin>',cls_ivl__disj__un_I22_J_0) ).
fof(c_0_168,axiom,
! [X12,X13,X14,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(X14,X13,X3),c_SetInterval_Oord__class_OatLeastAtMost(X13,X12,X3),tc_fun(X3,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X14,X12,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X13),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X13)) ),
file('<stdin>',cls_ivl__disj__un_I21_J_0) ).
fof(c_0_169,axiom,
! [X9,X5,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X5,c_HOL_Ominus__class_Ominus(X9,X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X9
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9)) ),
file('<stdin>',cls_Diff__partition_0) ).
fof(c_0_170,axiom,
! [X2,X9,X5,X6,X3] :
( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X9,X6,tc_fun(X3,tc_bool))
| hAPP(X9,X2) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X2,X5,X6)) ),
file('<stdin>',cls_UNION__empty__conv_I1_J_0) ).
fof(c_0_171,axiom,
! [X2,X9,X5,X6,X3] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X9,X6,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| hAPP(X9,X2) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X2,X5,X6)) ),
file('<stdin>',cls_UNION__empty__conv_I2_J_0) ).
fof(c_0_172,axiom,
! [X8,X5,X3] : c_Set_Oinsert(X8,c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3) = c_Set_Oinsert(X8,X5,X3),
file('<stdin>',cls_insert__Diff__single_0) ).
fof(c_0_173,axiom,
! [X53,X32,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X32,X53,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),X53),X32)) ),
file('<stdin>',cls_asm_0) ).
fof(c_0_174,axiom,
! [X11,X9,X5,X3] :
( c_HOL_Oord__class_Oless(X5,X11,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X11))
| ~ c_HOL_Oord__class_Oless(X5,X9,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_psubset__subset__trans_0) ).
fof(c_0_175,axiom,
! [X11,X9,X5,X3] :
( c_HOL_Oord__class_Oless(X5,X11,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X9,X11,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9)) ),
file('<stdin>',cls_subset__psubset__trans_0) ).
fof(c_0_176,axiom,
! [X5,X3] :
( X5 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))) ),
file('<stdin>',cls_subset__empty_0) ).
fof(c_0_177,axiom,
! [X8,X9,X5,X3] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X8,X9,X3),tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),X3) ),
file('<stdin>',cls_finite__Diff__insert_1) ).
fof(c_0_178,axiom,
! [X2,X15,X5,X6,X3] :
( c_Set_Oimage(c_COMBK(X15,X6,X3),X5,X3,X6) = c_Set_Oinsert(X15,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)),X6)
| ~ hBOOL(c_in(X2,X5,X3)) ),
file('<stdin>',cls_image__constant_0) ).
fof(c_0_179,axiom,
! [X10,X4,X6,X3] :
( ~ class_HOL_Oord(X6)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,X6)),X10),X4))
| ~ c_HOL_Oord__class_Oless(X4,X10,tc_fun(X3,X6)) ),
file('<stdin>',cls_less__fun__def_1) ).
fof(c_0_180,axiom,
! [X8,X9,X5,X3] : c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X8,X9,X3),tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),
file('<stdin>',cls_Diff__insert_0) ).
fof(c_0_181,axiom,
! [X16,X8,X5,X3] :
( hBOOL(c_in(X8,X5,X3))
| X8 = X16
| ~ hBOOL(c_in(X8,c_Set_Oinsert(X16,X5,X3),X3)) ),
file('<stdin>',cls_insertE_0) ).
fof(c_0_182,axiom,
! [X12,X14,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),c_SetInterval_Oord__class_OgreaterThanAtMost(X14,X12,X3),tc_fun(X3,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X14,X12,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X12)) ),
file('<stdin>',cls_ivl__disj__un_I5_J_0) ).
fof(c_0_183,axiom,
! [X12,X14,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(X14,X12,X3),c_Set_Oinsert(X12,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X14,X12,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X12)) ),
file('<stdin>',cls_ivl__disj__un_I6_J_0) ).
fof(c_0_184,axiom,
! [X11,X9,X5,X3] : c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),X11,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X5,X11,tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X9,X11,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
file('<stdin>',cls_Un__Diff_0) ).
fof(c_0_185,axiom,
! [X16,X8,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| hAPP(c_Complete__Lattice_OSup__class_OSup(X3),c_Set_Oinsert(X8,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)) = c_Lattices_Oupper__semilattice__class_Osup(X8,X16,X3) ),
file('<stdin>',cls_Sup__binary_0) ).
fof(c_0_186,axiom,
! [X3] : hBOOL(hAPP(hAPP(c_lessequals(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)))),
file('<stdin>',cls_subset__empty_1) ).
fof(c_0_187,axiom,
! [X9,X5,X3] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)))),
file('<stdin>',cls_Un__upper1_0) ).
fof(c_0_188,axiom,
! [X9,X5,X3] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)))),
file('<stdin>',cls_Un__upper2_0) ).
fof(c_0_189,axiom,
! [X15,X9,X5,X3] :
( hBOOL(c_in(X15,c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),X3))
| ~ hBOOL(c_in(X15,X5,X3)) ),
file('<stdin>',cls_UnCI_1) ).
fof(c_0_190,axiom,
! [X15,X9,X5,X3] :
( hBOOL(c_in(X15,c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),X3))
| ~ hBOOL(c_in(X15,X9,X3)) ),
file('<stdin>',cls_UnCI_0) ).
fof(c_0_191,axiom,
! [X2,X9,X5,X3] :
( hBOOL(hAPP(X9,X2))
| hBOOL(hAPP(X5,X2))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),X2)) ),
file('<stdin>',cls_sup1E_0) ).
fof(c_0_192,axiom,
! [X15,X5,X3] :
( ~ hBOOL(c_in(X15,X5,X3))
| ~ hBOOL(c_in(X15,c_HOL_Ouminus__class_Ouminus(X5,tc_fun(X3,tc_bool)),X3)) ),
file('<stdin>',cls_ComplD_0) ).
fof(c_0_193,axiom,
! [X18,X15,X16,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X8,X16,X3),c_SetInterval_Oord__class_OatLeastAtMost(X15,X18,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X15),X18))
| hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X16)) ),
file('<stdin>',cls_atLeastatMost__psubset__iff_4) ).
fof(c_0_194,axiom,
! [X18,X15,X16,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X15),X18))
| ~ c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X8,X16,X3),c_SetInterval_Oord__class_OatLeastAtMost(X15,X18,X3),tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_atLeastatMost__psubset__iff_3) ).
fof(c_0_195,axiom,
! [X5,X6,X3] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,c_COMBK(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool),X6),X6,tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
file('<stdin>',cls_UN__empty2_0) ).
fof(c_0_196,axiom,
! [X16,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ouminus__class_Ouminus(X8,X3)),X16))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ouminus__class_Ouminus(X16,X3)),X8)) ),
file('<stdin>',cls_minus__le__iff_1) ).
fof(c_0_197,axiom,
! [X16,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ouminus__class_Ouminus(X16,X3)),X8))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ouminus__class_Ouminus(X8,X3)),X16)) ),
file('<stdin>',cls_minus__le__iff_0) ).
fof(c_0_198,axiom,
! [X2,X9,X5,X3] :
( c_HOL_Oord__class_Oless(X5,X9,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X2,X9,X3))
| ~ c_HOL_Oord__class_Oless(X5,c_Set_Oinsert(X2,X9,X3),tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_psubset__insert__iff_0) ).
fof(c_0_199,axiom,
! [X9,X5,X3] :
( c_HOL_Oord__class_Oless(X5,X9,tc_fun(X3,tc_bool))
| X5 = X9
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9)) ),
file('<stdin>',cls_psubset__eq_2) ).
fof(c_0_200,axiom,
! [X9,X5,X3] :
( X5 = X9
| c_HOL_Oord__class_Oless(X5,X9,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9)) ),
file('<stdin>',cls_subset__iff__psubset__eq_0) ).
fof(c_0_201,axiom,
! [X9,X5,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)) = X9
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9)) ),
file('<stdin>',cls_Un__absorb1_0) ).
fof(c_0_202,axiom,
! [X9,X5,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)) = X5
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X5)) ),
file('<stdin>',cls_Un__absorb2_0) ).
fof(c_0_203,axiom,
! [X2,X28,X29,X3] :
( hBOOL(hAPP(X28,X2))
| ~ hBOOL(hAPP(X29,X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X29),X28)) ),
file('<stdin>',cls_predicate1D_0) ).
fof(c_0_204,axiom,
! [X2,X28,X29,X3] :
( hBOOL(hAPP(X28,X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X29),X28))
| ~ hBOOL(hAPP(X29,X2)) ),
file('<stdin>',cls_rev__predicate1D_0) ).
fof(c_0_205,axiom,
! [X2,X3] : hBOOL(c_in(X2,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)),
file('<stdin>',cls_singleton__iff_1) ).
fof(c_0_206,axiom,
! [X43,X2,X3] : c_Set_Oinsert(X43,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = c_Set_Oinsert(X2,c_Set_Oinsert(X43,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),
file('<stdin>',cls_doubleton__eq__iff_4) ).
fof(c_0_207,axiom,
! [X34,X33,X6,X3] :
( c_Finite__Set_Ofinite(c_Set_Oimage(X34,X33,X3,X6),X6)
| ~ c_Finite__Set_Ofinite(X33,X3) ),
file('<stdin>',cls_finite__imageI_0) ).
fof(c_0_208,axiom,
! [X16,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X16))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ouminus__class_Ouminus(X16,X3)),c_HOL_Ouminus__class_Ouminus(X8,X3))) ),
file('<stdin>',cls_neg__le__iff__le_0) ).
fof(c_0_209,axiom,
! [X37,X13,X38,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Ominus__class_Ominus(c_SetInterval_Oord__class_OatLeastLessThan(X38,X13,X3),c_SetInterval_Oord__class_OatLeastLessThan(X38,X37,X3),tc_fun(X3,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X37,X13,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X38),X37)) ),
file('<stdin>',cls_ivl__diff_0) ).
fof(c_0_210,axiom,
! [X2,X5,X3] :
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X2,X5,X3),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) = X5
| hBOOL(c_in(X2,X5,X3)) ),
file('<stdin>',cls_Diff__insert__absorb_0) ).
fof(c_0_211,axiom,
! [X8,X9,X3] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),c_Set_Oinsert(X8,X9,X3))),
file('<stdin>',cls_subset__insertI_0) ).
fof(c_0_212,axiom,
! [X2,X9,X5,X3] :
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X2,X5,X3),X9,tc_fun(X3,tc_bool)) = c_Set_Oinsert(X2,c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),X3)
| hBOOL(c_in(X2,X9,X3)) ),
file('<stdin>',cls_insert__Diff__if_1) ).
fof(c_0_213,axiom,
! [X15,X6,X3] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)),c_COMBK(X15,tc_fun(X3,tc_bool),X6),X6,tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
file('<stdin>',cls_UN__constant_0) ).
fof(c_0_214,axiom,
! [X16,X8,X9,X3] :
( hBOOL(c_in(X8,c_Set_Oinsert(X16,X9,X3),X3))
| ~ hBOOL(c_in(X8,X9,X3)) ),
file('<stdin>',cls_insertCI_0) ).
fof(c_0_215,axiom,
! [X16,X8,X5,X3] :
( hBOOL(c_in(X8,c_Set_Oinsert(X16,X5,X3),X3))
| ~ hBOOL(c_in(X8,X5,X3)) ),
file('<stdin>',cls_insert__iff_2) ).
fof(c_0_216,axiom,
! [X5,X3] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),X5)),
file('<stdin>',cls_empty__subsetI_0) ).
fof(c_0_217,axiom,
! [X2,X16,X8,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X2),c_Lattices_Oupper__semilattice__class_Osup(X8,X16,X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X8)) ),
file('<stdin>',cls_le__supI1_0) ).
fof(c_0_218,axiom,
! [X2,X16,X8,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X2),c_Lattices_Oupper__semilattice__class_Osup(X8,X16,X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X16)) ),
file('<stdin>',cls_le__supI2_0) ).
fof(c_0_219,axiom,
! [X9,X5,X3] :
( c_Finite__Set_Ofinite(X5,X3)
| ~ c_Finite__Set_Ofinite(X9,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9)) ),
file('<stdin>',cls_finite__subset_0) ).
fof(c_0_220,axiom,
! [X9,X5,X3] :
( c_Finite__Set_Ofinite(X5,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_rev__finite__subset_0) ).
fof(c_0_221,axiom,
! [X15,X5,X6,X3] :
( c_Set_Oimage(c_COMBK(X15,X3,X6),X5,X6,X3) = c_Set_Oinsert(X15,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| X5 = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)) ),
file('<stdin>',cls_image__constant__conv_1) ).
fof(c_0_222,axiom,
! [X2,X9,X5,X3] :
( c_HOL_Oord__class_Oless(X5,c_Set_Oinsert(X2,X9,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X2,X9,X3))
| ~ c_HOL_Oord__class_Oless(X5,X9,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_psubset__insert__iff_6) ).
fof(c_0_223,axiom,
! [X11,X9,X5,X3] : c_Lattices_Oupper__semilattice__class_Osup(X5,c_Lattices_Oupper__semilattice__class_Osup(X9,X11,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X9,c_Lattices_Oupper__semilattice__class_Osup(X5,X11,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
file('<stdin>',cls_Un__left__commute_0) ).
fof(c_0_224,axiom,
! [X11,X9,X5,X3] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),X11,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X5,c_Lattices_Oupper__semilattice__class_Osup(X9,X11,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
file('<stdin>',cls_Un__assoc_0) ).
fof(c_0_225,axiom,
! [X4,X5,X6,X3] :
( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_Set_Oimage(X4,X5,X6,X3)
| X5 = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)) ),
file('<stdin>',cls_empty__is__image_0) ).
fof(c_0_226,axiom,
! [X4,X5,X6,X3] :
( c_Set_Oimage(X4,X5,X6,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X5 = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)) ),
file('<stdin>',cls_image__is__empty_0) ).
fof(c_0_227,axiom,
! [X35,X1,X36,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ominus__class_Ominus(X36,X35,X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X35),X36)) ),
file('<stdin>',cls_le__eqI_1) ).
fof(c_0_228,axiom,
! [X35,X1,X36,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ominus__class_Ominus(X36,X35,X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X35),X36))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2)) ),
file('<stdin>',cls_le__eqI_0) ).
fof(c_0_229,axiom,
! [X15,X5,X6,X3] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,c_COMBK(X15,tc_fun(X3,tc_bool),X6),X6,tc_fun(X3,tc_bool)) = X15
| X5 = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)) ),
file('<stdin>',cls_UN__constant_1) ).
fof(c_0_230,axiom,
! [X7,X1,X2,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X7),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X7),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2)) ),
file('<stdin>',cls_xt1_I6_J_0) ).
fof(c_0_231,axiom,
! [X7,X1,X2,X3] :
( ~ class_Orderings_Opreorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X7))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X7))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1)) ),
file('<stdin>',cls_order__trans_0) ).
fof(c_0_232,axiom,
! [X10,X4,X6,X3] :
( ~ class_HOL_Oord(X6)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,X6)),X4),X10))
| ~ c_HOL_Oord__class_Oless(X4,X10,tc_fun(X3,X6)) ),
file('<stdin>',cls_less__fun__def_0) ).
fof(c_0_233,axiom,
! [X2,X5,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(c_Complete__Lattice_OInf__class_OInf(X3),X5)),X2))
| ~ hBOOL(c_in(X2,X5,X3)) ),
file('<stdin>',cls_Inf__lower_0) ).
fof(c_0_234,axiom,
! [X16,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ouminus__class_Ouminus(X16,X3)),c_HOL_Ouminus__class_Ouminus(X8,X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X16)) ),
file('<stdin>',cls_le__imp__neg__le_0) ).
fof(c_0_235,axiom,
! [X2,X9,X5,X3] :
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X2,X5,X3),X9,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X2,X9,X3)) ),
file('<stdin>',cls_insert__Diff1_0) ).
fof(c_0_236,axiom,
! [X15,X6,X3] : c_Set_Oimage(c_COMBK(X15,X3,X6),c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)),X6,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
file('<stdin>',cls_image__constant__conv_0) ).
fof(c_0_237,axiom,
! [X1,X2,X5,X3] :
( hBOOL(hAPP(X5,X2))
| X1 = X2
| ~ hBOOL(hAPP(c_Set_Oinsert(X1,X5,X3),X2)) ),
file('<stdin>',cls_insert__code_0) ).
fof(c_0_238,axiom,
! [X2,X5,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_Finite__Set_Olinorder__class_OMin(X5,X3)),X2))
| ~ hBOOL(c_in(X2,X5,X3))
| ~ c_Finite__Set_Ofinite(X5,X3) ),
file('<stdin>',cls_Min__le_0) ).
fof(c_0_239,axiom,
! [X16,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X8),c_HOL_Ouminus__class_Ouminus(X16,X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X16),c_HOL_Ouminus__class_Ouminus(X8,X3))) ),
file('<stdin>',cls_le__minus__iff_1) ).
fof(c_0_240,axiom,
! [X16,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X16),c_HOL_Ouminus__class_Ouminus(X8,X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),c_HOL_Ouminus__class_Ouminus(X16,X3))) ),
file('<stdin>',cls_le__minus__iff_0) ).
fof(c_0_241,axiom,
! [X9,X5,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)) != X9
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9)) ),
file('<stdin>',cls_subset__Un__eq_1) ).
fof(c_0_242,axiom,
! [X9,X5,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9))
| ~ c_HOL_Oord__class_Oless(X5,X9,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_psubset__eq_0) ).
fof(c_0_243,axiom,
! [X15,X9,X5,X3] :
( hBOOL(c_in(X15,X9,X3))
| ~ hBOOL(c_in(X15,X5,X3))
| ~ c_HOL_Oord__class_Oless(X5,X9,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_psubsetD_0) ).
fof(c_0_244,axiom,
! [X2,X9,X5,X3] :
( c_Set_Oinsert(X2,X5,X3) != c_Set_Oinsert(X2,X9,X3)
| hBOOL(c_in(X2,X9,X3))
| hBOOL(c_in(X2,X5,X3))
| X5 = X9 ),
file('<stdin>',cls_insert__ident_0) ).
fof(c_0_245,axiom,
! [X8,X11,X9,X3] : c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X8,X9,X3),X11,tc_fun(X3,tc_bool)) = c_Set_Oinsert(X8,c_Lattices_Oupper__semilattice__class_Osup(X9,X11,tc_fun(X3,tc_bool)),X3),
file('<stdin>',cls_Un__insert__left_0) ).
fof(c_0_246,axiom,
! [X8,X9,X5,X3] : c_Lattices_Oupper__semilattice__class_Osup(X5,c_Set_Oinsert(X8,X9,X3),tc_fun(X3,tc_bool)) = c_Set_Oinsert(X8,c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),X3),
file('<stdin>',cls_Un__insert__right_0) ).
fof(c_0_247,axiom,
! [X39,X5,X6,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X6)
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,c_COMBK(X39,X6,X3),X3,X6) = X39
| X5 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_SUP__const_0) ).
fof(c_0_248,axiom,
! [X2,X29,X3] :
( ~ hBOOL(hAPP(X29,X2))
| ~ hBOOL(c_in(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)) ),
file('<stdin>',cls_bex__empty_0) ).
fof(c_0_249,axiom,
! [X2,X9,X5,X3] :
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),X2))
| ~ hBOOL(hAPP(X5,X2)) ),
file('<stdin>',cls_sup1CI_1) ).
fof(c_0_250,axiom,
! [X2,X9,X5,X3] :
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),X2))
| ~ hBOOL(hAPP(X9,X2)) ),
file('<stdin>',cls_sup1CI_0) ).
fof(c_0_251,axiom,
! [X2,X29,X3] :
( hBOOL(hAPP(X29,X2))
| ~ hBOOL(c_in(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)) ),
file('<stdin>',cls_ball__empty_0) ).
fof(c_0_252,axiom,
! [X15,X5,X3] :
( hBOOL(c_in(X15,c_HOL_Ouminus__class_Ouminus(X5,tc_fun(X3,tc_bool)),X3))
| hBOOL(c_in(X15,X5,X3)) ),
file('<stdin>',cls_ComplI_0) ).
fof(c_0_253,axiom,
! [X2,X5,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X2),hAPP(c_Complete__Lattice_OSup__class_OSup(X3),X5)))
| ~ hBOOL(c_in(X2,X5,X3)) ),
file('<stdin>',cls_Sup__upper_0) ).
fof(c_0_254,axiom,
! [X2,X5,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X2),c_Finite__Set_Olinorder__class_OMax(X5,X3)))
| ~ hBOOL(c_in(X2,X5,X3))
| ~ c_Finite__Set_Ofinite(X5,X3) ),
file('<stdin>',cls_Max__ge_0) ).
fof(c_0_255,axiom,
! [X1,X2,X3] :
( ~ class_Orderings_Oorder(X3)
| X2 = X1
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1)) ),
file('<stdin>',cls_order__eq__iff_2) ).
fof(c_0_256,axiom,
! [X1,X2,X3] :
( ~ class_Orderings_Oorder(X3)
| X2 = X1
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1)) ),
file('<stdin>',cls_order__antisym_0) ).
fof(c_0_257,axiom,
! [X1,X2,X3] :
( ~ class_Orderings_Oorder(X3)
| X2 = X1
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2)) ),
file('<stdin>',cls_order__antisym__conv_0) ).
fof(c_0_258,axiom,
! [X8,X5,X3] : c_Set_Oinsert(X8,X5,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X5,tc_fun(X3,tc_bool)),
file('<stdin>',cls_insert__is__Un_0) ).
fof(c_0_259,axiom,
! [X9,X5,X3] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X5,tc_fun(X3,tc_bool)),X9,tc_fun(X3,tc_bool)),
file('<stdin>',cls_Compl__Diff__eq_0) ).
fof(c_0_260,axiom,
! [X8,X3] : ~ hBOOL(c_in(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)),
file('<stdin>',cls_emptyE_0) ).
fof(c_0_261,axiom,
! [X15,X3] : ~ hBOOL(c_in(X15,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)),
file('<stdin>',cls_empty__iff_0) ).
fof(c_0_262,axiom,
! [X2,X3] : ~ hBOOL(c_in(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)),
file('<stdin>',cls_ex__in__conv_0) ).
fof(c_0_263,axiom,
! [X16,X8,X3] :
( c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) != c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| X8 = X16 ),
file('<stdin>',cls_singleton__inject_0) ).
fof(c_0_264,axiom,
! [X1,X2,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1)) ),
file('<stdin>',cls_less__le__not__le_2) ).
fof(c_0_265,axiom,
! [X7,X1,X2,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3),X7,X3) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X7,X3),X3) ),
file('<stdin>',cls_sup__assoc_0) ).
fof(c_0_266,axiom,
! [X7,X1,X2,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X7,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X7,X3),X3) ),
file('<stdin>',cls_sup__left__commute_0) ).
fof(c_0_267,axiom,
! [X7,X1,X2,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X7,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X7,X3),X3) ),
file('<stdin>',cls_inf__sup__aci_I7_J_0) ).
fof(c_0_268,axiom,
! [X7,X1,X2,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3),X7,X3) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X7,X3),X3) ),
file('<stdin>',cls_inf__sup__aci_I6_J_0) ).
fof(c_0_269,axiom,
! [X1,X2,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X2),c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3))) ),
file('<stdin>',cls_sup__ge1_0) ).
fof(c_0_270,axiom,
! [X1,X2,X3] :
( ~ class_Lattices_Olattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X2),c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3))) ),
file('<stdin>',cls_inf__sup__ord_I3_J_0) ).
fof(c_0_271,axiom,
! [X1,X2,X3] :
( ~ class_Lattices_Olattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3))) ),
file('<stdin>',cls_inf__sup__ord_I4_J_0) ).
fof(c_0_272,axiom,
! [X1,X2,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3))) ),
file('<stdin>',cls_sup__ge2_0) ).
fof(c_0_273,axiom,
! [X4,X6,X3] : c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = c_Set_Oimage(X4,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)),X6,X3),
file('<stdin>',cls_empty__is__image_1) ).
fof(c_0_274,axiom,
! [X4,X6,X3] : c_Set_Oimage(X4,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)),X6,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
file('<stdin>',cls_image__empty_0) ).
fof(c_0_275,axiom,
! [X2,X9,X3] : hBOOL(c_in(X2,c_Set_Oinsert(X2,X9,X3),X3)),
file('<stdin>',cls_insertCI_1) ).
fof(c_0_276,axiom,
! [X8,X9,X3] : hBOOL(c_in(X8,c_Set_Oinsert(X8,X9,X3),X3)),
file('<stdin>',cls_insertI1_0) ).
fof(c_0_277,axiom,
! [X2,X5,X3] : hBOOL(c_in(X2,c_Set_Oinsert(X2,X5,X3),X3)),
file('<stdin>',cls_insert__iff_1) ).
fof(c_0_278,axiom,
! [X1,X2,X5,X3] : c_Set_Oinsert(X2,c_Set_Oinsert(X1,X5,X3),X3) = c_Set_Oinsert(X1,c_Set_Oinsert(X2,X5,X3),X3),
file('<stdin>',cls_insert__commute_0) ).
fof(c_0_279,axiom,
! [X11,X9,X5,X3] :
( c_HOL_Oord__class_Oless(X5,X11,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X9,X11,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X5,X9,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_psubset__trans_0) ).
fof(c_0_280,axiom,
! [X35,X1,X36,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ominus__class_Ominus(X36,X35,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X36,X35,X3) ),
file('<stdin>',cls_less__eqI_1) ).
fof(c_0_281,axiom,
! [X35,X1,X36,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ominus__class_Ominus(X36,X35,X3)
| c_HOL_Oord__class_Oless(X36,X35,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
file('<stdin>',cls_less__eqI_0) ).
fof(c_0_282,axiom,
! [X7,X1,X2,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_HOL_Oord__class_Oless(X2,X7,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X7))
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
file('<stdin>',cls_order__less__le__trans_0) ).
fof(c_0_283,axiom,
! [X7,X1,X2,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_HOL_Oord__class_Oless(X2,X7,X3)
| ~ c_HOL_Oord__class_Oless(X1,X7,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1)) ),
file('<stdin>',cls_order__le__less__trans_0) ).
fof(c_0_284,axiom,
! [X7,X1,X2,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X7,X2,X3)
| ~ c_HOL_Oord__class_Oless(X7,X1,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2)) ),
file('<stdin>',cls_xt1_I8_J_0) ).
fof(c_0_285,axiom,
! [X7,X1,X2,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X7,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X7),X1))
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
file('<stdin>',cls_xt1_I7_J_0) ).
fof(c_0_286,axiom,
! [X9,X5,X3] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),X9,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),
file('<stdin>',cls_Diff__idemp_0) ).
fof(c_0_287,axiom,
! [X9,X5,X3] : c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X9,X5,tc_fun(X3,tc_bool)),X5,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X9,X5,tc_fun(X3,tc_bool)),
file('<stdin>',cls_Un__Diff__cancel2_0) ).
fof(c_0_288,axiom,
! [X9,X5,X3] : c_Lattices_Oupper__semilattice__class_Osup(X5,c_HOL_Ominus__class_Ominus(X9,X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),
file('<stdin>',cls_Un__Diff__cancel_0) ).
fof(c_0_289,axiom,
! [X9,X5,X3] : c_Lattices_Oupper__semilattice__class_Osup(X5,c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),
file('<stdin>',cls_Un__left__absorb_0) ).
fof(c_0_290,axiom,
! [X16,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_SetInterval_Oord__class_OatLeastAtMost(X8,X16,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X16)) ),
file('<stdin>',cls_atLeastatMost__empty__iff2_0) ).
fof(c_0_291,axiom,
! [X16,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_SetInterval_Oord__class_OatLeastAtMost(X8,X16,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X16)) ),
file('<stdin>',cls_atLeastatMost__empty__iff_0) ).
fof(c_0_292,axiom,
! [X9,X5,X3] :
( c_Finite__Set_Ofinite(X5,X3)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_finite__Diff2_0) ).
fof(c_0_293,axiom,
! [X1,X2,X5,X3] :
( hBOOL(hAPP(c_Set_Oinsert(X1,X5,X3),X2))
| ~ hBOOL(hAPP(X5,X2)) ),
file('<stdin>',cls_insert__code_2) ).
fof(c_0_294,axiom,
! [X2,X3] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X2),X2)),
file('<stdin>',cls_equalityE_0) ).
fof(c_0_295,axiom,
! [X5,X3] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X5)),
file('<stdin>',cls_subset__refl_0) ).
fof(c_0_296,axiom,
! [X8,X29,X3] :
( hBOOL(hAPP(X29,X8))
| ~ hBOOL(c_in(X8,c_Collect(X29,X3),X3)) ),
file('<stdin>',cls_CollectD_0) ).
fof(c_0_297,axiom,
! [X32,X33,X3] :
( c_Finite__Set_Ofinite(X32,X3)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X33,X32,tc_fun(X3,tc_bool)),X3) ),
file('<stdin>',cls_finite__Un_1) ).
fof(c_0_298,axiom,
! [X32,X33,X3] :
( c_Finite__Set_Ofinite(X33,X3)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X33,X32,tc_fun(X3,tc_bool)),X3) ),
file('<stdin>',cls_finite__Un_0) ).
fof(c_0_299,axiom,
! [X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_Complete__Lattice_Ocomplete__lattice__axioms(c_Complete__Lattice_OInf__class_OInf(X3),c_Complete__Lattice_OSup__class_OSup(X3),c_lessequals(X3),X3) ),
file('<stdin>',cls_complete__lattice__class_Oaxioms_0) ).
fof(c_0_300,axiom,
! [X10,X4,X6] :
( ~ class_Lattices_Olattice(X6)
| hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,X10,tc_fun(t_a,X6)),v_x) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(X4,v_x),hAPP(X10,v_x),X6) ),
file('<stdin>',cls_sup__fun__eq_0) ).
fof(c_0_301,axiom,
! [X9,X5,X6] :
( ~ class_HOL_Ominus(X6)
| hAPP(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(t_a,X6)),v_x) = c_HOL_Ominus__class_Ominus(hAPP(X5,v_x),hAPP(X9,v_x),X6) ),
file('<stdin>',cls_fun__diff__def_0) ).
fof(c_0_302,axiom,
! [X4,X8,X3] : c_Finite__Set_Ofold1(X4,c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = X8,
file('<stdin>',cls_fold1__singleton_0) ).
fof(c_0_303,axiom,
! [X1,X2,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
file('<stdin>',cls_less__le__not__le_1) ).
fof(c_0_304,axiom,
! [X1,X2,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1))
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
file('<stdin>',cls_linorder__not__le_1) ).
fof(c_0_305,axiom,
! [X1,X2,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2)) ),
file('<stdin>',cls_linorder__not__less_1) ).
fof(c_0_306,axiom,
! [X2,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X2))
| ~ c_HOL_Oord__class_Oless(X2,X2,X3) ),
file('<stdin>',cls_linorder__antisym__conv2_1) ).
fof(c_0_307,axiom,
! [X16,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_SetInterval_Oord__class_OatLeastLessThan(X8,X16,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X16),X8)) ),
file('<stdin>',cls_atLeastLessThan__empty_0) ).
fof(c_0_308,axiom,
! [X14,X31,X3] :
( ~ class_Orderings_Oorder(X3)
| c_SetInterval_Oord__class_OgreaterThanAtMost(X31,X14,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X31)) ),
file('<stdin>',cls_greaterThanAtMost__empty_0) ).
fof(c_0_309,axiom,
! [X2,X16,X8,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_HOL_Oord__class_Oless(X2,c_Lattices_Oupper__semilattice__class_Osup(X8,X16,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,X8,X3) ),
file('<stdin>',cls_less__supI1_0) ).
fof(c_0_310,axiom,
! [X2,X16,X8,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_HOL_Oord__class_Oless(X2,c_Lattices_Oupper__semilattice__class_Osup(X8,X16,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,X16,X3) ),
file('<stdin>',cls_less__supI2_0) ).
fof(c_0_311,axiom,
! [X2,X5,X3] : hBOOL(hAPP(c_Set_Oinsert(X2,X5,X3),X2)),
file('<stdin>',cls_insert__code_1) ).
fof(c_0_312,axiom,
! [X43,X2,X3] :
( c_Set_Oinsert(X2,X43,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| hBOOL(c_in(X2,X43,X3)) ),
file('<stdin>',cls_comm__monoid__add_Ononempty__iff_2) ).
fof(c_0_313,axiom,
! [X8,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| hAPP(c_Complete__Lattice_OInf__class_OInf(X3),c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)) = X8 ),
file('<stdin>',cls_Inf__singleton_0) ).
fof(c_0_314,axiom,
! [X8,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| hAPP(c_Complete__Lattice_OSup__class_OSup(X3),c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)) = X8 ),
file('<stdin>',cls_Sup__singleton_0) ).
fof(c_0_315,axiom,
! [X7,X1,X2,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_HOL_Oord__class_Oless(X2,X7,X3)
| ~ c_HOL_Oord__class_Oless(X1,X7,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
file('<stdin>',cls_order__less__trans_0) ).
fof(c_0_316,axiom,
! [X7,X1,X2,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X7,X2,X3)
| ~ c_HOL_Oord__class_Oless(X7,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
file('<stdin>',cls_xt1_I10_J_0) ).
fof(c_0_317,axiom,
! [X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_Finite__Set_Olinorder__class_OMax(c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = X8 ),
file('<stdin>',cls_Max__singleton_0) ).
fof(c_0_318,axiom,
! [X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_Finite__Set_Olinorder__class_OMin(c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = X8 ),
file('<stdin>',cls_Min__singleton_0) ).
fof(c_0_319,axiom,
! [X1,X2,X3] :
( ~ class_Orderings_Olinorder(X3)
| X2 = X1
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1)) ),
file('<stdin>',cls_linorder__antisym__conv2_0) ).
fof(c_0_320,axiom,
! [X1,X2,X3] :
( ~ class_Orderings_Olinorder(X3)
| X2 = X1
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1))
| c_HOL_Oord__class_Oless(X2,X1,X3) ),
file('<stdin>',cls_linorder__antisym__conv1_0) ).
fof(c_0_321,axiom,
! [X16,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X8,X16,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X16))
| X8 = X16 ),
file('<stdin>',cls_order__neq__le__trans_0) ).
fof(c_0_322,axiom,
! [X16,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X8,X16,X3)
| X8 = X16
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X16)) ),
file('<stdin>',cls_order__le__neq__trans_0) ).
fof(c_0_323,axiom,
! [X1,X2,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X2 = X1
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1)) ),
file('<stdin>',cls_order__less__le_2) ).
fof(c_0_324,axiom,
! [X1,X2,X3] :
( ~ class_Orderings_Oorder(X3)
| X2 = X1
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1)) ),
file('<stdin>',cls_order__le__less_0) ).
fof(c_0_325,axiom,
! [X16,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X16,X8,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X16),X8))
| X8 = X16 ),
file('<stdin>',cls_xt1_I12_J_0) ).
fof(c_0_326,axiom,
! [X16,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X16,X8,X3)
| X8 = X16
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X16),X8)) ),
file('<stdin>',cls_xt1_I11_J_0) ).
fof(c_0_327,axiom,
! [X1,X2,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3) = X1
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1)) ),
file('<stdin>',cls_le__iff__sup_0) ).
fof(c_0_328,axiom,
! [X1,X2,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3) = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2)) ),
file('<stdin>',cls_sup__absorb1_0) ).
fof(c_0_329,axiom,
! [X8,X5,X3] :
( c_Set_Oinsert(X8,X5,X3) = X5
| ~ hBOOL(c_in(X8,X5,X3)) ),
file('<stdin>',cls_insert__absorb_0) ).
fof(c_0_330,axiom,
! [X16,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X8,X16,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X16,X3),c_HOL_Ouminus__class_Ouminus(X8,X3),X3) ),
file('<stdin>',cls_neg__less__iff__less_0) ).
fof(c_0_331,axiom,
! [X53,X55,X32,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X32,X53,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X32,X55,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X55,X53,X3) ),
file('<stdin>',cls_cut_0) ).
fof(c_0_332,axiom,
! [X8,X5,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| hAPP(c_Complete__Lattice_OSup__class_OSup(X3),c_Set_Oinsert(X8,X5,X3)) = c_Lattices_Oupper__semilattice__class_Osup(X8,hAPP(c_Complete__Lattice_OSup__class_OSup(X3),X5),X3) ),
file('<stdin>',cls_Sup__insert_0) ).
fof(c_0_333,axiom,
! [X2,X3] : c_Set_Ocontents(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = X2,
file('<stdin>',cls_contents__eq_0) ).
fof(c_0_334,axiom,
! [X2,X3] : c_The(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = X2,
file('<stdin>',cls_Nitpick_OThe__psimp_0) ).
fof(c_0_335,axiom,
! [X1,X2,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3) ),
file('<stdin>',cls_sup__left__idem_0) ).
fof(c_0_336,axiom,
! [X1,X2,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3) ),
file('<stdin>',cls_inf__sup__aci_I8_J_0) ).
fof(c_0_337,axiom,
! [X14,X31,X3] :
( ~ class_Orderings_Oorder(X3)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(X31,X14,X3)
| ~ c_HOL_Oord__class_Oless(X31,X14,X3) ),
file('<stdin>',cls_greaterThanAtMost__empty__iff2_0) ).
fof(c_0_338,axiom,
! [X16,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_SetInterval_Oord__class_OatLeastLessThan(X8,X16,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X8,X16,X3) ),
file('<stdin>',cls_atLeastLessThan__empty__iff_0) ).
fof(c_0_339,axiom,
! [X14,X31,X3] :
( ~ class_Orderings_Oorder(X3)
| c_SetInterval_Oord__class_OgreaterThanAtMost(X31,X14,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X31,X14,X3) ),
file('<stdin>',cls_greaterThanAtMost__empty__iff_0) ).
fof(c_0_340,axiom,
! [X16,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_SetInterval_Oord__class_OatLeastLessThan(X8,X16,X3)
| ~ c_HOL_Oord__class_Oless(X8,X16,X3) ),
file('<stdin>',cls_atLeastLessThan__empty__iff2_0) ).
fof(c_0_341,axiom,
! [X5,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(c_in(c_Finite__Set_Olinorder__class_OMax(X5,X3),X5,X3))
| X5 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X5,X3) ),
file('<stdin>',cls_Max__in_0) ).
fof(c_0_342,axiom,
! [X5,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(c_in(c_Finite__Set_Olinorder__class_OMin(X5,X3),X5,X3))
| X5 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X5,X3) ),
file('<stdin>',cls_Min__in_0) ).
fof(c_0_343,axiom,
! [X1,X2,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1)) ),
file('<stdin>',cls_linorder__linear_0) ).
fof(c_0_344,axiom,
! [X2,X5,X3] : c_Set_Oinsert(X2,c_Set_Oinsert(X2,X5,X3),X3) = c_Set_Oinsert(X2,X5,X3),
file('<stdin>',cls_insert__absorb2_0) ).
fof(c_0_345,axiom,
! [X16,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X16,c_HOL_Ouminus__class_Ouminus(X8,X3),X3)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ouminus__class_Ouminus(X16,X3),X3) ),
file('<stdin>',cls_less__minus__iff_0) ).
fof(c_0_346,axiom,
! [X16,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ouminus__class_Ouminus(X16,X3),X3)
| ~ c_HOL_Oord__class_Oless(X16,c_HOL_Ouminus__class_Ouminus(X8,X3),X3) ),
file('<stdin>',cls_less__minus__iff_1) ).
fof(c_0_347,axiom,
! [X16,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X16,X3),X8,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X8,X3),X16,X3) ),
file('<stdin>',cls_minus__less__iff_0) ).
fof(c_0_348,axiom,
! [X16,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X8,X3),X16,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X16,X3),X8,X3) ),
file('<stdin>',cls_minus__less__iff_1) ).
fof(c_0_349,axiom,
! [X32,X33,X3] :
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X33,X32,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X32,X3)
| ~ c_Finite__Set_Ofinite(X33,X3) ),
file('<stdin>',cls_finite__UnI_0) ).
fof(c_0_350,axiom,
! [X32,X33,X3] :
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X33,X32,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X32,X3)
| ~ c_Finite__Set_Ofinite(X33,X3) ),
file('<stdin>',cls_finite__Un_2) ).
fof(c_0_351,axiom,
! [X9,X5,X3] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X5,X3)
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_finite__Diff2_1) ).
fof(c_0_352,axiom,
! [X8,X29,X3] :
( hBOOL(c_in(X8,c_Collect(X29,X3),X3))
| ~ hBOOL(hAPP(X29,X8)) ),
file('<stdin>',cls_CollectI_0) ).
fof(c_0_353,axiom,
! [X2,X3] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X2)),
file('<stdin>',cls_bot1E_0) ).
fof(c_0_354,axiom,
! [X3] : c_Lattices_Oupper__semilattice__class_Osup(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)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
file('<stdin>',cls_Un__empty_2) ).
fof(c_0_355,axiom,
! [X2,X44,X3] :
( hBOOL(hAPP(X44,X2))
| ~ hBOOL(c_in(X2,X44,X3)) ),
file('<stdin>',cls_mem__def_0) ).
fof(c_0_356,axiom,
! [X8,X5,X3] :
( c_Finite__Set_Ofinite(X5,X3)
| ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X8,X5,X3),X3) ),
file('<stdin>',cls_finite__insert_0) ).
fof(c_0_357,axiom,
! [X5,X3] : ~ c_HOL_Oord__class_Oless(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
file('<stdin>',cls_not__psubset__empty_0) ).
fof(c_0_358,axiom,
! [X1,X2,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3) != X1
| hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1)) ),
file('<stdin>',cls_le__iff__sup_1) ).
fof(c_0_359,axiom,
! [X16,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X16,X3),c_HOL_Ouminus__class_Ouminus(X8,X3),X3)
| ~ c_HOL_Oord__class_Oless(X8,X16,X3) ),
file('<stdin>',cls_neg__less__iff__less_1) ).
fof(c_0_360,axiom,
! [X1,X2,X3] :
( ~ class_Orderings_Opreorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1))
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
file('<stdin>',cls_order__less__imp__le_0) ).
fof(c_0_361,axiom,
! [X1,X2,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1))
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
file('<stdin>',cls_order__le__less_1) ).
fof(c_0_362,axiom,
! [X16,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X8,X16,X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X16)) ),
file('<stdin>',cls_atLeastatMost__empty__iff2_1) ).
fof(c_0_363,axiom,
! [X16,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_SetInterval_Oord__class_OatLeastAtMost(X8,X16,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X16)) ),
file('<stdin>',cls_atLeastatMost__empty__iff_1) ).
fof(c_0_364,axiom,
! [X9,X5,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X5 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Un__empty_0) ).
fof(c_0_365,axiom,
! [X9,X5,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Un__empty_1) ).
fof(c_0_366,axiom,
! [X9,X5,X3] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X5,X3) ),
file('<stdin>',cls_finite__Diff_0) ).
fof(c_0_367,axiom,
! [X16,X8,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X8,X16,X3),X3) = c_HOL_Ominus__class_Ominus(X16,X8,X3) ),
file('<stdin>',cls_minus__diff__eq_0) ).
fof(c_0_368,axiom,
! [X1,X43,X2,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X43,X1,X3) != c_HOL_Ominus__class_Ominus(X2,X2,X3)
| X43 = X1 ),
file('<stdin>',cls_eq__eqI_1) ).
fof(c_0_369,axiom,
! [X35,X36,X2,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X2,X2,X3) != c_HOL_Ominus__class_Ominus(X36,X35,X3)
| X36 = X35 ),
file('<stdin>',cls_eq__eqI_0) ).
fof(c_0_370,axiom,
! [X16,X8,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X16,X8,X3)
| ~ c_HOL_Oord__class_Oless(X8,X16,X3) ),
file('<stdin>',cls_order__less__asym_H_0) ).
fof(c_0_371,axiom,
! [X1,X2,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
file('<stdin>',cls_order__less__asym_0) ).
fof(c_0_372,axiom,
! [X1,X2,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
file('<stdin>',cls_not__less__iff__gr__or__eq_1) ).
fof(c_0_373,axiom,
! [X16,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X8,X16,X3)
| ~ c_HOL_Oord__class_Oless(X16,X8,X3) ),
file('<stdin>',cls_xt1_I9_J_0) ).
fof(c_0_374,axiom,
! [X4,X5,X3] : c_Finite__Set_Ofold1(X4,X5,X3) = c_The(c_Finite__Set_Ofold1Set(X4,X5,X3),X3),
file('<stdin>',cls_fold1__def_0) ).
fof(c_0_375,axiom,
! [X16,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_SetInterval_Oord__class_OatLeastAtMost(X8,X16,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X16,X8,X3) ),
file('<stdin>',cls_atLeastatMost__empty_0) ).
fof(c_0_376,axiom,
! [X64,X65,X3] :
( X65 = X64
| ~ hBOOL(hAPP(hAPP(c_fequal(X3),X65),X64)) ),
file('<stdin>',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
fof(c_0_377,axiom,
! [X1,X2,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1)) ),
file('<stdin>',cls_linorder__not__le_0) ).
fof(c_0_378,axiom,
! [X1,X2,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| c_HOL_Oord__class_Oless(X2,X1,X3) ),
file('<stdin>',cls_linorder__not__less_0) ).
fof(c_0_379,axiom,
! [X2,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X2,X2,X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X2)) ),
file('<stdin>',cls_linorder__antisym__conv1_1) ).
fof(c_0_380,axiom,
! [X1,X2,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2)) ),
file('<stdin>',cls_not__leE_0) ).
fof(c_0_381,axiom,
! [X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_SetInterval_Oord__class_OatLeastAtMost(X8,X8,X3) = c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) ),
file('<stdin>',cls_atLeastAtMost__singleton_0) ).
fof(c_0_382,axiom,
! [X2,X44,X3] :
( hBOOL(c_in(X2,X44,X3))
| ~ hBOOL(hAPP(X44,X2)) ),
file('<stdin>',cls_mem__def_1) ).
fof(c_0_383,axiom,
! [X8,X3] : c_Collect(hAPP(c_fequal(X3),X8),X3) = c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),
file('<stdin>',cls_singleton__conv2_0) ).
fof(c_0_384,axiom,
! [X5,X3] : c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X5,tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
file('<stdin>',cls_empty__Diff_0) ).
fof(c_0_385,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_386,axiom,
! [X9,X5,X3] : c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X9,X5,tc_fun(X3,tc_bool)),
file('<stdin>',cls_Un__commute_0) ).
fof(c_0_387,axiom,
! [X8,X5,X3] :
( c_Finite__Set_Ofinite(c_Set_Oinsert(X8,X5,X3),X3)
| ~ c_Finite__Set_Ofinite(X5,X3) ),
file('<stdin>',cls_finite__insert_1) ).
fof(c_0_388,axiom,
! [X14,X31,X3] :
( ~ class_Orderings_Oorder(X3)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X31,X14,X3)
| c_HOL_Oord__class_Oless(X31,X14,X3) ),
file('<stdin>',cls_greaterThanAtMost__empty__iff2_1) ).
fof(c_0_389,axiom,
! [X16,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_SetInterval_Oord__class_OatLeastLessThan(X8,X16,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X8,X16,X3) ),
file('<stdin>',cls_atLeastLessThan__empty__iff_1) ).
fof(c_0_390,axiom,
! [X14,X31,X3] :
( ~ class_Orderings_Oorder(X3)
| c_SetInterval_Oord__class_OgreaterThanAtMost(X31,X14,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X31,X14,X3) ),
file('<stdin>',cls_greaterThanAtMost__empty__iff_1) ).
fof(c_0_391,axiom,
! [X16,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X8,X16,X3)
| c_HOL_Oord__class_Oless(X8,X16,X3) ),
file('<stdin>',cls_atLeastLessThan__empty__iff2_1) ).
fof(c_0_392,axiom,
! [X2,X3] :
( ~ class_Orderings_Obot(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_Orderings_Obot__class_Obot(X3)),X2)) ),
file('<stdin>',cls_bot__least_0) ).
fof(c_0_393,axiom,
! [X32,X3] : c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),X3),
file('<stdin>',cls_empty_0) ).
fof(c_0_394,axiom,
! [X5,X3] : c_HOL_Ominus__class_Ominus(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X5,
file('<stdin>',cls_Diff__empty_0) ).
fof(c_0_395,axiom,
! [X9,X3] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X9,tc_fun(X3,tc_bool)) = X9,
file('<stdin>',cls_Un__empty__left_0) ).
fof(c_0_396,axiom,
! [X5,X3] : c_Lattices_Oupper__semilattice__class_Osup(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X5,
file('<stdin>',cls_Un__empty__right_0) ).
fof(c_0_397,axiom,
! [X5,X6] :
( ~ class_HOL_Ouminus(X6)
| hAPP(c_HOL_Ouminus__class_Ouminus(X5,tc_fun(t_a,X6)),v_x) = c_HOL_Ouminus__class_Ouminus(hAPP(X5,v_x),X6) ),
file('<stdin>',cls_fun__Compl__def_0) ).
fof(c_0_398,axiom,
! [X8,X5,X3] : c_Set_Oinsert(X8,X5,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
file('<stdin>',cls_insert__not__empty_0) ).
fof(c_0_399,axiom,
! [X8,X5,X3] : c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_Set_Oinsert(X8,X5,X3),
file('<stdin>',cls_empty__not__insert_0) ).
fof(c_0_400,axiom,
! [X2,X3] : ~ c_HOL_Oord__class_Oless(X2,X2,tc_fun(X3,tc_bool)),
file('<stdin>',cls_psubset__eq_1) ).
fof(c_0_401,axiom,
! [X28,X29,X6,X3] : hAPP(c_COMBK(X29,X3,X6),X28) = X29,
file('<stdin>',cls_COMBK__def_0) ).
fof(c_0_402,axiom,
! [X1,X2,X3] :
( ~ class_Orderings_Olinorder(X3)
| X2 = X1
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3) ),
file('<stdin>',cls_linorder__antisym__conv3_0) ).
fof(c_0_403,axiom,
! [X1,X2,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X2 = X1
| c_HOL_Oord__class_Oless(X2,X1,X3) ),
file('<stdin>',cls_linorder__less__linear_0) ).
fof(c_0_404,axiom,
! [X1,X2,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X2 = X1 ),
file('<stdin>',cls_linorder__neqE_0) ).
fof(c_0_405,axiom,
! [X1,X2,X3] :
( ~ class_Orderings_Olinorder(X3)
| X2 = X1
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3) ),
file('<stdin>',cls_not__less__iff__gr__or__eq_0) ).
fof(c_0_406,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X2 = X1 ),
file('<stdin>',cls_linorder__neqE__ordered__idom_0) ).
fof(c_0_407,axiom,
! [X9,X5,X3] :
( c_HOL_Ouminus__class_Ouminus(X5,tc_fun(X3,tc_bool)) != c_HOL_Ouminus__class_Ouminus(X9,tc_fun(X3,tc_bool))
| X5 = X9 ),
file('<stdin>',cls_Compl__eq__Compl__iff_0) ).
fof(c_0_408,axiom,
! [X1,X2,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) ),
file('<stdin>',cls_sup__commute_0) ).
fof(c_0_409,axiom,
! [X1,X2,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) ),
file('<stdin>',cls_inf__sup__aci_I5_J_0) ).
fof(c_0_410,axiom,
! [X2,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X2)) ),
file('<stdin>',cls_order__eq__iff_0) ).
fof(c_0_411,axiom,
! [X2,X3] :
( ~ class_Orderings_Opreorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X2)) ),
file('<stdin>',cls_order__eq__refl_0) ).
fof(c_0_412,axiom,
! [X2,X29,X3] :
( c_Collect(X29,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(X29,X2)) ),
file('<stdin>',cls_Collect__empty__eq_0) ).
fof(c_0_413,axiom,
! [X2,X29,X3] :
( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_Collect(X29,X3)
| ~ hBOOL(hAPP(X29,X2)) ),
file('<stdin>',cls_empty__Collect__eq_0) ).
fof(c_0_414,axiom,
( ~ class_HOL_Ouminus(t_b)
| hAPP(c_HOL_Ouminus__class_Ouminus(v_A,tc_fun(t_a,t_b)),v_x) = c_HOL_Ouminus__class_Ouminus(hAPP(v_A,v_x),t_b) ),
file('<stdin>',cls_fun__Compl__def__raw_0) ).
fof(c_0_415,axiom,
hAPP(c_COMBK(v_P,t_a,t_b),v_Q) = v_P,
file('<stdin>',cls_COMBK__def__raw_0) ).
fof(c_0_416,axiom,
! [X5,X3] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X5,
file('<stdin>',cls_double__complement_0) ).
fof(c_0_417,axiom,
! [X2,X3] : hBOOL(hAPP(hAPP(c_fequal(X3),X2),X2)),
file('<stdin>',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
fof(c_0_418,axiom,
! [X9,X5,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X5,X9,X3) != c_Orderings_Obot__class_Obot(X3)
| X9 = c_Orderings_Obot__class_Obot(X3) ),
file('<stdin>',cls_sup__eq__bot__eq2_0) ).
fof(c_0_419,axiom,
! [X9,X5,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X5,X9,X3) != c_Orderings_Obot__class_Obot(X3)
| X5 = c_Orderings_Obot__class_Obot(X3) ),
file('<stdin>',cls_sup__eq__bot__eq1_0) ).
fof(c_0_420,axiom,
! [X5,X3] : c_HOL_Ominus__class_Ominus(X5,X5,tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
file('<stdin>',cls_Diff__cancel_0) ).
fof(c_0_421,axiom,
! [X2,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X2,X3) ),
file('<stdin>',cls_order__less__irrefl_0) ).
fof(c_0_422,axiom,
! [X2,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X2,X3) ),
file('<stdin>',cls_linorder__neq__iff_1) ).
fof(c_0_423,axiom,
! [X2,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X2,X3) ),
file('<stdin>',cls_order__less__le_1) ).
fof(c_0_424,axiom,
! [X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| hAPP(c_Complete__Lattice_OSup__class_OSup(X3),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))) = c_Orderings_Obot__class_Obot(X3) ),
file('<stdin>',cls_Sup__empty_0) ).
fof(c_0_425,axiom,
! [X5,X3] : c_Lattices_Oupper__semilattice__class_Osup(X5,X5,tc_fun(X3,tc_bool)) = X5,
file('<stdin>',cls_Un__absorb_0) ).
fof(c_0_426,axiom,
! [X6] :
( ~ class_Orderings_Obot(X6)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X6)),v_x) = c_Orderings_Obot__class_Obot(X6) ),
file('<stdin>',cls_bot__fun__eq_0) ).
fof(c_0_427,axiom,
! [X2,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X2,c_Orderings_Obot__class_Obot(X3),X3) = X2 ),
file('<stdin>',cls_sup__bot__right_0) ).
fof(c_0_428,axiom,
! [X2,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X3),X2,X3) = X2 ),
file('<stdin>',cls_sup__bot__left_0) ).
fof(c_0_429,axiom,
! [X3] : c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),
file('<stdin>',cls_finite_OemptyI_0) ).
fof(c_0_430,axiom,
! [X2,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X2,X2,X3) = X2 ),
file('<stdin>',cls_sup__idem_0) ).
fof(c_0_431,axiom,
! [X16,X8,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(X8,X3) != c_HOL_Ouminus__class_Ouminus(X16,X3)
| X8 = X16 ),
file('<stdin>',cls_neg__equal__iff__equal_0) ).
fof(c_0_432,axiom,
! [X1,X2,X3] :
( ~ class_Lattices_Oboolean__algebra(X3)
| c_HOL_Ouminus__class_Ouminus(X2,X3) != c_HOL_Ouminus__class_Ouminus(X1,X3)
| X2 = X1 ),
file('<stdin>',cls_compl__eq__compl__iff_0) ).
fof(c_0_433,axiom,
! [X2,X3] : c_The(hAPP(c_fequal(X3),X2),X3) = X2,
file('<stdin>',cls_the__sym__eq__trivial_0) ).
fof(c_0_434,axiom,
! [X8,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X8,X3),X3) = X8 ),
file('<stdin>',cls_minus__minus_0) ).
fof(c_0_435,axiom,
! [X2,X3] :
( ~ class_Lattices_Oboolean__algebra(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = X2 ),
file('<stdin>',cls_double__compl_0) ).
fof(c_0_436,axiom,
! [X16,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| X16 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X16,X3),X3) ),
file('<stdin>',cls_equation__minus__iff_0) ).
fof(c_0_437,axiom,
! [X8,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| X8 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X8,X3),X3) ),
file('<stdin>',cls_equation__minus__iff_1) ).
fof(c_0_438,axiom,
! [X16,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X16,X3),X3) = X16 ),
file('<stdin>',cls_minus__equation__iff_1) ).
fof(c_0_439,axiom,
! [X45,X46,X47,X48] :
( c_Com_Ocom_OSemi(X48,X46) != c_Com_Ocom_OSemi(X47,X45)
| X48 = X47 ),
file('<stdin>',cls_com_Osimps_I3_J_0) ).
fof(c_0_440,axiom,
! [X45,X46,X47,X48] :
( c_Com_Ocom_OSemi(X48,X46) != c_Com_Ocom_OSemi(X47,X45)
| X46 = X45 ),
file('<stdin>',cls_com_Osimps_I3_J_1) ).
fof(c_0_441,axiom,
! [X62,X63] :
( class_Finite__Set_Ofinite_Ofinite(tc_fun(X62,X63))
| ~ class_Finite__Set_Ofinite_Ofinite(X63)
| ~ class_Finite__Set_Ofinite_Ofinite(X62) ),
file('<stdin>',clsarity_fun__Finite__Set_Ofinite_Ofinite) ).
fof(c_0_442,axiom,
! [X62,X63] :
( class_HOL_Oord(tc_fun(X62,X63))
| ~ class_HOL_Oord(X63) ),
file('<stdin>',clsarity_fun__HOL_Oord) ).
fof(c_0_443,axiom,
! [X62,X63] :
( class_HOL_Ominus(tc_fun(X62,X63))
| ~ class_HOL_Ominus(X63) ),
file('<stdin>',clsarity_fun__HOL_Ominus) ).
fof(c_0_444,axiom,
! [X62,X63] :
( class_HOL_Ouminus(tc_fun(X62,X63))
| ~ class_HOL_Ouminus(X63) ),
file('<stdin>',clsarity_fun__HOL_Ouminus) ).
fof(c_0_445,axiom,
! [X62,X63] :
( class_Orderings_Obot(tc_fun(X62,X63))
| ~ class_Orderings_Obot(X63) ),
file('<stdin>',clsarity_fun__Orderings_Obot) ).
fof(c_0_446,axiom,
! [X62,X63] :
( class_Orderings_Oorder(tc_fun(X62,X63))
| ~ class_Orderings_Oorder(X63) ),
file('<stdin>',clsarity_fun__Orderings_Oorder) ).
fof(c_0_447,axiom,
! [X62,X63] :
( class_Lattices_Olattice(tc_fun(X62,X63))
| ~ class_Lattices_Olattice(X63) ),
file('<stdin>',clsarity_fun__Lattices_Olattice) ).
fof(c_0_448,axiom,
! [X62,X63] :
( class_Orderings_Opreorder(tc_fun(X62,X63))
| ~ class_Orderings_Opreorder(X63) ),
file('<stdin>',clsarity_fun__Orderings_Opreorder) ).
fof(c_0_449,axiom,
! [X62,X63] :
( class_Lattices_Oboolean__algebra(tc_fun(X62,X63))
| ~ class_Lattices_Oboolean__algebra(X63) ),
file('<stdin>',clsarity_fun__Lattices_Oboolean__algebra) ).
fof(c_0_450,axiom,
! [X62,X63] :
( class_Lattices_Obounded__lattice(tc_fun(X62,X63))
| ~ class_Lattices_Obounded__lattice(X63) ),
file('<stdin>',clsarity_fun__Lattices_Obounded__lattice) ).
fof(c_0_451,axiom,
! [X62,X63] :
( class_Lattices_Oupper__semilattice(tc_fun(X62,X63))
| ~ class_Lattices_Olattice(X63) ),
file('<stdin>',clsarity_fun__Lattices_Oupper__semilattice) ).
fof(c_0_452,axiom,
! [X62,X63] :
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X62,X63))
| ~ class_Complete__Lattice_Ocomplete__lattice(X63) ),
file('<stdin>',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).
fof(c_0_453,axiom,
! [X45,X47] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(X47,X45),
file('<stdin>',cls_com_Osimps_I12_J_0) ).
fof(c_0_454,axiom,
! [X45,X47] : c_Com_Ocom_OSemi(X47,X45) != c_Com_Ocom_OSKIP,
file('<stdin>',cls_com_Osimps_I13_J_0) ).
fof(c_0_455,axiom,
! [X5,X3] :
( ~ class_Finite__Set_Ofinite_Ofinite(X3)
| c_Finite__Set_Ofinite(X5,X3) ),
file('<stdin>',cls_finite_0) ).
fof(c_0_456,axiom,
! [X29,X3] : c_Collect(X29,X3) = X29,
file('<stdin>',cls_Collect__def_0) ).
fof(c_0_457,axiom,
class_HOL_Oord(tc_bool),
file('<stdin>',clsarity_bool__HOL_Oord) ).
fof(c_0_458,axiom,
class_HOL_Ominus(tc_bool),
file('<stdin>',clsarity_bool__HOL_Ominus) ).
fof(c_0_459,axiom,
class_HOL_Ouminus(tc_bool),
file('<stdin>',clsarity_bool__HOL_Ouminus) ).
fof(c_0_460,axiom,
class_Orderings_Obot(tc_bool),
file('<stdin>',clsarity_bool__Orderings_Obot) ).
fof(c_0_461,axiom,
class_Orderings_Oorder(tc_bool),
file('<stdin>',clsarity_bool__Orderings_Oorder) ).
fof(c_0_462,axiom,
class_Lattices_Olattice(tc_bool),
file('<stdin>',clsarity_bool__Lattices_Olattice) ).
fof(c_0_463,axiom,
class_Orderings_Opreorder(tc_bool),
file('<stdin>',clsarity_bool__Orderings_Opreorder) ).
fof(c_0_464,axiom,
class_Finite__Set_Ofinite_Ofinite(tc_bool),
file('<stdin>',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).
fof(c_0_465,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
file('<stdin>',clsarity_bool__Lattices_Oboolean__algebra) ).
fof(c_0_466,axiom,
class_Lattices_Obounded__lattice(tc_bool),
file('<stdin>',clsarity_bool__Lattices_Obounded__lattice) ).
fof(c_0_467,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
file('<stdin>',clsarity_bool__Lattices_Oupper__semilattice) ).
fof(c_0_468,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
file('<stdin>',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).
fof(c_0_469,axiom,
class_HOL_Oord(tc_nat),
file('<stdin>',clsarity_nat__HOL_Oord) ).
fof(c_0_470,axiom,
class_HOL_Ominus(tc_nat),
file('<stdin>',clsarity_nat__HOL_Ominus) ).
fof(c_0_471,axiom,
class_Orderings_Obot(tc_nat),
file('<stdin>',clsarity_nat__Orderings_Obot) ).
fof(c_0_472,axiom,
class_Orderings_Oorder(tc_nat),
file('<stdin>',clsarity_nat__Orderings_Oorder) ).
fof(c_0_473,axiom,
class_Lattices_Olattice(tc_nat),
file('<stdin>',clsarity_nat__Lattices_Olattice) ).
fof(c_0_474,axiom,
class_Orderings_Olinorder(tc_nat),
file('<stdin>',clsarity_nat__Orderings_Olinorder) ).
fof(c_0_475,axiom,
class_Orderings_Opreorder(tc_nat),
file('<stdin>',clsarity_nat__Orderings_Opreorder) ).
fof(c_0_476,axiom,
class_Lattices_Oupper__semilattice(tc_nat),
file('<stdin>',clsarity_nat__Lattices_Oupper__semilattice) ).
fof(c_0_477,plain,
! [X19,X20,X21,X22,X23,X24,X25,X26,X3] :
( c_Complete__Lattice_Ocomplete__lattice(X25,X26,c_COMBC(X21,X3,X3,tc_bool),c_COMBC(X22,X3,X3,tc_bool),X20,X23,X19,X24,X3)
| ~ c_Complete__Lattice_Ocomplete__lattice(X26,X25,X21,X22,X23,X20,X24,X19,X3) ),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_478,plain,
! [X19,X20,X21,X22,X23,X38,X24,X25,X39,X26,X5,X6,X3] :
( hBOOL(hAPP(hAPP(X21,c_Complete__Lattice_Ocomplete__lattice_OINFI(X26,X5,X39,X3,X6)),hAPP(X39,X38)))
| ~ hBOOL(c_in(X38,X5,X6))
| ~ c_Complete__Lattice_Ocomplete__lattice(X26,X25,X21,X22,X23,X20,X24,X19,X3) ),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_479,plain,
! [X19,X20,X21,X22,X23,X38,X24,X25,X39,X26,X5,X6,X3] :
( hBOOL(hAPP(hAPP(X21,hAPP(X39,X38)),c_Complete__Lattice_Ocomplete__lattice_OSUPR(X25,X5,X39,X3,X6)))
| ~ hBOOL(c_in(X38,X5,X6))
| ~ c_Complete__Lattice_Ocomplete__lattice(X26,X25,X21,X22,X23,X20,X24,X19,X3) ),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_480,plain,
! [X19,X20,X21,X22,X23,X24,X25,X39,X26,X5,X6,X3] :
( c_Complete__Lattice_Ocomplete__lattice_OINFI(X26,X5,c_COMBK(X39,X3,X6),X3,X6) = X39
| X5 = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool))
| ~ c_Complete__Lattice_Ocomplete__lattice(X26,X25,X21,X22,X23,X20,X24,X19,X3) ),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_481,plain,
! [X19,X20,X21,X22,X23,X24,X25,X39,X26,X5,X6,X3] :
( c_Complete__Lattice_Ocomplete__lattice_OSUPR(X25,X5,c_COMBK(X39,X3,X6),X3,X6) = X39
| X5 = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool))
| ~ c_Complete__Lattice_Ocomplete__lattice(X26,X25,X21,X22,X23,X20,X24,X19,X3) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_482,plain,
! [X19,X20,X21,X22,X23,X24,X16,X8,X25,X26,X3] :
( hAPP(X25,c_Set_Oinsert(X8,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)) = hAPP(hAPP(X20,X8),X16)
| ~ c_Complete__Lattice_Ocomplete__lattice(X26,X25,X21,X22,X23,X20,X24,X19,X3) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_483,plain,
! [X19,X20,X21,X22,X23,X24,X16,X8,X25,X26,X3] :
( hAPP(X26,c_Set_Oinsert(X8,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)) = hAPP(hAPP(X23,X8),X16)
| ~ c_Complete__Lattice_Ocomplete__lattice(X26,X25,X21,X22,X23,X20,X24,X19,X3) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_484,plain,
! [X2,X19,X20,X21,X22,X23,X24,X25,X26,X5,X3] :
( hBOOL(hAPP(hAPP(X21,hAPP(X26,X5)),X2))
| ~ hBOOL(c_in(X2,X5,X3))
| ~ c_Complete__Lattice_Ocomplete__lattice(X26,X25,X21,X22,X23,X20,X24,X19,X3) ),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_485,plain,
! [X2,X19,X20,X21,X22,X23,X24,X25,X26,X5,X3] :
( hBOOL(hAPP(hAPP(X21,X2),hAPP(X25,X5)))
| ~ hBOOL(c_in(X2,X5,X3))
| ~ c_Complete__Lattice_Ocomplete__lattice(X26,X25,X21,X22,X23,X20,X24,X19,X3) ),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
fof(c_0_486,plain,
! [X19,X20,X21,X22,X23,X24,X8,X25,X26,X3] :
( hAPP(X25,c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)) = X8
| ~ c_Complete__Lattice_Ocomplete__lattice(X26,X25,X21,X22,X23,X20,X24,X19,X3) ),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_487,plain,
! [X19,X20,X21,X22,X23,X24,X8,X25,X26,X3] :
( hAPP(X26,c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)) = X8
| ~ c_Complete__Lattice_Ocomplete__lattice(X26,X25,X21,X22,X23,X20,X24,X19,X3) ),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_488,plain,
! [X19,X20,X21,X22,X23,X24,X8,X25,X26,X5,X3] :
( hAPP(X25,c_Set_Oinsert(X8,X5,X3)) = hAPP(hAPP(X20,X8),hAPP(X25,X5))
| ~ c_Complete__Lattice_Ocomplete__lattice(X26,X25,X21,X22,X23,X20,X24,X19,X3) ),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_489,plain,
! [X19,X20,X21,X22,X23,X24,X8,X25,X26,X5,X3] :
( hAPP(X26,c_Set_Oinsert(X8,X5,X3)) = hAPP(hAPP(X23,X8),hAPP(X26,X5))
| ~ c_Complete__Lattice_Ocomplete__lattice(X26,X25,X21,X22,X23,X20,X24,X19,X3) ),
inference(fof_simplification,[status(thm)],[c_0_12]) ).
fof(c_0_490,plain,
! [X19,X20,X21,X22,X23,X24,X25,X26,X3] :
( hAPP(X25,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))) = X24
| ~ c_Complete__Lattice_Ocomplete__lattice(X26,X25,X21,X22,X23,X20,X24,X19,X3) ),
inference(fof_simplification,[status(thm)],[c_0_13]) ).
fof(c_0_491,plain,
! [X19,X20,X21,X22,X23,X24,X25,X26,X3] :
( hAPP(X26,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))) = X19
| ~ c_Complete__Lattice_Ocomplete__lattice(X26,X25,X21,X22,X23,X20,X24,X19,X3) ),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_492,plain,
! [X43,X2,X15,X28,X29,X32] :
( c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X15,X28,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X28,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X32,X29,X28,X15)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X32,X29,X28,X15,X2,X43)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,X15,X43,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_493,plain,
! [X43,X2,X15,X28,X29,X32] :
( c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X15,X28,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X28,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X32,X29,X28,X15)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X32,X29,X28,X15,X2,X43)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,X15,X43,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(fof_simplification,[status(thm)],[c_0_16]) ).
fof(c_0_494,plain,
! [X15,X28,X29,X32] :
( c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X15,X28,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(hAPP(c_COMBC(c_fequal(tc_Com_Ostate),tc_Com_Ostate,tc_Com_Ostate,tc_bool),v_sko__Hoare__Mirabelle__Xescape__2(X32,X29,X28,X15)),tc_fun(tc_Com_Ostate,tc_bool),t_a),X15,c_COMBK(hAPP(X28,v_sko__Hoare__Mirabelle__Xescape__1(X32,X29,X28,X15)),tc_fun(tc_Com_Ostate,tc_bool),t_a),t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(fof_simplification,[status(thm)],[c_0_17]) ).
fof(c_0_495,plain,
! [X43,X2,X15,X50,X28,X29,X32] :
( c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X15,X28,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X43,X50),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X32,X29,X28,X15,X2,X43)))
| ~ hBOOL(hAPP(hAPP(X2,X50),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X32,X29,X28,X15)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,X15,X43,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(fof_simplification,[status(thm)],[c_0_18]) ).
fof(c_0_496,plain,
! [X43,X2,X15,X50,X28,X29,X32] :
( c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X15,X28,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X43,X50),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X32,X29,X28,X15,X2,X43)))
| ~ hBOOL(hAPP(hAPP(X2,X50),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X32,X29,X28,X15)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,X15,X43,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(fof_simplification,[status(thm)],[c_0_19]) ).
fof(c_0_497,plain,
! [X7,X1,X2,X4,X5,X6,X3] :
( c_Nitpick_Ofold__graph_H(X4,X7,X5,hAPP(hAPP(X4,X2),X1),X3,X6)
| ~ c_Nitpick_Ofold__graph_H(X4,X7,c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X1,X3,X6)
| ~ hBOOL(c_in(X2,X5,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_20]) ).
fof(c_0_498,plain,
! [X7,X1,X2,X4,X5,X6,X3] :
( c_Finite__Set_Ofold__graph(X4,X7,X5,hAPP(hAPP(X4,X2),X1),X3,X6)
| ~ hBOOL(c_in(X2,X5,X3))
| ~ c_Finite__Set_Ofold__graph(X4,X7,c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X1,X3,X6) ),
inference(fof_simplification,[status(thm)],[c_0_21]) ).
fof(c_0_499,plain,
! [X7,X1,X2,X4,X5,X6,X3] :
( c_Finite__Set_Ofold__graph(X4,X7,c_Set_Oinsert(X2,X5,X3),hAPP(hAPP(X4,X2),X1),X3,X6)
| ~ c_Finite__Set_Ofold__graph(X4,X7,X5,X1,X3,X6)
| hBOOL(c_in(X2,X5,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_22]) ).
fof(c_0_500,axiom,
! [X4,X9,X5,X6,X3] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(c_Set_Oimage(X4,X5,X6,X3),c_Set_Oimage(X4,X9,X6,X3),tc_fun(X3,tc_bool))),c_Set_Oimage(X4,c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X6,tc_bool)),X6,X3))),
c_0_23 ).
fof(c_0_501,plain,
! [X2,X4,X8,X5,X3] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X4,c_Set_Oinsert(X8,X5,X3),X3),X2))
| hBOOL(c_in(X8,X5,X3))
| ~ c_Finite__Set_Ofold__graph(X4,X8,X5,X2,X3,X3) ),
inference(fof_simplification,[status(thm)],[c_0_24]) ).
fof(c_0_502,plain,
! [X7,X2,X4,X6,X3] :
( X2 = X7
| ~ c_Finite__Set_Ofold__graph(X4,X7,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X2,X3,X6) ),
inference(fof_simplification,[status(thm)],[c_0_25]) ).
fof(c_0_503,plain,
! [X7,X2,X4,X5,X6,X3] :
( c_Finite__Set_Ofinite(X5,X3)
| ~ c_Finite__Set_Ofold__graph(X4,X7,X5,X2,X3,X6) ),
inference(fof_simplification,[status(thm)],[c_0_26]) ).
fof(c_0_504,plain,
! [X15,X51,X28,X52,X29,X32] :
( c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X15,X28,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X28,v_sko__Hoare__Mirabelle__Xconseq12__1(X29,X52,X28,X51)),v_sko__Hoare__Mirabelle__Xconseq12__3(X29,X52,X28,X51)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X52,X15,X51,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(fof_simplification,[status(thm)],[c_0_27]) ).
fof(c_0_505,plain,
! [X15,X51,X28,X52,X29,X32] :
( c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X15,X28,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X29,v_sko__Hoare__Mirabelle__Xconseq12__1(X29,X52,X28,X51)),v_sko__Hoare__Mirabelle__Xconseq12__2(X29,X52,X28,X51)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X52,X15,X51,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(fof_simplification,[status(thm)],[c_0_28]) ).
fof(c_0_506,axiom,
! [X7,X4,X6,X3] : c_Nitpick_Ofold__graph_H(X4,X7,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X7,X3,X6),
c_0_29 ).
fof(c_0_507,axiom,
! [X7,X4,X6,X3] : c_Finite__Set_Ofold__graph(X4,X7,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X7,X3,X6),
c_0_30 ).
fof(c_0_508,plain,
! [X15,X50,X51,X28,X52,X29,X32] :
( c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X15,X28,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X51,X50),v_sko__Hoare__Mirabelle__Xconseq12__3(X29,X52,X28,X51)))
| ~ hBOOL(hAPP(hAPP(X52,X50),v_sko__Hoare__Mirabelle__Xconseq12__2(X29,X52,X28,X51)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X52,X15,X51,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(fof_simplification,[status(thm)],[c_0_31]) ).
fof(c_0_509,plain,
! [X18,X15,X27,X28,X29,X32,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OSemi(X15,X18),X27,X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X28,X18,X27,X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X15,X28,X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_32]) ).
fof(c_0_510,plain,
! [X2,X9,X5,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),c_Set_Oinsert(X2,X9,X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool))),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_33]) ).
fof(c_0_511,plain,
! [X2,X9,X5,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),c_Set_Oinsert(X2,X9,X3)))
| ~ hBOOL(c_in(X2,X5,X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool))),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_34]) ).
fof(c_0_512,plain,
! [X2,X9,X5,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),c_Set_Oinsert(X2,X9,X3)))
| ~ hBOOL(c_in(X2,X5,X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool))),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_35]) ).
fof(c_0_513,plain,
! [X2,X49,X9,X5,X6,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),hAPP(X5,X2)),X9))
| ~ hBOOL(c_in(X2,X49,X6))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X49,X5,X6,tc_fun(X3,tc_bool))),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_36]) ).
fof(c_0_514,axiom,
! [X15,X28,X29,X32] :
( c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X15,X28,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X29,v_sko__Hoare__Mirabelle__Xescape__1(X32,X29,X28,X15)),v_sko__Hoare__Mirabelle__Xescape__2(X32,X29,X28,X15))) ),
c_0_37 ).
fof(c_0_515,axiom,
! [X15,X28,X29,X32] :
( c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X15,X28,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X29,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X32,X29,X28,X15)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X32,X29,X28,X15))) ),
c_0_38 ).
fof(c_0_516,axiom,
! [X15,X28,X29,X32] :
( c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X15,X28,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X29,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X32,X29,X28,X15)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X32,X29,X28,X15))) ),
c_0_39 ).
fof(c_0_517,plain,
! [X2,X4,X9,X5,X6,X3] :
( hBOOL(c_in(hAPP(X4,X2),X9,X3))
| ~ hBOOL(c_in(X2,X5,X6))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_Set_Oimage(X4,X5,X6,X3)),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_40]) ).
fof(c_0_518,plain,
! [X4,X9,X5,X6,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X6,tc_bool)),c_Set_Oimage(X4,X5,X3,X6)),c_Set_Oimage(X4,X9,X3,X6)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_41]) ).
fof(c_0_519,plain,
! [X2,X4,X5,X6,X3] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X6,tc_bool)),X2),X5))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_Set_Oimage(X4,X2,X6,X3)),c_Set_Oimage(X4,X5,X6,X3))) ),
inference(fof_simplification,[status(thm)],[c_0_42]) ).
fof(c_0_520,plain,
! [X15,X51,X28,X29,X32] :
( c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X15,X28,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X28,v_sko__Hoare__Mirabelle__Xconseq2__1(X28,X51)),v_sko__Hoare__Mirabelle__Xconseq2__2(X28,X51)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X15,X51,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(fof_simplification,[status(thm)],[c_0_43]) ).
fof(c_0_521,plain,
! [X15,X28,X52,X29,X32] :
( c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X15,X28,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X52,v_sko__Hoare__Mirabelle__Xconseq1__1(X29,X52)),v_sko__Hoare__Mirabelle__Xconseq1__2(X29,X52)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X52,X15,X28,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(fof_simplification,[status(thm)],[c_0_44]) ).
fof(c_0_522,plain,
! [X2,X9,X5,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool))),X9))
| ~ hBOOL(c_in(X2,X5,X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),c_Set_Oinsert(X2,X9,X3))) ),
inference(fof_simplification,[status(thm)],[c_0_45]) ).
fof(c_0_523,plain,
! [X15,X28,X52,X29,X32] :
( c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X15,X28,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X29,v_sko__Hoare__Mirabelle__Xconseq1__1(X29,X52)),v_sko__Hoare__Mirabelle__Xconseq1__2(X29,X52)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X52,X15,X28,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(fof_simplification,[status(thm)],[c_0_46]) ).
fof(c_0_524,plain,
! [X15,X51,X28,X29,X32] :
( c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X15,X28,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X51,v_sko__Hoare__Mirabelle__Xconseq2__1(X28,X51)),v_sko__Hoare__Mirabelle__Xconseq2__2(X28,X51)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,X15,X51,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(fof_simplification,[status(thm)],[c_0_47]) ).
fof(c_0_525,axiom,
! [X8,X9,X3] : c_Set_Oinsert(X8,X9,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X3),X3,X3,tc_bool),X8),X3),X9,tc_fun(X3,tc_bool)),
c_0_48 ).
fof(c_0_526,plain,
! [X42,X11,X9,X5,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool))),c_HOL_Ominus__class_Ominus(X11,X42,tc_fun(X3,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X42),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X11)) ),
inference(fof_simplification,[status(thm)],[c_0_49]) ).
fof(c_0_527,plain,
! [X42,X11,X9,X5,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(X11,X42,tc_fun(X3,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X42))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X11)) ),
inference(fof_simplification,[status(thm)],[c_0_50]) ).
fof(c_0_528,plain,
! [X4,X9,X5,X6,X3] :
( c_Finite__Set_Ofinite(X9,X6)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X6,tc_bool)),X9),c_Set_Oimage(X4,X5,X3,X6)))
| ~ c_Finite__Set_Ofinite(X5,X3) ),
inference(fof_simplification,[status(thm)],[c_0_51]) ).
fof(c_0_529,plain,
! [X11,X9,X5,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),c_Lattices_Oupper__semilattice__class_Osup(X9,X11,tc_fun(X3,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool))),X11)) ),
inference(fof_simplification,[status(thm)],[c_0_52]) ).
fof(c_0_530,plain,
! [X4,X9,X5,X6,X3] :
( ~ class_OrderedGroup_Oab__group__add(X6)
| c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),X3,X6) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X4,X5,X3,X6),c_Finite__Set_Osetsum(X4,X9,X3,X6),X6)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X5))
| ~ c_Finite__Set_Ofinite(X5,X3) ),
inference(fof_simplification,[status(thm)],[c_0_53]) ).
fof(c_0_531,plain,
! [X11,X9,X5,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool))),X11))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),c_Lattices_Oupper__semilattice__class_Osup(X9,X11,tc_fun(X3,tc_bool)))) ),
inference(fof_simplification,[status(thm)],[c_0_54]) ).
fof(c_0_532,plain,
! [X11,X9,X5,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool))),X11))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X11))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X11)) ),
inference(fof_simplification,[status(thm)],[c_0_55]) ).
fof(c_0_533,plain,
! [X11,X9,X5,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool))),X11))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X11))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X11)) ),
inference(fof_simplification,[status(thm)],[c_0_56]) ).
fof(c_0_534,plain,
! [X2,X9,X5,X3] :
( c_HOL_Oord__class_Oless(X5,c_Set_Oinsert(X2,X9,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X9,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X5,X9,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_57]) ).
fof(c_0_535,plain,
! [X2,X9,X5,X3] :
( c_HOL_Oord__class_Oless(X5,c_Set_Oinsert(X2,X9,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X9,tc_fun(X3,tc_bool))
| hBOOL(c_in(X2,X9,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_58]) ).
fof(c_0_536,plain,
! [X18,X15,X16,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X16),X18))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X16))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X8,X16,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X15,X18,X3))) ),
inference(fof_simplification,[status(thm)],[c_0_59]) ).
fof(c_0_537,plain,
! [X18,X15,X16,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X15),X8))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X16))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X8,X16,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X15,X18,X3))) ),
inference(fof_simplification,[status(thm)],[c_0_60]) ).
fof(c_0_538,plain,
! [X4,X16,X8,X3] :
( X8 = X16
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X4,c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),X16)) ),
inference(fof_simplification,[status(thm)],[c_0_61]) ).
fof(c_0_539,plain,
! [X11,X9,X5,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X11))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool))),X11)) ),
inference(fof_simplification,[status(thm)],[c_0_62]) ).
fof(c_0_540,plain,
! [X11,X9,X5,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X11))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool))),X11)) ),
inference(fof_simplification,[status(thm)],[c_0_63]) ).
fof(c_0_541,plain,
! [X18,X15,X16,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X15),X8))
| hBOOL(hAPP(hAPP(c_lessequals(X3),X16),X8))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X8,X16,X3)),c_SetInterval_Oord__class_OatLeastLessThan(X15,X18,X3))) ),
inference(fof_simplification,[status(thm)],[c_0_64]) ).
fof(c_0_542,plain,
! [X18,X15,X16,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X16),X18))
| hBOOL(hAPP(hAPP(c_lessequals(X3),X16),X8))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X8,X16,X3)),c_SetInterval_Oord__class_OatLeastLessThan(X15,X18,X3))) ),
inference(fof_simplification,[status(thm)],[c_0_65]) ).
fof(c_0_543,plain,
! [X8,X9,X5,X6,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X6,tc_bool)),hAPP(X9,X8)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X9,X3,tc_fun(X6,tc_bool))))
| ~ hBOOL(c_in(X8,X5,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_66]) ).
fof(c_0_544,plain,
! [X2,X16,X9,X5,X6,X3] :
( hBOOL(c_in(X16,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X9,X6,tc_fun(X3,tc_bool)),X3))
| ~ hBOOL(c_in(X16,hAPP(X9,X2),X3))
| ~ hBOOL(c_in(X2,X5,X6)) ),
inference(fof_simplification,[status(thm)],[c_0_67]) ).
fof(c_0_545,plain,
! [X16,X8,X9,X5,X6,X3] :
( hBOOL(c_in(X16,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X9,X3,tc_fun(X6,tc_bool)),X6))
| ~ hBOOL(c_in(X16,hAPP(X9,X8),X6))
| ~ hBOOL(c_in(X8,X5,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_68]) ).
fof(c_0_546,plain,
! [X4,X8,X5,X6,X3] :
( ~ class_OrderedGroup_Oab__group__add(X6)
| c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3,X6) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X4,X5,X3,X6),hAPP(X4,X8),X6)
| ~ hBOOL(c_in(X8,X5,X3))
| ~ c_Finite__Set_Ofinite(X5,X3) ),
inference(fof_simplification,[status(thm)],[c_0_69]) ).
fof(c_0_547,plain,
! [X4,X8,X5,X6,X3] :
( ~ class_Ring__and__Field_Oring(X6)
| c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3,X6) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X4,X5,X3,X6),hAPP(X4,X8),X6)
| ~ hBOOL(c_in(X8,X5,X3))
| ~ c_Finite__Set_Ofinite(X5,X3) ),
inference(fof_simplification,[status(thm)],[c_0_70]) ).
fof(c_0_548,axiom,
! [X39,X9,X5,X6,X3] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X6,tc_bool)),X39,X6,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X39,X6,tc_fun(X3,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,X39,X6,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
c_0_71 ).
fof(c_0_549,plain,
! [X2,X9,X5,X3] :
( c_HOL_Oord__class_Oless(X5,c_Set_Oinsert(X2,X9,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X2,X5,X3))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X9,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X5,X9,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_72]) ).
fof(c_0_550,plain,
! [X2,X9,X5,X3] :
( c_HOL_Oord__class_Oless(X5,c_Set_Oinsert(X2,X9,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X2,X5,X3))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X9,tc_fun(X3,tc_bool))
| hBOOL(c_in(X2,X9,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_73]) ).
fof(c_0_551,axiom,
! [X4,X9,X5,X6,X3] : c_Set_Oimage(X4,c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X6,tc_bool)),X6,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(X4,X5,X6,X3),c_Set_Oimage(X4,X9,X6,X3),tc_fun(X3,tc_bool)),
c_0_74 ).
fof(c_0_552,plain,
! [X9,X5,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_HOL_Ouminus__class_Ouminus(X5,tc_fun(X3,tc_bool))),c_HOL_Ouminus__class_Ouminus(X9,tc_fun(X3,tc_bool)))) ),
inference(fof_simplification,[status(thm)],[c_0_75]) ).
fof(c_0_553,plain,
! [X2,X9,X5,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_Set_Oinsert(X2,X5,X3)),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_76]) ).
fof(c_0_554,plain,
! [X2,X16,X9,X5,X6,X3] :
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X9,X3,tc_fun(X6,tc_bool)),X16))
| ~ hBOOL(hAPP(hAPP(X9,X2),X16))
| ~ hBOOL(c_in(X2,X5,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_77]) ).
fof(c_0_555,plain,
! [X16,X8,X9,X5,X6,X3] :
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X9,X3,tc_fun(X6,tc_bool)),X16))
| ~ hBOOL(hAPP(hAPP(X9,X8),X16))
| ~ hBOOL(c_in(X8,X5,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_78]) ).
fof(c_0_556,plain,
! [X8,X42,X11,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_Set_Oinsert(X8,X11,X3)),c_Set_Oinsert(X8,X42,X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X11),X42)) ),
inference(fof_simplification,[status(thm)],[c_0_79]) ).
fof(c_0_557,plain,
! [X38,X39,X5,X6,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X6)
| hBOOL(hAPP(hAPP(c_lessequals(X6),hAPP(X39,X38)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X39,X3,X6)))
| ~ hBOOL(c_in(X38,X5,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_80]) ).
fof(c_0_558,plain,
! [X2,X9,X5,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_Set_Oinsert(X2,X5,X3)),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9))
| ~ hBOOL(c_in(X2,X9,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_81]) ).
fof(c_0_559,axiom,
! [X2,X3] : hBOOL(hAPP(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3))),
c_0_82 ).
fof(c_0_560,plain,
! [X2,X4,X5,X17,X3] :
( ~ hBOOL(c_in(X2,X5,X17))
| hBOOL(c_in(hAPP(X4,X2),c_Set_Oimage(X4,X5,X17,X3),X3)) ),
inference(fof_simplification,[status(thm)],[c_0_83]) ).
fof(c_0_561,plain,
! [X2,X4,X5,X6,X3] :
( ~ hBOOL(c_in(X2,X5,X6))
| hBOOL(c_in(hAPP(X4,X2),c_Set_Oimage(X4,X5,X6,X3),X3)) ),
inference(fof_simplification,[status(thm)],[c_0_84]) ).
fof(c_0_562,plain,
! [X2,X4,X5,X6,X3] :
( hBOOL(c_in(hAPP(X4,X2),c_Set_Oimage(X4,X5,X6,X3),X3))
| ~ hBOOL(c_in(X2,X5,X6)) ),
inference(fof_simplification,[status(thm)],[c_0_85]) ).
fof(c_0_563,plain,
! [X2,X4,X5,X6,X3] :
( hBOOL(c_in(hAPP(X4,X2),c_Set_Oimage(X4,X5,X3,X6),X6))
| ~ hBOOL(c_in(X2,X5,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_86]) ).
fof(c_0_564,axiom,
! [X29,X32,X3] : c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X29,c_Com_Ocom_OSKIP,X29,X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3),
c_0_87 ).
fof(c_0_565,plain,
! [X18,X15,X16,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X8,X16,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X15,X18,X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X16),X18))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X15),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_88]) ).
fof(c_0_566,plain,
! [X2,X5,X3] :
( X5 = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| X5 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3))) ),
inference(fof_simplification,[status(thm)],[c_0_89]) ).
fof(c_0_567,plain,
! [X2,X9,X5,X3] :
( hBOOL(c_in(X2,X9,X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_Set_Oinsert(X2,X5,X3)),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_90]) ).
fof(c_0_568,plain,
! [X2,X9,X5,X3] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X9,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X2,X5,X3))
| hBOOL(c_in(X2,X9,X3))
| ~ c_HOL_Oord__class_Oless(X5,c_Set_Oinsert(X2,X9,X3),tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_91]) ).
fof(c_0_569,plain,
! [X4,X8,X5,X6,X3] :
( ~ class_OrderedGroup_Oab__group__add(X6)
| c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3,X6) = c_Finite__Set_Osetsum(X4,X5,X3,X6)
| hBOOL(c_in(X8,X5,X3))
| ~ c_Finite__Set_Ofinite(X5,X3) ),
inference(fof_simplification,[status(thm)],[c_0_92]) ).
fof(c_0_570,plain,
! [X11,X9,X5,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X11))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X11))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_93]) ).
fof(c_0_571,plain,
! [X2,X9,X5,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),c_Set_Oinsert(X2,X9,X3)))
| hBOOL(c_in(X2,X5,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_94]) ).
fof(c_0_572,plain,
! [X2,X9,X5,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9))
| hBOOL(c_in(X2,X5,X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),c_Set_Oinsert(X2,X9,X3))) ),
inference(fof_simplification,[status(thm)],[c_0_95]) ).
fof(c_0_573,axiom,
! [X4,X8,X5,X3] :
( c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3,tc_nat) = c_Finite__Set_Osetsum(X4,X5,X3,tc_nat)
| hBOOL(c_in(X8,X5,X3)) ),
c_0_96 ).
fof(c_0_574,plain,
! [X9,X5,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_HOL_Ouminus__class_Ouminus(X9,tc_fun(X3,tc_bool))),c_HOL_Ouminus__class_Ouminus(X5,tc_fun(X3,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_97]) ).
fof(c_0_575,plain,
! [X9,X5,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_HOL_Ouminus__class_Ouminus(X5,tc_fun(X3,tc_bool))),c_HOL_Ouminus__class_Ouminus(X9,tc_fun(X3,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X5)) ),
inference(fof_simplification,[status(thm)],[c_0_98]) ).
fof(c_0_576,axiom,
! [X8,X3] : c_Collect(hAPP(c_COMBC(c_fequal(X3),X3,X3,tc_bool),X8),X3) = c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),
c_0_99 ).
fof(c_0_577,plain,
! [X11,X9,X5,X3] :
( c_HOL_Ominus__class_Ominus(X9,c_HOL_Ominus__class_Ominus(X11,X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X5
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X11))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_100]) ).
fof(c_0_578,plain,
! [X2,X9,X5,X6,X3] :
( c_Finite__Set_Ofinite(hAPP(X9,X2),X6)
| ~ hBOOL(c_in(X2,X5,X3))
| ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X9,X3,tc_fun(X6,tc_bool)),X6)
| ~ c_Finite__Set_Ofinite(X5,X3) ),
inference(fof_simplification,[status(thm)],[c_0_101]) ).
fof(c_0_579,plain,
! [X31,X49,X5,X6,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(X5,X31),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X49,X5,X3,tc_fun(X6,tc_bool)),tc_fun(X6,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X49,X5,X3,tc_fun(X6,tc_bool))
| ~ hBOOL(c_in(X31,X49,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_102]) ).
fof(c_0_580,axiom,
! [X2,X4,X3] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(X4,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),X2)),
c_0_103 ).
fof(c_0_581,plain,
! [X2,X9,X5,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),c_Set_Oinsert(X2,X9,X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9))
| hBOOL(c_in(X2,X5,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_104]) ).
fof(c_0_582,plain,
! [X2,X9,X5,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),c_Set_Oinsert(X2,X9,X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9))
| hBOOL(c_in(X2,X5,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_105]) ).
fof(c_0_583,axiom,
! [X27,X28,X29,X30,X6,X3] : hAPP(hAPP(c_COMBC(X29,X6,X30,X3),X28),X27) = hAPP(hAPP(X29,X27),X28),
c_0_106 ).
fof(c_0_584,axiom,
! [X8,X3] : c_The(hAPP(c_COMBC(c_fequal(X3),X3,X3,tc_bool),X8),X3) = X8,
c_0_107 ).
fof(c_0_585,plain,
! [X18,X15,X16,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X8,X16,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X15,X18,X3)))
| hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X16)) ),
inference(fof_simplification,[status(thm)],[c_0_108]) ).
fof(c_0_586,axiom,
! [X8,X9,X5,X6,X3] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oinsert(X8,X5,X6),X9,X6,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(X9,X8),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X9,X6,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
c_0_109 ).
fof(c_0_587,plain,
! [X2,X4,X5,X6,X3] :
( c_Set_Oinsert(hAPP(X4,X2),c_Set_Oimage(X4,X5,X3,X6),X6) = c_Set_Oimage(X4,X5,X3,X6)
| ~ hBOOL(c_in(X2,X5,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_110]) ).
fof(c_0_588,plain,
! [X16,X9,X5,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),c_Set_Oinsert(X16,X9,X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_111]) ).
fof(c_0_589,plain,
! [X2,X16,X8,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_Lattices_Oupper__semilattice__class_Osup(X8,X16,X3)),X2)) ),
inference(fof_simplification,[status(thm)],[c_0_112]) ).
fof(c_0_590,plain,
! [X2,X16,X8,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X16),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_Lattices_Oupper__semilattice__class_Osup(X8,X16,X3)),X2)) ),
inference(fof_simplification,[status(thm)],[c_0_113]) ).
fof(c_0_591,plain,
! [X7,X1,X2,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X7))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3)),X7)) ),
inference(fof_simplification,[status(thm)],[c_0_114]) ).
fof(c_0_592,plain,
! [X7,X1,X2,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X7))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3)),X7)) ),
inference(fof_simplification,[status(thm)],[c_0_115]) ).
fof(c_0_593,plain,
! [X1,X2,X3] :
( X1 = c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)
| ~ hBOOL(hAPP(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X1)) ),
inference(fof_simplification,[status(thm)],[c_0_116]) ).
fof(c_0_594,axiom,
! [X4,X8,X9,X6,X3] : c_Set_Oimage(X4,c_Set_Oinsert(X8,X9,X6),X6,X3) = c_Set_Oinsert(hAPP(X4,X8),c_Set_Oimage(X4,X9,X6,X3),X3),
c_0_117 ).
fof(c_0_595,plain,
! [X9,X5,X3] :
( X5 = X9
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_118]) ).
fof(c_0_596,plain,
! [X9,X5,X3] :
( X5 = X9
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_119]) ).
fof(c_0_597,axiom,
! [X9,X5,X3] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool))),X5)),
c_0_120 ).
fof(c_0_598,plain,
! [X10,X4,X6,X3] :
( ~ class_HOL_Oord(X6)
| c_HOL_Oord__class_Oless(X4,X10,tc_fun(X3,X6))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,X6)),X10),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,X6)),X4),X10)) ),
inference(fof_simplification,[status(thm)],[c_0_121]) ).
fof(c_0_599,plain,
! [X18,X15,X16,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X8,X16,X3),c_SetInterval_Oord__class_OatLeastAtMost(X15,X18,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X15),X18))
| ~ c_HOL_Oord__class_Oless(X15,X8,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X16),X18))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X15),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_122]) ).
fof(c_0_600,plain,
! [X18,X15,X16,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X8,X16,X3),c_SetInterval_Oord__class_OatLeastAtMost(X15,X18,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X15),X18))
| ~ c_HOL_Oord__class_Oless(X16,X18,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X16),X18))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X15),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_123]) ).
fof(c_0_601,plain,
! [X15,X9,X5,X3] :
( hBOOL(c_in(X15,X9,X3))
| hBOOL(c_in(X15,X5,X3))
| ~ hBOOL(c_in(X15,c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),X3)) ),
inference(fof_simplification,[status(thm)],[c_0_124]) ).
fof(c_0_602,plain,
! [X2,X16,X8,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_Lattices_Oupper__semilattice__class_Osup(X8,X16,X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X16),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X2)) ),
inference(fof_simplification,[status(thm)],[c_0_125]) ).
fof(c_0_603,plain,
! [X7,X1,X2,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3)),X7))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X7))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X7)) ),
inference(fof_simplification,[status(thm)],[c_0_126]) ).
fof(c_0_604,plain,
! [X7,X1,X2,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_Lattices_Oupper__semilattice__class_Osup(X1,X7,X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X7),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2)) ),
inference(fof_simplification,[status(thm)],[c_0_127]) ).
fof(c_0_605,plain,
! [X2,X9,X5,X3] :
( c_HOL_Oord__class_Oless(X5,c_Set_Oinsert(X2,X9,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9))
| hBOOL(c_in(X2,X5,X3))
| ~ c_HOL_Oord__class_Oless(X5,X9,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_128]) ).
fof(c_0_606,plain,
! [X2,X9,X5,X3] :
( c_HOL_Oord__class_Oless(X5,c_Set_Oinsert(X2,X9,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9))
| hBOOL(c_in(X2,X5,X3))
| hBOOL(c_in(X2,X9,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_129]) ).
fof(c_0_607,axiom,
! [X3] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)))),
c_0_130 ).
fof(c_0_608,plain,
! [X16,X8,X3] :
( X16 = X8
| ~ hBOOL(c_in(X16,c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)) ),
inference(fof_simplification,[status(thm)],[c_0_131]) ).
fof(c_0_609,axiom,
! [X18,X15,X16,X8,X3] :
( c_Set_Oinsert(X8,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X15,c_Set_Oinsert(X18,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)
| X8 = X18
| X8 = X15 ),
c_0_132 ).
fof(c_0_610,axiom,
! [X18,X15,X16,X8,X3] :
( c_Set_Oinsert(X8,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X15,c_Set_Oinsert(X18,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)
| X16 = X15
| X8 = X15 ),
c_0_133 ).
fof(c_0_611,axiom,
! [X18,X15,X16,X8,X3] :
( c_Set_Oinsert(X8,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X15,c_Set_Oinsert(X18,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)
| X8 = X18
| X16 = X18 ),
c_0_134 ).
fof(c_0_612,axiom,
! [X18,X15,X16,X8,X3] :
( c_Set_Oinsert(X8,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X15,c_Set_Oinsert(X18,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)
| X16 = X15
| X16 = X18 ),
c_0_135 ).
fof(c_0_613,axiom,
! [X8,X9,X5,X3] : c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X8,X9,X3),tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X9,tc_fun(X3,tc_bool)),
c_0_136 ).
fof(c_0_614,plain,
! [X15,X9,X5,X3] :
( ~ hBOOL(c_in(X15,X9,X3))
| ~ hBOOL(c_in(X15,c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),X3)) ),
inference(fof_simplification,[status(thm)],[c_0_137]) ).
fof(c_0_615,plain,
! [X8,X5,X3] :
( c_Set_Oinsert(X8,c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3) = X5
| ~ hBOOL(c_in(X8,X5,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_138]) ).
fof(c_0_616,axiom,
! [X8,X9,X6,X3] : c_Set_Oinsert(X8,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)),X9,X6,tc_fun(X3,tc_bool)),X3) = c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),
c_0_139 ).
fof(c_0_617,plain,
! [X2,X9,X5,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9))
| hBOOL(c_in(X2,X5,X3))
| hBOOL(c_in(X2,X9,X3))
| ~ c_HOL_Oord__class_Oless(X5,c_Set_Oinsert(X2,X9,X3),tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_140]) ).
fof(c_0_618,axiom,
! [X56,X57,X58,X59,X60,X61,X3] :
( c_Hoare__Mirabelle_Otriple_Otriple(X59,X61,X57,X3) != c_Hoare__Mirabelle_Otriple_Otriple(X58,X60,X56,X3)
| X59 = X58 ),
c_0_141 ).
fof(c_0_619,axiom,
! [X56,X57,X58,X59,X60,X61,X3] :
( c_Hoare__Mirabelle_Otriple_Otriple(X59,X61,X57,X3) != c_Hoare__Mirabelle_Otriple_Otriple(X58,X60,X56,X3)
| X61 = X60 ),
c_0_142 ).
fof(c_0_620,axiom,
! [X56,X57,X58,X59,X60,X61,X3] :
( c_Hoare__Mirabelle_Otriple_Otriple(X59,X61,X57,X3) != c_Hoare__Mirabelle_Otriple_Otriple(X58,X60,X56,X3)
| X57 = X56 ),
c_0_143 ).
fof(c_0_621,plain,
! [X40,X39,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_Finite__Set_Olinorder__class_OMax(X39,X3)),c_Finite__Set_Olinorder__class_OMax(X40,X3)))
| ~ c_Finite__Set_Ofinite(X40,X3)
| X39 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X39),X40)) ),
inference(fof_simplification,[status(thm)],[c_0_144]) ).
fof(c_0_622,plain,
! [X40,X39,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_Finite__Set_Olinorder__class_OMin(X40,X3)),c_Finite__Set_Olinorder__class_OMin(X39,X3)))
| ~ c_Finite__Set_Ofinite(X40,X3)
| X39 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X39),X40)) ),
inference(fof_simplification,[status(thm)],[c_0_145]) ).
fof(c_0_623,plain,
! [X53,X41,X32,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(X41,X53,tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X32,X53,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Set_Oinsert(X41,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_146]) ).
fof(c_0_624,plain,
! [X15,X9,X5,X3] :
( hBOOL(c_in(X15,X5,X3))
| ~ hBOOL(c_in(X15,c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),X3)) ),
inference(fof_simplification,[status(thm)],[c_0_147]) ).
fof(c_0_625,plain,
! [X8,X9,X5,X3] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X8,X9,X3),tc_fun(X3,tc_bool)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_148]) ).
fof(c_0_626,plain,
! [X2,X10,X4,X6,X3] :
( ~ class_HOL_Oord(X6)
| hBOOL(hAPP(hAPP(c_lessequals(X6),hAPP(X4,X2)),hAPP(X10,X2)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,X6)),X4),X10)) ),
inference(fof_simplification,[status(thm)],[c_0_149]) ).
fof(c_0_627,plain,
! [X54,X53,X32,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X32,X53,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),X53),X54))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X32,X54,X3) ),
inference(fof_simplification,[status(thm)],[c_0_150]) ).
fof(c_0_628,plain,
! [X18,X15,X16,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X16,X18,X3)
| c_HOL_Oord__class_Oless(X15,X8,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X16))
| ~ c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X8,X16,X3),c_SetInterval_Oord__class_OatLeastAtMost(X15,X18,X3),tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_151]) ).
fof(c_0_629,plain,
! [X2,X9,X5,X3] :
( hBOOL(c_in(X2,X9,X3))
| ~ hBOOL(c_in(X2,X5,X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_152]) ).
fof(c_0_630,plain,
! [X15,X9,X5,X3] :
( hBOOL(c_in(X15,X9,X3))
| ~ hBOOL(c_in(X15,X5,X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_153]) ).
fof(c_0_631,plain,
! [X2,X9,X5,X3] :
( hBOOL(c_in(X2,X9,X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9))
| ~ hBOOL(c_in(X2,X5,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_154]) ).
fof(c_0_632,plain,
! [X41,X9,X5,X3] :
( hBOOL(c_in(X41,X9,X3))
| ~ hBOOL(c_in(X41,X5,X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_155]) ).
fof(c_0_633,plain,
! [X18,X15,X16,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X15),X8))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X16))
| ~ c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X8,X16,X3),c_SetInterval_Oord__class_OatLeastAtMost(X15,X18,X3),tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_156]) ).
fof(c_0_634,plain,
! [X18,X15,X16,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X16),X18))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X16))
| ~ c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X8,X16,X3),c_SetInterval_Oord__class_OatLeastAtMost(X15,X18,X3),tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_157]) ).
fof(c_0_635,axiom,
! [X9,X5,X6,X3] : c_Lattices_Oupper__semilattice__class_Osup(X5,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)),X9,X6,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X5,
c_0_158 ).
fof(c_0_636,axiom,
! [X9,X5,X6,X3] : c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)),X5,X6,tc_fun(X3,tc_bool)),X9,tc_fun(X3,tc_bool)) = X9,
c_0_159 ).
fof(c_0_637,axiom,
! [X9,X5,X6,X3] : c_HOL_Ominus__class_Ominus(X5,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)),X9,X6,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X5,
c_0_160 ).
fof(c_0_638,plain,
! [X2,X4,X3] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X2)),
inference(fof_simplification,[status(thm)],[c_0_161]) ).
fof(c_0_639,plain,
! [X5,X3] :
( X5 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),c_HOL_Ouminus__class_Ouminus(X5,tc_fun(X3,tc_bool)))) ),
inference(fof_simplification,[status(thm)],[c_0_162]) ).
fof(c_0_640,plain,
! [X15,X9,X5,X3] :
( hBOOL(c_in(X15,c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),X3))
| hBOOL(c_in(X15,X9,X3))
| ~ hBOOL(c_in(X15,X5,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_163]) ).
fof(c_0_641,plain,
! [X15,X9,X5,X3] :
( hBOOL(c_in(X15,c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),X3))
| hBOOL(c_in(X15,X9,X3))
| ~ hBOOL(c_in(X15,X5,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_164]) ).
fof(c_0_642,plain,
! [X12,X13,X14,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(X14,X13,X3),c_SetInterval_Oord__class_OatLeastLessThan(X13,X12,X3),tc_fun(X3,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X14,X12,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X13),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X13)) ),
inference(fof_simplification,[status(thm)],[c_0_165]) ).
fof(c_0_643,plain,
! [X12,X13,X14,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OgreaterThanAtMost(X14,X13,X3),c_SetInterval_Oord__class_OgreaterThanAtMost(X13,X12,X3),tc_fun(X3,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X14,X12,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X13),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X13)) ),
inference(fof_simplification,[status(thm)],[c_0_166]) ).
fof(c_0_644,plain,
! [X12,X13,X14,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastAtMost(X14,X13,X3),c_SetInterval_Oord__class_OgreaterThanAtMost(X13,X12,X3),tc_fun(X3,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X14,X12,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X13),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X13)) ),
inference(fof_simplification,[status(thm)],[c_0_167]) ).
fof(c_0_645,plain,
! [X12,X13,X14,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(X14,X13,X3),c_SetInterval_Oord__class_OatLeastAtMost(X13,X12,X3),tc_fun(X3,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X14,X12,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X13),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X13)) ),
inference(fof_simplification,[status(thm)],[c_0_168]) ).
fof(c_0_646,plain,
! [X9,X5,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X5,c_HOL_Ominus__class_Ominus(X9,X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X9
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_169]) ).
fof(c_0_647,plain,
! [X2,X9,X5,X6,X3] :
( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X9,X6,tc_fun(X3,tc_bool))
| hAPP(X9,X2) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X2,X5,X6)) ),
inference(fof_simplification,[status(thm)],[c_0_170]) ).
fof(c_0_648,plain,
! [X2,X9,X5,X6,X3] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X9,X6,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| hAPP(X9,X2) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X2,X5,X6)) ),
inference(fof_simplification,[status(thm)],[c_0_171]) ).
fof(c_0_649,axiom,
! [X8,X5,X3] : c_Set_Oinsert(X8,c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3) = c_Set_Oinsert(X8,X5,X3),
c_0_172 ).
fof(c_0_650,plain,
! [X53,X32,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X32,X53,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),X53),X32)) ),
inference(fof_simplification,[status(thm)],[c_0_173]) ).
fof(c_0_651,plain,
! [X11,X9,X5,X3] :
( c_HOL_Oord__class_Oless(X5,X11,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X11))
| ~ c_HOL_Oord__class_Oless(X5,X9,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_174]) ).
fof(c_0_652,plain,
! [X11,X9,X5,X3] :
( c_HOL_Oord__class_Oless(X5,X11,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X9,X11,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_175]) ).
fof(c_0_653,plain,
! [X5,X3] :
( X5 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))) ),
inference(fof_simplification,[status(thm)],[c_0_176]) ).
fof(c_0_654,plain,
! [X8,X9,X5,X3] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X8,X9,X3),tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_177]) ).
fof(c_0_655,plain,
! [X2,X15,X5,X6,X3] :
( c_Set_Oimage(c_COMBK(X15,X6,X3),X5,X3,X6) = c_Set_Oinsert(X15,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)),X6)
| ~ hBOOL(c_in(X2,X5,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_178]) ).
fof(c_0_656,plain,
! [X10,X4,X6,X3] :
( ~ class_HOL_Oord(X6)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,X6)),X10),X4))
| ~ c_HOL_Oord__class_Oless(X4,X10,tc_fun(X3,X6)) ),
inference(fof_simplification,[status(thm)],[c_0_179]) ).
fof(c_0_657,axiom,
! [X8,X9,X5,X3] : c_HOL_Ominus__class_Ominus(X5,c_Set_Oinsert(X8,X9,X3),tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),
c_0_180 ).
fof(c_0_658,plain,
! [X16,X8,X5,X3] :
( hBOOL(c_in(X8,X5,X3))
| X8 = X16
| ~ hBOOL(c_in(X8,c_Set_Oinsert(X16,X5,X3),X3)) ),
inference(fof_simplification,[status(thm)],[c_0_181]) ).
fof(c_0_659,plain,
! [X12,X14,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),c_SetInterval_Oord__class_OgreaterThanAtMost(X14,X12,X3),tc_fun(X3,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X14,X12,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_182]) ).
fof(c_0_660,plain,
! [X12,X14,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(X14,X12,X3),c_Set_Oinsert(X12,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X14,X12,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_183]) ).
fof(c_0_661,axiom,
! [X11,X9,X5,X3] : c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),X11,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X5,X11,tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X9,X11,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
c_0_184 ).
fof(c_0_662,plain,
! [X16,X8,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| hAPP(c_Complete__Lattice_OSup__class_OSup(X3),c_Set_Oinsert(X8,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)) = c_Lattices_Oupper__semilattice__class_Osup(X8,X16,X3) ),
inference(fof_simplification,[status(thm)],[c_0_185]) ).
fof(c_0_663,axiom,
! [X3] : hBOOL(hAPP(hAPP(c_lessequals(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_0_186 ).
fof(c_0_664,axiom,
! [X9,X5,X3] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)))),
c_0_187 ).
fof(c_0_665,axiom,
! [X9,X5,X3] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)))),
c_0_188 ).
fof(c_0_666,plain,
! [X15,X9,X5,X3] :
( hBOOL(c_in(X15,c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),X3))
| ~ hBOOL(c_in(X15,X5,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_189]) ).
fof(c_0_667,plain,
! [X15,X9,X5,X3] :
( hBOOL(c_in(X15,c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),X3))
| ~ hBOOL(c_in(X15,X9,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_190]) ).
fof(c_0_668,plain,
! [X2,X9,X5,X3] :
( hBOOL(hAPP(X9,X2))
| hBOOL(hAPP(X5,X2))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),X2)) ),
inference(fof_simplification,[status(thm)],[c_0_191]) ).
fof(c_0_669,plain,
! [X15,X5,X3] :
( ~ hBOOL(c_in(X15,X5,X3))
| ~ hBOOL(c_in(X15,c_HOL_Ouminus__class_Ouminus(X5,tc_fun(X3,tc_bool)),X3)) ),
inference(fof_simplification,[status(thm)],[c_0_192]) ).
fof(c_0_670,plain,
! [X18,X15,X16,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X8,X16,X3),c_SetInterval_Oord__class_OatLeastAtMost(X15,X18,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X15),X18))
| hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X16)) ),
inference(fof_simplification,[status(thm)],[c_0_193]) ).
fof(c_0_671,plain,
! [X18,X15,X16,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X15),X18))
| ~ c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X8,X16,X3),c_SetInterval_Oord__class_OatLeastAtMost(X15,X18,X3),tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_194]) ).
fof(c_0_672,axiom,
! [X5,X6,X3] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,c_COMBK(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool),X6),X6,tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
c_0_195 ).
fof(c_0_673,plain,
! [X16,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ouminus__class_Ouminus(X8,X3)),X16))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ouminus__class_Ouminus(X16,X3)),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_196]) ).
fof(c_0_674,plain,
! [X16,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ouminus__class_Ouminus(X16,X3)),X8))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ouminus__class_Ouminus(X8,X3)),X16)) ),
inference(fof_simplification,[status(thm)],[c_0_197]) ).
fof(c_0_675,plain,
! [X2,X9,X5,X3] :
( c_HOL_Oord__class_Oless(X5,X9,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X2,X9,X3))
| ~ c_HOL_Oord__class_Oless(X5,c_Set_Oinsert(X2,X9,X3),tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_198]) ).
fof(c_0_676,plain,
! [X9,X5,X3] :
( c_HOL_Oord__class_Oless(X5,X9,tc_fun(X3,tc_bool))
| X5 = X9
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_199]) ).
fof(c_0_677,plain,
! [X9,X5,X3] :
( X5 = X9
| c_HOL_Oord__class_Oless(X5,X9,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_200]) ).
fof(c_0_678,plain,
! [X9,X5,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)) = X9
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_201]) ).
fof(c_0_679,plain,
! [X9,X5,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)) = X5
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X5)) ),
inference(fof_simplification,[status(thm)],[c_0_202]) ).
fof(c_0_680,plain,
! [X2,X28,X29,X3] :
( hBOOL(hAPP(X28,X2))
| ~ hBOOL(hAPP(X29,X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X29),X28)) ),
inference(fof_simplification,[status(thm)],[c_0_203]) ).
fof(c_0_681,plain,
! [X2,X28,X29,X3] :
( hBOOL(hAPP(X28,X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X29),X28))
| ~ hBOOL(hAPP(X29,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_204]) ).
fof(c_0_682,axiom,
! [X2,X3] : hBOOL(c_in(X2,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)),
c_0_205 ).
fof(c_0_683,axiom,
! [X43,X2,X3] : c_Set_Oinsert(X43,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = c_Set_Oinsert(X2,c_Set_Oinsert(X43,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),
c_0_206 ).
fof(c_0_684,plain,
! [X34,X33,X6,X3] :
( c_Finite__Set_Ofinite(c_Set_Oimage(X34,X33,X3,X6),X6)
| ~ c_Finite__Set_Ofinite(X33,X3) ),
inference(fof_simplification,[status(thm)],[c_0_207]) ).
fof(c_0_685,plain,
! [X16,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X16))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ouminus__class_Ouminus(X16,X3)),c_HOL_Ouminus__class_Ouminus(X8,X3))) ),
inference(fof_simplification,[status(thm)],[c_0_208]) ).
fof(c_0_686,plain,
! [X37,X13,X38,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Ominus__class_Ominus(c_SetInterval_Oord__class_OatLeastLessThan(X38,X13,X3),c_SetInterval_Oord__class_OatLeastLessThan(X38,X37,X3),tc_fun(X3,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X37,X13,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X38),X37)) ),
inference(fof_simplification,[status(thm)],[c_0_209]) ).
fof(c_0_687,axiom,
! [X2,X5,X3] :
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X2,X5,X3),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) = X5
| hBOOL(c_in(X2,X5,X3)) ),
c_0_210 ).
fof(c_0_688,axiom,
! [X8,X9,X3] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),c_Set_Oinsert(X8,X9,X3))),
c_0_211 ).
fof(c_0_689,axiom,
! [X2,X9,X5,X3] :
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X2,X5,X3),X9,tc_fun(X3,tc_bool)) = c_Set_Oinsert(X2,c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),X3)
| hBOOL(c_in(X2,X9,X3)) ),
c_0_212 ).
fof(c_0_690,axiom,
! [X15,X6,X3] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)),c_COMBK(X15,tc_fun(X3,tc_bool),X6),X6,tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
c_0_213 ).
fof(c_0_691,plain,
! [X16,X8,X9,X3] :
( hBOOL(c_in(X8,c_Set_Oinsert(X16,X9,X3),X3))
| ~ hBOOL(c_in(X8,X9,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_214]) ).
fof(c_0_692,plain,
! [X16,X8,X5,X3] :
( hBOOL(c_in(X8,c_Set_Oinsert(X16,X5,X3),X3))
| ~ hBOOL(c_in(X8,X5,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_215]) ).
fof(c_0_693,axiom,
! [X5,X3] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),X5)),
c_0_216 ).
fof(c_0_694,plain,
! [X2,X16,X8,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X2),c_Lattices_Oupper__semilattice__class_Osup(X8,X16,X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_217]) ).
fof(c_0_695,plain,
! [X2,X16,X8,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X2),c_Lattices_Oupper__semilattice__class_Osup(X8,X16,X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X16)) ),
inference(fof_simplification,[status(thm)],[c_0_218]) ).
fof(c_0_696,plain,
! [X9,X5,X3] :
( c_Finite__Set_Ofinite(X5,X3)
| ~ c_Finite__Set_Ofinite(X9,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_219]) ).
fof(c_0_697,plain,
! [X9,X5,X3] :
( c_Finite__Set_Ofinite(X5,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_220]) ).
fof(c_0_698,axiom,
! [X15,X5,X6,X3] :
( c_Set_Oimage(c_COMBK(X15,X3,X6),X5,X6,X3) = c_Set_Oinsert(X15,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| X5 = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)) ),
c_0_221 ).
fof(c_0_699,plain,
! [X2,X9,X5,X3] :
( c_HOL_Oord__class_Oless(X5,c_Set_Oinsert(X2,X9,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X2,X9,X3))
| ~ c_HOL_Oord__class_Oless(X5,X9,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_222]) ).
fof(c_0_700,axiom,
! [X11,X9,X5,X3] : c_Lattices_Oupper__semilattice__class_Osup(X5,c_Lattices_Oupper__semilattice__class_Osup(X9,X11,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X9,c_Lattices_Oupper__semilattice__class_Osup(X5,X11,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
c_0_223 ).
fof(c_0_701,axiom,
! [X11,X9,X5,X3] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),X11,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X5,c_Lattices_Oupper__semilattice__class_Osup(X9,X11,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
c_0_224 ).
fof(c_0_702,axiom,
! [X4,X5,X6,X3] :
( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_Set_Oimage(X4,X5,X6,X3)
| X5 = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)) ),
c_0_225 ).
fof(c_0_703,axiom,
! [X4,X5,X6,X3] :
( c_Set_Oimage(X4,X5,X6,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X5 = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)) ),
c_0_226 ).
fof(c_0_704,plain,
! [X35,X1,X36,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ominus__class_Ominus(X36,X35,X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X35),X36)) ),
inference(fof_simplification,[status(thm)],[c_0_227]) ).
fof(c_0_705,plain,
! [X35,X1,X36,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ominus__class_Ominus(X36,X35,X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X35),X36))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2)) ),
inference(fof_simplification,[status(thm)],[c_0_228]) ).
fof(c_0_706,axiom,
! [X15,X5,X6,X3] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,c_COMBK(X15,tc_fun(X3,tc_bool),X6),X6,tc_fun(X3,tc_bool)) = X15
| X5 = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)) ),
c_0_229 ).
fof(c_0_707,plain,
! [X7,X1,X2,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X7),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X7),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2)) ),
inference(fof_simplification,[status(thm)],[c_0_230]) ).
fof(c_0_708,plain,
! [X7,X1,X2,X3] :
( ~ class_Orderings_Opreorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X7))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X7))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1)) ),
inference(fof_simplification,[status(thm)],[c_0_231]) ).
fof(c_0_709,plain,
! [X10,X4,X6,X3] :
( ~ class_HOL_Oord(X6)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,X6)),X4),X10))
| ~ c_HOL_Oord__class_Oless(X4,X10,tc_fun(X3,X6)) ),
inference(fof_simplification,[status(thm)],[c_0_232]) ).
fof(c_0_710,plain,
! [X2,X5,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(c_Complete__Lattice_OInf__class_OInf(X3),X5)),X2))
| ~ hBOOL(c_in(X2,X5,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_233]) ).
fof(c_0_711,plain,
! [X16,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ouminus__class_Ouminus(X16,X3)),c_HOL_Ouminus__class_Ouminus(X8,X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X16)) ),
inference(fof_simplification,[status(thm)],[c_0_234]) ).
fof(c_0_712,plain,
! [X2,X9,X5,X3] :
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X2,X5,X3),X9,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X2,X9,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_235]) ).
fof(c_0_713,axiom,
! [X15,X6,X3] : c_Set_Oimage(c_COMBK(X15,X3,X6),c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)),X6,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
c_0_236 ).
fof(c_0_714,plain,
! [X1,X2,X5,X3] :
( hBOOL(hAPP(X5,X2))
| X1 = X2
| ~ hBOOL(hAPP(c_Set_Oinsert(X1,X5,X3),X2)) ),
inference(fof_simplification,[status(thm)],[c_0_237]) ).
fof(c_0_715,plain,
! [X2,X5,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_Finite__Set_Olinorder__class_OMin(X5,X3)),X2))
| ~ hBOOL(c_in(X2,X5,X3))
| ~ c_Finite__Set_Ofinite(X5,X3) ),
inference(fof_simplification,[status(thm)],[c_0_238]) ).
fof(c_0_716,plain,
! [X16,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X8),c_HOL_Ouminus__class_Ouminus(X16,X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X16),c_HOL_Ouminus__class_Ouminus(X8,X3))) ),
inference(fof_simplification,[status(thm)],[c_0_239]) ).
fof(c_0_717,plain,
! [X16,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X16),c_HOL_Ouminus__class_Ouminus(X8,X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),c_HOL_Ouminus__class_Ouminus(X16,X3))) ),
inference(fof_simplification,[status(thm)],[c_0_240]) ).
fof(c_0_718,axiom,
! [X9,X5,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)) != X9
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9)) ),
c_0_241 ).
fof(c_0_719,plain,
! [X9,X5,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X9))
| ~ c_HOL_Oord__class_Oless(X5,X9,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_242]) ).
fof(c_0_720,plain,
! [X15,X9,X5,X3] :
( hBOOL(c_in(X15,X9,X3))
| ~ hBOOL(c_in(X15,X5,X3))
| ~ c_HOL_Oord__class_Oless(X5,X9,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_243]) ).
fof(c_0_721,axiom,
! [X2,X9,X5,X3] :
( c_Set_Oinsert(X2,X5,X3) != c_Set_Oinsert(X2,X9,X3)
| hBOOL(c_in(X2,X9,X3))
| hBOOL(c_in(X2,X5,X3))
| X5 = X9 ),
c_0_244 ).
fof(c_0_722,axiom,
! [X8,X11,X9,X3] : c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X8,X9,X3),X11,tc_fun(X3,tc_bool)) = c_Set_Oinsert(X8,c_Lattices_Oupper__semilattice__class_Osup(X9,X11,tc_fun(X3,tc_bool)),X3),
c_0_245 ).
fof(c_0_723,axiom,
! [X8,X9,X5,X3] : c_Lattices_Oupper__semilattice__class_Osup(X5,c_Set_Oinsert(X8,X9,X3),tc_fun(X3,tc_bool)) = c_Set_Oinsert(X8,c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),X3),
c_0_246 ).
fof(c_0_724,plain,
! [X39,X5,X6,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X6)
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,c_COMBK(X39,X6,X3),X3,X6) = X39
| X5 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_247]) ).
fof(c_0_725,plain,
! [X2,X29,X3] :
( ~ hBOOL(hAPP(X29,X2))
| ~ hBOOL(c_in(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)) ),
inference(fof_simplification,[status(thm)],[c_0_248]) ).
fof(c_0_726,plain,
! [X2,X9,X5,X3] :
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),X2))
| ~ hBOOL(hAPP(X5,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_249]) ).
fof(c_0_727,plain,
! [X2,X9,X5,X3] :
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),X2))
| ~ hBOOL(hAPP(X9,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_250]) ).
fof(c_0_728,plain,
! [X2,X29,X3] :
( hBOOL(hAPP(X29,X2))
| ~ hBOOL(c_in(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)) ),
inference(fof_simplification,[status(thm)],[c_0_251]) ).
fof(c_0_729,axiom,
! [X15,X5,X3] :
( hBOOL(c_in(X15,c_HOL_Ouminus__class_Ouminus(X5,tc_fun(X3,tc_bool)),X3))
| hBOOL(c_in(X15,X5,X3)) ),
c_0_252 ).
fof(c_0_730,plain,
! [X2,X5,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X2),hAPP(c_Complete__Lattice_OSup__class_OSup(X3),X5)))
| ~ hBOOL(c_in(X2,X5,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_253]) ).
fof(c_0_731,plain,
! [X2,X5,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X2),c_Finite__Set_Olinorder__class_OMax(X5,X3)))
| ~ hBOOL(c_in(X2,X5,X3))
| ~ c_Finite__Set_Ofinite(X5,X3) ),
inference(fof_simplification,[status(thm)],[c_0_254]) ).
fof(c_0_732,plain,
! [X1,X2,X3] :
( ~ class_Orderings_Oorder(X3)
| X2 = X1
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1)) ),
inference(fof_simplification,[status(thm)],[c_0_255]) ).
fof(c_0_733,plain,
! [X1,X2,X3] :
( ~ class_Orderings_Oorder(X3)
| X2 = X1
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1)) ),
inference(fof_simplification,[status(thm)],[c_0_256]) ).
fof(c_0_734,plain,
! [X1,X2,X3] :
( ~ class_Orderings_Oorder(X3)
| X2 = X1
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2)) ),
inference(fof_simplification,[status(thm)],[c_0_257]) ).
fof(c_0_735,axiom,
! [X8,X5,X3] : c_Set_Oinsert(X8,X5,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X5,tc_fun(X3,tc_bool)),
c_0_258 ).
fof(c_0_736,axiom,
! [X9,X5,X3] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X5,tc_fun(X3,tc_bool)),X9,tc_fun(X3,tc_bool)),
c_0_259 ).
fof(c_0_737,plain,
! [X8,X3] : ~ hBOOL(c_in(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)),
inference(fof_simplification,[status(thm)],[c_0_260]) ).
fof(c_0_738,plain,
! [X15,X3] : ~ hBOOL(c_in(X15,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)),
inference(fof_simplification,[status(thm)],[c_0_261]) ).
fof(c_0_739,plain,
! [X2,X3] : ~ hBOOL(c_in(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)),
inference(fof_simplification,[status(thm)],[c_0_262]) ).
fof(c_0_740,axiom,
! [X16,X8,X3] :
( c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) != c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| X8 = X16 ),
c_0_263 ).
fof(c_0_741,plain,
! [X1,X2,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1)) ),
inference(fof_simplification,[status(thm)],[c_0_264]) ).
fof(c_0_742,plain,
! [X7,X1,X2,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3),X7,X3) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X7,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_265]) ).
fof(c_0_743,plain,
! [X7,X1,X2,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X7,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X7,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_266]) ).
fof(c_0_744,plain,
! [X7,X1,X2,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X7,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X7,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_267]) ).
fof(c_0_745,plain,
! [X7,X1,X2,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3),X7,X3) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X7,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_268]) ).
fof(c_0_746,plain,
! [X1,X2,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X2),c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3))) ),
inference(fof_simplification,[status(thm)],[c_0_269]) ).
fof(c_0_747,plain,
! [X1,X2,X3] :
( ~ class_Lattices_Olattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X2),c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3))) ),
inference(fof_simplification,[status(thm)],[c_0_270]) ).
fof(c_0_748,plain,
! [X1,X2,X3] :
( ~ class_Lattices_Olattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3))) ),
inference(fof_simplification,[status(thm)],[c_0_271]) ).
fof(c_0_749,plain,
! [X1,X2,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3))) ),
inference(fof_simplification,[status(thm)],[c_0_272]) ).
fof(c_0_750,axiom,
! [X4,X6,X3] : c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = c_Set_Oimage(X4,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)),X6,X3),
c_0_273 ).
fof(c_0_751,axiom,
! [X4,X6,X3] : c_Set_Oimage(X4,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)),X6,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
c_0_274 ).
fof(c_0_752,axiom,
! [X2,X9,X3] : hBOOL(c_in(X2,c_Set_Oinsert(X2,X9,X3),X3)),
c_0_275 ).
fof(c_0_753,axiom,
! [X8,X9,X3] : hBOOL(c_in(X8,c_Set_Oinsert(X8,X9,X3),X3)),
c_0_276 ).
fof(c_0_754,axiom,
! [X2,X5,X3] : hBOOL(c_in(X2,c_Set_Oinsert(X2,X5,X3),X3)),
c_0_277 ).
fof(c_0_755,axiom,
! [X1,X2,X5,X3] : c_Set_Oinsert(X2,c_Set_Oinsert(X1,X5,X3),X3) = c_Set_Oinsert(X1,c_Set_Oinsert(X2,X5,X3),X3),
c_0_278 ).
fof(c_0_756,plain,
! [X11,X9,X5,X3] :
( c_HOL_Oord__class_Oless(X5,X11,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X9,X11,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X5,X9,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_279]) ).
fof(c_0_757,plain,
! [X35,X1,X36,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ominus__class_Ominus(X36,X35,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X36,X35,X3) ),
inference(fof_simplification,[status(thm)],[c_0_280]) ).
fof(c_0_758,plain,
! [X35,X1,X36,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ominus__class_Ominus(X36,X35,X3)
| c_HOL_Oord__class_Oless(X36,X35,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_281]) ).
fof(c_0_759,plain,
! [X7,X1,X2,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_HOL_Oord__class_Oless(X2,X7,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X7))
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_282]) ).
fof(c_0_760,plain,
! [X7,X1,X2,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_HOL_Oord__class_Oless(X2,X7,X3)
| ~ c_HOL_Oord__class_Oless(X1,X7,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1)) ),
inference(fof_simplification,[status(thm)],[c_0_283]) ).
fof(c_0_761,plain,
! [X7,X1,X2,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X7,X2,X3)
| ~ c_HOL_Oord__class_Oless(X7,X1,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2)) ),
inference(fof_simplification,[status(thm)],[c_0_284]) ).
fof(c_0_762,plain,
! [X7,X1,X2,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X7,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X7),X1))
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_285]) ).
fof(c_0_763,axiom,
! [X9,X5,X3] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),X9,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),
c_0_286 ).
fof(c_0_764,axiom,
! [X9,X5,X3] : c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X9,X5,tc_fun(X3,tc_bool)),X5,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X9,X5,tc_fun(X3,tc_bool)),
c_0_287 ).
fof(c_0_765,axiom,
! [X9,X5,X3] : c_Lattices_Oupper__semilattice__class_Osup(X5,c_HOL_Ominus__class_Ominus(X9,X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),
c_0_288 ).
fof(c_0_766,axiom,
! [X9,X5,X3] : c_Lattices_Oupper__semilattice__class_Osup(X5,c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)),
c_0_289 ).
fof(c_0_767,plain,
! [X16,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_SetInterval_Oord__class_OatLeastAtMost(X8,X16,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X16)) ),
inference(fof_simplification,[status(thm)],[c_0_290]) ).
fof(c_0_768,plain,
! [X16,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_SetInterval_Oord__class_OatLeastAtMost(X8,X16,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X16)) ),
inference(fof_simplification,[status(thm)],[c_0_291]) ).
fof(c_0_769,plain,
! [X9,X5,X3] :
( c_Finite__Set_Ofinite(X5,X3)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_292]) ).
fof(c_0_770,plain,
! [X1,X2,X5,X3] :
( hBOOL(hAPP(c_Set_Oinsert(X1,X5,X3),X2))
| ~ hBOOL(hAPP(X5,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_293]) ).
fof(c_0_771,axiom,
! [X2,X3] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X2),X2)),
c_0_294 ).
fof(c_0_772,axiom,
! [X5,X3] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X5)),
c_0_295 ).
fof(c_0_773,plain,
! [X8,X29,X3] :
( hBOOL(hAPP(X29,X8))
| ~ hBOOL(c_in(X8,c_Collect(X29,X3),X3)) ),
inference(fof_simplification,[status(thm)],[c_0_296]) ).
fof(c_0_774,plain,
! [X32,X33,X3] :
( c_Finite__Set_Ofinite(X32,X3)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X33,X32,tc_fun(X3,tc_bool)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_297]) ).
fof(c_0_775,plain,
! [X32,X33,X3] :
( c_Finite__Set_Ofinite(X33,X3)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X33,X32,tc_fun(X3,tc_bool)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_298]) ).
fof(c_0_776,plain,
! [X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_Complete__Lattice_Ocomplete__lattice__axioms(c_Complete__Lattice_OInf__class_OInf(X3),c_Complete__Lattice_OSup__class_OSup(X3),c_lessequals(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_299]) ).
fof(c_0_777,plain,
! [X10,X4,X6] :
( ~ class_Lattices_Olattice(X6)
| hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,X10,tc_fun(t_a,X6)),v_x) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(X4,v_x),hAPP(X10,v_x),X6) ),
inference(fof_simplification,[status(thm)],[c_0_300]) ).
fof(c_0_778,plain,
! [X9,X5,X6] :
( ~ class_HOL_Ominus(X6)
| hAPP(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(t_a,X6)),v_x) = c_HOL_Ominus__class_Ominus(hAPP(X5,v_x),hAPP(X9,v_x),X6) ),
inference(fof_simplification,[status(thm)],[c_0_301]) ).
fof(c_0_779,axiom,
! [X4,X8,X3] : c_Finite__Set_Ofold1(X4,c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = X8,
c_0_302 ).
fof(c_0_780,plain,
! [X1,X2,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_303]) ).
fof(c_0_781,plain,
! [X1,X2,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1))
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_304]) ).
fof(c_0_782,plain,
! [X1,X2,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2)) ),
inference(fof_simplification,[status(thm)],[c_0_305]) ).
fof(c_0_783,plain,
! [X2,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X2))
| ~ c_HOL_Oord__class_Oless(X2,X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_306]) ).
fof(c_0_784,plain,
! [X16,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_SetInterval_Oord__class_OatLeastLessThan(X8,X16,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X16),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_307]) ).
fof(c_0_785,plain,
! [X14,X31,X3] :
( ~ class_Orderings_Oorder(X3)
| c_SetInterval_Oord__class_OgreaterThanAtMost(X31,X14,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X31)) ),
inference(fof_simplification,[status(thm)],[c_0_308]) ).
fof(c_0_786,plain,
! [X2,X16,X8,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_HOL_Oord__class_Oless(X2,c_Lattices_Oupper__semilattice__class_Osup(X8,X16,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,X8,X3) ),
inference(fof_simplification,[status(thm)],[c_0_309]) ).
fof(c_0_787,plain,
! [X2,X16,X8,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_HOL_Oord__class_Oless(X2,c_Lattices_Oupper__semilattice__class_Osup(X8,X16,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,X16,X3) ),
inference(fof_simplification,[status(thm)],[c_0_310]) ).
fof(c_0_788,axiom,
! [X2,X5,X3] : hBOOL(hAPP(c_Set_Oinsert(X2,X5,X3),X2)),
c_0_311 ).
fof(c_0_789,axiom,
! [X43,X2,X3] :
( c_Set_Oinsert(X2,X43,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| hBOOL(c_in(X2,X43,X3)) ),
c_0_312 ).
fof(c_0_790,plain,
! [X8,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| hAPP(c_Complete__Lattice_OInf__class_OInf(X3),c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_313]) ).
fof(c_0_791,plain,
! [X8,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| hAPP(c_Complete__Lattice_OSup__class_OSup(X3),c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_314]) ).
fof(c_0_792,plain,
! [X7,X1,X2,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_HOL_Oord__class_Oless(X2,X7,X3)
| ~ c_HOL_Oord__class_Oless(X1,X7,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_315]) ).
fof(c_0_793,plain,
! [X7,X1,X2,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X7,X2,X3)
| ~ c_HOL_Oord__class_Oless(X7,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_316]) ).
fof(c_0_794,plain,
! [X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_Finite__Set_Olinorder__class_OMax(c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_317]) ).
fof(c_0_795,plain,
! [X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_Finite__Set_Olinorder__class_OMin(c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_318]) ).
fof(c_0_796,plain,
! [X1,X2,X3] :
( ~ class_Orderings_Olinorder(X3)
| X2 = X1
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1)) ),
inference(fof_simplification,[status(thm)],[c_0_319]) ).
fof(c_0_797,plain,
! [X1,X2,X3] :
( ~ class_Orderings_Olinorder(X3)
| X2 = X1
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1))
| c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_320]) ).
fof(c_0_798,plain,
! [X16,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X8,X16,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X16))
| X8 = X16 ),
inference(fof_simplification,[status(thm)],[c_0_321]) ).
fof(c_0_799,plain,
! [X16,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X8,X16,X3)
| X8 = X16
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X16)) ),
inference(fof_simplification,[status(thm)],[c_0_322]) ).
fof(c_0_800,plain,
! [X1,X2,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X2 = X1
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1)) ),
inference(fof_simplification,[status(thm)],[c_0_323]) ).
fof(c_0_801,plain,
! [X1,X2,X3] :
( ~ class_Orderings_Oorder(X3)
| X2 = X1
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1)) ),
inference(fof_simplification,[status(thm)],[c_0_324]) ).
fof(c_0_802,plain,
! [X16,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X16,X8,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X16),X8))
| X8 = X16 ),
inference(fof_simplification,[status(thm)],[c_0_325]) ).
fof(c_0_803,plain,
! [X16,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X16,X8,X3)
| X8 = X16
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X16),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_326]) ).
fof(c_0_804,plain,
! [X1,X2,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3) = X1
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1)) ),
inference(fof_simplification,[status(thm)],[c_0_327]) ).
fof(c_0_805,plain,
! [X1,X2,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3) = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2)) ),
inference(fof_simplification,[status(thm)],[c_0_328]) ).
fof(c_0_806,plain,
! [X8,X5,X3] :
( c_Set_Oinsert(X8,X5,X3) = X5
| ~ hBOOL(c_in(X8,X5,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_329]) ).
fof(c_0_807,plain,
! [X16,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X8,X16,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X16,X3),c_HOL_Ouminus__class_Ouminus(X8,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_330]) ).
fof(c_0_808,plain,
! [X53,X55,X32,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X32,X53,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X32,X55,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X55,X53,X3) ),
inference(fof_simplification,[status(thm)],[c_0_331]) ).
fof(c_0_809,plain,
! [X8,X5,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| hAPP(c_Complete__Lattice_OSup__class_OSup(X3),c_Set_Oinsert(X8,X5,X3)) = c_Lattices_Oupper__semilattice__class_Osup(X8,hAPP(c_Complete__Lattice_OSup__class_OSup(X3),X5),X3) ),
inference(fof_simplification,[status(thm)],[c_0_332]) ).
fof(c_0_810,axiom,
! [X2,X3] : c_Set_Ocontents(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = X2,
c_0_333 ).
fof(c_0_811,axiom,
! [X2,X3] : c_The(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = X2,
c_0_334 ).
fof(c_0_812,plain,
! [X1,X2,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_335]) ).
fof(c_0_813,plain,
! [X1,X2,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_336]) ).
fof(c_0_814,plain,
! [X14,X31,X3] :
( ~ class_Orderings_Oorder(X3)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(X31,X14,X3)
| ~ c_HOL_Oord__class_Oless(X31,X14,X3) ),
inference(fof_simplification,[status(thm)],[c_0_337]) ).
fof(c_0_815,plain,
! [X16,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_SetInterval_Oord__class_OatLeastLessThan(X8,X16,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X8,X16,X3) ),
inference(fof_simplification,[status(thm)],[c_0_338]) ).
fof(c_0_816,plain,
! [X14,X31,X3] :
( ~ class_Orderings_Oorder(X3)
| c_SetInterval_Oord__class_OgreaterThanAtMost(X31,X14,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X31,X14,X3) ),
inference(fof_simplification,[status(thm)],[c_0_339]) ).
fof(c_0_817,plain,
! [X16,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_SetInterval_Oord__class_OatLeastLessThan(X8,X16,X3)
| ~ c_HOL_Oord__class_Oless(X8,X16,X3) ),
inference(fof_simplification,[status(thm)],[c_0_340]) ).
fof(c_0_818,plain,
! [X5,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(c_in(c_Finite__Set_Olinorder__class_OMax(X5,X3),X5,X3))
| X5 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X5,X3) ),
inference(fof_simplification,[status(thm)],[c_0_341]) ).
fof(c_0_819,plain,
! [X5,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(c_in(c_Finite__Set_Olinorder__class_OMin(X5,X3),X5,X3))
| X5 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X5,X3) ),
inference(fof_simplification,[status(thm)],[c_0_342]) ).
fof(c_0_820,plain,
! [X1,X2,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1)) ),
inference(fof_simplification,[status(thm)],[c_0_343]) ).
fof(c_0_821,axiom,
! [X2,X5,X3] : c_Set_Oinsert(X2,c_Set_Oinsert(X2,X5,X3),X3) = c_Set_Oinsert(X2,X5,X3),
c_0_344 ).
fof(c_0_822,plain,
! [X16,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X16,c_HOL_Ouminus__class_Ouminus(X8,X3),X3)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ouminus__class_Ouminus(X16,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_345]) ).
fof(c_0_823,plain,
! [X16,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ouminus__class_Ouminus(X16,X3),X3)
| ~ c_HOL_Oord__class_Oless(X16,c_HOL_Ouminus__class_Ouminus(X8,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_346]) ).
fof(c_0_824,plain,
! [X16,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X16,X3),X8,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X8,X3),X16,X3) ),
inference(fof_simplification,[status(thm)],[c_0_347]) ).
fof(c_0_825,plain,
! [X16,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X8,X3),X16,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X16,X3),X8,X3) ),
inference(fof_simplification,[status(thm)],[c_0_348]) ).
fof(c_0_826,plain,
! [X32,X33,X3] :
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X33,X32,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X32,X3)
| ~ c_Finite__Set_Ofinite(X33,X3) ),
inference(fof_simplification,[status(thm)],[c_0_349]) ).
fof(c_0_827,plain,
! [X32,X33,X3] :
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X33,X32,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X32,X3)
| ~ c_Finite__Set_Ofinite(X33,X3) ),
inference(fof_simplification,[status(thm)],[c_0_350]) ).
fof(c_0_828,plain,
! [X9,X5,X3] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X5,X3)
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_351]) ).
fof(c_0_829,plain,
! [X8,X29,X3] :
( hBOOL(c_in(X8,c_Collect(X29,X3),X3))
| ~ hBOOL(hAPP(X29,X8)) ),
inference(fof_simplification,[status(thm)],[c_0_352]) ).
fof(c_0_830,plain,
! [X2,X3] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X2)),
inference(fof_simplification,[status(thm)],[c_0_353]) ).
fof(c_0_831,axiom,
! [X3] : c_Lattices_Oupper__semilattice__class_Osup(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)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
c_0_354 ).
fof(c_0_832,plain,
! [X2,X44,X3] :
( hBOOL(hAPP(X44,X2))
| ~ hBOOL(c_in(X2,X44,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_355]) ).
fof(c_0_833,plain,
! [X8,X5,X3] :
( c_Finite__Set_Ofinite(X5,X3)
| ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X8,X5,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_356]) ).
fof(c_0_834,plain,
! [X5,X3] : ~ c_HOL_Oord__class_Oless(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
inference(fof_simplification,[status(thm)],[c_0_357]) ).
fof(c_0_835,plain,
! [X1,X2,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3) != X1
| hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1)) ),
inference(fof_simplification,[status(thm)],[c_0_358]) ).
fof(c_0_836,plain,
! [X16,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X16,X3),c_HOL_Ouminus__class_Ouminus(X8,X3),X3)
| ~ c_HOL_Oord__class_Oless(X8,X16,X3) ),
inference(fof_simplification,[status(thm)],[c_0_359]) ).
fof(c_0_837,plain,
! [X1,X2,X3] :
( ~ class_Orderings_Opreorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1))
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_360]) ).
fof(c_0_838,plain,
! [X1,X2,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1))
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_361]) ).
fof(c_0_839,plain,
! [X16,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X8,X16,X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X16)) ),
inference(fof_simplification,[status(thm)],[c_0_362]) ).
fof(c_0_840,plain,
! [X16,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_SetInterval_Oord__class_OatLeastAtMost(X8,X16,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X16)) ),
inference(fof_simplification,[status(thm)],[c_0_363]) ).
fof(c_0_841,axiom,
! [X9,X5,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X5 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
c_0_364 ).
fof(c_0_842,axiom,
! [X9,X5,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
c_0_365 ).
fof(c_0_843,plain,
! [X9,X5,X3] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X5,X9,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X5,X3) ),
inference(fof_simplification,[status(thm)],[c_0_366]) ).
fof(c_0_844,plain,
! [X16,X8,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X8,X16,X3),X3) = c_HOL_Ominus__class_Ominus(X16,X8,X3) ),
inference(fof_simplification,[status(thm)],[c_0_367]) ).
fof(c_0_845,plain,
! [X1,X43,X2,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X43,X1,X3) != c_HOL_Ominus__class_Ominus(X2,X2,X3)
| X43 = X1 ),
inference(fof_simplification,[status(thm)],[c_0_368]) ).
fof(c_0_846,plain,
! [X35,X36,X2,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X2,X2,X3) != c_HOL_Ominus__class_Ominus(X36,X35,X3)
| X36 = X35 ),
inference(fof_simplification,[status(thm)],[c_0_369]) ).
fof(c_0_847,plain,
! [X16,X8,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X16,X8,X3)
| ~ c_HOL_Oord__class_Oless(X8,X16,X3) ),
inference(fof_simplification,[status(thm)],[c_0_370]) ).
fof(c_0_848,plain,
! [X1,X2,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_371]) ).
fof(c_0_849,plain,
! [X1,X2,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_372]) ).
fof(c_0_850,plain,
! [X16,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X8,X16,X3)
| ~ c_HOL_Oord__class_Oless(X16,X8,X3) ),
inference(fof_simplification,[status(thm)],[c_0_373]) ).
fof(c_0_851,axiom,
! [X4,X5,X3] : c_Finite__Set_Ofold1(X4,X5,X3) = c_The(c_Finite__Set_Ofold1Set(X4,X5,X3),X3),
c_0_374 ).
fof(c_0_852,plain,
! [X16,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_SetInterval_Oord__class_OatLeastAtMost(X8,X16,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X16,X8,X3) ),
inference(fof_simplification,[status(thm)],[c_0_375]) ).
fof(c_0_853,plain,
! [X64,X65,X3] :
( X65 = X64
| ~ hBOOL(hAPP(hAPP(c_fequal(X3),X65),X64)) ),
inference(fof_simplification,[status(thm)],[c_0_376]) ).
fof(c_0_854,plain,
! [X1,X2,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1)) ),
inference(fof_simplification,[status(thm)],[c_0_377]) ).
fof(c_0_855,plain,
! [X1,X2,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_378]) ).
fof(c_0_856,plain,
! [X2,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X2,X2,X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X2)) ),
inference(fof_simplification,[status(thm)],[c_0_379]) ).
fof(c_0_857,plain,
! [X1,X2,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2)) ),
inference(fof_simplification,[status(thm)],[c_0_380]) ).
fof(c_0_858,plain,
! [X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_SetInterval_Oord__class_OatLeastAtMost(X8,X8,X3) = c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_381]) ).
fof(c_0_859,plain,
! [X2,X44,X3] :
( hBOOL(c_in(X2,X44,X3))
| ~ hBOOL(hAPP(X44,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_382]) ).
fof(c_0_860,axiom,
! [X8,X3] : c_Collect(hAPP(c_fequal(X3),X8),X3) = c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),
c_0_383 ).
fof(c_0_861,axiom,
! [X5,X3] : c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X5,tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
c_0_384 ).
fof(c_0_862,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_385 ).
fof(c_0_863,axiom,
! [X9,X5,X3] : c_Lattices_Oupper__semilattice__class_Osup(X5,X9,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X9,X5,tc_fun(X3,tc_bool)),
c_0_386 ).
fof(c_0_864,plain,
! [X8,X5,X3] :
( c_Finite__Set_Ofinite(c_Set_Oinsert(X8,X5,X3),X3)
| ~ c_Finite__Set_Ofinite(X5,X3) ),
inference(fof_simplification,[status(thm)],[c_0_387]) ).
fof(c_0_865,plain,
! [X14,X31,X3] :
( ~ class_Orderings_Oorder(X3)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X31,X14,X3)
| c_HOL_Oord__class_Oless(X31,X14,X3) ),
inference(fof_simplification,[status(thm)],[c_0_388]) ).
fof(c_0_866,plain,
! [X16,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_SetInterval_Oord__class_OatLeastLessThan(X8,X16,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X8,X16,X3) ),
inference(fof_simplification,[status(thm)],[c_0_389]) ).
fof(c_0_867,plain,
! [X14,X31,X3] :
( ~ class_Orderings_Oorder(X3)
| c_SetInterval_Oord__class_OgreaterThanAtMost(X31,X14,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X31,X14,X3) ),
inference(fof_simplification,[status(thm)],[c_0_390]) ).
fof(c_0_868,plain,
! [X16,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X8,X16,X3)
| c_HOL_Oord__class_Oless(X8,X16,X3) ),
inference(fof_simplification,[status(thm)],[c_0_391]) ).
fof(c_0_869,plain,
! [X2,X3] :
( ~ class_Orderings_Obot(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_Orderings_Obot__class_Obot(X3)),X2)) ),
inference(fof_simplification,[status(thm)],[c_0_392]) ).
fof(c_0_870,axiom,
! [X32,X3] : c_Hoare__Mirabelle_Ohoare__derivs(X32,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),X3),
c_0_393 ).
fof(c_0_871,axiom,
! [X5,X3] : c_HOL_Ominus__class_Ominus(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X5,
c_0_394 ).
fof(c_0_872,axiom,
! [X9,X3] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X9,tc_fun(X3,tc_bool)) = X9,
c_0_395 ).
fof(c_0_873,axiom,
! [X5,X3] : c_Lattices_Oupper__semilattice__class_Osup(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X5,
c_0_396 ).
fof(c_0_874,plain,
! [X5,X6] :
( ~ class_HOL_Ouminus(X6)
| hAPP(c_HOL_Ouminus__class_Ouminus(X5,tc_fun(t_a,X6)),v_x) = c_HOL_Ouminus__class_Ouminus(hAPP(X5,v_x),X6) ),
inference(fof_simplification,[status(thm)],[c_0_397]) ).
fof(c_0_875,axiom,
! [X8,X5,X3] : c_Set_Oinsert(X8,X5,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
c_0_398 ).
fof(c_0_876,axiom,
! [X8,X5,X3] : c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_Set_Oinsert(X8,X5,X3),
c_0_399 ).
fof(c_0_877,plain,
! [X2,X3] : ~ c_HOL_Oord__class_Oless(X2,X2,tc_fun(X3,tc_bool)),
inference(fof_simplification,[status(thm)],[c_0_400]) ).
fof(c_0_878,axiom,
! [X28,X29,X6,X3] : hAPP(c_COMBK(X29,X3,X6),X28) = X29,
c_0_401 ).
fof(c_0_879,plain,
! [X1,X2,X3] :
( ~ class_Orderings_Olinorder(X3)
| X2 = X1
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_402]) ).
fof(c_0_880,plain,
! [X1,X2,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X2 = X1
| c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_403]) ).
fof(c_0_881,plain,
! [X1,X2,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X2 = X1 ),
inference(fof_simplification,[status(thm)],[c_0_404]) ).
fof(c_0_882,plain,
! [X1,X2,X3] :
( ~ class_Orderings_Olinorder(X3)
| X2 = X1
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_405]) ).
fof(c_0_883,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X2 = X1 ),
inference(fof_simplification,[status(thm)],[c_0_406]) ).
fof(c_0_884,axiom,
! [X9,X5,X3] :
( c_HOL_Ouminus__class_Ouminus(X5,tc_fun(X3,tc_bool)) != c_HOL_Ouminus__class_Ouminus(X9,tc_fun(X3,tc_bool))
| X5 = X9 ),
c_0_407 ).
fof(c_0_885,plain,
! [X1,X2,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_408]) ).
fof(c_0_886,plain,
! [X1,X2,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_409]) ).
fof(c_0_887,plain,
! [X2,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X2)) ),
inference(fof_simplification,[status(thm)],[c_0_410]) ).
fof(c_0_888,plain,
! [X2,X3] :
( ~ class_Orderings_Opreorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X2)) ),
inference(fof_simplification,[status(thm)],[c_0_411]) ).
fof(c_0_889,plain,
! [X2,X29,X3] :
( c_Collect(X29,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(X29,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_412]) ).
fof(c_0_890,plain,
! [X2,X29,X3] :
( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_Collect(X29,X3)
| ~ hBOOL(hAPP(X29,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_413]) ).
fof(c_0_891,plain,
( ~ class_HOL_Ouminus(t_b)
| hAPP(c_HOL_Ouminus__class_Ouminus(v_A,tc_fun(t_a,t_b)),v_x) = c_HOL_Ouminus__class_Ouminus(hAPP(v_A,v_x),t_b) ),
inference(fof_simplification,[status(thm)],[c_0_414]) ).
fof(c_0_892,axiom,
hAPP(c_COMBK(v_P,t_a,t_b),v_Q) = v_P,
c_0_415 ).
fof(c_0_893,axiom,
! [X5,X3] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X5,
c_0_416 ).
fof(c_0_894,axiom,
! [X2,X3] : hBOOL(hAPP(hAPP(c_fequal(X3),X2),X2)),
c_0_417 ).
fof(c_0_895,plain,
! [X9,X5,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X5,X9,X3) != c_Orderings_Obot__class_Obot(X3)
| X9 = c_Orderings_Obot__class_Obot(X3) ),
inference(fof_simplification,[status(thm)],[c_0_418]) ).
fof(c_0_896,plain,
! [X9,X5,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X5,X9,X3) != c_Orderings_Obot__class_Obot(X3)
| X5 = c_Orderings_Obot__class_Obot(X3) ),
inference(fof_simplification,[status(thm)],[c_0_419]) ).
fof(c_0_897,axiom,
! [X5,X3] : c_HOL_Ominus__class_Ominus(X5,X5,tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
c_0_420 ).
fof(c_0_898,plain,
! [X2,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_421]) ).
fof(c_0_899,plain,
! [X2,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_422]) ).
fof(c_0_900,plain,
! [X2,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_423]) ).
fof(c_0_901,plain,
! [X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| hAPP(c_Complete__Lattice_OSup__class_OSup(X3),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))) = c_Orderings_Obot__class_Obot(X3) ),
inference(fof_simplification,[status(thm)],[c_0_424]) ).
fof(c_0_902,axiom,
! [X5,X3] : c_Lattices_Oupper__semilattice__class_Osup(X5,X5,tc_fun(X3,tc_bool)) = X5,
c_0_425 ).
fof(c_0_903,plain,
! [X6] :
( ~ class_Orderings_Obot(X6)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X6)),v_x) = c_Orderings_Obot__class_Obot(X6) ),
inference(fof_simplification,[status(thm)],[c_0_426]) ).
fof(c_0_904,plain,
! [X2,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X2,c_Orderings_Obot__class_Obot(X3),X3) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_427]) ).
fof(c_0_905,plain,
! [X2,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X3),X2,X3) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_428]) ).
fof(c_0_906,axiom,
! [X3] : c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),
c_0_429 ).
fof(c_0_907,plain,
! [X2,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X2,X2,X3) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_430]) ).
fof(c_0_908,plain,
! [X16,X8,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(X8,X3) != c_HOL_Ouminus__class_Ouminus(X16,X3)
| X8 = X16 ),
inference(fof_simplification,[status(thm)],[c_0_431]) ).
fof(c_0_909,plain,
! [X1,X2,X3] :
( ~ class_Lattices_Oboolean__algebra(X3)
| c_HOL_Ouminus__class_Ouminus(X2,X3) != c_HOL_Ouminus__class_Ouminus(X1,X3)
| X2 = X1 ),
inference(fof_simplification,[status(thm)],[c_0_432]) ).
fof(c_0_910,axiom,
! [X2,X3] : c_The(hAPP(c_fequal(X3),X2),X3) = X2,
c_0_433 ).
fof(c_0_911,plain,
! [X8,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X8,X3),X3) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_434]) ).
fof(c_0_912,plain,
! [X2,X3] :
( ~ class_Lattices_Oboolean__algebra(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_435]) ).
fof(c_0_913,plain,
! [X16,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| X16 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X16,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_436]) ).
fof(c_0_914,plain,
! [X8,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| X8 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X8,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_437]) ).
fof(c_0_915,plain,
! [X16,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X16,X3),X3) = X16 ),
inference(fof_simplification,[status(thm)],[c_0_438]) ).
fof(c_0_916,axiom,
! [X45,X46,X47,X48] :
( c_Com_Ocom_OSemi(X48,X46) != c_Com_Ocom_OSemi(X47,X45)
| X48 = X47 ),
c_0_439 ).
fof(c_0_917,axiom,
! [X45,X46,X47,X48] :
( c_Com_Ocom_OSemi(X48,X46) != c_Com_Ocom_OSemi(X47,X45)
| X46 = X45 ),
c_0_440 ).
fof(c_0_918,plain,
! [X62,X63] :
( class_Finite__Set_Ofinite_Ofinite(tc_fun(X62,X63))
| ~ class_Finite__Set_Ofinite_Ofinite(X63)
| ~ class_Finite__Set_Ofinite_Ofinite(X62) ),
inference(fof_simplification,[status(thm)],[c_0_441]) ).
fof(c_0_919,plain,
! [X62,X63] :
( class_HOL_Oord(tc_fun(X62,X63))
| ~ class_HOL_Oord(X63) ),
inference(fof_simplification,[status(thm)],[c_0_442]) ).
fof(c_0_920,plain,
! [X62,X63] :
( class_HOL_Ominus(tc_fun(X62,X63))
| ~ class_HOL_Ominus(X63) ),
inference(fof_simplification,[status(thm)],[c_0_443]) ).
fof(c_0_921,plain,
! [X62,X63] :
( class_HOL_Ouminus(tc_fun(X62,X63))
| ~ class_HOL_Ouminus(X63) ),
inference(fof_simplification,[status(thm)],[c_0_444]) ).
fof(c_0_922,plain,
! [X62,X63] :
( class_Orderings_Obot(tc_fun(X62,X63))
| ~ class_Orderings_Obot(X63) ),
inference(fof_simplification,[status(thm)],[c_0_445]) ).
fof(c_0_923,plain,
! [X62,X63] :
( class_Orderings_Oorder(tc_fun(X62,X63))
| ~ class_Orderings_Oorder(X63) ),
inference(fof_simplification,[status(thm)],[c_0_446]) ).
fof(c_0_924,plain,
! [X62,X63] :
( class_Lattices_Olattice(tc_fun(X62,X63))
| ~ class_Lattices_Olattice(X63) ),
inference(fof_simplification,[status(thm)],[c_0_447]) ).
fof(c_0_925,plain,
! [X62,X63] :
( class_Orderings_Opreorder(tc_fun(X62,X63))
| ~ class_Orderings_Opreorder(X63) ),
inference(fof_simplification,[status(thm)],[c_0_448]) ).
fof(c_0_926,plain,
! [X62,X63] :
( class_Lattices_Oboolean__algebra(tc_fun(X62,X63))
| ~ class_Lattices_Oboolean__algebra(X63) ),
inference(fof_simplification,[status(thm)],[c_0_449]) ).
fof(c_0_927,plain,
! [X62,X63] :
( class_Lattices_Obounded__lattice(tc_fun(X62,X63))
| ~ class_Lattices_Obounded__lattice(X63) ),
inference(fof_simplification,[status(thm)],[c_0_450]) ).
fof(c_0_928,plain,
! [X62,X63] :
( class_Lattices_Oupper__semilattice(tc_fun(X62,X63))
| ~ class_Lattices_Olattice(X63) ),
inference(fof_simplification,[status(thm)],[c_0_451]) ).
fof(c_0_929,plain,
! [X62,X63] :
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X62,X63))
| ~ class_Complete__Lattice_Ocomplete__lattice(X63) ),
inference(fof_simplification,[status(thm)],[c_0_452]) ).
fof(c_0_930,axiom,
! [X45,X47] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(X47,X45),
c_0_453 ).
fof(c_0_931,axiom,
! [X45,X47] : c_Com_Ocom_OSemi(X47,X45) != c_Com_Ocom_OSKIP,
c_0_454 ).
fof(c_0_932,plain,
! [X5,X3] :
( ~ class_Finite__Set_Ofinite_Ofinite(X3)
| c_Finite__Set_Ofinite(X5,X3) ),
inference(fof_simplification,[status(thm)],[c_0_455]) ).
fof(c_0_933,axiom,
! [X29,X3] : c_Collect(X29,X3) = X29,
c_0_456 ).
fof(c_0_934,axiom,
class_HOL_Oord(tc_bool),
c_0_457 ).
fof(c_0_935,axiom,
class_HOL_Ominus(tc_bool),
c_0_458 ).
fof(c_0_936,axiom,
class_HOL_Ouminus(tc_bool),
c_0_459 ).
fof(c_0_937,axiom,
class_Orderings_Obot(tc_bool),
c_0_460 ).
fof(c_0_938,axiom,
class_Orderings_Oorder(tc_bool),
c_0_461 ).
fof(c_0_939,axiom,
class_Lattices_Olattice(tc_bool),
c_0_462 ).
fof(c_0_940,axiom,
class_Orderings_Opreorder(tc_bool),
c_0_463 ).
fof(c_0_941,axiom,
class_Finite__Set_Ofinite_Ofinite(tc_bool),
c_0_464 ).
fof(c_0_942,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
c_0_465 ).
fof(c_0_943,axiom,
class_Lattices_Obounded__lattice(tc_bool),
c_0_466 ).
fof(c_0_944,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
c_0_467 ).
fof(c_0_945,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
c_0_468 ).
fof(c_0_946,axiom,
class_HOL_Oord(tc_nat),
c_0_469 ).
fof(c_0_947,axiom,
class_HOL_Ominus(tc_nat),
c_0_470 ).
fof(c_0_948,axiom,
class_Orderings_Obot(tc_nat),
c_0_471 ).
fof(c_0_949,axiom,
class_Orderings_Oorder(tc_nat),
c_0_472 ).
fof(c_0_950,axiom,
class_Lattices_Olattice(tc_nat),
c_0_473 ).
fof(c_0_951,axiom,
class_Orderings_Olinorder(tc_nat),
c_0_474 ).
fof(c_0_952,axiom,
class_Orderings_Opreorder(tc_nat),
c_0_475 ).
fof(c_0_953,axiom,
class_Lattices_Oupper__semilattice(tc_nat),
c_0_476 ).
fof(c_0_954,plain,
! [X27,X28,X29,X30,X31,X32,X33,X34,X35] :
( c_Complete__Lattice_Ocomplete__lattice(X33,X34,c_COMBC(X29,X35,X35,tc_bool),c_COMBC(X30,X35,X35,tc_bool),X28,X31,X27,X32,X35)
| ~ c_Complete__Lattice_Ocomplete__lattice(X34,X33,X29,X30,X31,X28,X32,X27,X35) ),
inference(variable_rename,[status(thm)],[c_0_477]) ).
fof(c_0_955,plain,
! [X40,X41,X42,X43,X44,X45,X46,X47,X48,X49,X50,X51,X52] :
( hBOOL(hAPP(hAPP(X42,c_Complete__Lattice_Ocomplete__lattice_OINFI(X49,X50,X48,X52,X51)),hAPP(X48,X45)))
| ~ hBOOL(c_in(X45,X50,X51))
| ~ c_Complete__Lattice_Ocomplete__lattice(X49,X47,X42,X43,X44,X41,X46,X40,X52) ),
inference(variable_rename,[status(thm)],[c_0_478]) ).
fof(c_0_956,plain,
! [X40,X41,X42,X43,X44,X45,X46,X47,X48,X49,X50,X51,X52] :
( hBOOL(hAPP(hAPP(X42,hAPP(X48,X45)),c_Complete__Lattice_Ocomplete__lattice_OSUPR(X47,X50,X48,X52,X51)))
| ~ hBOOL(c_in(X45,X50,X51))
| ~ c_Complete__Lattice_Ocomplete__lattice(X49,X47,X42,X43,X44,X41,X46,X40,X52) ),
inference(variable_rename,[status(thm)],[c_0_479]) ).
fof(c_0_957,plain,
! [X40,X41,X42,X43,X44,X45,X46,X47,X48,X49,X50,X51] :
( c_Complete__Lattice_Ocomplete__lattice_OINFI(X48,X49,c_COMBK(X47,X51,X50),X51,X50) = X47
| X49 = c_Orderings_Obot__class_Obot(tc_fun(X50,tc_bool))
| ~ c_Complete__Lattice_Ocomplete__lattice(X48,X46,X42,X43,X44,X41,X45,X40,X51) ),
inference(variable_rename,[status(thm)],[c_0_480]) ).
fof(c_0_958,plain,
! [X40,X41,X42,X43,X44,X45,X46,X47,X48,X49,X50,X51] :
( c_Complete__Lattice_Ocomplete__lattice_OSUPR(X46,X49,c_COMBK(X47,X51,X50),X51,X50) = X47
| X49 = c_Orderings_Obot__class_Obot(tc_fun(X50,tc_bool))
| ~ c_Complete__Lattice_Ocomplete__lattice(X48,X46,X42,X43,X44,X41,X45,X40,X51) ),
inference(variable_rename,[status(thm)],[c_0_481]) ).
fof(c_0_959,plain,
! [X27,X28,X29,X30,X31,X32,X33,X34,X35,X36,X37] :
( hAPP(X35,c_Set_Oinsert(X34,c_Set_Oinsert(X33,c_Orderings_Obot__class_Obot(tc_fun(X37,tc_bool)),X37),X37)) = hAPP(hAPP(X28,X34),X33)
| ~ c_Complete__Lattice_Ocomplete__lattice(X36,X35,X29,X30,X31,X28,X32,X27,X37) ),
inference(variable_rename,[status(thm)],[c_0_482]) ).
fof(c_0_960,plain,
! [X27,X28,X29,X30,X31,X32,X33,X34,X35,X36,X37] :
( hAPP(X36,c_Set_Oinsert(X34,c_Set_Oinsert(X33,c_Orderings_Obot__class_Obot(tc_fun(X37,tc_bool)),X37),X37)) = hAPP(hAPP(X31,X34),X33)
| ~ c_Complete__Lattice_Ocomplete__lattice(X36,X35,X29,X30,X31,X28,X32,X27,X37) ),
inference(variable_rename,[status(thm)],[c_0_483]) ).
fof(c_0_961,plain,
! [X27,X28,X29,X30,X31,X32,X33,X34,X35,X36,X37] :
( hBOOL(hAPP(hAPP(X30,hAPP(X35,X36)),X27))
| ~ hBOOL(c_in(X27,X36,X37))
| ~ c_Complete__Lattice_Ocomplete__lattice(X35,X34,X30,X31,X32,X29,X33,X28,X37) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_484])])]) ).
fof(c_0_962,plain,
! [X27,X28,X29,X30,X31,X32,X33,X34,X35,X36,X37] :
( hBOOL(hAPP(hAPP(X30,X27),hAPP(X34,X36)))
| ~ hBOOL(c_in(X27,X36,X37))
| ~ c_Complete__Lattice_Ocomplete__lattice(X35,X34,X30,X31,X32,X29,X33,X28,X37) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_485])])]) ).
fof(c_0_963,plain,
! [X27,X28,X29,X30,X31,X32,X33,X34,X35,X36] :
( hAPP(X34,c_Set_Oinsert(X33,c_Orderings_Obot__class_Obot(tc_fun(X36,tc_bool)),X36)) = X33
| ~ c_Complete__Lattice_Ocomplete__lattice(X35,X34,X29,X30,X31,X28,X32,X27,X36) ),
inference(variable_rename,[status(thm)],[c_0_486]) ).
fof(c_0_964,plain,
! [X27,X28,X29,X30,X31,X32,X33,X34,X35,X36] :
( hAPP(X35,c_Set_Oinsert(X33,c_Orderings_Obot__class_Obot(tc_fun(X36,tc_bool)),X36)) = X33
| ~ c_Complete__Lattice_Ocomplete__lattice(X35,X34,X29,X30,X31,X28,X32,X27,X36) ),
inference(variable_rename,[status(thm)],[c_0_487]) ).
fof(c_0_965,plain,
! [X27,X28,X29,X30,X31,X32,X33,X34,X35,X36,X37] :
( hAPP(X34,c_Set_Oinsert(X33,X36,X37)) = hAPP(hAPP(X28,X33),hAPP(X34,X36))
| ~ c_Complete__Lattice_Ocomplete__lattice(X35,X34,X29,X30,X31,X28,X32,X27,X37) ),
inference(variable_rename,[status(thm)],[c_0_488]) ).
fof(c_0_966,plain,
! [X27,X28,X29,X30,X31,X32,X33,X34,X35,X36,X37] :
( hAPP(X35,c_Set_Oinsert(X33,X36,X37)) = hAPP(hAPP(X31,X33),hAPP(X35,X36))
| ~ c_Complete__Lattice_Ocomplete__lattice(X35,X34,X29,X30,X31,X28,X32,X27,X37) ),
inference(variable_rename,[status(thm)],[c_0_489]) ).
fof(c_0_967,plain,
! [X27,X28,X29,X30,X31,X32,X33,X34,X35] :
( hAPP(X33,c_Orderings_Obot__class_Obot(tc_fun(X35,tc_bool))) = X32
| ~ c_Complete__Lattice_Ocomplete__lattice(X34,X33,X29,X30,X31,X28,X32,X27,X35) ),
inference(variable_rename,[status(thm)],[c_0_490]) ).
fof(c_0_968,plain,
! [X27,X28,X29,X30,X31,X32,X33,X34,X35] :
( hAPP(X34,c_Orderings_Obot__class_Obot(tc_fun(X35,tc_bool))) = X27
| ~ c_Complete__Lattice_Ocomplete__lattice(X34,X33,X29,X30,X31,X28,X32,X27,X35) ),
inference(variable_rename,[status(thm)],[c_0_491]) ).
fof(c_0_969,plain,
! [X44,X45,X46,X47,X48,X49] :
( c_Hoare__Mirabelle_Ohoare__derivs(X49,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X48,X46,X47,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X47,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X49,X48,X47,X46)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X49,X48,X47,X46,X45,X44)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X49,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X45,X46,X44,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(variable_rename,[status(thm)],[c_0_492]) ).
fof(c_0_970,plain,
! [X44,X45,X46,X47,X48,X49] :
( c_Hoare__Mirabelle_Ohoare__derivs(X49,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X48,X46,X47,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X47,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X49,X48,X47,X46)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X49,X48,X47,X46,X45,X44)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X49,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X45,X46,X44,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(variable_rename,[status(thm)],[c_0_493]) ).
fof(c_0_971,plain,
! [X33,X34,X35,X36] :
( c_Hoare__Mirabelle_Ohoare__derivs(X36,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X35,X33,X34,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X36,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(hAPP(c_COMBC(c_fequal(tc_Com_Ostate),tc_Com_Ostate,tc_Com_Ostate,tc_bool),v_sko__Hoare__Mirabelle__Xescape__2(X36,X35,X34,X33)),tc_fun(tc_Com_Ostate,tc_bool),t_a),X33,c_COMBK(hAPP(X34,v_sko__Hoare__Mirabelle__Xescape__1(X36,X35,X34,X33)),tc_fun(tc_Com_Ostate,tc_bool),t_a),t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(variable_rename,[status(thm)],[c_0_494]) ).
fof(c_0_972,plain,
! [X51,X52,X53,X54,X55,X56,X57] :
( c_Hoare__Mirabelle_Ohoare__derivs(X57,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X56,X53,X55,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X51,X54),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X57,X56,X55,X53,X52,X51)))
| ~ hBOOL(hAPP(hAPP(X52,X54),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X57,X56,X55,X53)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X57,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X52,X53,X51,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(variable_rename,[status(thm)],[c_0_495]) ).
fof(c_0_973,plain,
! [X51,X52,X53,X54,X55,X56,X57] :
( c_Hoare__Mirabelle_Ohoare__derivs(X57,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X56,X53,X55,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X51,X54),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X57,X56,X55,X53,X52,X51)))
| ~ hBOOL(hAPP(hAPP(X52,X54),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X57,X56,X55,X53)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X57,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X52,X53,X51,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(variable_rename,[status(thm)],[c_0_496]) ).
fof(c_0_974,plain,
! [X8,X9,X10,X11,X12,X13,X14] :
( c_Nitpick_Ofold__graph_H(X11,X8,X12,hAPP(hAPP(X11,X10),X9),X14,X13)
| ~ c_Nitpick_Ofold__graph_H(X11,X8,c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool)),X14),tc_fun(X14,tc_bool)),X9,X14,X13)
| ~ hBOOL(c_in(X10,X12,X14)) ),
inference(variable_rename,[status(thm)],[c_0_497]) ).
fof(c_0_975,plain,
! [X8,X9,X10,X11,X12,X13,X14] :
( c_Finite__Set_Ofold__graph(X11,X8,X12,hAPP(hAPP(X11,X10),X9),X14,X13)
| ~ hBOOL(c_in(X10,X12,X14))
| ~ c_Finite__Set_Ofold__graph(X11,X8,c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool)),X14),tc_fun(X14,tc_bool)),X9,X14,X13) ),
inference(variable_rename,[status(thm)],[c_0_498]) ).
fof(c_0_976,plain,
! [X8,X9,X10,X11,X12,X13,X14] :
( c_Finite__Set_Ofold__graph(X11,X8,c_Set_Oinsert(X10,X12,X14),hAPP(hAPP(X11,X10),X9),X14,X13)
| ~ c_Finite__Set_Ofold__graph(X11,X8,X12,X9,X14,X13)
| hBOOL(c_in(X10,X12,X14)) ),
inference(variable_rename,[status(thm)],[c_0_499]) ).
fof(c_0_977,plain,
! [X10,X11,X12,X13,X14] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X14,tc_bool)),c_HOL_Ominus__class_Ominus(c_Set_Oimage(X10,X12,X13,X14),c_Set_Oimage(X10,X11,X13,X14),tc_fun(X14,tc_bool))),c_Set_Oimage(X10,c_HOL_Ominus__class_Ominus(X12,X11,tc_fun(X13,tc_bool)),X13,X14))),
inference(variable_rename,[status(thm)],[c_0_500]) ).
fof(c_0_978,plain,
! [X9,X10,X11,X12,X13] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X10,c_Set_Oinsert(X11,X12,X13),X13),X9))
| hBOOL(c_in(X11,X12,X13))
| ~ c_Finite__Set_Ofold__graph(X10,X11,X12,X9,X13,X13) ),
inference(variable_rename,[status(thm)],[c_0_501]) ).
fof(c_0_979,plain,
! [X8,X9,X10,X11,X12] :
( X9 = X8
| ~ c_Finite__Set_Ofold__graph(X10,X8,c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)),X9,X12,X11) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_502])])]) ).
fof(c_0_980,plain,
! [X8,X9,X10,X11,X12,X13] :
( c_Finite__Set_Ofinite(X11,X13)
| ~ c_Finite__Set_Ofold__graph(X10,X8,X11,X9,X13,X12) ),
inference(variable_rename,[status(thm)],[c_0_503]) ).
fof(c_0_981,plain,
! [X53,X54,X55,X56,X57,X58] :
( c_Hoare__Mirabelle_Ohoare__derivs(X58,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X57,X53,X55,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X55,v_sko__Hoare__Mirabelle__Xconseq12__1(X57,X56,X55,X54)),v_sko__Hoare__Mirabelle__Xconseq12__3(X57,X56,X55,X54)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X58,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X56,X53,X54,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(variable_rename,[status(thm)],[c_0_504]) ).
fof(c_0_982,plain,
! [X53,X54,X55,X56,X57,X58] :
( c_Hoare__Mirabelle_Ohoare__derivs(X58,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X57,X53,X55,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X57,v_sko__Hoare__Mirabelle__Xconseq12__1(X57,X56,X55,X54)),v_sko__Hoare__Mirabelle__Xconseq12__2(X57,X56,X55,X54)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X58,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X56,X53,X54,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(variable_rename,[status(thm)],[c_0_505]) ).
fof(c_0_983,plain,
! [X8,X9,X10,X11] : c_Nitpick_Ofold__graph_H(X9,X8,c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)),X8,X11,X10),
inference(variable_rename,[status(thm)],[c_0_506]) ).
fof(c_0_984,plain,
! [X8,X9,X10,X11] : c_Finite__Set_Ofold__graph(X9,X8,c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)),X8,X11,X10),
inference(variable_rename,[status(thm)],[c_0_507]) ).
fof(c_0_985,plain,
! [X53,X54,X55,X56,X57,X58,X59] :
( c_Hoare__Mirabelle_Ohoare__derivs(X59,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X58,X53,X56,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X55,X54),v_sko__Hoare__Mirabelle__Xconseq12__3(X58,X57,X56,X55)))
| ~ hBOOL(hAPP(hAPP(X57,X54),v_sko__Hoare__Mirabelle__Xconseq12__2(X58,X57,X56,X55)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X59,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X57,X53,X55,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(variable_rename,[status(thm)],[c_0_508]) ).
fof(c_0_986,plain,
! [X33,X34,X35,X36,X37,X38,X39] :
( c_Hoare__Mirabelle_Ohoare__derivs(X38,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X37,c_Com_Ocom_OSemi(X34,X33),X35,X39),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X39),tc_bool)),tc_Hoare__Mirabelle_Otriple(X39)),X39)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X38,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X36,X33,X35,X39),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X39),tc_bool)),tc_Hoare__Mirabelle_Otriple(X39)),X39)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X38,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X37,X34,X36,X39),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X39),tc_bool)),tc_Hoare__Mirabelle_Otriple(X39)),X39) ),
inference(variable_rename,[status(thm)],[c_0_509]) ).
fof(c_0_987,plain,
! [X10,X11,X12,X13] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X13,tc_bool)),X12),c_Set_Oinsert(X10,X11,X13)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X13,tc_bool)),X12),X11))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X13,tc_bool)),c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool)),X13),tc_fun(X13,tc_bool))),X11)) ),
inference(variable_rename,[status(thm)],[c_0_510]) ).
fof(c_0_988,plain,
! [X10,X11,X12,X13] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X13,tc_bool)),X12),c_Set_Oinsert(X10,X11,X13)))
| ~ hBOOL(c_in(X10,X12,X13))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X13,tc_bool)),c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool)),X13),tc_fun(X13,tc_bool))),X11)) ),
inference(variable_rename,[status(thm)],[c_0_511]) ).
fof(c_0_989,plain,
! [X10,X11,X12,X13] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X13,tc_bool)),X12),c_Set_Oinsert(X10,X11,X13)))
| ~ hBOOL(c_in(X10,X12,X13))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X13,tc_bool)),c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool)),X13),tc_fun(X13,tc_bool))),X11)) ),
inference(variable_rename,[status(thm)],[c_0_512]) ).
fof(c_0_990,plain,
! [X50,X51,X52,X53,X54,X55] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X55,tc_bool)),hAPP(X53,X50)),X52))
| ~ hBOOL(c_in(X50,X51,X54))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X55,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X51,X53,X54,tc_fun(X55,tc_bool))),X52)) ),
inference(variable_rename,[status(thm)],[c_0_513]) ).
fof(c_0_991,plain,
! [X33,X34,X35,X36] :
( c_Hoare__Mirabelle_Ohoare__derivs(X36,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X35,X33,X34,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X35,v_sko__Hoare__Mirabelle__Xescape__1(X36,X35,X34,X33)),v_sko__Hoare__Mirabelle__Xescape__2(X36,X35,X34,X33))) ),
inference(variable_rename,[status(thm)],[c_0_514]) ).
fof(c_0_992,plain,
! [X33,X34,X35,X36] :
( c_Hoare__Mirabelle_Ohoare__derivs(X36,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X35,X33,X34,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X35,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X36,X35,X34,X33)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X36,X35,X34,X33))) ),
inference(variable_rename,[status(thm)],[c_0_515]) ).
fof(c_0_993,plain,
! [X33,X34,X35,X36] :
( c_Hoare__Mirabelle_Ohoare__derivs(X36,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X35,X33,X34,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X35,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X36,X35,X34,X33)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X36,X35,X34,X33))) ),
inference(variable_rename,[status(thm)],[c_0_516]) ).
fof(c_0_994,plain,
! [X10,X11,X12,X13,X14,X15] :
( hBOOL(c_in(hAPP(X11,X10),X12,X15))
| ~ hBOOL(c_in(X10,X13,X14))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X15,tc_bool)),c_Set_Oimage(X11,X13,X14,X15)),X12)) ),
inference(variable_rename,[status(thm)],[c_0_517]) ).
fof(c_0_995,plain,
! [X10,X11,X12,X13,X14] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X13,tc_bool)),c_Set_Oimage(X10,X12,X14,X13)),c_Set_Oimage(X10,X11,X14,X13)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X14,tc_bool)),X12),X11)) ),
inference(variable_rename,[status(thm)],[c_0_518]) ).
fof(c_0_996,plain,
! [X7,X8,X9,X10,X11] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X10,tc_bool)),X7),X9))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X11,tc_bool)),c_Set_Oimage(X8,X7,X10,X11)),c_Set_Oimage(X8,X9,X10,X11))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_519])])]) ).
fof(c_0_997,plain,
! [X52,X53,X54,X55,X56] :
( c_Hoare__Mirabelle_Ohoare__derivs(X56,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X55,X52,X54,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X54,v_sko__Hoare__Mirabelle__Xconseq2__1(X54,X53)),v_sko__Hoare__Mirabelle__Xconseq2__2(X54,X53)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X56,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X55,X52,X53,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(variable_rename,[status(thm)],[c_0_520]) ).
fof(c_0_998,plain,
! [X53,X54,X55,X56,X57] :
( c_Hoare__Mirabelle_Ohoare__derivs(X57,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X56,X53,X54,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X55,v_sko__Hoare__Mirabelle__Xconseq1__1(X56,X55)),v_sko__Hoare__Mirabelle__Xconseq1__2(X56,X55)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X57,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X55,X53,X54,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(variable_rename,[status(thm)],[c_0_521]) ).
fof(c_0_999,plain,
! [X10,X11,X12,X13] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X13,tc_bool)),c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool)),X13),tc_fun(X13,tc_bool))),X11))
| ~ hBOOL(c_in(X10,X12,X13))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X13,tc_bool)),X12),c_Set_Oinsert(X10,X11,X13))) ),
inference(variable_rename,[status(thm)],[c_0_522]) ).
fof(c_0_1000,plain,
! [X53,X54,X55,X56,X57] :
( c_Hoare__Mirabelle_Ohoare__derivs(X57,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X56,X53,X54,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X56,v_sko__Hoare__Mirabelle__Xconseq1__1(X56,X55)),v_sko__Hoare__Mirabelle__Xconseq1__2(X56,X55)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X57,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X55,X53,X54,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(variable_rename,[status(thm)],[c_0_523]) ).
fof(c_0_1001,plain,
! [X52,X53,X54,X55,X56] :
( c_Hoare__Mirabelle_Ohoare__derivs(X56,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X55,X52,X54,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X53,v_sko__Hoare__Mirabelle__Xconseq2__1(X54,X53)),v_sko__Hoare__Mirabelle__Xconseq2__2(X54,X53)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X56,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X55,X52,X53,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(variable_rename,[status(thm)],[c_0_524]) ).
fof(c_0_1002,plain,
! [X10,X11,X12] : c_Set_Oinsert(X10,X11,X12) = c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X12),X12,X12,tc_bool),X10),X12),X11,tc_fun(X12,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_525]) ).
fof(c_0_1003,plain,
! [X43,X44,X45,X46,X47] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X47,tc_bool)),c_HOL_Ominus__class_Ominus(X46,X45,tc_fun(X47,tc_bool))),c_HOL_Ominus__class_Ominus(X44,X43,tc_fun(X47,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X47,tc_bool)),X43),X45))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X47,tc_bool)),X46),X44)) ),
inference(variable_rename,[status(thm)],[c_0_526]) ).
fof(c_0_1004,plain,
! [X43,X44,X45,X46,X47] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X47,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X46,X45,tc_fun(X47,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(X44,X43,tc_fun(X47,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X47,tc_bool)),X45),X43))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X47,tc_bool)),X46),X44)) ),
inference(variable_rename,[status(thm)],[c_0_527]) ).
fof(c_0_1005,plain,
! [X10,X11,X12,X13,X14] :
( c_Finite__Set_Ofinite(X11,X13)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X13,tc_bool)),X11),c_Set_Oimage(X10,X12,X14,X13)))
| ~ c_Finite__Set_Ofinite(X12,X14) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_528])])]) ).
fof(c_0_1006,plain,
! [X12,X13,X14,X15] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X15,tc_bool)),X14),c_Lattices_Oupper__semilattice__class_Osup(X13,X12,tc_fun(X15,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X15,tc_bool)),c_HOL_Ominus__class_Ominus(X14,X13,tc_fun(X15,tc_bool))),X12)) ),
inference(variable_rename,[status(thm)],[c_0_529]) ).
fof(c_0_1007,plain,
! [X10,X11,X12,X13,X14] :
( ~ class_OrderedGroup_Oab__group__add(X13)
| c_Finite__Set_Osetsum(X10,c_HOL_Ominus__class_Ominus(X12,X11,tc_fun(X14,tc_bool)),X14,X13) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X10,X12,X14,X13),c_Finite__Set_Osetsum(X10,X11,X14,X13),X13)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X14,tc_bool)),X11),X12))
| ~ c_Finite__Set_Ofinite(X12,X14) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_530])])]) ).
fof(c_0_1008,plain,
! [X12,X13,X14,X15] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X15,tc_bool)),c_HOL_Ominus__class_Ominus(X14,X13,tc_fun(X15,tc_bool))),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X15,tc_bool)),X14),c_Lattices_Oupper__semilattice__class_Osup(X13,X12,tc_fun(X15,tc_bool)))) ),
inference(variable_rename,[status(thm)],[c_0_531]) ).
fof(c_0_1009,plain,
! [X12,X13,X14,X15] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X15,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X14,X13,tc_fun(X15,tc_bool))),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X15,tc_bool)),X13),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X15,tc_bool)),X14),X12)) ),
inference(variable_rename,[status(thm)],[c_0_532]) ).
fof(c_0_1010,plain,
! [X12,X13,X14,X15] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X15,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X14,X13,tc_fun(X15,tc_bool))),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X15,tc_bool)),X13),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X15,tc_bool)),X14),X12)) ),
inference(variable_rename,[status(thm)],[c_0_533]) ).
fof(c_0_1011,plain,
! [X10,X11,X12,X13] :
( c_HOL_Oord__class_Oless(X12,c_Set_Oinsert(X10,X11,X13),tc_fun(X13,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X13,tc_bool)),X12),X11))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool)),X13),tc_fun(X13,tc_bool)),X11,tc_fun(X13,tc_bool))
| ~ c_HOL_Oord__class_Oless(X12,X11,tc_fun(X13,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_534]) ).
fof(c_0_1012,plain,
! [X10,X11,X12,X13] :
( c_HOL_Oord__class_Oless(X12,c_Set_Oinsert(X10,X11,X13),tc_fun(X13,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X13,tc_bool)),X12),X11))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool)),X13),tc_fun(X13,tc_bool)),X11,tc_fun(X13,tc_bool))
| hBOOL(c_in(X10,X11,X13)) ),
inference(variable_rename,[status(thm)],[c_0_535]) ).
fof(c_0_1013,plain,
! [X19,X20,X21,X22,X23] :
( ~ class_Orderings_Oorder(X23)
| hBOOL(hAPP(hAPP(c_lessequals(X23),X21),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X23),X22),X21))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X23,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X22,X21,X23)),c_SetInterval_Oord__class_OatLeastAtMost(X20,X19,X23))) ),
inference(variable_rename,[status(thm)],[c_0_536]) ).
fof(c_0_1014,plain,
! [X19,X20,X21,X22,X23] :
( ~ class_Orderings_Oorder(X23)
| hBOOL(hAPP(hAPP(c_lessequals(X23),X20),X22))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X23),X22),X21))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X23,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X22,X21,X23)),c_SetInterval_Oord__class_OatLeastAtMost(X20,X19,X23))) ),
inference(variable_rename,[status(thm)],[c_0_537]) ).
fof(c_0_1015,plain,
! [X17,X18,X19,X20] :
( X19 = X18
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X17,c_Set_Oinsert(X19,c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X20),X20),X18)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_538])])]) ).
fof(c_0_1016,plain,
! [X12,X13,X14,X15] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X15,tc_bool)),X14),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X15,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X14,X13,tc_fun(X15,tc_bool))),X12)) ),
inference(variable_rename,[status(thm)],[c_0_539]) ).
fof(c_0_1017,plain,
! [X12,X13,X14,X15] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X15,tc_bool)),X13),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X15,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X14,X13,tc_fun(X15,tc_bool))),X12)) ),
inference(variable_rename,[status(thm)],[c_0_540]) ).
fof(c_0_1018,plain,
! [X19,X20,X21,X22,X23] :
( ~ class_Orderings_Olinorder(X23)
| hBOOL(hAPP(hAPP(c_lessequals(X23),X20),X22))
| hBOOL(hAPP(hAPP(c_lessequals(X23),X21),X22))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X23,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X22,X21,X23)),c_SetInterval_Oord__class_OatLeastLessThan(X20,X19,X23))) ),
inference(variable_rename,[status(thm)],[c_0_541]) ).
fof(c_0_1019,plain,
! [X19,X20,X21,X22,X23] :
( ~ class_Orderings_Olinorder(X23)
| hBOOL(hAPP(hAPP(c_lessequals(X23),X21),X19))
| hBOOL(hAPP(hAPP(c_lessequals(X23),X21),X22))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X23,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X22,X21,X23)),c_SetInterval_Oord__class_OatLeastLessThan(X20,X19,X23))) ),
inference(variable_rename,[status(thm)],[c_0_542]) ).
fof(c_0_1020,plain,
! [X10,X11,X12,X13,X14] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X13,tc_bool)),hAPP(X11,X10)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,X11,X14,tc_fun(X13,tc_bool))))
| ~ hBOOL(c_in(X10,X12,X14)) ),
inference(variable_rename,[status(thm)],[c_0_543]) ).
fof(c_0_1021,plain,
! [X17,X18,X19,X20,X21,X22] :
( hBOOL(c_in(X18,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,X19,X21,tc_fun(X22,tc_bool)),X22))
| ~ hBOOL(c_in(X18,hAPP(X19,X17),X22))
| ~ hBOOL(c_in(X17,X20,X21)) ),
inference(variable_rename,[status(thm)],[c_0_544]) ).
fof(c_0_1022,plain,
! [X17,X18,X19,X20,X21,X22] :
( hBOOL(c_in(X17,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,X19,X22,tc_fun(X21,tc_bool)),X21))
| ~ hBOOL(c_in(X17,hAPP(X19,X18),X21))
| ~ hBOOL(c_in(X18,X20,X22)) ),
inference(variable_rename,[status(thm)],[c_0_545]) ).
fof(c_0_1023,plain,
! [X9,X10,X11,X12,X13] :
( ~ class_OrderedGroup_Oab__group__add(X12)
| c_Finite__Set_Osetsum(X9,c_HOL_Ominus__class_Ominus(X11,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool)),X13),tc_fun(X13,tc_bool)),X13,X12) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X9,X11,X13,X12),hAPP(X9,X10),X12)
| ~ hBOOL(c_in(X10,X11,X13))
| ~ c_Finite__Set_Ofinite(X11,X13) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_546])])]) ).
fof(c_0_1024,plain,
! [X9,X10,X11,X12,X13] :
( ~ class_Ring__and__Field_Oring(X12)
| c_Finite__Set_Osetsum(X9,c_HOL_Ominus__class_Ominus(X11,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool)),X13),tc_fun(X13,tc_bool)),X13,X12) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X9,X11,X13,X12),hAPP(X9,X10),X12)
| ~ hBOOL(c_in(X10,X11,X13))
| ~ c_Finite__Set_Ofinite(X11,X13) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_547])])]) ).
fof(c_0_1025,plain,
! [X40,X41,X42,X43,X44] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Lattices_Oupper__semilattice__class_Osup(X42,X41,tc_fun(X43,tc_bool)),X40,X43,tc_fun(X44,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X42,X40,X43,tc_fun(X44,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X41,X40,X43,tc_fun(X44,tc_bool)),tc_fun(X44,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_548]) ).
fof(c_0_1026,plain,
! [X10,X11,X12,X13] :
( c_HOL_Oord__class_Oless(X12,c_Set_Oinsert(X10,X11,X13),tc_fun(X13,tc_bool))
| ~ hBOOL(c_in(X10,X12,X13))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool)),X13),tc_fun(X13,tc_bool)),X11,tc_fun(X13,tc_bool))
| ~ c_HOL_Oord__class_Oless(X12,X11,tc_fun(X13,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_549]) ).
fof(c_0_1027,plain,
! [X10,X11,X12,X13] :
( c_HOL_Oord__class_Oless(X12,c_Set_Oinsert(X10,X11,X13),tc_fun(X13,tc_bool))
| ~ hBOOL(c_in(X10,X12,X13))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool)),X13),tc_fun(X13,tc_bool)),X11,tc_fun(X13,tc_bool))
| hBOOL(c_in(X10,X11,X13)) ),
inference(variable_rename,[status(thm)],[c_0_550]) ).
fof(c_0_1028,plain,
! [X10,X11,X12,X13,X14] : c_Set_Oimage(X10,c_Lattices_Oupper__semilattice__class_Osup(X12,X11,tc_fun(X13,tc_bool)),X13,X14) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(X10,X12,X13,X14),c_Set_Oimage(X10,X11,X13,X14),tc_fun(X14,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_551]) ).
fof(c_0_1029,plain,
! [X10,X11,X12] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X12,tc_bool)),X10),X11))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X12,tc_bool)),c_HOL_Ouminus__class_Ouminus(X11,tc_fun(X12,tc_bool))),c_HOL_Ouminus__class_Ouminus(X10,tc_fun(X12,tc_bool)))) ),
inference(variable_rename,[status(thm)],[c_0_552]) ).
fof(c_0_1030,plain,
! [X10,X11,X12,X13] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X13,tc_bool)),X12),X11))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X13,tc_bool)),c_Set_Oinsert(X10,X12,X13)),X11)) ),
inference(variable_rename,[status(thm)],[c_0_553]) ).
fof(c_0_1031,plain,
! [X17,X18,X19,X20,X21,X22] :
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,X19,X22,tc_fun(X21,tc_bool)),X18))
| ~ hBOOL(hAPP(hAPP(X19,X17),X18))
| ~ hBOOL(c_in(X17,X20,X22)) ),
inference(variable_rename,[status(thm)],[c_0_554]) ).
fof(c_0_1032,plain,
! [X17,X18,X19,X20,X21,X22] :
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,X19,X22,tc_fun(X21,tc_bool)),X17))
| ~ hBOOL(hAPP(hAPP(X19,X18),X17))
| ~ hBOOL(c_in(X18,X20,X22)) ),
inference(variable_rename,[status(thm)],[c_0_555]) ).
fof(c_0_1033,plain,
! [X43,X44,X45,X46] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X46,tc_bool)),c_Set_Oinsert(X43,X45,X46)),c_Set_Oinsert(X43,X44,X46)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X46,tc_bool)),X45),X44)) ),
inference(variable_rename,[status(thm)],[c_0_556]) ).
fof(c_0_1034,plain,
! [X40,X41,X42,X43,X44] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X43)
| hBOOL(hAPP(hAPP(c_lessequals(X43),hAPP(X41,X40)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X42,X41,X44,X43)))
| ~ hBOOL(c_in(X40,X42,X44)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_557])])]) ).
fof(c_0_1035,plain,
! [X10,X11,X12,X13] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X13,tc_bool)),c_Set_Oinsert(X10,X12,X13)),X11))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X13,tc_bool)),X12),X11))
| ~ hBOOL(c_in(X10,X11,X13)) ),
inference(variable_rename,[status(thm)],[c_0_558]) ).
fof(c_0_1036,plain,
! [X4,X5] : hBOOL(hAPP(c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5))),
inference(variable_rename,[status(thm)],[c_0_559]) ).
fof(c_0_1037,plain,
! [X18,X19,X20,X21,X22] :
( ~ hBOOL(c_in(X18,X20,X21))
| hBOOL(c_in(hAPP(X19,X18),c_Set_Oimage(X19,X20,X21,X22),X22)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_560])])]) ).
fof(c_0_1038,plain,
! [X7,X8,X9,X10,X11] :
( ~ hBOOL(c_in(X7,X9,X10))
| hBOOL(c_in(hAPP(X8,X7),c_Set_Oimage(X8,X9,X10,X11),X11)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_561])])]) ).
fof(c_0_1039,plain,
! [X7,X8,X9,X10,X11] :
( hBOOL(c_in(hAPP(X8,X7),c_Set_Oimage(X8,X9,X10,X11),X11))
| ~ hBOOL(c_in(X7,X9,X10)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_562])])]) ).
fof(c_0_1040,plain,
! [X7,X8,X9,X10,X11] :
( hBOOL(c_in(hAPP(X8,X7),c_Set_Oimage(X8,X9,X11,X10),X10))
| ~ hBOOL(c_in(X7,X9,X11)) ),
inference(variable_rename,[status(thm)],[c_0_563]) ).
fof(c_0_1041,plain,
! [X33,X34,X35] : c_Hoare__Mirabelle_Ohoare__derivs(X34,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X33,c_Com_Ocom_OSKIP,X33,X35),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X35),tc_bool)),tc_Hoare__Mirabelle_Otriple(X35)),X35),
inference(variable_rename,[status(thm)],[c_0_564]) ).
fof(c_0_1042,plain,
! [X19,X20,X21,X22,X23] :
( ~ class_Orderings_Oorder(X23)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X23,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X22,X21,X23)),c_SetInterval_Oord__class_OatLeastAtMost(X20,X19,X23)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X23),X21),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X23),X20),X22)) ),
inference(variable_rename,[status(thm)],[c_0_565]) ).
fof(c_0_1043,plain,
! [X6,X7,X8] :
( X7 = c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool)),X8)
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X8,tc_bool)),X7),c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool)),X8))) ),
inference(variable_rename,[status(thm)],[c_0_566]) ).
fof(c_0_1044,plain,
! [X10,X11,X12,X13] :
( hBOOL(c_in(X10,X11,X13))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X13,tc_bool)),c_Set_Oinsert(X10,X12,X13)),X11)) ),
inference(variable_rename,[status(thm)],[c_0_567]) ).
fof(c_0_1045,plain,
! [X10,X11,X12,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool)),X13),tc_fun(X13,tc_bool)),X11,tc_fun(X13,tc_bool))
| ~ hBOOL(c_in(X10,X12,X13))
| hBOOL(c_in(X10,X11,X13))
| ~ c_HOL_Oord__class_Oless(X12,c_Set_Oinsert(X10,X11,X13),tc_fun(X13,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_568]) ).
fof(c_0_1046,plain,
! [X9,X10,X11,X12,X13] :
( ~ class_OrderedGroup_Oab__group__add(X12)
| c_Finite__Set_Osetsum(X9,c_HOL_Ominus__class_Ominus(X11,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool)),X13),tc_fun(X13,tc_bool)),X13,X12) = c_Finite__Set_Osetsum(X9,X11,X13,X12)
| hBOOL(c_in(X10,X11,X13))
| ~ c_Finite__Set_Ofinite(X11,X13) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_569])])]) ).
fof(c_0_1047,plain,
! [X12,X13,X14,X15] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X15,tc_bool)),X14),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X15,tc_bool)),X13),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X15,tc_bool)),X14),X13)) ),
inference(variable_rename,[status(thm)],[c_0_570]) ).
fof(c_0_1048,plain,
! [X10,X11,X12,X13] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X13,tc_bool)),X12),X11))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X13,tc_bool)),X12),c_Set_Oinsert(X10,X11,X13)))
| hBOOL(c_in(X10,X12,X13)) ),
inference(variable_rename,[status(thm)],[c_0_571]) ).
fof(c_0_1049,plain,
! [X10,X11,X12,X13] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X13,tc_bool)),X12),X11))
| hBOOL(c_in(X10,X12,X13))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X13,tc_bool)),X12),c_Set_Oinsert(X10,X11,X13))) ),
inference(variable_rename,[status(thm)],[c_0_572]) ).
fof(c_0_1050,plain,
! [X9,X10,X11,X12] :
( c_Finite__Set_Osetsum(X9,c_HOL_Ominus__class_Ominus(X11,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)),X12),tc_fun(X12,tc_bool)),X12,tc_nat) = c_Finite__Set_Osetsum(X9,X11,X12,tc_nat)
| hBOOL(c_in(X10,X11,X12)) ),
inference(variable_rename,[status(thm)],[c_0_573]) ).
fof(c_0_1051,plain,
! [X10,X11,X12] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X12,tc_bool)),c_HOL_Ouminus__class_Ouminus(X10,tc_fun(X12,tc_bool))),c_HOL_Ouminus__class_Ouminus(X11,tc_fun(X12,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X12,tc_bool)),X11),X10)) ),
inference(variable_rename,[status(thm)],[c_0_574]) ).
fof(c_0_1052,plain,
! [X10,X11,X12] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X12,tc_bool)),c_HOL_Ouminus__class_Ouminus(X11,tc_fun(X12,tc_bool))),c_HOL_Ouminus__class_Ouminus(X10,tc_fun(X12,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X12,tc_bool)),X10),X11)) ),
inference(variable_rename,[status(thm)],[c_0_575]) ).
fof(c_0_1053,plain,
! [X9,X10] : c_Collect(hAPP(c_COMBC(c_fequal(X10),X10,X10,tc_bool),X9),X10) = c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool)),X10),
inference(variable_rename,[status(thm)],[c_0_576]) ).
fof(c_0_1054,plain,
! [X12,X13,X14,X15] :
( c_HOL_Ominus__class_Ominus(X13,c_HOL_Ominus__class_Ominus(X12,X14,tc_fun(X15,tc_bool)),tc_fun(X15,tc_bool)) = X14
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X15,tc_bool)),X13),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X15,tc_bool)),X14),X13)) ),
inference(variable_rename,[status(thm)],[c_0_577]) ).
fof(c_0_1055,plain,
! [X10,X11,X12,X13,X14] :
( c_Finite__Set_Ofinite(hAPP(X11,X10),X13)
| ~ hBOOL(c_in(X10,X12,X14))
| ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,X11,X14,tc_fun(X13,tc_bool)),X13)
| ~ c_Finite__Set_Ofinite(X12,X14) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_578])])]) ).
fof(c_0_1056,plain,
! [X50,X51,X52,X53,X54] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(X52,X50),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X51,X52,X54,tc_fun(X53,tc_bool)),tc_fun(X53,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X51,X52,X54,tc_fun(X53,tc_bool))
| ~ hBOOL(c_in(X50,X51,X54)) ),
inference(variable_rename,[status(thm)],[c_0_579]) ).
fof(c_0_1057,plain,
! [X5,X6,X7] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(X6,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_bool)),X7),X7),X5)),
inference(variable_rename,[status(thm)],[c_0_580]) ).
fof(c_0_1058,plain,
! [X10,X11,X12,X13] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X13,tc_bool)),X12),c_Set_Oinsert(X10,X11,X13)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X13,tc_bool)),X12),X11))
| hBOOL(c_in(X10,X12,X13)) ),
inference(variable_rename,[status(thm)],[c_0_581]) ).
fof(c_0_1059,plain,
! [X10,X11,X12,X13] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X13,tc_bool)),X12),c_Set_Oinsert(X10,X11,X13)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X13,tc_bool)),X12),X11))
| hBOOL(c_in(X10,X12,X13)) ),
inference(variable_rename,[status(thm)],[c_0_582]) ).
fof(c_0_1060,plain,
! [X31,X32,X33,X34,X35,X36] : hAPP(hAPP(c_COMBC(X33,X35,X34,X36),X32),X31) = hAPP(hAPP(X33,X31),X32),
inference(variable_rename,[status(thm)],[c_0_583]) ).
fof(c_0_1061,plain,
! [X9,X10] : c_The(hAPP(c_COMBC(c_fequal(X10),X10,X10,tc_bool),X9),X10) = X9,
inference(variable_rename,[status(thm)],[c_0_584]) ).
fof(c_0_1062,plain,
! [X19,X20,X21,X22,X23] :
( ~ class_Orderings_Oorder(X23)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X23,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X22,X21,X23)),c_SetInterval_Oord__class_OatLeastAtMost(X20,X19,X23)))
| hBOOL(hAPP(hAPP(c_lessequals(X23),X22),X21)) ),
inference(variable_rename,[status(thm)],[c_0_585]) ).
fof(c_0_1063,plain,
! [X10,X11,X12,X13,X14] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oinsert(X10,X12,X13),X11,X13,tc_fun(X14,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(X11,X10),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,X11,X13,tc_fun(X14,tc_bool)),tc_fun(X14,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_586]) ).
fof(c_0_1064,plain,
! [X7,X8,X9,X10,X11] :
( c_Set_Oinsert(hAPP(X8,X7),c_Set_Oimage(X8,X9,X11,X10),X10) = c_Set_Oimage(X8,X9,X11,X10)
| ~ hBOOL(c_in(X7,X9,X11)) ),
inference(variable_rename,[status(thm)],[c_0_587]) ).
fof(c_0_1065,plain,
! [X17,X18,X19,X20] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X20,tc_bool)),X19),c_Set_Oinsert(X17,X18,X20)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X20,tc_bool)),X19),X18)) ),
inference(variable_rename,[status(thm)],[c_0_588]) ).
fof(c_0_1066,plain,
! [X17,X18,X19,X20] :
( ~ class_Lattices_Oupper__semilattice(X20)
| hBOOL(hAPP(hAPP(c_lessequals(X20),X19),X17))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X20),c_Lattices_Oupper__semilattice__class_Osup(X19,X18,X20)),X17)) ),
inference(variable_rename,[status(thm)],[c_0_589]) ).
fof(c_0_1067,plain,
! [X17,X18,X19,X20] :
( ~ class_Lattices_Oupper__semilattice(X20)
| hBOOL(hAPP(hAPP(c_lessequals(X20),X18),X17))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X20),c_Lattices_Oupper__semilattice__class_Osup(X19,X18,X20)),X17)) ),
inference(variable_rename,[status(thm)],[c_0_590]) ).
fof(c_0_1068,plain,
! [X8,X9,X10,X11] :
( ~ class_Lattices_Oupper__semilattice(X11)
| hBOOL(hAPP(hAPP(c_lessequals(X11),X10),X8))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X11),c_Lattices_Oupper__semilattice__class_Osup(X10,X9,X11)),X8)) ),
inference(variable_rename,[status(thm)],[c_0_591]) ).
fof(c_0_1069,plain,
! [X8,X9,X10,X11] :
( ~ class_Lattices_Oupper__semilattice(X11)
| hBOOL(hAPP(hAPP(c_lessequals(X11),X9),X8))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X11),c_Lattices_Oupper__semilattice__class_Osup(X10,X9,X11)),X8)) ),
inference(variable_rename,[status(thm)],[c_0_592]) ).
fof(c_0_1070,plain,
! [X4,X5,X6] :
( X4 = c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)),X6),X6)
| ~ hBOOL(hAPP(c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)),X6),X4)) ),
inference(variable_rename,[status(thm)],[c_0_593]) ).
fof(c_0_1071,plain,
! [X10,X11,X12,X13,X14] : c_Set_Oimage(X10,c_Set_Oinsert(X11,X12,X13),X13,X14) = c_Set_Oinsert(hAPP(X10,X11),c_Set_Oimage(X10,X12,X13,X14),X14),
inference(variable_rename,[status(thm)],[c_0_594]) ).
fof(c_0_1072,plain,
! [X10,X11,X12] :
( X11 = X10
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X12,tc_bool)),X10),X11))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X12,tc_bool)),X11),X10)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_595])])]) ).
fof(c_0_1073,plain,
! [X10,X11,X12] :
( X11 = X10
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X12,tc_bool)),X10),X11))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X12,tc_bool)),X11),X10)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_596])])]) ).
fof(c_0_1074,plain,
! [X10,X11,X12] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X12,tc_bool)),c_HOL_Ominus__class_Ominus(X11,X10,tc_fun(X12,tc_bool))),X11)),
inference(variable_rename,[status(thm)],[c_0_597]) ).
fof(c_0_1075,plain,
! [X11,X12,X13,X14] :
( ~ class_HOL_Oord(X13)
| c_HOL_Oord__class_Oless(X12,X11,tc_fun(X14,X13))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X14,X13)),X11),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X14,X13)),X12),X11)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_598])])]) ).
fof(c_0_1076,plain,
! [X19,X20,X21,X22,X23] :
( ~ class_Orderings_Oorder(X23)
| c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X22,X21,X23),c_SetInterval_Oord__class_OatLeastAtMost(X20,X19,X23),tc_fun(X23,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X23),X20),X19))
| ~ c_HOL_Oord__class_Oless(X20,X22,X23)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X23),X21),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X23),X20),X22)) ),
inference(variable_rename,[status(thm)],[c_0_599]) ).
fof(c_0_1077,plain,
! [X19,X20,X21,X22,X23] :
( ~ class_Orderings_Oorder(X23)
| c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X22,X21,X23),c_SetInterval_Oord__class_OatLeastAtMost(X20,X19,X23),tc_fun(X23,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X23),X20),X19))
| ~ c_HOL_Oord__class_Oless(X21,X19,X23)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X23),X21),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X23),X20),X22)) ),
inference(variable_rename,[status(thm)],[c_0_600]) ).
fof(c_0_1078,plain,
! [X16,X17,X18,X19] :
( hBOOL(c_in(X16,X17,X19))
| hBOOL(c_in(X16,X18,X19))
| ~ hBOOL(c_in(X16,c_Lattices_Oupper__semilattice__class_Osup(X18,X17,tc_fun(X19,tc_bool)),X19)) ),
inference(variable_rename,[status(thm)],[c_0_601]) ).
fof(c_0_1079,plain,
! [X17,X18,X19,X20] :
( ~ class_Lattices_Oupper__semilattice(X20)
| hBOOL(hAPP(hAPP(c_lessequals(X20),c_Lattices_Oupper__semilattice__class_Osup(X19,X18,X20)),X17))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X20),X18),X17))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X20),X19),X17)) ),
inference(variable_rename,[status(thm)],[c_0_602]) ).
fof(c_0_1080,plain,
! [X8,X9,X10,X11] :
( ~ class_Lattices_Oupper__semilattice(X11)
| hBOOL(hAPP(hAPP(c_lessequals(X11),c_Lattices_Oupper__semilattice__class_Osup(X10,X9,X11)),X8))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X11),X9),X8))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X11),X10),X8)) ),
inference(variable_rename,[status(thm)],[c_0_603]) ).
fof(c_0_1081,plain,
! [X8,X9,X10,X11] :
( ~ class_Lattices_Oupper__semilattice(X11)
| hBOOL(hAPP(hAPP(c_lessequals(X11),c_Lattices_Oupper__semilattice__class_Osup(X9,X8,X11)),X10))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X11),X8),X10))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X11),X9),X10)) ),
inference(variable_rename,[status(thm)],[c_0_604]) ).
fof(c_0_1082,plain,
! [X10,X11,X12,X13] :
( c_HOL_Oord__class_Oless(X12,c_Set_Oinsert(X10,X11,X13),tc_fun(X13,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X13,tc_bool)),X12),X11))
| hBOOL(c_in(X10,X12,X13))
| ~ c_HOL_Oord__class_Oless(X12,X11,tc_fun(X13,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_605]) ).
fof(c_0_1083,plain,
! [X10,X11,X12,X13] :
( c_HOL_Oord__class_Oless(X12,c_Set_Oinsert(X10,X11,X13),tc_fun(X13,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X13,tc_bool)),X12),X11))
| hBOOL(c_in(X10,X12,X13))
| hBOOL(c_in(X10,X11,X13)) ),
inference(variable_rename,[status(thm)],[c_0_606]) ).
fof(c_0_1084,plain,
! [X4] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))),c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)))),
inference(variable_rename,[status(thm)],[c_0_607]) ).
fof(c_0_1085,plain,
! [X17,X18,X19] :
( X17 = X18
| ~ hBOOL(c_in(X17,c_Set_Oinsert(X18,c_Orderings_Obot__class_Obot(tc_fun(X19,tc_bool)),X19),X19)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_608])])]) ).
fof(c_0_1086,plain,
! [X19,X20,X21,X22,X23] :
( c_Set_Oinsert(X22,c_Set_Oinsert(X21,c_Orderings_Obot__class_Obot(tc_fun(X23,tc_bool)),X23),X23) != c_Set_Oinsert(X20,c_Set_Oinsert(X19,c_Orderings_Obot__class_Obot(tc_fun(X23,tc_bool)),X23),X23)
| X22 = X19
| X22 = X20 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_609])])]) ).
fof(c_0_1087,plain,
! [X19,X20,X21,X22,X23] :
( c_Set_Oinsert(X22,c_Set_Oinsert(X21,c_Orderings_Obot__class_Obot(tc_fun(X23,tc_bool)),X23),X23) != c_Set_Oinsert(X20,c_Set_Oinsert(X19,c_Orderings_Obot__class_Obot(tc_fun(X23,tc_bool)),X23),X23)
| X21 = X20
| X22 = X20 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_610])])]) ).
fof(c_0_1088,plain,
! [X19,X20,X21,X22,X23] :
( c_Set_Oinsert(X22,c_Set_Oinsert(X21,c_Orderings_Obot__class_Obot(tc_fun(X23,tc_bool)),X23),X23) != c_Set_Oinsert(X20,c_Set_Oinsert(X19,c_Orderings_Obot__class_Obot(tc_fun(X23,tc_bool)),X23),X23)
| X22 = X19
| X21 = X19 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_611])])]) ).
fof(c_0_1089,plain,
! [X19,X20,X21,X22,X23] :
( c_Set_Oinsert(X22,c_Set_Oinsert(X21,c_Orderings_Obot__class_Obot(tc_fun(X23,tc_bool)),X23),X23) != c_Set_Oinsert(X20,c_Set_Oinsert(X19,c_Orderings_Obot__class_Obot(tc_fun(X23,tc_bool)),X23),X23)
| X21 = X20
| X21 = X19 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_612])])]) ).
fof(c_0_1090,plain,
! [X10,X11,X12,X13] : c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X10,X11,X13),tc_fun(X13,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool)),X13),tc_fun(X13,tc_bool)),X11,tc_fun(X13,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_613]) ).
fof(c_0_1091,plain,
! [X16,X17,X18,X19] :
( ~ hBOOL(c_in(X16,X17,X19))
| ~ hBOOL(c_in(X16,c_HOL_Ominus__class_Ominus(X18,X17,tc_fun(X19,tc_bool)),X19)) ),
inference(variable_rename,[status(thm)],[c_0_614]) ).
fof(c_0_1092,plain,
! [X9,X10,X11] :
( c_Set_Oinsert(X9,c_HOL_Ominus__class_Ominus(X10,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)),X11),tc_fun(X11,tc_bool)),X11) = X10
| ~ hBOOL(c_in(X9,X10,X11)) ),
inference(variable_rename,[status(thm)],[c_0_615]) ).
fof(c_0_1093,plain,
! [X10,X11,X12,X13] : c_Set_Oinsert(X10,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)),X11,X12,tc_fun(X13,tc_bool)),X13) = c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool)),X13),
inference(variable_rename,[status(thm)],[c_0_616]) ).
fof(c_0_1094,plain,
! [X10,X11,X12,X13] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X13,tc_bool)),X12),X11))
| hBOOL(c_in(X10,X12,X13))
| hBOOL(c_in(X10,X11,X13))
| ~ c_HOL_Oord__class_Oless(X12,c_Set_Oinsert(X10,X11,X13),tc_fun(X13,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_617]) ).
fof(c_0_1095,plain,
! [X62,X63,X64,X65,X66,X67,X68] :
( c_Hoare__Mirabelle_Otriple_Otriple(X65,X67,X63,X68) != c_Hoare__Mirabelle_Otriple_Otriple(X64,X66,X62,X68)
| X65 = X64 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_618])])]) ).
fof(c_0_1096,plain,
! [X62,X63,X64,X65,X66,X67,X68] :
( c_Hoare__Mirabelle_Otriple_Otriple(X65,X67,X63,X68) != c_Hoare__Mirabelle_Otriple_Otriple(X64,X66,X62,X68)
| X67 = X66 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_619])])]) ).
fof(c_0_1097,plain,
! [X62,X63,X64,X65,X66,X67,X68] :
( c_Hoare__Mirabelle_Otriple_Otriple(X65,X67,X63,X68) != c_Hoare__Mirabelle_Otriple_Otriple(X64,X66,X62,X68)
| X63 = X62 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_620])])]) ).
fof(c_0_1098,plain,
! [X41,X42,X43] :
( ~ class_Orderings_Olinorder(X43)
| hBOOL(hAPP(hAPP(c_lessequals(X43),c_Finite__Set_Olinorder__class_OMax(X42,X43)),c_Finite__Set_Olinorder__class_OMax(X41,X43)))
| ~ c_Finite__Set_Ofinite(X41,X43)
| X42 = c_Orderings_Obot__class_Obot(tc_fun(X43,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X43,tc_bool)),X42),X41)) ),
inference(variable_rename,[status(thm)],[c_0_621]) ).
fof(c_0_1099,plain,
! [X41,X42,X43] :
( ~ class_Orderings_Olinorder(X43)
| hBOOL(hAPP(hAPP(c_lessequals(X43),c_Finite__Set_Olinorder__class_OMin(X41,X43)),c_Finite__Set_Olinorder__class_OMin(X42,X43)))
| ~ c_Finite__Set_Ofinite(X41,X43)
| X42 = c_Orderings_Obot__class_Obot(tc_fun(X43,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X43,tc_bool)),X42),X41)) ),
inference(variable_rename,[status(thm)],[c_0_622]) ).
fof(c_0_1100,plain,
! [X54,X55,X56,X57] :
( c_Hoare__Mirabelle_Ohoare__derivs(X56,c_Set_Oinsert(X55,X54,tc_Hoare__Mirabelle_Otriple(X57)),X57)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X56,X54,X57)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X56,c_Set_Oinsert(X55,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X57),tc_bool)),tc_Hoare__Mirabelle_Otriple(X57)),X57) ),
inference(variable_rename,[status(thm)],[c_0_623]) ).
fof(c_0_1101,plain,
! [X16,X17,X18,X19] :
( hBOOL(c_in(X16,X18,X19))
| ~ hBOOL(c_in(X16,c_HOL_Ominus__class_Ominus(X18,X17,tc_fun(X19,tc_bool)),X19)) ),
inference(variable_rename,[status(thm)],[c_0_624]) ).
fof(c_0_1102,plain,
! [X10,X11,X12,X13] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X12,X11,tc_fun(X13,tc_bool)),X13)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X10,X11,X13),tc_fun(X13,tc_bool)),X13) ),
inference(variable_rename,[status(thm)],[c_0_625]) ).
fof(c_0_1103,plain,
! [X11,X12,X13,X14,X15] :
( ~ class_HOL_Oord(X14)
| hBOOL(hAPP(hAPP(c_lessequals(X14),hAPP(X13,X11)),hAPP(X12,X11)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X15,X14)),X13),X12)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_626])])]) ).
fof(c_0_1104,plain,
! [X55,X56,X57,X58] :
( c_Hoare__Mirabelle_Ohoare__derivs(X57,X56,X58)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(X58),tc_bool)),X56),X55))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X57,X55,X58) ),
inference(variable_rename,[status(thm)],[c_0_627]) ).
fof(c_0_1105,plain,
! [X19,X20,X21,X22,X23] :
( ~ class_Orderings_Oorder(X23)
| c_HOL_Oord__class_Oless(X21,X19,X23)
| c_HOL_Oord__class_Oless(X20,X22,X23)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X23),X22),X21))
| ~ c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X22,X21,X23),c_SetInterval_Oord__class_OatLeastAtMost(X20,X19,X23),tc_fun(X23,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_628]) ).
fof(c_0_1106,plain,
! [X10,X11,X12,X13] :
( hBOOL(c_in(X10,X11,X13))
| ~ hBOOL(c_in(X10,X12,X13))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X13,tc_bool)),X12),X11)) ),
inference(variable_rename,[status(thm)],[c_0_629]) ).
fof(c_0_1107,plain,
! [X16,X17,X18,X19] :
( hBOOL(c_in(X16,X17,X19))
| ~ hBOOL(c_in(X16,X18,X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X19,tc_bool)),X18),X17)) ),
inference(variable_rename,[status(thm)],[c_0_630]) ).
fof(c_0_1108,plain,
! [X10,X11,X12,X13] :
( hBOOL(c_in(X10,X11,X13))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X13,tc_bool)),X12),X11))
| ~ hBOOL(c_in(X10,X12,X13)) ),
inference(variable_rename,[status(thm)],[c_0_631]) ).
fof(c_0_1109,plain,
! [X42,X43,X44,X45] :
( hBOOL(c_in(X42,X43,X45))
| ~ hBOOL(c_in(X42,X44,X45))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X45,tc_bool)),X44),X43)) ),
inference(variable_rename,[status(thm)],[c_0_632]) ).
fof(c_0_1110,plain,
! [X19,X20,X21,X22,X23] :
( ~ class_Orderings_Oorder(X23)
| hBOOL(hAPP(hAPP(c_lessequals(X23),X20),X22))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X23),X22),X21))
| ~ c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X22,X21,X23),c_SetInterval_Oord__class_OatLeastAtMost(X20,X19,X23),tc_fun(X23,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_633]) ).
fof(c_0_1111,plain,
! [X19,X20,X21,X22,X23] :
( ~ class_Orderings_Oorder(X23)
| hBOOL(hAPP(hAPP(c_lessequals(X23),X21),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X23),X22),X21))
| ~ c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X22,X21,X23),c_SetInterval_Oord__class_OatLeastAtMost(X20,X19,X23),tc_fun(X23,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_634]) ).
fof(c_0_1112,plain,
! [X10,X11,X12,X13] : c_Lattices_Oupper__semilattice__class_Osup(X11,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)),X10,X12,tc_fun(X13,tc_bool)),tc_fun(X13,tc_bool)) = X11,
inference(variable_rename,[status(thm)],[c_0_635]) ).
fof(c_0_1113,plain,
! [X10,X11,X12,X13] : c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)),X11,X12,tc_fun(X13,tc_bool)),X10,tc_fun(X13,tc_bool)) = X10,
inference(variable_rename,[status(thm)],[c_0_636]) ).
fof(c_0_1114,plain,
! [X10,X11,X12,X13] : c_HOL_Ominus__class_Ominus(X11,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)),X10,X12,tc_fun(X13,tc_bool)),tc_fun(X13,tc_bool)) = X11,
inference(variable_rename,[status(thm)],[c_0_637]) ).
fof(c_0_1115,plain,
! [X5,X6,X7] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X6,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_bool)),X7),X5)),
inference(variable_rename,[status(thm)],[c_0_638]) ).
fof(c_0_1116,plain,
! [X6,X7] :
( X6 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X7,tc_bool)),X6),c_HOL_Ouminus__class_Ouminus(X6,tc_fun(X7,tc_bool)))) ),
inference(variable_rename,[status(thm)],[c_0_639]) ).
fof(c_0_1117,plain,
! [X16,X17,X18,X19] :
( hBOOL(c_in(X16,c_HOL_Ominus__class_Ominus(X18,X17,tc_fun(X19,tc_bool)),X19))
| hBOOL(c_in(X16,X17,X19))
| ~ hBOOL(c_in(X16,X18,X19)) ),
inference(variable_rename,[status(thm)],[c_0_640]) ).
fof(c_0_1118,plain,
! [X16,X17,X18,X19] :
( hBOOL(c_in(X16,c_HOL_Ominus__class_Ominus(X18,X17,tc_fun(X19,tc_bool)),X19))
| hBOOL(c_in(X16,X17,X19))
| ~ hBOOL(c_in(X16,X18,X19)) ),
inference(variable_rename,[status(thm)],[c_0_641]) ).
fof(c_0_1119,plain,
! [X15,X16,X17,X18] :
( ~ class_Orderings_Olinorder(X18)
| c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(X17,X16,X18),c_SetInterval_Oord__class_OatLeastLessThan(X16,X15,X18),tc_fun(X18,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X17,X15,X18)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X18),X16),X15))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X18),X17),X16)) ),
inference(variable_rename,[status(thm)],[c_0_642]) ).
fof(c_0_1120,plain,
! [X15,X16,X17,X18] :
( ~ class_Orderings_Olinorder(X18)
| c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OgreaterThanAtMost(X17,X16,X18),c_SetInterval_Oord__class_OgreaterThanAtMost(X16,X15,X18),tc_fun(X18,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X17,X15,X18)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X18),X16),X15))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X18),X17),X16)) ),
inference(variable_rename,[status(thm)],[c_0_643]) ).
fof(c_0_1121,plain,
! [X15,X16,X17,X18] :
( ~ class_Orderings_Olinorder(X18)
| c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastAtMost(X17,X16,X18),c_SetInterval_Oord__class_OgreaterThanAtMost(X16,X15,X18),tc_fun(X18,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X17,X15,X18)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X18),X16),X15))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X18),X17),X16)) ),
inference(variable_rename,[status(thm)],[c_0_644]) ).
fof(c_0_1122,plain,
! [X15,X16,X17,X18] :
( ~ class_Orderings_Olinorder(X18)
| c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(X17,X16,X18),c_SetInterval_Oord__class_OatLeastAtMost(X16,X15,X18),tc_fun(X18,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X17,X15,X18)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X18),X16),X15))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X18),X17),X16)) ),
inference(variable_rename,[status(thm)],[c_0_645]) ).
fof(c_0_1123,plain,
! [X10,X11,X12] :
( c_Lattices_Oupper__semilattice__class_Osup(X11,c_HOL_Ominus__class_Ominus(X10,X11,tc_fun(X12,tc_bool)),tc_fun(X12,tc_bool)) = X10
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X12,tc_bool)),X11),X10)) ),
inference(variable_rename,[status(thm)],[c_0_646]) ).
fof(c_0_1124,plain,
! [X10,X11,X12,X13,X14] :
( c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,X11,X13,tc_fun(X14,tc_bool))
| hAPP(X11,X10) = c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool))
| ~ hBOOL(c_in(X10,X12,X13)) ),
inference(variable_rename,[status(thm)],[c_0_647]) ).
fof(c_0_1125,plain,
! [X10,X11,X12,X13,X14] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,X11,X13,tc_fun(X14,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool))
| hAPP(X11,X10) = c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool))
| ~ hBOOL(c_in(X10,X12,X13)) ),
inference(variable_rename,[status(thm)],[c_0_648]) ).
fof(c_0_1126,plain,
! [X9,X10,X11] : c_Set_Oinsert(X9,c_HOL_Ominus__class_Ominus(X10,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)),X11),tc_fun(X11,tc_bool)),X11) = c_Set_Oinsert(X9,X10,X11),
inference(variable_rename,[status(thm)],[c_0_649]) ).
fof(c_0_1127,plain,
! [X54,X55,X56] :
( c_Hoare__Mirabelle_Ohoare__derivs(X55,X54,X56)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(X56),tc_bool)),X54),X55)) ),
inference(variable_rename,[status(thm)],[c_0_650]) ).
fof(c_0_1128,plain,
! [X12,X13,X14,X15] :
( c_HOL_Oord__class_Oless(X14,X12,tc_fun(X15,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X15,tc_bool)),X13),X12))
| ~ c_HOL_Oord__class_Oless(X14,X13,tc_fun(X15,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_651]) ).
fof(c_0_1129,plain,
! [X12,X13,X14,X15] :
( c_HOL_Oord__class_Oless(X14,X12,tc_fun(X15,tc_bool))
| ~ c_HOL_Oord__class_Oless(X13,X12,tc_fun(X15,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X15,tc_bool)),X14),X13)) ),
inference(variable_rename,[status(thm)],[c_0_652]) ).
fof(c_0_1130,plain,
! [X6,X7] :
( X6 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X7,tc_bool)),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_bool)))) ),
inference(variable_rename,[status(thm)],[c_0_653]) ).
fof(c_0_1131,plain,
! [X10,X11,X12,X13] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X10,X11,X13),tc_fun(X13,tc_bool)),X13)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X12,X11,tc_fun(X13,tc_bool)),X13) ),
inference(variable_rename,[status(thm)],[c_0_654]) ).
fof(c_0_1132,plain,
! [X16,X17,X18,X19,X20] :
( c_Set_Oimage(c_COMBK(X17,X19,X20),X18,X20,X19) = c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X19,tc_bool)),X19)
| ~ hBOOL(c_in(X16,X18,X20)) ),
inference(variable_rename,[status(thm)],[c_0_655]) ).
fof(c_0_1133,plain,
! [X11,X12,X13,X14] :
( ~ class_HOL_Oord(X13)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X14,X13)),X11),X12))
| ~ c_HOL_Oord__class_Oless(X12,X11,tc_fun(X14,X13)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_656])])]) ).
fof(c_0_1134,plain,
! [X10,X11,X12,X13] : c_HOL_Ominus__class_Ominus(X12,c_Set_Oinsert(X10,X11,X13),tc_fun(X13,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X12,X11,tc_fun(X13,tc_bool)),c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool)),X13),tc_fun(X13,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_657]) ).
fof(c_0_1135,plain,
! [X17,X18,X19,X20] :
( hBOOL(c_in(X18,X19,X20))
| X18 = X17
| ~ hBOOL(c_in(X18,c_Set_Oinsert(X17,X19,X20),X20)) ),
inference(variable_rename,[status(thm)],[c_0_658]) ).
fof(c_0_1136,plain,
! [X15,X16,X17] :
( ~ class_Orderings_Olinorder(X17)
| c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X17,tc_bool)),X17),c_SetInterval_Oord__class_OgreaterThanAtMost(X16,X15,X17),tc_fun(X17,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X16,X15,X17)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X17),X16),X15)) ),
inference(variable_rename,[status(thm)],[c_0_659]) ).
fof(c_0_1137,plain,
! [X15,X16,X17] :
( ~ class_Orderings_Olinorder(X17)
| c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(X16,X15,X17),c_Set_Oinsert(X15,c_Orderings_Obot__class_Obot(tc_fun(X17,tc_bool)),X17),tc_fun(X17,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X16,X15,X17)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X17),X16),X15)) ),
inference(variable_rename,[status(thm)],[c_0_660]) ).
fof(c_0_1138,plain,
! [X12,X13,X14,X15] : c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(X14,X13,tc_fun(X15,tc_bool)),X12,tc_fun(X15,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X14,X12,tc_fun(X15,tc_bool)),c_HOL_Ominus__class_Ominus(X13,X12,tc_fun(X15,tc_bool)),tc_fun(X15,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_661]) ).
fof(c_0_1139,plain,
! [X17,X18,X19] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X19)
| hAPP(c_Complete__Lattice_OSup__class_OSup(X19),c_Set_Oinsert(X18,c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X19,tc_bool)),X19),X19)) = c_Lattices_Oupper__semilattice__class_Osup(X18,X17,X19) ),
inference(variable_rename,[status(thm)],[c_0_662]) ).
fof(c_0_1140,plain,
! [X4] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))),
inference(variable_rename,[status(thm)],[c_0_663]) ).
fof(c_0_1141,plain,
! [X10,X11,X12] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X12,tc_bool)),X11),c_Lattices_Oupper__semilattice__class_Osup(X11,X10,tc_fun(X12,tc_bool)))),
inference(variable_rename,[status(thm)],[c_0_664]) ).
fof(c_0_1142,plain,
! [X10,X11,X12] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X12,tc_bool)),X10),c_Lattices_Oupper__semilattice__class_Osup(X11,X10,tc_fun(X12,tc_bool)))),
inference(variable_rename,[status(thm)],[c_0_665]) ).
fof(c_0_1143,plain,
! [X16,X17,X18,X19] :
( hBOOL(c_in(X16,c_Lattices_Oupper__semilattice__class_Osup(X18,X17,tc_fun(X19,tc_bool)),X19))
| ~ hBOOL(c_in(X16,X18,X19)) ),
inference(variable_rename,[status(thm)],[c_0_666]) ).
fof(c_0_1144,plain,
! [X16,X17,X18,X19] :
( hBOOL(c_in(X16,c_Lattices_Oupper__semilattice__class_Osup(X18,X17,tc_fun(X19,tc_bool)),X19))
| ~ hBOOL(c_in(X16,X17,X19)) ),
inference(variable_rename,[status(thm)],[c_0_667]) ).
fof(c_0_1145,plain,
! [X10,X11,X12,X13] :
( hBOOL(hAPP(X11,X10))
| hBOOL(hAPP(X12,X10))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X12,X11,tc_fun(X13,tc_bool)),X10)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_668])])]) ).
fof(c_0_1146,plain,
! [X16,X17,X18] :
( ~ hBOOL(c_in(X16,X17,X18))
| ~ hBOOL(c_in(X16,c_HOL_Ouminus__class_Ouminus(X17,tc_fun(X18,tc_bool)),X18)) ),
inference(variable_rename,[status(thm)],[c_0_669]) ).
fof(c_0_1147,plain,
! [X19,X20,X21,X22,X23] :
( ~ class_Orderings_Oorder(X23)
| c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X22,X21,X23),c_SetInterval_Oord__class_OatLeastAtMost(X20,X19,X23),tc_fun(X23,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X23),X20),X19))
| hBOOL(hAPP(hAPP(c_lessequals(X23),X22),X21)) ),
inference(variable_rename,[status(thm)],[c_0_670]) ).
fof(c_0_1148,plain,
! [X19,X20,X21,X22,X23] :
( ~ class_Orderings_Oorder(X23)
| hBOOL(hAPP(hAPP(c_lessequals(X23),X20),X19))
| ~ c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X22,X21,X23),c_SetInterval_Oord__class_OatLeastAtMost(X20,X19,X23),tc_fun(X23,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_671]) ).
fof(c_0_1149,plain,
! [X7,X8,X9] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,c_COMBK(c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),tc_fun(X9,tc_bool),X8),X8,tc_fun(X9,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_672]) ).
fof(c_0_1150,plain,
! [X17,X18,X19] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X19)
| hBOOL(hAPP(hAPP(c_lessequals(X19),c_HOL_Ouminus__class_Ouminus(X18,X19)),X17))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X19),c_HOL_Ouminus__class_Ouminus(X17,X19)),X18)) ),
inference(variable_rename,[status(thm)],[c_0_673]) ).
fof(c_0_1151,plain,
! [X17,X18,X19] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X19)
| hBOOL(hAPP(hAPP(c_lessequals(X19),c_HOL_Ouminus__class_Ouminus(X17,X19)),X18))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X19),c_HOL_Ouminus__class_Ouminus(X18,X19)),X17)) ),
inference(variable_rename,[status(thm)],[c_0_674]) ).
fof(c_0_1152,plain,
! [X10,X11,X12,X13] :
( c_HOL_Oord__class_Oless(X12,X11,tc_fun(X13,tc_bool))
| ~ hBOOL(c_in(X10,X11,X13))
| ~ c_HOL_Oord__class_Oless(X12,c_Set_Oinsert(X10,X11,X13),tc_fun(X13,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_675]) ).
fof(c_0_1153,plain,
! [X10,X11,X12] :
( c_HOL_Oord__class_Oless(X11,X10,tc_fun(X12,tc_bool))
| X11 = X10
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X12,tc_bool)),X11),X10)) ),
inference(variable_rename,[status(thm)],[c_0_676]) ).
fof(c_0_1154,plain,
! [X10,X11,X12] :
( X11 = X10
| c_HOL_Oord__class_Oless(X11,X10,tc_fun(X12,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X12,tc_bool)),X11),X10)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_677])])]) ).
fof(c_0_1155,plain,
! [X10,X11,X12] :
( c_Lattices_Oupper__semilattice__class_Osup(X11,X10,tc_fun(X12,tc_bool)) = X10
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X12,tc_bool)),X11),X10)) ),
inference(variable_rename,[status(thm)],[c_0_678]) ).
fof(c_0_1156,plain,
! [X10,X11,X12] :
( c_Lattices_Oupper__semilattice__class_Osup(X11,X10,tc_fun(X12,tc_bool)) = X11
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X12,tc_bool)),X10),X11)) ),
inference(variable_rename,[status(thm)],[c_0_679]) ).
fof(c_0_1157,plain,
! [X30,X31,X32,X33] :
( hBOOL(hAPP(X31,X30))
| ~ hBOOL(hAPP(X32,X30))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X33,tc_bool)),X32),X31)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_680])])]) ).
fof(c_0_1158,plain,
! [X30,X31,X32,X33] :
( hBOOL(hAPP(X31,X30))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X33,tc_bool)),X32),X31))
| ~ hBOOL(hAPP(X32,X30)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_681])])]) ).
fof(c_0_1159,plain,
! [X4,X5] : hBOOL(c_in(X4,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5)),
inference(variable_rename,[status(thm)],[c_0_682]) ).
fof(c_0_1160,plain,
! [X44,X45,X46] : c_Set_Oinsert(X44,c_Set_Oinsert(X45,c_Orderings_Obot__class_Obot(tc_fun(X46,tc_bool)),X46),X46) = c_Set_Oinsert(X45,c_Set_Oinsert(X44,c_Orderings_Obot__class_Obot(tc_fun(X46,tc_bool)),X46),X46),
inference(variable_rename,[status(thm)],[c_0_683]) ).
fof(c_0_1161,plain,
! [X35,X36,X37,X38] :
( c_Finite__Set_Ofinite(c_Set_Oimage(X35,X36,X38,X37),X37)
| ~ c_Finite__Set_Ofinite(X36,X38) ),
inference(variable_rename,[status(thm)],[c_0_684]) ).
fof(c_0_1162,plain,
! [X17,X18,X19] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X19)
| hBOOL(hAPP(hAPP(c_lessequals(X19),X18),X17))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X19),c_HOL_Ouminus__class_Ouminus(X17,X19)),c_HOL_Ouminus__class_Ouminus(X18,X19))) ),
inference(variable_rename,[status(thm)],[c_0_685]) ).
fof(c_0_1163,plain,
! [X39,X40,X41,X42] :
( ~ class_Orderings_Olinorder(X42)
| c_HOL_Ominus__class_Ominus(c_SetInterval_Oord__class_OatLeastLessThan(X41,X40,X42),c_SetInterval_Oord__class_OatLeastLessThan(X41,X39,X42),tc_fun(X42,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X39,X40,X42)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X42),X41),X39)) ),
inference(variable_rename,[status(thm)],[c_0_686]) ).
fof(c_0_1164,plain,
! [X6,X7,X8] :
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X6,X7,X8),c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool)),X8),tc_fun(X8,tc_bool)) = X7
| hBOOL(c_in(X6,X7,X8)) ),
inference(variable_rename,[status(thm)],[c_0_687]) ).
fof(c_0_1165,plain,
! [X10,X11,X12] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X12,tc_bool)),X11),c_Set_Oinsert(X10,X11,X12))),
inference(variable_rename,[status(thm)],[c_0_688]) ).
fof(c_0_1166,plain,
! [X10,X11,X12,X13] :
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X10,X12,X13),X11,tc_fun(X13,tc_bool)) = c_Set_Oinsert(X10,c_HOL_Ominus__class_Ominus(X12,X11,tc_fun(X13,tc_bool)),X13)
| hBOOL(c_in(X10,X11,X13)) ),
inference(variable_rename,[status(thm)],[c_0_689]) ).
fof(c_0_1167,plain,
! [X16,X17,X18] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X17,tc_bool)),c_COMBK(X16,tc_fun(X18,tc_bool),X17),X17,tc_fun(X18,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X18,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_690]) ).
fof(c_0_1168,plain,
! [X17,X18,X19,X20] :
( hBOOL(c_in(X18,c_Set_Oinsert(X17,X19,X20),X20))
| ~ hBOOL(c_in(X18,X19,X20)) ),
inference(variable_rename,[status(thm)],[c_0_691]) ).
fof(c_0_1169,plain,
! [X17,X18,X19,X20] :
( hBOOL(c_in(X18,c_Set_Oinsert(X17,X19,X20),X20))
| ~ hBOOL(c_in(X18,X19,X20)) ),
inference(variable_rename,[status(thm)],[c_0_692]) ).
fof(c_0_1170,plain,
! [X6,X7] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X7,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_bool))),X6)),
inference(variable_rename,[status(thm)],[c_0_693]) ).
fof(c_0_1171,plain,
! [X17,X18,X19,X20] :
( ~ class_Lattices_Oupper__semilattice(X20)
| hBOOL(hAPP(hAPP(c_lessequals(X20),X17),c_Lattices_Oupper__semilattice__class_Osup(X19,X18,X20)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X20),X17),X19)) ),
inference(variable_rename,[status(thm)],[c_0_694]) ).
fof(c_0_1172,plain,
! [X17,X18,X19,X20] :
( ~ class_Lattices_Oupper__semilattice(X20)
| hBOOL(hAPP(hAPP(c_lessequals(X20),X17),c_Lattices_Oupper__semilattice__class_Osup(X19,X18,X20)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X20),X17),X18)) ),
inference(variable_rename,[status(thm)],[c_0_695]) ).
fof(c_0_1173,plain,
! [X10,X11,X12] :
( c_Finite__Set_Ofinite(X11,X12)
| ~ c_Finite__Set_Ofinite(X10,X12)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X12,tc_bool)),X11),X10)) ),
inference(variable_rename,[status(thm)],[c_0_696]) ).
fof(c_0_1174,plain,
! [X10,X11,X12] :
( c_Finite__Set_Ofinite(X11,X12)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X12,tc_bool)),X11),X10))
| ~ c_Finite__Set_Ofinite(X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_697]) ).
fof(c_0_1175,plain,
! [X16,X17,X18,X19] :
( c_Set_Oimage(c_COMBK(X16,X19,X18),X17,X18,X19) = c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X19,tc_bool)),X19)
| X17 = 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_698])])]) ).
fof(c_0_1176,plain,
! [X10,X11,X12,X13] :
( c_HOL_Oord__class_Oless(X12,c_Set_Oinsert(X10,X11,X13),tc_fun(X13,tc_bool))
| ~ hBOOL(c_in(X10,X11,X13))
| ~ c_HOL_Oord__class_Oless(X12,X11,tc_fun(X13,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_699]) ).
fof(c_0_1177,plain,
! [X12,X13,X14,X15] : c_Lattices_Oupper__semilattice__class_Osup(X14,c_Lattices_Oupper__semilattice__class_Osup(X13,X12,tc_fun(X15,tc_bool)),tc_fun(X15,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X13,c_Lattices_Oupper__semilattice__class_Osup(X14,X12,tc_fun(X15,tc_bool)),tc_fun(X15,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_700]) ).
fof(c_0_1178,plain,
! [X12,X13,X14,X15] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X14,X13,tc_fun(X15,tc_bool)),X12,tc_fun(X15,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X14,c_Lattices_Oupper__semilattice__class_Osup(X13,X12,tc_fun(X15,tc_bool)),tc_fun(X15,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_701]) ).
fof(c_0_1179,plain,
! [X7,X8,X9,X10] :
( c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool)) != c_Set_Oimage(X7,X8,X9,X10)
| X8 = c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_702])])]) ).
fof(c_0_1180,plain,
! [X7,X8,X9,X10] :
( c_Set_Oimage(X7,X8,X9,X10) != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool))
| X8 = c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_703])])]) ).
fof(c_0_1181,plain,
! [X37,X38,X39,X40,X41] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X41)
| c_HOL_Ominus__class_Ominus(X40,X38,X41) != c_HOL_Ominus__class_Ominus(X39,X37,X41)
| hBOOL(hAPP(hAPP(c_lessequals(X41),X38),X40))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X41),X37),X39)) ),
inference(variable_rename,[status(thm)],[c_0_704]) ).
fof(c_0_1182,plain,
! [X37,X38,X39,X40,X41] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X41)
| c_HOL_Ominus__class_Ominus(X40,X38,X41) != c_HOL_Ominus__class_Ominus(X39,X37,X41)
| hBOOL(hAPP(hAPP(c_lessequals(X41),X37),X39))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X41),X38),X40)) ),
inference(variable_rename,[status(thm)],[c_0_705]) ).
fof(c_0_1183,plain,
! [X16,X17,X18,X19] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,c_COMBK(X16,tc_fun(X19,tc_bool),X18),X18,tc_fun(X19,tc_bool)) = X16
| X17 = 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_706])])]) ).
fof(c_0_1184,plain,
! [X8,X9,X10,X11] :
( ~ class_Orderings_Oorder(X11)
| hBOOL(hAPP(hAPP(c_lessequals(X11),X8),X10))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X11),X8),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X11),X9),X10)) ),
inference(variable_rename,[status(thm)],[c_0_707]) ).
fof(c_0_1185,plain,
! [X8,X9,X10,X11] :
( ~ class_Orderings_Opreorder(X11)
| hBOOL(hAPP(hAPP(c_lessequals(X11),X10),X8))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X11),X9),X8))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X11),X10),X9)) ),
inference(variable_rename,[status(thm)],[c_0_708]) ).
fof(c_0_1186,plain,
! [X11,X12,X13,X14] :
( ~ class_HOL_Oord(X13)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X14,X13)),X12),X11))
| ~ c_HOL_Oord__class_Oless(X12,X11,tc_fun(X14,X13)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_709])])]) ).
fof(c_0_1187,plain,
! [X6,X7,X8] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X8)
| hBOOL(hAPP(hAPP(c_lessequals(X8),hAPP(c_Complete__Lattice_OInf__class_OInf(X8),X7)),X6))
| ~ hBOOL(c_in(X6,X7,X8)) ),
inference(variable_rename,[status(thm)],[c_0_710]) ).
fof(c_0_1188,plain,
! [X17,X18,X19] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X19)
| hBOOL(hAPP(hAPP(c_lessequals(X19),c_HOL_Ouminus__class_Ouminus(X17,X19)),c_HOL_Ouminus__class_Ouminus(X18,X19)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X19),X18),X17)) ),
inference(variable_rename,[status(thm)],[c_0_711]) ).
fof(c_0_1189,plain,
! [X10,X11,X12,X13] :
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X10,X12,X13),X11,tc_fun(X13,tc_bool)) = c_HOL_Ominus__class_Ominus(X12,X11,tc_fun(X13,tc_bool))
| ~ hBOOL(c_in(X10,X11,X13)) ),
inference(variable_rename,[status(thm)],[c_0_712]) ).
fof(c_0_1190,plain,
! [X16,X17,X18] : c_Set_Oimage(c_COMBK(X16,X18,X17),c_Orderings_Obot__class_Obot(tc_fun(X17,tc_bool)),X17,X18) = c_Orderings_Obot__class_Obot(tc_fun(X18,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_713]) ).
fof(c_0_1191,plain,
! [X6,X7,X8,X9] :
( hBOOL(hAPP(X8,X7))
| X6 = X7
| ~ hBOOL(hAPP(c_Set_Oinsert(X6,X8,X9),X7)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_714])])]) ).
fof(c_0_1192,plain,
! [X6,X7,X8] :
( ~ class_Orderings_Olinorder(X8)
| hBOOL(hAPP(hAPP(c_lessequals(X8),c_Finite__Set_Olinorder__class_OMin(X7,X8)),X6))
| ~ hBOOL(c_in(X6,X7,X8))
| ~ c_Finite__Set_Ofinite(X7,X8) ),
inference(variable_rename,[status(thm)],[c_0_715]) ).
fof(c_0_1193,plain,
! [X17,X18,X19] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X19)
| hBOOL(hAPP(hAPP(c_lessequals(X19),X18),c_HOL_Ouminus__class_Ouminus(X17,X19)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X19),X17),c_HOL_Ouminus__class_Ouminus(X18,X19))) ),
inference(variable_rename,[status(thm)],[c_0_716]) ).
fof(c_0_1194,plain,
! [X17,X18,X19] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X19)
| hBOOL(hAPP(hAPP(c_lessequals(X19),X17),c_HOL_Ouminus__class_Ouminus(X18,X19)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X19),X18),c_HOL_Ouminus__class_Ouminus(X17,X19))) ),
inference(variable_rename,[status(thm)],[c_0_717]) ).
fof(c_0_1195,plain,
! [X10,X11,X12] :
( c_Lattices_Oupper__semilattice__class_Osup(X11,X10,tc_fun(X12,tc_bool)) != X10
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X12,tc_bool)),X11),X10)) ),
inference(variable_rename,[status(thm)],[c_0_718]) ).
fof(c_0_1196,plain,
! [X10,X11,X12] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X12,tc_bool)),X11),X10))
| ~ c_HOL_Oord__class_Oless(X11,X10,tc_fun(X12,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_719]) ).
fof(c_0_1197,plain,
! [X16,X17,X18,X19] :
( hBOOL(c_in(X16,X17,X19))
| ~ hBOOL(c_in(X16,X18,X19))
| ~ c_HOL_Oord__class_Oless(X18,X17,tc_fun(X19,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_720]) ).
fof(c_0_1198,plain,
! [X10,X11,X12,X13] :
( c_Set_Oinsert(X10,X12,X13) != c_Set_Oinsert(X10,X11,X13)
| hBOOL(c_in(X10,X11,X13))
| hBOOL(c_in(X10,X12,X13))
| X12 = X11 ),
inference(variable_rename,[status(thm)],[c_0_721]) ).
fof(c_0_1199,plain,
! [X12,X13,X14,X15] : c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X12,X14,X15),X13,tc_fun(X15,tc_bool)) = c_Set_Oinsert(X12,c_Lattices_Oupper__semilattice__class_Osup(X14,X13,tc_fun(X15,tc_bool)),X15),
inference(variable_rename,[status(thm)],[c_0_722]) ).
fof(c_0_1200,plain,
! [X10,X11,X12,X13] : c_Lattices_Oupper__semilattice__class_Osup(X12,c_Set_Oinsert(X10,X11,X13),tc_fun(X13,tc_bool)) = c_Set_Oinsert(X10,c_Lattices_Oupper__semilattice__class_Osup(X12,X11,tc_fun(X13,tc_bool)),X13),
inference(variable_rename,[status(thm)],[c_0_723]) ).
fof(c_0_1201,plain,
! [X40,X41,X42,X43] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X42)
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X41,c_COMBK(X40,X42,X43),X43,X42) = X40
| X41 = c_Orderings_Obot__class_Obot(tc_fun(X43,tc_bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_724])])]) ).
fof(c_0_1202,plain,
! [X30,X31,X32] :
( ~ hBOOL(hAPP(X31,X30))
| ~ hBOOL(c_in(X30,c_Orderings_Obot__class_Obot(tc_fun(X32,tc_bool)),X32)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_725])])]) ).
fof(c_0_1203,plain,
! [X10,X11,X12,X13] :
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X12,X11,tc_fun(X13,tc_bool)),X10))
| ~ hBOOL(hAPP(X12,X10)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_726])])]) ).
fof(c_0_1204,plain,
! [X10,X11,X12,X13] :
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X12,X11,tc_fun(X13,tc_bool)),X10))
| ~ hBOOL(hAPP(X11,X10)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_727])])]) ).
fof(c_0_1205,plain,
! [X30,X31,X32] :
( hBOOL(hAPP(X31,X30))
| ~ hBOOL(c_in(X30,c_Orderings_Obot__class_Obot(tc_fun(X32,tc_bool)),X32)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_728])])]) ).
fof(c_0_1206,plain,
! [X16,X17,X18] :
( hBOOL(c_in(X16,c_HOL_Ouminus__class_Ouminus(X17,tc_fun(X18,tc_bool)),X18))
| hBOOL(c_in(X16,X17,X18)) ),
inference(variable_rename,[status(thm)],[c_0_729]) ).
fof(c_0_1207,plain,
! [X6,X7,X8] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X8)
| hBOOL(hAPP(hAPP(c_lessequals(X8),X6),hAPP(c_Complete__Lattice_OSup__class_OSup(X8),X7)))
| ~ hBOOL(c_in(X6,X7,X8)) ),
inference(variable_rename,[status(thm)],[c_0_730]) ).
fof(c_0_1208,plain,
! [X6,X7,X8] :
( ~ class_Orderings_Olinorder(X8)
| hBOOL(hAPP(hAPP(c_lessequals(X8),X6),c_Finite__Set_Olinorder__class_OMax(X7,X8)))
| ~ hBOOL(c_in(X6,X7,X8))
| ~ c_Finite__Set_Ofinite(X7,X8) ),
inference(variable_rename,[status(thm)],[c_0_731]) ).
fof(c_0_1209,plain,
! [X4,X5,X6] :
( ~ class_Orderings_Oorder(X6)
| X5 = X4
| ~ hBOOL(hAPP(hAPP(c_lessequals(X6),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X6),X5),X4)) ),
inference(variable_rename,[status(thm)],[c_0_732]) ).
fof(c_0_1210,plain,
! [X4,X5,X6] :
( ~ class_Orderings_Oorder(X6)
| X5 = X4
| ~ hBOOL(hAPP(hAPP(c_lessequals(X6),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X6),X5),X4)) ),
inference(variable_rename,[status(thm)],[c_0_733]) ).
fof(c_0_1211,plain,
! [X4,X5,X6] :
( ~ class_Orderings_Oorder(X6)
| X5 = X4
| ~ hBOOL(hAPP(hAPP(c_lessequals(X6),X5),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X6),X4),X5)) ),
inference(variable_rename,[status(thm)],[c_0_734]) ).
fof(c_0_1212,plain,
! [X9,X10,X11] : c_Set_Oinsert(X9,X10,X11) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)),X11),X10,tc_fun(X11,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_735]) ).
fof(c_0_1213,plain,
! [X10,X11,X12] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X11,X10,tc_fun(X12,tc_bool)),tc_fun(X12,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X11,tc_fun(X12,tc_bool)),X10,tc_fun(X12,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_736]) ).
fof(c_0_1214,plain,
! [X9,X10] : ~ hBOOL(c_in(X9,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool)),X10)),
inference(variable_rename,[status(thm)],[c_0_737]) ).
fof(c_0_1215,plain,
! [X16,X17] : ~ hBOOL(c_in(X16,c_Orderings_Obot__class_Obot(tc_fun(X17,tc_bool)),X17)),
inference(variable_rename,[status(thm)],[c_0_738]) ).
fof(c_0_1216,plain,
! [X4,X5] : ~ hBOOL(c_in(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5)),
inference(variable_rename,[status(thm)],[c_0_739]) ).
fof(c_0_1217,plain,
! [X17,X18,X19] :
( c_Set_Oinsert(X18,c_Orderings_Obot__class_Obot(tc_fun(X19,tc_bool)),X19) != c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X19,tc_bool)),X19)
| X18 = X17 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_740])])]) ).
fof(c_0_1218,plain,
! [X4,X5,X6] :
( ~ class_Orderings_Opreorder(X6)
| c_HOL_Oord__class_Oless(X5,X4,X6)
| hBOOL(hAPP(hAPP(c_lessequals(X6),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X6),X5),X4)) ),
inference(variable_rename,[status(thm)],[c_0_741]) ).
fof(c_0_1219,plain,
! [X8,X9,X10,X11] :
( ~ class_Lattices_Oupper__semilattice(X11)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X10,X9,X11),X8,X11) = c_Lattices_Oupper__semilattice__class_Osup(X10,c_Lattices_Oupper__semilattice__class_Osup(X9,X8,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_742]) ).
fof(c_0_1220,plain,
! [X8,X9,X10,X11] :
( ~ class_Lattices_Oupper__semilattice(X11)
| c_Lattices_Oupper__semilattice__class_Osup(X10,c_Lattices_Oupper__semilattice__class_Osup(X9,X8,X11),X11) = c_Lattices_Oupper__semilattice__class_Osup(X9,c_Lattices_Oupper__semilattice__class_Osup(X10,X8,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_743]) ).
fof(c_0_1221,plain,
! [X8,X9,X10,X11] :
( ~ class_Lattices_Olattice(X11)
| c_Lattices_Oupper__semilattice__class_Osup(X10,c_Lattices_Oupper__semilattice__class_Osup(X9,X8,X11),X11) = c_Lattices_Oupper__semilattice__class_Osup(X9,c_Lattices_Oupper__semilattice__class_Osup(X10,X8,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_744]) ).
fof(c_0_1222,plain,
! [X8,X9,X10,X11] :
( ~ class_Lattices_Olattice(X11)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X10,X9,X11),X8,X11) = c_Lattices_Oupper__semilattice__class_Osup(X10,c_Lattices_Oupper__semilattice__class_Osup(X9,X8,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_745]) ).
fof(c_0_1223,plain,
! [X4,X5,X6] :
( ~ class_Lattices_Oupper__semilattice(X6)
| hBOOL(hAPP(hAPP(c_lessequals(X6),X5),c_Lattices_Oupper__semilattice__class_Osup(X5,X4,X6))) ),
inference(variable_rename,[status(thm)],[c_0_746]) ).
fof(c_0_1224,plain,
! [X4,X5,X6] :
( ~ class_Lattices_Olattice(X6)
| hBOOL(hAPP(hAPP(c_lessequals(X6),X5),c_Lattices_Oupper__semilattice__class_Osup(X5,X4,X6))) ),
inference(variable_rename,[status(thm)],[c_0_747]) ).
fof(c_0_1225,plain,
! [X4,X5,X6] :
( ~ class_Lattices_Olattice(X6)
| hBOOL(hAPP(hAPP(c_lessequals(X6),X4),c_Lattices_Oupper__semilattice__class_Osup(X5,X4,X6))) ),
inference(variable_rename,[status(thm)],[c_0_748]) ).
fof(c_0_1226,plain,
! [X4,X5,X6] :
( ~ class_Lattices_Oupper__semilattice(X6)
| hBOOL(hAPP(hAPP(c_lessequals(X6),X4),c_Lattices_Oupper__semilattice__class_Osup(X5,X4,X6))) ),
inference(variable_rename,[status(thm)],[c_0_749]) ).
fof(c_0_1227,plain,
! [X7,X8,X9] : c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)) = c_Set_Oimage(X7,c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool)),X8,X9),
inference(variable_rename,[status(thm)],[c_0_750]) ).
fof(c_0_1228,plain,
! [X7,X8,X9] : c_Set_Oimage(X7,c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool)),X8,X9) = c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_751]) ).
fof(c_0_1229,plain,
! [X10,X11,X12] : hBOOL(c_in(X10,c_Set_Oinsert(X10,X11,X12),X12)),
inference(variable_rename,[status(thm)],[c_0_752]) ).
fof(c_0_1230,plain,
! [X10,X11,X12] : hBOOL(c_in(X10,c_Set_Oinsert(X10,X11,X12),X12)),
inference(variable_rename,[status(thm)],[c_0_753]) ).
fof(c_0_1231,plain,
! [X6,X7,X8] : hBOOL(c_in(X6,c_Set_Oinsert(X6,X7,X8),X8)),
inference(variable_rename,[status(thm)],[c_0_754]) ).
fof(c_0_1232,plain,
! [X6,X7,X8,X9] : c_Set_Oinsert(X7,c_Set_Oinsert(X6,X8,X9),X9) = c_Set_Oinsert(X6,c_Set_Oinsert(X7,X8,X9),X9),
inference(variable_rename,[status(thm)],[c_0_755]) ).
fof(c_0_1233,plain,
! [X12,X13,X14,X15] :
( c_HOL_Oord__class_Oless(X14,X12,tc_fun(X15,tc_bool))
| ~ c_HOL_Oord__class_Oless(X13,X12,tc_fun(X15,tc_bool))
| ~ c_HOL_Oord__class_Oless(X14,X13,tc_fun(X15,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_756]) ).
fof(c_0_1234,plain,
! [X37,X38,X39,X40,X41] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X41)
| c_HOL_Ominus__class_Ominus(X40,X38,X41) != c_HOL_Ominus__class_Ominus(X39,X37,X41)
| c_HOL_Oord__class_Oless(X40,X38,X41)
| ~ c_HOL_Oord__class_Oless(X39,X37,X41) ),
inference(variable_rename,[status(thm)],[c_0_757]) ).
fof(c_0_1235,plain,
! [X37,X38,X39,X40,X41] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X41)
| c_HOL_Ominus__class_Ominus(X40,X38,X41) != c_HOL_Ominus__class_Ominus(X39,X37,X41)
| c_HOL_Oord__class_Oless(X39,X37,X41)
| ~ c_HOL_Oord__class_Oless(X40,X38,X41) ),
inference(variable_rename,[status(thm)],[c_0_758]) ).
fof(c_0_1236,plain,
! [X8,X9,X10,X11] :
( ~ class_Orderings_Opreorder(X11)
| c_HOL_Oord__class_Oless(X10,X8,X11)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X11),X9),X8))
| ~ c_HOL_Oord__class_Oless(X10,X9,X11) ),
inference(variable_rename,[status(thm)],[c_0_759]) ).
fof(c_0_1237,plain,
! [X8,X9,X10,X11] :
( ~ class_Orderings_Opreorder(X11)
| c_HOL_Oord__class_Oless(X10,X8,X11)
| ~ c_HOL_Oord__class_Oless(X9,X8,X11)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X11),X10),X9)) ),
inference(variable_rename,[status(thm)],[c_0_760]) ).
fof(c_0_1238,plain,
! [X8,X9,X10,X11] :
( ~ class_Orderings_Oorder(X11)
| c_HOL_Oord__class_Oless(X8,X10,X11)
| ~ c_HOL_Oord__class_Oless(X8,X9,X11)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X11),X9),X10)) ),
inference(variable_rename,[status(thm)],[c_0_761]) ).
fof(c_0_1239,plain,
! [X8,X9,X10,X11] :
( ~ class_Orderings_Oorder(X11)
| c_HOL_Oord__class_Oless(X8,X10,X11)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X11),X8),X9))
| ~ c_HOL_Oord__class_Oless(X9,X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_762]) ).
fof(c_0_1240,plain,
! [X10,X11,X12] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X11,X10,tc_fun(X12,tc_bool)),X10,tc_fun(X12,tc_bool)) = c_HOL_Ominus__class_Ominus(X11,X10,tc_fun(X12,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_763]) ).
fof(c_0_1241,plain,
! [X10,X11,X12] : c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X10,X11,tc_fun(X12,tc_bool)),X11,tc_fun(X12,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X10,X11,tc_fun(X12,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_764]) ).
fof(c_0_1242,plain,
! [X10,X11,X12] : c_Lattices_Oupper__semilattice__class_Osup(X11,c_HOL_Ominus__class_Ominus(X10,X11,tc_fun(X12,tc_bool)),tc_fun(X12,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X11,X10,tc_fun(X12,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_765]) ).
fof(c_0_1243,plain,
! [X10,X11,X12] : c_Lattices_Oupper__semilattice__class_Osup(X11,c_Lattices_Oupper__semilattice__class_Osup(X11,X10,tc_fun(X12,tc_bool)),tc_fun(X12,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X11,X10,tc_fun(X12,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_766]) ).
fof(c_0_1244,plain,
! [X17,X18,X19] :
( ~ class_Orderings_Oorder(X19)
| c_Orderings_Obot__class_Obot(tc_fun(X19,tc_bool)) != c_SetInterval_Oord__class_OatLeastAtMost(X18,X17,X19)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X19),X18),X17)) ),
inference(variable_rename,[status(thm)],[c_0_767]) ).
fof(c_0_1245,plain,
! [X17,X18,X19] :
( ~ class_Orderings_Oorder(X19)
| c_SetInterval_Oord__class_OatLeastAtMost(X18,X17,X19) != c_Orderings_Obot__class_Obot(tc_fun(X19,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X19),X18),X17)) ),
inference(variable_rename,[status(thm)],[c_0_768]) ).
fof(c_0_1246,plain,
! [X10,X11,X12] :
( c_Finite__Set_Ofinite(X11,X12)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X11,X10,tc_fun(X12,tc_bool)),X12)
| ~ c_Finite__Set_Ofinite(X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_769]) ).
fof(c_0_1247,plain,
! [X6,X7,X8,X9] :
( hBOOL(hAPP(c_Set_Oinsert(X6,X8,X9),X7))
| ~ hBOOL(hAPP(X8,X7)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_770])])]) ).
fof(c_0_1248,plain,
! [X4,X5] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X5,tc_bool)),X4),X4)),
inference(variable_rename,[status(thm)],[c_0_771]) ).
fof(c_0_1249,plain,
! [X6,X7] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X7,tc_bool)),X6),X6)),
inference(variable_rename,[status(thm)],[c_0_772]) ).
fof(c_0_1250,plain,
! [X30,X31,X32] :
( hBOOL(hAPP(X31,X30))
| ~ hBOOL(c_in(X30,c_Collect(X31,X32),X32)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_773])])]) ).
fof(c_0_1251,plain,
! [X34,X35,X36] :
( c_Finite__Set_Ofinite(X34,X36)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X35,X34,tc_fun(X36,tc_bool)),X36) ),
inference(variable_rename,[status(thm)],[c_0_774]) ).
fof(c_0_1252,plain,
! [X34,X35,X36] :
( c_Finite__Set_Ofinite(X35,X36)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X35,X34,tc_fun(X36,tc_bool)),X36) ),
inference(variable_rename,[status(thm)],[c_0_775]) ).
fof(c_0_1253,plain,
! [X4] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X4)
| c_Complete__Lattice_Ocomplete__lattice__axioms(c_Complete__Lattice_OInf__class_OInf(X4),c_Complete__Lattice_OSup__class_OSup(X4),c_lessequals(X4),X4) ),
inference(variable_rename,[status(thm)],[c_0_776]) ).
fof(c_0_1254,plain,
! [X11,X12,X13] :
( ~ class_Lattices_Olattice(X13)
| hAPP(c_Lattices_Oupper__semilattice__class_Osup(X12,X11,tc_fun(t_a,X13)),v_x) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(X12,v_x),hAPP(X11,v_x),X13) ),
inference(variable_rename,[status(thm)],[c_0_777]) ).
fof(c_0_1255,plain,
! [X10,X11,X12] :
( ~ class_HOL_Ominus(X12)
| hAPP(c_HOL_Ominus__class_Ominus(X11,X10,tc_fun(t_a,X12)),v_x) = c_HOL_Ominus__class_Ominus(hAPP(X11,v_x),hAPP(X10,v_x),X12) ),
inference(variable_rename,[status(thm)],[c_0_778]) ).
fof(c_0_1256,plain,
! [X9,X10,X11] : c_Finite__Set_Ofold1(X9,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)),X11),X11) = X10,
inference(variable_rename,[status(thm)],[c_0_779]) ).
fof(c_0_1257,plain,
! [X4,X5,X6] :
( ~ class_Orderings_Opreorder(X6)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X6),X4),X5))
| ~ c_HOL_Oord__class_Oless(X5,X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_780]) ).
fof(c_0_1258,plain,
! [X4,X5,X6] :
( ~ class_Orderings_Olinorder(X6)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X6),X5),X4))
| ~ c_HOL_Oord__class_Oless(X4,X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_781]) ).
fof(c_0_1259,plain,
! [X4,X5,X6] :
( ~ class_Orderings_Olinorder(X6)
| ~ c_HOL_Oord__class_Oless(X5,X4,X6)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X6),X4),X5)) ),
inference(variable_rename,[status(thm)],[c_0_782]) ).
fof(c_0_1260,plain,
! [X4,X5] :
( ~ class_Orderings_Olinorder(X5)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X5),X4),X4))
| ~ c_HOL_Oord__class_Oless(X4,X4,X5) ),
inference(variable_rename,[status(thm)],[c_0_783]) ).
fof(c_0_1261,plain,
! [X17,X18,X19] :
( ~ class_Orderings_Oorder(X19)
| c_SetInterval_Oord__class_OatLeastLessThan(X18,X17,X19) = c_Orderings_Obot__class_Obot(tc_fun(X19,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X19),X17),X18)) ),
inference(variable_rename,[status(thm)],[c_0_784]) ).
fof(c_0_1262,plain,
! [X32,X33,X34] :
( ~ class_Orderings_Oorder(X34)
| c_SetInterval_Oord__class_OgreaterThanAtMost(X33,X32,X34) = c_Orderings_Obot__class_Obot(tc_fun(X34,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X34),X32),X33)) ),
inference(variable_rename,[status(thm)],[c_0_785]) ).
fof(c_0_1263,plain,
! [X17,X18,X19,X20] :
( ~ class_Lattices_Oupper__semilattice(X20)
| c_HOL_Oord__class_Oless(X17,c_Lattices_Oupper__semilattice__class_Osup(X19,X18,X20),X20)
| ~ c_HOL_Oord__class_Oless(X17,X19,X20) ),
inference(variable_rename,[status(thm)],[c_0_786]) ).
fof(c_0_1264,plain,
! [X17,X18,X19,X20] :
( ~ class_Lattices_Oupper__semilattice(X20)
| c_HOL_Oord__class_Oless(X17,c_Lattices_Oupper__semilattice__class_Osup(X19,X18,X20),X20)
| ~ c_HOL_Oord__class_Oless(X17,X18,X20) ),
inference(variable_rename,[status(thm)],[c_0_787]) ).
fof(c_0_1265,plain,
! [X6,X7,X8] : hBOOL(hAPP(c_Set_Oinsert(X6,X7,X8),X6)),
inference(variable_rename,[status(thm)],[c_0_788]) ).
fof(c_0_1266,plain,
! [X44,X45,X46] :
( c_Set_Oinsert(X45,X44,X46) != c_Orderings_Obot__class_Obot(tc_fun(X46,tc_bool))
| hBOOL(c_in(X45,X44,X46)) ),
inference(variable_rename,[status(thm)],[c_0_789]) ).
fof(c_0_1267,plain,
! [X9,X10] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X10)
| hAPP(c_Complete__Lattice_OInf__class_OInf(X10),c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool)),X10)) = X9 ),
inference(variable_rename,[status(thm)],[c_0_790]) ).
fof(c_0_1268,plain,
! [X9,X10] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X10)
| hAPP(c_Complete__Lattice_OSup__class_OSup(X10),c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool)),X10)) = X9 ),
inference(variable_rename,[status(thm)],[c_0_791]) ).
fof(c_0_1269,plain,
! [X8,X9,X10,X11] :
( ~ class_Orderings_Opreorder(X11)
| c_HOL_Oord__class_Oless(X10,X8,X11)
| ~ c_HOL_Oord__class_Oless(X9,X8,X11)
| ~ c_HOL_Oord__class_Oless(X10,X9,X11) ),
inference(variable_rename,[status(thm)],[c_0_792]) ).
fof(c_0_1270,plain,
! [X8,X9,X10,X11] :
( ~ class_Orderings_Oorder(X11)
| c_HOL_Oord__class_Oless(X8,X10,X11)
| ~ c_HOL_Oord__class_Oless(X8,X9,X11)
| ~ c_HOL_Oord__class_Oless(X9,X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_793]) ).
fof(c_0_1271,plain,
! [X9,X10] :
( ~ class_Orderings_Olinorder(X10)
| c_Finite__Set_Olinorder__class_OMax(c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool)),X10),X10) = X9 ),
inference(variable_rename,[status(thm)],[c_0_794]) ).
fof(c_0_1272,plain,
! [X9,X10] :
( ~ class_Orderings_Olinorder(X10)
| c_Finite__Set_Olinorder__class_OMin(c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool)),X10),X10) = X9 ),
inference(variable_rename,[status(thm)],[c_0_795]) ).
fof(c_0_1273,plain,
! [X4,X5,X6] :
( ~ class_Orderings_Olinorder(X6)
| X5 = X4
| c_HOL_Oord__class_Oless(X5,X4,X6)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X6),X5),X4)) ),
inference(variable_rename,[status(thm)],[c_0_796]) ).
fof(c_0_1274,plain,
! [X4,X5,X6] :
( ~ class_Orderings_Olinorder(X6)
| X5 = X4
| ~ hBOOL(hAPP(hAPP(c_lessequals(X6),X5),X4))
| c_HOL_Oord__class_Oless(X5,X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_797]) ).
fof(c_0_1275,plain,
! [X17,X18,X19] :
( ~ class_Orderings_Oorder(X19)
| c_HOL_Oord__class_Oless(X18,X17,X19)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X19),X18),X17))
| X18 = X17 ),
inference(variable_rename,[status(thm)],[c_0_798]) ).
fof(c_0_1276,plain,
! [X17,X18,X19] :
( ~ class_Orderings_Oorder(X19)
| c_HOL_Oord__class_Oless(X18,X17,X19)
| X18 = X17
| ~ hBOOL(hAPP(hAPP(c_lessequals(X19),X18),X17)) ),
inference(variable_rename,[status(thm)],[c_0_799]) ).
fof(c_0_1277,plain,
! [X4,X5,X6] :
( ~ class_Orderings_Oorder(X6)
| c_HOL_Oord__class_Oless(X5,X4,X6)
| X5 = X4
| ~ hBOOL(hAPP(hAPP(c_lessequals(X6),X5),X4)) ),
inference(variable_rename,[status(thm)],[c_0_800]) ).
fof(c_0_1278,plain,
! [X4,X5,X6] :
( ~ class_Orderings_Oorder(X6)
| X5 = X4
| c_HOL_Oord__class_Oless(X5,X4,X6)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X6),X5),X4)) ),
inference(variable_rename,[status(thm)],[c_0_801]) ).
fof(c_0_1279,plain,
! [X17,X18,X19] :
( ~ class_Orderings_Oorder(X19)
| c_HOL_Oord__class_Oless(X17,X18,X19)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X19),X17),X18))
| X18 = X17 ),
inference(variable_rename,[status(thm)],[c_0_802]) ).
fof(c_0_1280,plain,
! [X17,X18,X19] :
( ~ class_Orderings_Oorder(X19)
| c_HOL_Oord__class_Oless(X17,X18,X19)
| X18 = X17
| ~ hBOOL(hAPP(hAPP(c_lessequals(X19),X17),X18)) ),
inference(variable_rename,[status(thm)],[c_0_803]) ).
fof(c_0_1281,plain,
! [X4,X5,X6] :
( ~ class_Lattices_Oupper__semilattice(X6)
| c_Lattices_Oupper__semilattice__class_Osup(X5,X4,X6) = X4
| ~ hBOOL(hAPP(hAPP(c_lessequals(X6),X5),X4)) ),
inference(variable_rename,[status(thm)],[c_0_804]) ).
fof(c_0_1282,plain,
! [X4,X5,X6] :
( ~ class_Lattices_Oupper__semilattice(X6)
| c_Lattices_Oupper__semilattice__class_Osup(X5,X4,X6) = X5
| ~ hBOOL(hAPP(hAPP(c_lessequals(X6),X4),X5)) ),
inference(variable_rename,[status(thm)],[c_0_805]) ).
fof(c_0_1283,plain,
! [X9,X10,X11] :
( c_Set_Oinsert(X9,X10,X11) = X10
| ~ hBOOL(c_in(X9,X10,X11)) ),
inference(variable_rename,[status(thm)],[c_0_806]) ).
fof(c_0_1284,plain,
! [X17,X18,X19] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X19)
| c_HOL_Oord__class_Oless(X18,X17,X19)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X17,X19),c_HOL_Ouminus__class_Ouminus(X18,X19),X19) ),
inference(variable_rename,[status(thm)],[c_0_807]) ).
fof(c_0_1285,plain,
! [X56,X57,X58,X59] :
( c_Hoare__Mirabelle_Ohoare__derivs(X58,X56,X59)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X58,X57,X59)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X57,X56,X59) ),
inference(variable_rename,[status(thm)],[c_0_808]) ).
fof(c_0_1286,plain,
! [X9,X10,X11] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X11)
| hAPP(c_Complete__Lattice_OSup__class_OSup(X11),c_Set_Oinsert(X9,X10,X11)) = c_Lattices_Oupper__semilattice__class_Osup(X9,hAPP(c_Complete__Lattice_OSup__class_OSup(X11),X10),X11) ),
inference(variable_rename,[status(thm)],[c_0_809]) ).
fof(c_0_1287,plain,
! [X4,X5] : c_Set_Ocontents(c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) = X4,
inference(variable_rename,[status(thm)],[c_0_810]) ).
fof(c_0_1288,plain,
! [X4,X5] : c_The(c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) = X4,
inference(variable_rename,[status(thm)],[c_0_811]) ).
fof(c_0_1289,plain,
! [X4,X5,X6] :
( ~ class_Lattices_Oupper__semilattice(X6)
| c_Lattices_Oupper__semilattice__class_Osup(X5,c_Lattices_Oupper__semilattice__class_Osup(X5,X4,X6),X6) = c_Lattices_Oupper__semilattice__class_Osup(X5,X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_812]) ).
fof(c_0_1290,plain,
! [X4,X5,X6] :
( ~ class_Lattices_Olattice(X6)
| c_Lattices_Oupper__semilattice__class_Osup(X5,c_Lattices_Oupper__semilattice__class_Osup(X5,X4,X6),X6) = c_Lattices_Oupper__semilattice__class_Osup(X5,X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_813]) ).
fof(c_0_1291,plain,
! [X32,X33,X34] :
( ~ class_Orderings_Oorder(X34)
| c_Orderings_Obot__class_Obot(tc_fun(X34,tc_bool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(X33,X32,X34)
| ~ c_HOL_Oord__class_Oless(X33,X32,X34) ),
inference(variable_rename,[status(thm)],[c_0_814]) ).
fof(c_0_1292,plain,
! [X17,X18,X19] :
( ~ class_Orderings_Oorder(X19)
| c_SetInterval_Oord__class_OatLeastLessThan(X18,X17,X19) != c_Orderings_Obot__class_Obot(tc_fun(X19,tc_bool))
| ~ c_HOL_Oord__class_Oless(X18,X17,X19) ),
inference(variable_rename,[status(thm)],[c_0_815]) ).
fof(c_0_1293,plain,
! [X32,X33,X34] :
( ~ class_Orderings_Oorder(X34)
| c_SetInterval_Oord__class_OgreaterThanAtMost(X33,X32,X34) != c_Orderings_Obot__class_Obot(tc_fun(X34,tc_bool))
| ~ c_HOL_Oord__class_Oless(X33,X32,X34) ),
inference(variable_rename,[status(thm)],[c_0_816]) ).
fof(c_0_1294,plain,
! [X17,X18,X19] :
( ~ class_Orderings_Oorder(X19)
| c_Orderings_Obot__class_Obot(tc_fun(X19,tc_bool)) != c_SetInterval_Oord__class_OatLeastLessThan(X18,X17,X19)
| ~ c_HOL_Oord__class_Oless(X18,X17,X19) ),
inference(variable_rename,[status(thm)],[c_0_817]) ).
fof(c_0_1295,plain,
! [X6,X7] :
( ~ class_Orderings_Olinorder(X7)
| hBOOL(c_in(c_Finite__Set_Olinorder__class_OMax(X6,X7),X6,X7))
| X6 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_bool))
| ~ c_Finite__Set_Ofinite(X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_818]) ).
fof(c_0_1296,plain,
! [X6,X7] :
( ~ class_Orderings_Olinorder(X7)
| hBOOL(c_in(c_Finite__Set_Olinorder__class_OMin(X6,X7),X6,X7))
| X6 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_bool))
| ~ c_Finite__Set_Ofinite(X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_819]) ).
fof(c_0_1297,plain,
! [X4,X5,X6] :
( ~ class_Orderings_Olinorder(X6)
| hBOOL(hAPP(hAPP(c_lessequals(X6),X4),X5))
| hBOOL(hAPP(hAPP(c_lessequals(X6),X5),X4)) ),
inference(variable_rename,[status(thm)],[c_0_820]) ).
fof(c_0_1298,plain,
! [X6,X7,X8] : c_Set_Oinsert(X6,c_Set_Oinsert(X6,X7,X8),X8) = c_Set_Oinsert(X6,X7,X8),
inference(variable_rename,[status(thm)],[c_0_821]) ).
fof(c_0_1299,plain,
! [X17,X18,X19] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X19)
| c_HOL_Oord__class_Oless(X17,c_HOL_Ouminus__class_Ouminus(X18,X19),X19)
| ~ c_HOL_Oord__class_Oless(X18,c_HOL_Ouminus__class_Ouminus(X17,X19),X19) ),
inference(variable_rename,[status(thm)],[c_0_822]) ).
fof(c_0_1300,plain,
! [X17,X18,X19] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X19)
| c_HOL_Oord__class_Oless(X18,c_HOL_Ouminus__class_Ouminus(X17,X19),X19)
| ~ c_HOL_Oord__class_Oless(X17,c_HOL_Ouminus__class_Ouminus(X18,X19),X19) ),
inference(variable_rename,[status(thm)],[c_0_823]) ).
fof(c_0_1301,plain,
! [X17,X18,X19] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X19)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X17,X19),X18,X19)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X18,X19),X17,X19) ),
inference(variable_rename,[status(thm)],[c_0_824]) ).
fof(c_0_1302,plain,
! [X17,X18,X19] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X19)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X18,X19),X17,X19)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X17,X19),X18,X19) ),
inference(variable_rename,[status(thm)],[c_0_825]) ).
fof(c_0_1303,plain,
! [X34,X35,X36] :
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X35,X34,tc_fun(X36,tc_bool)),X36)
| ~ c_Finite__Set_Ofinite(X34,X36)
| ~ c_Finite__Set_Ofinite(X35,X36) ),
inference(variable_rename,[status(thm)],[c_0_826]) ).
fof(c_0_1304,plain,
! [X34,X35,X36] :
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X35,X34,tc_fun(X36,tc_bool)),X36)
| ~ c_Finite__Set_Ofinite(X34,X36)
| ~ c_Finite__Set_Ofinite(X35,X36) ),
inference(variable_rename,[status(thm)],[c_0_827]) ).
fof(c_0_1305,plain,
! [X10,X11,X12] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X11,X10,tc_fun(X12,tc_bool)),X12)
| ~ c_Finite__Set_Ofinite(X11,X12)
| ~ c_Finite__Set_Ofinite(X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_828]) ).
fof(c_0_1306,plain,
! [X30,X31,X32] :
( hBOOL(c_in(X30,c_Collect(X31,X32),X32))
| ~ hBOOL(hAPP(X31,X30)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_829])])]) ).
fof(c_0_1307,plain,
! [X4,X5] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X4)),
inference(variable_rename,[status(thm)],[c_0_830]) ).
fof(c_0_1308,plain,
! [X4] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_831]) ).
fof(c_0_1309,plain,
! [X45,X46,X47] :
( hBOOL(hAPP(X46,X45))
| ~ hBOOL(c_in(X45,X46,X47)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_832])])]) ).
fof(c_0_1310,plain,
! [X9,X10,X11] :
( c_Finite__Set_Ofinite(X10,X11)
| ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X9,X10,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_833]) ).
fof(c_0_1311,plain,
! [X6,X7] : ~ c_HOL_Oord__class_Oless(X6,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_bool)),tc_fun(X7,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_834]) ).
fof(c_0_1312,plain,
! [X4,X5,X6] :
( ~ class_Lattices_Oupper__semilattice(X6)
| c_Lattices_Oupper__semilattice__class_Osup(X5,X4,X6) != X4
| hBOOL(hAPP(hAPP(c_lessequals(X6),X5),X4)) ),
inference(variable_rename,[status(thm)],[c_0_835]) ).
fof(c_0_1313,plain,
! [X17,X18,X19] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X19)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X17,X19),c_HOL_Ouminus__class_Ouminus(X18,X19),X19)
| ~ c_HOL_Oord__class_Oless(X18,X17,X19) ),
inference(variable_rename,[status(thm)],[c_0_836]) ).
fof(c_0_1314,plain,
! [X4,X5,X6] :
( ~ class_Orderings_Opreorder(X6)
| hBOOL(hAPP(hAPP(c_lessequals(X6),X5),X4))
| ~ c_HOL_Oord__class_Oless(X5,X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_837]) ).
fof(c_0_1315,plain,
! [X4,X5,X6] :
( ~ class_Orderings_Oorder(X6)
| hBOOL(hAPP(hAPP(c_lessequals(X6),X5),X4))
| ~ c_HOL_Oord__class_Oless(X5,X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_838]) ).
fof(c_0_1316,plain,
! [X17,X18,X19] :
( ~ class_Orderings_Oorder(X19)
| c_Orderings_Obot__class_Obot(tc_fun(X19,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X18,X17,X19)
| hBOOL(hAPP(hAPP(c_lessequals(X19),X18),X17)) ),
inference(variable_rename,[status(thm)],[c_0_839]) ).
fof(c_0_1317,plain,
! [X17,X18,X19] :
( ~ class_Orderings_Oorder(X19)
| c_SetInterval_Oord__class_OatLeastAtMost(X18,X17,X19) = c_Orderings_Obot__class_Obot(tc_fun(X19,tc_bool))
| hBOOL(hAPP(hAPP(c_lessequals(X19),X18),X17)) ),
inference(variable_rename,[status(thm)],[c_0_840]) ).
fof(c_0_1318,plain,
! [X10,X11,X12] :
( c_Lattices_Oupper__semilattice__class_Osup(X11,X10,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_841]) ).
fof(c_0_1319,plain,
! [X10,X11,X12] :
( c_Lattices_Oupper__semilattice__class_Osup(X11,X10,tc_fun(X12,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool))
| X10 = c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_842]) ).
fof(c_0_1320,plain,
! [X10,X11,X12] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X11,X10,tc_fun(X12,tc_bool)),X12)
| ~ c_Finite__Set_Ofinite(X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_843]) ).
fof(c_0_1321,plain,
! [X17,X18,X19] :
( ~ class_OrderedGroup_Oab__group__add(X19)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X18,X17,X19),X19) = c_HOL_Ominus__class_Ominus(X17,X18,X19) ),
inference(variable_rename,[status(thm)],[c_0_844]) ).
fof(c_0_1322,plain,
! [X44,X45,X46,X47] :
( ~ class_OrderedGroup_Oab__group__add(X47)
| c_HOL_Ominus__class_Ominus(X45,X44,X47) != c_HOL_Ominus__class_Ominus(X46,X46,X47)
| X45 = X44 ),
inference(variable_rename,[status(thm)],[c_0_845]) ).
fof(c_0_1323,plain,
! [X37,X38,X39,X40] :
( ~ class_OrderedGroup_Oab__group__add(X40)
| c_HOL_Ominus__class_Ominus(X39,X39,X40) != c_HOL_Ominus__class_Ominus(X38,X37,X40)
| X38 = X37 ),
inference(variable_rename,[status(thm)],[c_0_846]) ).
fof(c_0_1324,plain,
! [X17,X18,X19] :
( ~ class_Orderings_Opreorder(X19)
| ~ c_HOL_Oord__class_Oless(X17,X18,X19)
| ~ c_HOL_Oord__class_Oless(X18,X17,X19) ),
inference(variable_rename,[status(thm)],[c_0_847]) ).
fof(c_0_1325,plain,
! [X4,X5,X6] :
( ~ class_Orderings_Opreorder(X6)
| ~ c_HOL_Oord__class_Oless(X4,X5,X6)
| ~ c_HOL_Oord__class_Oless(X5,X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_848]) ).
fof(c_0_1326,plain,
! [X4,X5,X6] :
( ~ class_Orderings_Olinorder(X6)
| ~ c_HOL_Oord__class_Oless(X5,X4,X6)
| ~ c_HOL_Oord__class_Oless(X4,X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_849]) ).
fof(c_0_1327,plain,
! [X17,X18,X19] :
( ~ class_Orderings_Oorder(X19)
| ~ c_HOL_Oord__class_Oless(X18,X17,X19)
| ~ c_HOL_Oord__class_Oless(X17,X18,X19) ),
inference(variable_rename,[status(thm)],[c_0_850]) ).
fof(c_0_1328,plain,
! [X6,X7,X8] : c_Finite__Set_Ofold1(X6,X7,X8) = c_The(c_Finite__Set_Ofold1Set(X6,X7,X8),X8),
inference(variable_rename,[status(thm)],[c_0_851]) ).
fof(c_0_1329,plain,
! [X17,X18,X19] :
( ~ class_Orderings_Oorder(X19)
| c_SetInterval_Oord__class_OatLeastAtMost(X18,X17,X19) = c_Orderings_Obot__class_Obot(tc_fun(X19,tc_bool))
| ~ c_HOL_Oord__class_Oless(X17,X18,X19) ),
inference(variable_rename,[status(thm)],[c_0_852]) ).
fof(c_0_1330,plain,
! [X66,X67,X68] :
( X67 = X66
| ~ hBOOL(hAPP(hAPP(c_fequal(X68),X67),X66)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_853])])]) ).
fof(c_0_1331,plain,
! [X4,X5,X6] :
( ~ class_Orderings_Olinorder(X6)
| c_HOL_Oord__class_Oless(X4,X5,X6)
| hBOOL(hAPP(hAPP(c_lessequals(X6),X5),X4)) ),
inference(variable_rename,[status(thm)],[c_0_854]) ).
fof(c_0_1332,plain,
! [X4,X5,X6] :
( ~ class_Orderings_Olinorder(X6)
| hBOOL(hAPP(hAPP(c_lessequals(X6),X4),X5))
| c_HOL_Oord__class_Oless(X5,X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_855]) ).
fof(c_0_1333,plain,
! [X4,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_HOL_Oord__class_Oless(X4,X4,X5)
| hBOOL(hAPP(hAPP(c_lessequals(X5),X4),X4)) ),
inference(variable_rename,[status(thm)],[c_0_856]) ).
fof(c_0_1334,plain,
! [X4,X5,X6] :
( ~ class_Orderings_Olinorder(X6)
| c_HOL_Oord__class_Oless(X5,X4,X6)
| hBOOL(hAPP(hAPP(c_lessequals(X6),X4),X5)) ),
inference(variable_rename,[status(thm)],[c_0_857]) ).
fof(c_0_1335,plain,
! [X9,X10] :
( ~ class_Orderings_Oorder(X10)
| c_SetInterval_Oord__class_OatLeastAtMost(X9,X9,X10) = c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool)),X10) ),
inference(variable_rename,[status(thm)],[c_0_858]) ).
fof(c_0_1336,plain,
! [X45,X46,X47] :
( hBOOL(c_in(X45,X46,X47))
| ~ hBOOL(hAPP(X46,X45)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_859])])]) ).
fof(c_0_1337,plain,
! [X9,X10] : c_Collect(hAPP(c_fequal(X10),X9),X10) = c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool)),X10),
inference(variable_rename,[status(thm)],[c_0_860]) ).
fof(c_0_1338,plain,
! [X6,X7] : c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X7,tc_bool)),X6,tc_fun(X7,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_861]) ).
fof(c_0_1339,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_862 ).
fof(c_0_1340,plain,
! [X10,X11,X12] : c_Lattices_Oupper__semilattice__class_Osup(X11,X10,tc_fun(X12,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X10,X11,tc_fun(X12,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_863]) ).
fof(c_0_1341,plain,
! [X9,X10,X11] :
( c_Finite__Set_Ofinite(c_Set_Oinsert(X9,X10,X11),X11)
| ~ c_Finite__Set_Ofinite(X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_864]) ).
fof(c_0_1342,plain,
! [X32,X33,X34] :
( ~ class_Orderings_Oorder(X34)
| c_Orderings_Obot__class_Obot(tc_fun(X34,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X33,X32,X34)
| c_HOL_Oord__class_Oless(X33,X32,X34) ),
inference(variable_rename,[status(thm)],[c_0_865]) ).
fof(c_0_1343,plain,
! [X17,X18,X19] :
( ~ class_Orderings_Oorder(X19)
| c_SetInterval_Oord__class_OatLeastLessThan(X18,X17,X19) = c_Orderings_Obot__class_Obot(tc_fun(X19,tc_bool))
| c_HOL_Oord__class_Oless(X18,X17,X19) ),
inference(variable_rename,[status(thm)],[c_0_866]) ).
fof(c_0_1344,plain,
! [X32,X33,X34] :
( ~ class_Orderings_Oorder(X34)
| c_SetInterval_Oord__class_OgreaterThanAtMost(X33,X32,X34) = c_Orderings_Obot__class_Obot(tc_fun(X34,tc_bool))
| c_HOL_Oord__class_Oless(X33,X32,X34) ),
inference(variable_rename,[status(thm)],[c_0_867]) ).
fof(c_0_1345,plain,
! [X17,X18,X19] :
( ~ class_Orderings_Oorder(X19)
| c_Orderings_Obot__class_Obot(tc_fun(X19,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X18,X17,X19)
| c_HOL_Oord__class_Oless(X18,X17,X19) ),
inference(variable_rename,[status(thm)],[c_0_868]) ).
fof(c_0_1346,plain,
! [X4,X5] :
( ~ class_Orderings_Obot(X5)
| hBOOL(hAPP(hAPP(c_lessequals(X5),c_Orderings_Obot__class_Obot(X5)),X4)) ),
inference(variable_rename,[status(thm)],[c_0_869]) ).
fof(c_0_1347,plain,
! [X33,X34] : c_Hoare__Mirabelle_Ohoare__derivs(X33,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X34),tc_bool)),X34),
inference(variable_rename,[status(thm)],[c_0_870]) ).
fof(c_0_1348,plain,
! [X6,X7] : c_HOL_Ominus__class_Ominus(X6,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_bool)),tc_fun(X7,tc_bool)) = X6,
inference(variable_rename,[status(thm)],[c_0_871]) ).
fof(c_0_1349,plain,
! [X10,X11] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)),X10,tc_fun(X11,tc_bool)) = X10,
inference(variable_rename,[status(thm)],[c_0_872]) ).
fof(c_0_1350,plain,
! [X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(X6,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_bool)),tc_fun(X7,tc_bool)) = X6,
inference(variable_rename,[status(thm)],[c_0_873]) ).
fof(c_0_1351,plain,
! [X7,X8] :
( ~ class_HOL_Ouminus(X8)
| hAPP(c_HOL_Ouminus__class_Ouminus(X7,tc_fun(t_a,X8)),v_x) = c_HOL_Ouminus__class_Ouminus(hAPP(X7,v_x),X8) ),
inference(variable_rename,[status(thm)],[c_0_874]) ).
fof(c_0_1352,plain,
! [X9,X10,X11] : c_Set_Oinsert(X9,X10,X11) != c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_875]) ).
fof(c_0_1353,plain,
! [X9,X10,X11] : c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)) != c_Set_Oinsert(X9,X10,X11),
inference(variable_rename,[status(thm)],[c_0_876]) ).
fof(c_0_1354,plain,
! [X4,X5] : ~ c_HOL_Oord__class_Oless(X4,X4,tc_fun(X5,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_877]) ).
fof(c_0_1355,plain,
! [X30,X31,X32,X33] : hAPP(c_COMBK(X31,X33,X32),X30) = X31,
inference(variable_rename,[status(thm)],[c_0_878]) ).
fof(c_0_1356,plain,
! [X4,X5,X6] :
( ~ class_Orderings_Olinorder(X6)
| X5 = X4
| c_HOL_Oord__class_Oless(X5,X4,X6)
| c_HOL_Oord__class_Oless(X4,X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_879]) ).
fof(c_0_1357,plain,
! [X4,X5,X6] :
( ~ class_Orderings_Olinorder(X6)
| c_HOL_Oord__class_Oless(X4,X5,X6)
| X5 = X4
| c_HOL_Oord__class_Oless(X5,X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_880]) ).
fof(c_0_1358,plain,
! [X4,X5,X6] :
( ~ class_Orderings_Olinorder(X6)
| c_HOL_Oord__class_Oless(X4,X5,X6)
| c_HOL_Oord__class_Oless(X5,X4,X6)
| X5 = X4 ),
inference(variable_rename,[status(thm)],[c_0_881]) ).
fof(c_0_1359,plain,
! [X4,X5,X6] :
( ~ class_Orderings_Olinorder(X6)
| X5 = X4
| c_HOL_Oord__class_Oless(X4,X5,X6)
| c_HOL_Oord__class_Oless(X5,X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_882]) ).
fof(c_0_1360,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__idom(X6)
| c_HOL_Oord__class_Oless(X4,X5,X6)
| c_HOL_Oord__class_Oless(X5,X4,X6)
| X5 = X4 ),
inference(variable_rename,[status(thm)],[c_0_883]) ).
fof(c_0_1361,plain,
! [X10,X11,X12] :
( c_HOL_Ouminus__class_Ouminus(X11,tc_fun(X12,tc_bool)) != c_HOL_Ouminus__class_Ouminus(X10,tc_fun(X12,tc_bool))
| X11 = X10 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_884])])]) ).
fof(c_0_1362,plain,
! [X4,X5,X6] :
( ~ class_Lattices_Oupper__semilattice(X6)
| c_Lattices_Oupper__semilattice__class_Osup(X5,X4,X6) = c_Lattices_Oupper__semilattice__class_Osup(X4,X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_885]) ).
fof(c_0_1363,plain,
! [X4,X5,X6] :
( ~ class_Lattices_Olattice(X6)
| c_Lattices_Oupper__semilattice__class_Osup(X5,X4,X6) = c_Lattices_Oupper__semilattice__class_Osup(X4,X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_886]) ).
fof(c_0_1364,plain,
! [X4,X5] :
( ~ class_Orderings_Oorder(X5)
| hBOOL(hAPP(hAPP(c_lessequals(X5),X4),X4)) ),
inference(variable_rename,[status(thm)],[c_0_887]) ).
fof(c_0_1365,plain,
! [X4,X5] :
( ~ class_Orderings_Opreorder(X5)
| hBOOL(hAPP(hAPP(c_lessequals(X5),X4),X4)) ),
inference(variable_rename,[status(thm)],[c_0_888]) ).
fof(c_0_1366,plain,
! [X30,X31,X32] :
( c_Collect(X31,X32) != c_Orderings_Obot__class_Obot(tc_fun(X32,tc_bool))
| ~ hBOOL(hAPP(X31,X30)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_889])])]) ).
fof(c_0_1367,plain,
! [X30,X31,X32] :
( c_Orderings_Obot__class_Obot(tc_fun(X32,tc_bool)) != c_Collect(X31,X32)
| ~ hBOOL(hAPP(X31,X30)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_890])])]) ).
fof(c_0_1368,plain,
( ~ class_HOL_Ouminus(t_b)
| hAPP(c_HOL_Ouminus__class_Ouminus(v_A,tc_fun(t_a,t_b)),v_x) = c_HOL_Ouminus__class_Ouminus(hAPP(v_A,v_x),t_b) ),
c_0_891 ).
fof(c_0_1369,axiom,
hAPP(c_COMBK(v_P,t_a,t_b),v_Q) = v_P,
c_0_892 ).
fof(c_0_1370,plain,
! [X6,X7] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X6,tc_fun(X7,tc_bool)),tc_fun(X7,tc_bool)) = X6,
inference(variable_rename,[status(thm)],[c_0_893]) ).
fof(c_0_1371,plain,
! [X4,X5] : hBOOL(hAPP(hAPP(c_fequal(X5),X4),X4)),
inference(variable_rename,[status(thm)],[c_0_894]) ).
fof(c_0_1372,plain,
! [X10,X11,X12] :
( ~ class_Lattices_Obounded__lattice(X12)
| c_Lattices_Oupper__semilattice__class_Osup(X11,X10,X12) != c_Orderings_Obot__class_Obot(X12)
| X10 = c_Orderings_Obot__class_Obot(X12) ),
inference(variable_rename,[status(thm)],[c_0_895]) ).
fof(c_0_1373,plain,
! [X10,X11,X12] :
( ~ class_Lattices_Obounded__lattice(X12)
| c_Lattices_Oupper__semilattice__class_Osup(X11,X10,X12) != c_Orderings_Obot__class_Obot(X12)
| X11 = c_Orderings_Obot__class_Obot(X12) ),
inference(variable_rename,[status(thm)],[c_0_896]) ).
fof(c_0_1374,plain,
! [X6,X7] : c_HOL_Ominus__class_Ominus(X6,X6,tc_fun(X7,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_897]) ).
fof(c_0_1375,plain,
! [X4,X5] :
( ~ class_Orderings_Opreorder(X5)
| ~ c_HOL_Oord__class_Oless(X4,X4,X5) ),
inference(variable_rename,[status(thm)],[c_0_898]) ).
fof(c_0_1376,plain,
! [X4,X5] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_HOL_Oord__class_Oless(X4,X4,X5) ),
inference(variable_rename,[status(thm)],[c_0_899]) ).
fof(c_0_1377,plain,
! [X4,X5] :
( ~ class_Orderings_Oorder(X5)
| ~ c_HOL_Oord__class_Oless(X4,X4,X5) ),
inference(variable_rename,[status(thm)],[c_0_900]) ).
fof(c_0_1378,plain,
! [X4] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X4)
| hAPP(c_Complete__Lattice_OSup__class_OSup(X4),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))) = c_Orderings_Obot__class_Obot(X4) ),
inference(variable_rename,[status(thm)],[c_0_901]) ).
fof(c_0_1379,plain,
! [X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(X6,X6,tc_fun(X7,tc_bool)) = X6,
inference(variable_rename,[status(thm)],[c_0_902]) ).
fof(c_0_1380,plain,
! [X7] :
( ~ class_Orderings_Obot(X7)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X7)),v_x) = c_Orderings_Obot__class_Obot(X7) ),
inference(variable_rename,[status(thm)],[c_0_903]) ).
fof(c_0_1381,plain,
! [X4,X5] :
( ~ class_Lattices_Obounded__lattice(X5)
| c_Lattices_Oupper__semilattice__class_Osup(X4,c_Orderings_Obot__class_Obot(X5),X5) = X4 ),
inference(variable_rename,[status(thm)],[c_0_904]) ).
fof(c_0_1382,plain,
! [X4,X5] :
( ~ class_Lattices_Obounded__lattice(X5)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X5),X4,X5) = X4 ),
inference(variable_rename,[status(thm)],[c_0_905]) ).
fof(c_0_1383,plain,
! [X4] : c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),
inference(variable_rename,[status(thm)],[c_0_906]) ).
fof(c_0_1384,plain,
! [X4,X5] :
( ~ class_Lattices_Oupper__semilattice(X5)
| c_Lattices_Oupper__semilattice__class_Osup(X4,X4,X5) = X4 ),
inference(variable_rename,[status(thm)],[c_0_907]) ).
fof(c_0_1385,plain,
! [X17,X18,X19] :
( ~ class_OrderedGroup_Ogroup__add(X19)
| c_HOL_Ouminus__class_Ouminus(X18,X19) != c_HOL_Ouminus__class_Ouminus(X17,X19)
| X18 = X17 ),
inference(variable_rename,[status(thm)],[c_0_908]) ).
fof(c_0_1386,plain,
! [X4,X5,X6] :
( ~ class_Lattices_Oboolean__algebra(X6)
| c_HOL_Ouminus__class_Ouminus(X5,X6) != c_HOL_Ouminus__class_Ouminus(X4,X6)
| X5 = X4 ),
inference(variable_rename,[status(thm)],[c_0_909]) ).
fof(c_0_1387,plain,
! [X4,X5] : c_The(hAPP(c_fequal(X5),X4),X5) = X4,
inference(variable_rename,[status(thm)],[c_0_910]) ).
fof(c_0_1388,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Ogroup__add(X10)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X9,X10),X10) = X9 ),
inference(variable_rename,[status(thm)],[c_0_911]) ).
fof(c_0_1389,plain,
! [X4,X5] :
( ~ class_Lattices_Oboolean__algebra(X5)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X4,X5),X5) = X4 ),
inference(variable_rename,[status(thm)],[c_0_912]) ).
fof(c_0_1390,plain,
! [X17,X18] :
( ~ class_OrderedGroup_Ogroup__add(X18)
| X17 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X17,X18),X18) ),
inference(variable_rename,[status(thm)],[c_0_913]) ).
fof(c_0_1391,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Ogroup__add(X10)
| X9 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X9,X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_914]) ).
fof(c_0_1392,plain,
! [X17,X18] :
( ~ class_OrderedGroup_Ogroup__add(X18)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X17,X18),X18) = X17 ),
inference(variable_rename,[status(thm)],[c_0_915]) ).
fof(c_0_1393,plain,
! [X49,X50,X51,X52] :
( c_Com_Ocom_OSemi(X52,X50) != c_Com_Ocom_OSemi(X51,X49)
| X52 = X51 ),
inference(variable_rename,[status(thm)],[c_0_916]) ).
fof(c_0_1394,plain,
! [X49,X50,X51,X52] :
( c_Com_Ocom_OSemi(X52,X50) != c_Com_Ocom_OSemi(X51,X49)
| X50 = X49 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_917])])]) ).
fof(c_0_1395,plain,
! [X64,X65] :
( class_Finite__Set_Ofinite_Ofinite(tc_fun(X64,X65))
| ~ class_Finite__Set_Ofinite_Ofinite(X65)
| ~ class_Finite__Set_Ofinite_Ofinite(X64) ),
inference(variable_rename,[status(thm)],[c_0_918]) ).
fof(c_0_1396,plain,
! [X64,X65] :
( class_HOL_Oord(tc_fun(X64,X65))
| ~ class_HOL_Oord(X65) ),
inference(variable_rename,[status(thm)],[c_0_919]) ).
fof(c_0_1397,plain,
! [X64,X65] :
( class_HOL_Ominus(tc_fun(X64,X65))
| ~ class_HOL_Ominus(X65) ),
inference(variable_rename,[status(thm)],[c_0_920]) ).
fof(c_0_1398,plain,
! [X64,X65] :
( class_HOL_Ouminus(tc_fun(X64,X65))
| ~ class_HOL_Ouminus(X65) ),
inference(variable_rename,[status(thm)],[c_0_921]) ).
fof(c_0_1399,plain,
! [X64,X65] :
( class_Orderings_Obot(tc_fun(X64,X65))
| ~ class_Orderings_Obot(X65) ),
inference(variable_rename,[status(thm)],[c_0_922]) ).
fof(c_0_1400,plain,
! [X64,X65] :
( class_Orderings_Oorder(tc_fun(X64,X65))
| ~ class_Orderings_Oorder(X65) ),
inference(variable_rename,[status(thm)],[c_0_923]) ).
fof(c_0_1401,plain,
! [X64,X65] :
( class_Lattices_Olattice(tc_fun(X64,X65))
| ~ class_Lattices_Olattice(X65) ),
inference(variable_rename,[status(thm)],[c_0_924]) ).
fof(c_0_1402,plain,
! [X64,X65] :
( class_Orderings_Opreorder(tc_fun(X64,X65))
| ~ class_Orderings_Opreorder(X65) ),
inference(variable_rename,[status(thm)],[c_0_925]) ).
fof(c_0_1403,plain,
! [X64,X65] :
( class_Lattices_Oboolean__algebra(tc_fun(X64,X65))
| ~ class_Lattices_Oboolean__algebra(X65) ),
inference(variable_rename,[status(thm)],[c_0_926]) ).
fof(c_0_1404,plain,
! [X64,X65] :
( class_Lattices_Obounded__lattice(tc_fun(X64,X65))
| ~ class_Lattices_Obounded__lattice(X65) ),
inference(variable_rename,[status(thm)],[c_0_927]) ).
fof(c_0_1405,plain,
! [X64,X65] :
( class_Lattices_Oupper__semilattice(tc_fun(X64,X65))
| ~ class_Lattices_Olattice(X65) ),
inference(variable_rename,[status(thm)],[c_0_928]) ).
fof(c_0_1406,plain,
! [X64,X65] :
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X64,X65))
| ~ class_Complete__Lattice_Ocomplete__lattice(X65) ),
inference(variable_rename,[status(thm)],[c_0_929]) ).
fof(c_0_1407,plain,
! [X48,X49] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(X49,X48),
inference(variable_rename,[status(thm)],[c_0_930]) ).
fof(c_0_1408,plain,
! [X48,X49] : c_Com_Ocom_OSemi(X49,X48) != c_Com_Ocom_OSKIP,
inference(variable_rename,[status(thm)],[c_0_931]) ).
fof(c_0_1409,plain,
! [X6,X7] :
( ~ class_Finite__Set_Ofinite_Ofinite(X7)
| c_Finite__Set_Ofinite(X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_932]) ).
fof(c_0_1410,plain,
! [X30,X31] : c_Collect(X30,X31) = X30,
inference(variable_rename,[status(thm)],[c_0_933]) ).
fof(c_0_1411,axiom,
class_HOL_Oord(tc_bool),
c_0_934 ).
fof(c_0_1412,axiom,
class_HOL_Ominus(tc_bool),
c_0_935 ).
fof(c_0_1413,axiom,
class_HOL_Ouminus(tc_bool),
c_0_936 ).
fof(c_0_1414,axiom,
class_Orderings_Obot(tc_bool),
c_0_937 ).
fof(c_0_1415,axiom,
class_Orderings_Oorder(tc_bool),
c_0_938 ).
fof(c_0_1416,axiom,
class_Lattices_Olattice(tc_bool),
c_0_939 ).
fof(c_0_1417,axiom,
class_Orderings_Opreorder(tc_bool),
c_0_940 ).
fof(c_0_1418,axiom,
class_Finite__Set_Ofinite_Ofinite(tc_bool),
c_0_941 ).
fof(c_0_1419,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
c_0_942 ).
fof(c_0_1420,axiom,
class_Lattices_Obounded__lattice(tc_bool),
c_0_943 ).
fof(c_0_1421,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
c_0_944 ).
fof(c_0_1422,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
c_0_945 ).
fof(c_0_1423,axiom,
class_HOL_Oord(tc_nat),
c_0_946 ).
fof(c_0_1424,axiom,
class_HOL_Ominus(tc_nat),
c_0_947 ).
fof(c_0_1425,axiom,
class_Orderings_Obot(tc_nat),
c_0_948 ).
fof(c_0_1426,axiom,
class_Orderings_Oorder(tc_nat),
c_0_949 ).
fof(c_0_1427,axiom,
class_Lattices_Olattice(tc_nat),
c_0_950 ).
fof(c_0_1428,axiom,
class_Orderings_Olinorder(tc_nat),
c_0_951 ).
fof(c_0_1429,axiom,
class_Orderings_Opreorder(tc_nat),
c_0_952 ).
fof(c_0_1430,axiom,
class_Lattices_Oupper__semilattice(tc_nat),
c_0_953 ).
cnf(c_0_1431,plain,
( c_Complete__Lattice_Ocomplete__lattice(X2,X1,c_COMBC(X3,X9,X9,tc_bool),c_COMBC(X4,X9,X9,tc_bool),X6,X5,X8,X7,X9)
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
inference(split_conjunct,[status(thm)],[c_0_954]) ).
cnf(c_0_1432,plain,
( hBOOL(hAPP(hAPP(X3,c_Complete__Lattice_Ocomplete__lattice_OINFI(X1,X11,X13,X9,X12)),hAPP(X13,X10)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| ~ hBOOL(c_in(X10,X11,X12)) ),
inference(split_conjunct,[status(thm)],[c_0_955]) ).
cnf(c_0_1433,plain,
( hBOOL(hAPP(hAPP(X3,hAPP(X13,X10)),c_Complete__Lattice_Ocomplete__lattice_OSUPR(X2,X11,X13,X9,X12)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| ~ hBOOL(c_in(X10,X11,X12)) ),
inference(split_conjunct,[status(thm)],[c_0_956]) ).
cnf(c_0_1434,plain,
( X10 = c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool))
| c_Complete__Lattice_Ocomplete__lattice_OINFI(X1,X10,c_COMBK(X12,X9,X11),X9,X11) = X12
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
inference(split_conjunct,[status(thm)],[c_0_957]) ).
cnf(c_0_1435,plain,
( X10 = c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool))
| c_Complete__Lattice_Ocomplete__lattice_OSUPR(X2,X10,c_COMBK(X12,X9,X11),X9,X11) = X12
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
inference(split_conjunct,[status(thm)],[c_0_958]) ).
cnf(c_0_1436,plain,
( hAPP(X2,c_Set_Oinsert(X10,c_Set_Oinsert(X11,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),X9),X9)) = 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_959]) ).
cnf(c_0_1437,plain,
( hAPP(X1,c_Set_Oinsert(X10,c_Set_Oinsert(X11,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),X9),X9)) = 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_960]) ).
cnf(c_0_1438,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_961]) ).
cnf(c_0_1439,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_962]) ).
cnf(c_0_1440,plain,
( hAPP(X2,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),X9)) = X10
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
inference(split_conjunct,[status(thm)],[c_0_963]) ).
cnf(c_0_1441,plain,
( hAPP(X1,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),X9)) = X10
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
inference(split_conjunct,[status(thm)],[c_0_964]) ).
cnf(c_0_1442,plain,
( hAPP(X2,c_Set_Oinsert(X10,X11,X9)) = 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_965]) ).
cnf(c_0_1443,plain,
( hAPP(X1,c_Set_Oinsert(X10,X11,X9)) = 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_966]) ).
cnf(c_0_1444,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_967]) ).
cnf(c_0_1445,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_968]) ).
cnf(c_0_1446,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),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_969]) ).
cnf(c_0_1447,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),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_970]) ).
cnf(c_0_1448,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,X4,X3,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(hAPP(c_COMBC(c_fequal(tc_Com_Ostate),tc_Com_Ostate,tc_Com_Ostate,tc_bool),v_sko__Hoare__Mirabelle__Xescape__2(X1,X2,X3,X4)),tc_fun(tc_Com_Ostate,tc_bool),t_a),X4,c_COMBK(hAPP(X3,v_sko__Hoare__Mirabelle__Xescape__1(X1,X2,X3,X4)),tc_fun(tc_Com_Ostate,tc_bool),t_a),t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(split_conjunct,[status(thm)],[c_0_971]) ).
cnf(c_0_1449,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,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),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_972]) ).
cnf(c_0_1450,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,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),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_973]) ).
cnf(c_0_1451,plain,
( c_Nitpick_Ofold__graph_H(X4,X5,X2,hAPP(hAPP(X4,X1),X6),X3,X7)
| ~ hBOOL(c_in(X1,X2,X3))
| ~ c_Nitpick_Ofold__graph_H(X4,X5,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X6,X3,X7) ),
inference(split_conjunct,[status(thm)],[c_0_974]) ).
cnf(c_0_1452,plain,
( c_Finite__Set_Ofold__graph(X1,X2,X3,hAPP(hAPP(X1,X4),X6),X5,X7)
| ~ c_Finite__Set_Ofold__graph(X1,X2,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),tc_fun(X5,tc_bool)),X6,X5,X7)
| ~ hBOOL(c_in(X4,X3,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_975]) ).
cnf(c_0_1453,plain,
( hBOOL(c_in(X1,X2,X3))
| c_Finite__Set_Ofold__graph(X4,X5,c_Set_Oinsert(X1,X2,X3),hAPP(hAPP(X4,X1),X6),X3,X7)
| ~ c_Finite__Set_Ofold__graph(X4,X5,X2,X6,X3,X7) ),
inference(split_conjunct,[status(thm)],[c_0_976]) ).
cnf(c_0_1454,plain,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(c_Set_Oimage(X2,X3,X4,X1),c_Set_Oimage(X2,X5,X4,X1),tc_fun(X1,tc_bool))),c_Set_Oimage(X2,c_HOL_Ominus__class_Ominus(X3,X5,tc_fun(X4,tc_bool)),X4,X1))),
inference(split_conjunct,[status(thm)],[c_0_977]) ).
cnf(c_0_1455,plain,
( hBOOL(c_in(X2,X3,X5))
| hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,c_Set_Oinsert(X2,X3,X5),X5),X4))
| ~ c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5,X5) ),
inference(split_conjunct,[status(thm)],[c_0_978]) ).
cnf(c_0_1456,plain,
( X4 = X2
| ~ c_Finite__Set_Ofold__graph(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X4,X3,X5) ),
inference(split_conjunct,[status(thm)],[c_0_979]) ).
cnf(c_0_1457,plain,
( c_Finite__Set_Ofinite(X3,X5)
| ~ c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_980]) ).
cnf(c_0_1458,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xconseq12__1(X6,X2,X5,X4)),v_sko__Hoare__Mirabelle__Xconseq12__3(X6,X2,X5,X4))) ),
inference(split_conjunct,[status(thm)],[c_0_981]) ).
cnf(c_0_1459,plain,
( hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xconseq12__1(X5,X2,X6,X4)),v_sko__Hoare__Mirabelle__Xconseq12__2(X5,X2,X6,X4)))
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X5,X3,X6,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(split_conjunct,[status(thm)],[c_0_982]) ).
cnf(c_0_1460,plain,
c_Nitpick_Ofold__graph_H(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_983]) ).
cnf(c_0_1461,plain,
c_Finite__Set_Ofold__graph(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_984]) ).
cnf(c_0_1462,plain,
( hBOOL(hAPP(hAPP(X4,X5),v_sko__Hoare__Mirabelle__Xconseq12__3(X6,X2,X7,X4)))
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X2,X5),v_sko__Hoare__Mirabelle__Xconseq12__2(X6,X2,X7,X4))) ),
inference(split_conjunct,[status(thm)],[c_0_985]) ).
cnf(c_0_1463,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,c_Com_Ocom_OSemi(X3,X6),X7,X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_bool)),tc_Hoare__Mirabelle_Otriple(X5)),X5)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_bool)),tc_Hoare__Mirabelle_Otriple(X5)),X5)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X4,X6,X7,X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_bool)),tc_Hoare__Mirabelle_Otriple(X5)),X5) ),
inference(split_conjunct,[status(thm)],[c_0_986]) ).
cnf(c_0_1464,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool))),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_987]) ).
cnf(c_0_1465,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool))),X4))
| ~ hBOOL(c_in(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_988]) ).
cnf(c_0_1466,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool))),X4))
| ~ hBOOL(c_in(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_989]) ).
cnf(c_0_1467,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(X3,X6)),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X3,X4,tc_fun(X1,tc_bool))),X5))
| ~ hBOOL(c_in(X6,X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_990]) ).
cnf(c_0_1468,plain,
( hBOOL(hAPP(hAPP(X1,v_sko__Hoare__Mirabelle__Xescape__1(X2,X1,X3,X4)),v_sko__Hoare__Mirabelle__Xescape__2(X2,X1,X3,X4)))
| c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(split_conjunct,[status(thm)],[c_0_991]) ).
cnf(c_0_1469,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,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(split_conjunct,[status(thm)],[c_0_992]) ).
cnf(c_0_1470,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,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(split_conjunct,[status(thm)],[c_0_993]) ).
cnf(c_0_1471,plain,
( hBOOL(c_in(hAPP(X2,X6),X5,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Set_Oimage(X2,X3,X4,X1)),X5))
| ~ hBOOL(c_in(X6,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_994]) ).
cnf(c_0_1472,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,tc_bool)),c_Set_Oimage(X5,X2,X1,X4)),c_Set_Oimage(X5,X3,X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_995]) ).
cnf(c_0_1473,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Set_Oimage(X2,X3,X4,X1)),c_Set_Oimage(X2,X5,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,tc_bool)),X3),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_996]) ).
cnf(c_0_1474,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X5,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xconseq2__1(X5,X4)),v_sko__Hoare__Mirabelle__Xconseq2__2(X5,X4))) ),
inference(split_conjunct,[status(thm)],[c_0_997]) ).
cnf(c_0_1475,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X5,X3,X4,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X2,v_sko__Hoare__Mirabelle__Xconseq1__1(X5,X2)),v_sko__Hoare__Mirabelle__Xconseq1__2(X5,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_998]) ).
cnf(c_0_1476,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool))),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)))
| ~ hBOOL(c_in(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_999]) ).
cnf(c_0_1477,plain,
( hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xconseq1__1(X5,X2)),v_sko__Hoare__Mirabelle__Xconseq1__2(X5,X2)))
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X5,X3,X4,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(split_conjunct,[status(thm)],[c_0_1000]) ).
cnf(c_0_1478,plain,
( hBOOL(hAPP(hAPP(X4,v_sko__Hoare__Mirabelle__Xconseq2__1(X5,X4)),v_sko__Hoare__Mirabelle__Xconseq2__2(X5,X4)))
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X5,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(split_conjunct,[status(thm)],[c_0_1001]) ).
cnf(c_0_1479,plain,
c_Set_Oinsert(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X3),X3,X3,tc_bool),X1),X3),X2,tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1002]) ).
cnf(c_0_1480,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X1,tc_bool))),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_1003]) ).
cnf(c_0_1481,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X1,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(X3,X5,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_1004]) ).
cnf(c_0_1482,plain,
( c_Finite__Set_Ofinite(X4,X3)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X4),c_Set_Oimage(X5,X1,X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_1005]) ).
cnf(c_0_1483,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X1,tc_bool))),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1006]) ).
cnf(c_0_1484,plain,
( c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),X2,X5) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X4,X1,X2,X5),c_Finite__Set_Osetsum(X4,X3,X2,X5),X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X3),X1))
| ~ class_OrderedGroup_Oab__group__add(X5) ),
inference(split_conjunct,[status(thm)],[c_0_1007]) ).
cnf(c_0_1485,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X1,tc_bool))),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,tc_fun(X1,tc_bool)))) ),
inference(split_conjunct,[status(thm)],[c_0_1008]) ).
cnf(c_0_1486,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X1,tc_bool))),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1009]) ).
cnf(c_0_1487,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X1,tc_bool))),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1010]) ).
cnf(c_0_1488,plain,
( c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1011]) ).
cnf(c_0_1489,plain,
( hBOOL(c_in(X1,X2,X3))
| c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X4),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1012]) ).
cnf(c_0_1490,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1013]) ).
cnf(c_0_1491,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1014]) ).
cnf(c_0_1492,plain,
( X2 = X4
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1015]) ).
cnf(c_0_1493,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X1,tc_bool))),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1016]) ).
cnf(c_0_1494,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X1,tc_bool))),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1017]) ).
cnf(c_0_1495,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastLessThan(X4,X5,X1)))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1018]) ).
cnf(c_0_1496,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastLessThan(X4,X5,X1)))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1019]) ).
cnf(c_0_1497,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,tc_bool)),hAPP(X5,X1)),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_1020]) ).
cnf(c_0_1498,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_1021]) ).
cnf(c_0_1499,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_1022]) ).
cnf(c_0_1500,plain,
( c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2,X5) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X4,X1,X2,X5),hAPP(X4,X3),X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(c_in(X3,X1,X2))
| ~ class_OrderedGroup_Oab__group__add(X5) ),
inference(split_conjunct,[status(thm)],[c_0_1023]) ).
cnf(c_0_1501,plain,
( c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2,X5) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X4,X1,X2,X5),hAPP(X4,X3),X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(c_in(X3,X1,X2))
| ~ class_Ring__and__Field_Oring(X5) ),
inference(split_conjunct,[status(thm)],[c_0_1024]) ).
cnf(c_0_1502,plain,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,X3,tc_fun(X5,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4,X3,tc_fun(X5,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1025]) ).
cnf(c_0_1503,plain,
( c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X4,X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1026]) ).
cnf(c_0_1504,plain,
( hBOOL(c_in(X1,X2,X3))
| c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X1,X4,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1027]) ).
cnf(c_0_1505,plain,
c_Set_Oimage(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4,X5) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(X1,X2,X4,X5),c_Set_Oimage(X1,X3,X4,X5),tc_fun(X5,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1028]) ).
cnf(c_0_1506,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X1,tc_bool))),c_HOL_Ouminus__class_Ouminus(X3,tc_fun(X1,tc_bool)))) ),
inference(split_conjunct,[status(thm)],[c_0_1029]) ).
cnf(c_0_1507,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Set_Oinsert(X2,X3,X1)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1030]) ).
cnf(c_0_1508,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_1031]) ).
cnf(c_0_1509,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_1032]) ).
cnf(c_0_1510,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Set_Oinsert(X4,X2,X1)),c_Set_Oinsert(X4,X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1033]) ).
cnf(c_0_1511,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X4),hAPP(X5,X1)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X5,X3,X4)))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1034]) ).
cnf(c_0_1512,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_Set_Oinsert(X1,X4,X3)),X2))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X4),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1035]) ).
cnf(c_0_1513,plain,
hBOOL(hAPP(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2))),
inference(split_conjunct,[status(thm)],[c_0_1036]) ).
cnf(c_0_1514,plain,
( hBOOL(c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5))
| ~ hBOOL(c_in(X2,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1037]) ).
cnf(c_0_1515,plain,
( hBOOL(c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5))
| ~ hBOOL(c_in(X2,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1038]) ).
cnf(c_0_1516,plain,
( hBOOL(c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1039]) ).
cnf(c_0_1517,plain,
( hBOOL(c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1040]) ).
cnf(c_0_1518,plain,
c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,c_Com_Ocom_OSKIP,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3),
inference(split_conjunct,[status(thm)],[c_0_1041]) ).
cnf(c_0_1519,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1042]) ).
cnf(c_0_1520,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| X2 = c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1043]) ).
cnf(c_0_1521,plain,
( hBOOL(c_in(X2,X4,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Set_Oinsert(X2,X3,X1)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1044]) ).
cnf(c_0_1522,plain,
( hBOOL(c_in(X2,X3,X4))
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| ~ hBOOL(c_in(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1045]) ).
cnf(c_0_1523,plain,
( hBOOL(c_in(X3,X1,X2))
| c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2,X5) = c_Finite__Set_Osetsum(X4,X1,X2,X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Oab__group__add(X5) ),
inference(split_conjunct,[status(thm)],[c_0_1046]) ).
cnf(c_0_1524,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1047]) ).
cnf(c_0_1525,plain,
( hBOOL(c_in(X1,X2,X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X2),c_Set_Oinsert(X1,X4,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_1048]) ).
cnf(c_0_1526,plain,
( hBOOL(c_in(X3,X2,X1))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1049]) ).
cnf(c_0_1527,plain,
( hBOOL(c_in(X1,X2,X3))
| c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3,tc_nat) = c_Finite__Set_Osetsum(X4,X2,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1050]) ).
cnf(c_0_1528,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ouminus__class_Ouminus(X3,tc_fun(X1,tc_bool))),c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1051]) ).
cnf(c_0_1529,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ouminus__class_Ouminus(X3,tc_fun(X1,tc_bool))),c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1052]) ).
cnf(c_0_1530,plain,
c_Collect(hAPP(c_COMBC(c_fequal(X1),X1,X1,tc_bool),X2),X1) = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
inference(split_conjunct,[status(thm)],[c_0_1053]) ).
cnf(c_0_1531,plain,
( c_HOL_Ominus__class_Ominus(X3,c_HOL_Ominus__class_Ominus(X4,X2,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1054]) ).
cnf(c_0_1532,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_1055]) ).
cnf(c_0_1533,plain,
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(X4,X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1056]) ).
cnf(c_0_1534,plain,
hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),X2)),
inference(split_conjunct,[status(thm)],[c_0_1057]) ).
cnf(c_0_1535,plain,
( hBOOL(c_in(X1,X2,X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X2),c_Set_Oinsert(X1,X4,X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1058]) ).
cnf(c_0_1536,plain,
( hBOOL(c_in(X1,X2,X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X2),c_Set_Oinsert(X1,X4,X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1059]) ).
cnf(c_0_1537,plain,
hAPP(hAPP(c_COMBC(X1,X2,X3,X4),X5),X6) = hAPP(hAPP(X1,X6),X5),
inference(split_conjunct,[status(thm)],[c_0_1060]) ).
cnf(c_0_1538,plain,
c_The(hAPP(c_COMBC(c_fequal(X1),X1,X1,tc_bool),X2),X1) = X2,
inference(split_conjunct,[status(thm)],[c_0_1061]) ).
cnf(c_0_1539,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1062]) ).
cnf(c_0_1540,plain,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oinsert(X1,X2,X3),X4,X3,tc_fun(X5,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(X4,X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1063]) ).
cnf(c_0_1541,plain,
( c_Set_Oinsert(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5) = c_Set_Oimage(X4,X2,X3,X5)
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1064]) ).
cnf(c_0_1542,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X4,X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1065]) ).
cnf(c_0_1543,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)),X4))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1066]) ).
cnf(c_0_1544,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)),X4))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1067]) ).
cnf(c_0_1545,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)),X4))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1068]) ).
cnf(c_0_1546,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)),X4))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1069]) ).
cnf(c_0_1547,plain,
( X3 = c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2)
| ~ hBOOL(hAPP(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1070]) ).
cnf(c_0_1548,plain,
c_Set_Oimage(X1,c_Set_Oinsert(X2,X3,X4),X4,X5) = c_Set_Oinsert(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5),
inference(split_conjunct,[status(thm)],[c_0_1071]) ).
cnf(c_0_1549,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1072]) ).
cnf(c_0_1550,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1073]) ).
cnf(c_0_1551,plain,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X1,tc_bool))),X2)),
inference(split_conjunct,[status(thm)],[c_0_1074]) ).
cnf(c_0_1552,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,X2)),X4),X3))
| c_HOL_Oord__class_Oless(X3,X4,tc_fun(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,X2)),X3),X4))
| ~ class_HOL_Oord(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1075]) ).
cnf(c_0_1553,plain,
( c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1),c_SetInterval_Oord__class_OatLeastAtMost(X2,X5,X1),tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X5))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1076]) ).
cnf(c_0_1554,plain,
( c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1),c_SetInterval_Oord__class_OatLeastAtMost(X2,X5,X1),tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ c_HOL_Oord__class_Oless(X4,X5,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X5))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1077]) ).
cnf(c_0_1555,plain,
( hBOOL(c_in(X1,X2,X4))
| hBOOL(c_in(X1,X3,X4))
| ~ hBOOL(c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1078]) ).
cnf(c_0_1556,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1079]) ).
cnf(c_0_1557,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1080]) ).
cnf(c_0_1558,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1081]) ).
cnf(c_0_1559,plain,
( hBOOL(c_in(X4,X1,X3))
| c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1082]) ).
cnf(c_0_1560,plain,
( hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(X1,X4,X3))
| c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X4),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1083]) ).
cnf(c_0_1561,plain,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)))),
inference(split_conjunct,[status(thm)],[c_0_1084]) ).
cnf(c_0_1562,plain,
( X1 = X2
| ~ hBOOL(c_in(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1085]) ).
cnf(c_0_1563,plain,
( X1 = X2
| X1 = X3
| c_Set_Oinsert(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) ),
inference(split_conjunct,[status(thm)],[c_0_1086]) ).
cnf(c_0_1564,plain,
( X1 = X2
| X3 = X2
| c_Set_Oinsert(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_1087]) ).
cnf(c_0_1565,plain,
( X1 = X2
| X3 = X2
| c_Set_Oinsert(X3,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_1088]) ).
cnf(c_0_1566,plain,
( X1 = X2
| X1 = X3
| c_Set_Oinsert(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) ),
inference(split_conjunct,[status(thm)],[c_0_1089]) ).
cnf(c_0_1567,plain,
c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1090]) ).
cnf(c_0_1568,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_1091]) ).
cnf(c_0_1569,plain,
( c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3) = X2
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1092]) ).
cnf(c_0_1570,plain,
c_Set_Oinsert(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)),X4) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),
inference(split_conjunct,[status(thm)],[c_0_1093]) ).
cnf(c_0_1571,plain,
( hBOOL(c_in(X2,X3,X4))
| hBOOL(c_in(X2,X1,X4))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,tc_bool)),X1),X3))
| ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1094]) ).
cnf(c_0_1572,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_1095]) ).
cnf(c_0_1573,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_1096]) ).
cnf(c_0_1574,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_1097]) ).
cnf(c_0_1575,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_Finite__Set_Olinorder__class_OMax(X2,X1)),c_Finite__Set_Olinorder__class_OMax(X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ c_Finite__Set_Ofinite(X3,X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1098]) ).
cnf(c_0_1576,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_Finite__Set_Olinorder__class_OMin(X3,X1)),c_Finite__Set_Olinorder__class_OMin(X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ c_Finite__Set_Ofinite(X3,X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1099]) ).
cnf(c_0_1577,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,X4,tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1100]) ).
cnf(c_0_1578,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_1101]) ).
cnf(c_0_1579,plain,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X4,tc_bool)),X4)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)),X4) ),
inference(split_conjunct,[status(thm)],[c_0_1102]) ).
cnf(c_0_1580,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X2),hAPP(X3,X5)),hAPP(X4,X5)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,X2)),X3),X4))
| ~ class_HOL_Oord(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1103]) ).
cnf(c_0_1581,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),X4),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1104]) ).
cnf(c_0_1582,plain,
( c_HOL_Oord__class_Oless(X4,X1,X3)
| c_HOL_Oord__class_Oless(X2,X5,X3)
| ~ c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1105]) ).
cnf(c_0_1583,plain,
( hBOOL(c_in(X4,X3,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(c_in(X4,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1106]) ).
cnf(c_0_1584,plain,
( hBOOL(c_in(X4,X3,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(c_in(X4,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1107]) ).
cnf(c_0_1585,plain,
( hBOOL(c_in(X1,X4,X3))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1108]) ).
cnf(c_0_1586,plain,
( hBOOL(c_in(X4,X3,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(c_in(X4,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1109]) ).
cnf(c_0_1587,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X3),X4),X1))
| ~ c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1110]) ).
cnf(c_0_1588,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X5))
| ~ c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1111]) ).
cnf(c_0_1589,plain,
c_Lattices_Oupper__semilattice__class_Osup(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_1112]) ).
cnf(c_0_1590,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X1,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = X4,
inference(split_conjunct,[status(thm)],[c_0_1113]) ).
cnf(c_0_1591,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_1114]) ).
cnf(c_0_1592,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_1115]) ).
cnf(c_0_1593,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X1,tc_bool)))) ),
inference(split_conjunct,[status(thm)],[c_0_1116]) ).
cnf(c_0_1594,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_1117]) ).
cnf(c_0_1595,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_1118]) ).
cnf(c_0_1596,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1),c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X2,X4,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1119]) ).
cnf(c_0_1597,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X1),c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X4,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1120]) ).
cnf(c_0_1598,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1),c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X4,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1121]) ).
cnf(c_0_1599,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X4,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1122]) ).
cnf(c_0_1600,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X2,c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1123]) ).
cnf(c_0_1601,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_1124]) ).
cnf(c_0_1602,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_1125]) ).
cnf(c_0_1603,plain,
c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3) = c_Set_Oinsert(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_1126]) ).
cnf(c_0_1604,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1127]) ).
cnf(c_0_1605,plain,
( c_HOL_Oord__class_Oless(X1,X4,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1128]) ).
cnf(c_0_1606,plain,
( c_HOL_Oord__class_Oless(X2,X4,tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_fun(X1,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1129]) ).
cnf(c_0_1607,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))) ),
inference(split_conjunct,[status(thm)],[c_0_1130]) ).
cnf(c_0_1608,plain,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X4,X2,X3),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_1131]) ).
cnf(c_0_1609,plain,
( c_Set_Oimage(c_COMBK(X4,X5,X3),X2,X3,X5) = c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5)
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1132]) ).
cnf(c_0_1610,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,X4)),X2),X1))
| ~ class_HOL_Oord(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1133]) ).
cnf(c_0_1611,plain,
c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X4,tc_bool)),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1134]) ).
cnf(c_0_1612,plain,
( X1 = X2
| hBOOL(c_in(X1,X3,X4))
| ~ hBOOL(c_in(X1,c_Set_Oinsert(X2,X3,X4),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1135]) ).
cnf(c_0_1613,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1136]) ).
cnf(c_0_1614,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1137]) ).
cnf(c_0_1615,plain,
c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X1,X4,tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1138]) ).
cnf(c_0_1616,plain,
( hAPP(c_Complete__Lattice_OSup__class_OSup(X1),c_Set_Oinsert(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1)) = c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1139]) ).
cnf(c_0_1617,plain,
hBOOL(hAPP(hAPP(c_lessequals(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_1140]) ).
cnf(c_0_1618,plain,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X1,tc_bool)))),
inference(split_conjunct,[status(thm)],[c_0_1141]) ).
cnf(c_0_1619,plain,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X1,tc_bool)))),
inference(split_conjunct,[status(thm)],[c_0_1142]) ).
cnf(c_0_1620,plain,
( hBOOL(c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1143]) ).
cnf(c_0_1621,plain,
( hBOOL(c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X4,X2,tc_fun(X3,tc_bool)),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1144]) ).
cnf(c_0_1622,plain,
( hBOOL(hAPP(X1,X4))
| hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1145]) ).
cnf(c_0_1623,plain,
( ~ hBOOL(c_in(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1146]) ).
cnf(c_0_1624,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1),tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1147]) ).
cnf(c_0_1625,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X3),X4),X5))
| ~ c_HOL_Oord__class_Oless(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_1148]) ).
cnf(c_0_1626,plain,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBK(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool),X3),X3,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1149]) ).
cnf(c_0_1627,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ouminus__class_Ouminus(X3,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),X3))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1150]) ).
cnf(c_0_1628,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ouminus__class_Ouminus(X3,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),X3))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1151]) ).
cnf(c_0_1629,plain,
( c_HOL_Oord__class_Oless(X1,X3,tc_fun(X4,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| ~ hBOOL(c_in(X2,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1152]) ).
cnf(c_0_1630,plain,
( X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1153]) ).
cnf(c_0_1631,plain,
( c_HOL_Oord__class_Oless(X2,X3,tc_fun(X1,tc_bool))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1154]) ).
cnf(c_0_1632,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X1,tc_bool)) = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1155]) ).
cnf(c_0_1633,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X1,tc_bool)) = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1156]) ).
cnf(c_0_1634,plain,
( hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1157]) ).
cnf(c_0_1635,plain,
( hBOOL(hAPP(X4,X2))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X1),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1158]) ).
cnf(c_0_1636,plain,
hBOOL(c_in(X1,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2)),
inference(split_conjunct,[status(thm)],[c_0_1159]) ).
cnf(c_0_1637,plain,
c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = c_Set_Oinsert(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),
inference(split_conjunct,[status(thm)],[c_0_1160]) ).
cnf(c_0_1638,plain,
( c_Finite__Set_Ofinite(c_Set_Oimage(X3,X1,X2,X4),X4)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1161]) ).
cnf(c_0_1639,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),c_HOL_Ouminus__class_Ouminus(X3,X1)))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1162]) ).
cnf(c_0_1640,plain,
( c_HOL_Ominus__class_Ominus(c_SetInterval_Oord__class_OatLeastLessThan(X2,X4,X1),c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1163]) ).
cnf(c_0_1641,plain,
( hBOOL(c_in(X1,X2,X3))
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X2,X3),c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_1164]) ).
cnf(c_0_1642,plain,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X2,X1))),
inference(split_conjunct,[status(thm)],[c_0_1165]) ).
cnf(c_0_1643,plain,
( hBOOL(c_in(X1,X2,X3))
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X4,X2,tc_fun(X3,tc_bool)),X3) ),
inference(split_conjunct,[status(thm)],[c_0_1166]) ).
cnf(c_0_1644,plain,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_COMBK(X2,tc_fun(X3,tc_bool),X1),X1,tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1167]) ).
cnf(c_0_1645,plain,
( hBOOL(c_in(X1,c_Set_Oinsert(X4,X2,X3),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1168]) ).
cnf(c_0_1646,plain,
( hBOOL(c_in(X1,c_Set_Oinsert(X4,X2,X3),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1169]) ).
cnf(c_0_1647,plain,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X2)),
inference(split_conjunct,[status(thm)],[c_0_1170]) ).
cnf(c_0_1648,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1171]) ).
cnf(c_0_1649,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X4,X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1172]) ).
cnf(c_0_1650,plain,
( c_Finite__Set_Ofinite(X2,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ c_Finite__Set_Ofinite(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_1173]) ).
cnf(c_0_1651,plain,
( c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X3),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1174]) ).
cnf(c_0_1652,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Set_Oimage(c_COMBK(X3,X4,X2),X1,X2,X4) = c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4) ),
inference(split_conjunct,[status(thm)],[c_0_1175]) ).
cnf(c_0_1653,plain,
( c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X4,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1176]) ).
cnf(c_0_1654,plain,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1177]) ).
cnf(c_0_1655,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1178]) ).
cnf(c_0_1656,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_Set_Oimage(X4,X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1179]) ).
cnf(c_0_1657,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Set_Oimage(X3,X1,X2,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1180]) ).
cnf(c_0_1658,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_HOL_Ominus__class_Ominus(X5,X4,X1) != c_HOL_Ominus__class_Ominus(X3,X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1181]) ).
cnf(c_0_1659,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_HOL_Ominus__class_Ominus(X3,X2,X1) != c_HOL_Ominus__class_Ominus(X5,X4,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1182]) ).
cnf(c_0_1660,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBK(X3,tc_fun(X4,tc_bool),X2),X2,tc_fun(X4,tc_bool)) = X3 ),
inference(split_conjunct,[status(thm)],[c_0_1183]) ).
cnf(c_0_1661,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X2))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1184]) ).
cnf(c_0_1662,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1185]) ).
cnf(c_0_1663,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,X4)),X1),X2))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,X4))
| ~ class_HOL_Oord(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1186]) ).
cnf(c_0_1664,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(c_Complete__Lattice_OInf__class_OInf(X3),X2)),X1))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1187]) ).
cnf(c_0_1665,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ouminus__class_Ouminus(X3,X1)),c_HOL_Ouminus__class_Ouminus(X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1188]) ).
cnf(c_0_1666,plain,
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X4,X3),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_1189]) ).
cnf(c_0_1667,plain,
c_Set_Oimage(c_COMBK(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1190]) ).
cnf(c_0_1668,plain,
( X1 = X4
| hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1191]) ).
cnf(c_0_1669,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X2),c_Finite__Set_Olinorder__class_OMin(X1,X2)),X3))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(c_in(X3,X1,X2))
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1192]) ).
cnf(c_0_1670,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ouminus__class_Ouminus(X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ouminus__class_Ouminus(X3,X1)))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1193]) ).
cnf(c_0_1671,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ouminus__class_Ouminus(X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ouminus__class_Ouminus(X3,X1)))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1194]) ).
cnf(c_0_1672,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X1,tc_bool)) != X3 ),
inference(split_conjunct,[status(thm)],[c_0_1195]) ).
cnf(c_0_1673,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X1),X2))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1196]) ).
cnf(c_0_1674,plain,
( hBOOL(c_in(X4,X2,X3))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X4,X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1197]) ).
cnf(c_0_1675,plain,
( X1 = X2
| hBOOL(c_in(X3,X1,X4))
| hBOOL(c_in(X3,X2,X4))
| c_Set_Oinsert(X3,X1,X4) != c_Set_Oinsert(X3,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_1198]) ).
cnf(c_0_1676,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),X3),
inference(split_conjunct,[status(thm)],[c_0_1199]) ).
cnf(c_0_1677,plain,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) = c_Set_Oinsert(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),X4),
inference(split_conjunct,[status(thm)],[c_0_1200]) ).
cnf(c_0_1678,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_1201]) ).
cnf(c_0_1679,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_1202]) ).
cnf(c_0_1680,plain,
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1203]) ).
cnf(c_0_1681,plain,
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X4,tc_bool)),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1204]) ).
cnf(c_0_1682,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_1205]) ).
cnf(c_0_1683,plain,
( hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1206]) ).
cnf(c_0_1684,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X3),X1),hAPP(c_Complete__Lattice_OSup__class_OSup(X3),X2)))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1207]) ).
cnf(c_0_1685,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X2),X3),c_Finite__Set_Olinorder__class_OMax(X1,X2)))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(c_in(X3,X1,X2))
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1208]) ).
cnf(c_0_1686,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1209]) ).
cnf(c_0_1687,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1210]) ).
cnf(c_0_1688,plain,
( X3 = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1211]) ).
cnf(c_0_1689,plain,
c_Set_Oinsert(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X2,tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1212]) ).
cnf(c_0_1690,plain,
c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1213]) ).
cnf(c_0_1691,plain,
~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
inference(split_conjunct,[status(thm)],[c_0_1214]) ).
cnf(c_0_1692,plain,
~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
inference(split_conjunct,[status(thm)],[c_0_1215]) ).
cnf(c_0_1693,plain,
~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
inference(split_conjunct,[status(thm)],[c_0_1216]) ).
cnf(c_0_1694,plain,
( X1 = X2
| c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) != c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) ),
inference(split_conjunct,[status(thm)],[c_0_1217]) ).
cnf(c_0_1695,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1218]) ).
cnf(c_0_1696,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1219]) ).
cnf(c_0_1697,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4),X4) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4),X4)
| ~ class_Lattices_Oupper__semilattice(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1220]) ).
cnf(c_0_1698,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4),X4) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4),X4)
| ~ class_Lattices_Olattice(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1221]) ).
cnf(c_0_1699,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3)
| ~ class_Lattices_Olattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1222]) ).
cnf(c_0_1700,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1223]) ).
cnf(c_0_1701,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1224]) ).
cnf(c_0_1702,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X1)))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1225]) ).
cnf(c_0_1703,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X1)))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1226]) ).
cnf(c_0_1704,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Set_Oimage(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,X1),
inference(split_conjunct,[status(thm)],[c_0_1227]) ).
cnf(c_0_1705,plain,
c_Set_Oimage(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1228]) ).
cnf(c_0_1706,plain,
hBOOL(c_in(X1,c_Set_Oinsert(X1,X2,X3),X3)),
inference(split_conjunct,[status(thm)],[c_0_1229]) ).
cnf(c_0_1707,plain,
hBOOL(c_in(X1,c_Set_Oinsert(X1,X2,X3),X3)),
inference(split_conjunct,[status(thm)],[c_0_1230]) ).
cnf(c_0_1708,plain,
hBOOL(c_in(X1,c_Set_Oinsert(X1,X2,X3),X3)),
inference(split_conjunct,[status(thm)],[c_0_1231]) ).
cnf(c_0_1709,plain,
c_Set_Oinsert(X1,c_Set_Oinsert(X2,X3,X4),X4) = c_Set_Oinsert(X2,c_Set_Oinsert(X1,X3,X4),X4),
inference(split_conjunct,[status(thm)],[c_0_1232]) ).
cnf(c_0_1710,plain,
( c_HOL_Oord__class_Oless(X1,X4,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X2,X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1233]) ).
cnf(c_0_1711,plain,
( c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X4,X5,X3) != c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1234]) ).
cnf(c_0_1712,plain,
( c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1235]) ).
cnf(c_0_1713,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X4))
| ~ class_Orderings_Opreorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1236]) ).
cnf(c_0_1714,plain,
( c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1237]) ).
cnf(c_0_1715,plain,
( c_HOL_Oord__class_Oless(X4,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ c_HOL_Oord__class_Oless(X4,X2,X1)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1238]) ).
cnf(c_0_1716,plain,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X4),X1))
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1239]) ).
cnf(c_0_1717,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_1240]) ).
cnf(c_0_1718,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1241]) ).
cnf(c_0_1719,plain,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1242]) ).
cnf(c_0_1720,plain,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1243]) ).
cnf(c_0_1721,plain,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1244]) ).
cnf(c_0_1722,plain,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| 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_1245]) ).
cnf(c_0_1723,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_1246]) ).
cnf(c_0_1724,plain,
( hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1247]) ).
cnf(c_0_1725,plain,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X2)),
inference(split_conjunct,[status(thm)],[c_0_1248]) ).
cnf(c_0_1726,plain,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X2)),
inference(split_conjunct,[status(thm)],[c_0_1249]) ).
cnf(c_0_1727,plain,
( hBOOL(hAPP(X2,X1))
| ~ hBOOL(c_in(X1,c_Collect(X2,X3),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1250]) ).
cnf(c_0_1728,plain,
( c_Finite__Set_Ofinite(X2,X3)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X3) ),
inference(split_conjunct,[status(thm)],[c_0_1251]) ).
cnf(c_0_1729,plain,
( c_Finite__Set_Ofinite(X1,X3)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X3) ),
inference(split_conjunct,[status(thm)],[c_0_1252]) ).
cnf(c_0_1730,plain,
( c_Complete__Lattice_Ocomplete__lattice__axioms(c_Complete__Lattice_OInf__class_OInf(X1),c_Complete__Lattice_OSup__class_OSup(X1),c_lessequals(X1),X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1253]) ).
cnf(c_0_1731,plain,
( hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(t_a,X3)),v_x) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(X1,v_x),hAPP(X2,v_x),X3)
| ~ class_Lattices_Olattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1254]) ).
cnf(c_0_1732,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_1255]) ).
cnf(c_0_1733,plain,
c_Finite__Set_Ofold1(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = X2,
inference(split_conjunct,[status(thm)],[c_0_1256]) ).
cnf(c_0_1734,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1))
| ~ class_Orderings_Opreorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1257]) ).
cnf(c_0_1735,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1))
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1258]) ).
cnf(c_0_1736,plain,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1259]) ).
cnf(c_0_1737,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),X1),X1))
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1260]) ).
cnf(c_0_1738,plain,
( c_SetInterval_Oord__class_OatLeastLessThan(X3,X2,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1261]) ).
cnf(c_0_1739,plain,
( c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X2,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1262]) ).
cnf(c_0_1740,plain,
( c_HOL_Oord__class_Oless(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1263]) ).
cnf(c_0_1741,plain,
( c_HOL_Oord__class_Oless(X1,c_Lattices_Oupper__semilattice__class_Osup(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1264]) ).
cnf(c_0_1742,plain,
hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X1)),
inference(split_conjunct,[status(thm)],[c_0_1265]) ).
cnf(c_0_1743,plain,
( hBOOL(c_in(X1,X2,X3))
| c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1266]) ).
cnf(c_0_1744,plain,
( hAPP(c_Complete__Lattice_OInf__class_OInf(X1),c_Set_Oinsert(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_1267]) ).
cnf(c_0_1745,plain,
( hAPP(c_Complete__Lattice_OSup__class_OSup(X1),c_Set_Oinsert(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_1268]) ).
cnf(c_0_1746,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1269]) ).
cnf(c_0_1747,plain,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1270]) ).
cnf(c_0_1748,plain,
( c_Finite__Set_Olinorder__class_OMax(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = X1
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1271]) ).
cnf(c_0_1749,plain,
( c_Finite__Set_Olinorder__class_OMin(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = X1
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1272]) ).
cnf(c_0_1750,plain,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1273]) ).
cnf(c_0_1751,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1274]) ).
cnf(c_0_1752,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1275]) ).
cnf(c_0_1753,plain,
( X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1276]) ).
cnf(c_0_1754,plain,
( X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1277]) ).
cnf(c_0_1755,plain,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1278]) ).
cnf(c_0_1756,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1))
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1279]) ).
cnf(c_0_1757,plain,
( X3 = X2
| c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1280]) ).
cnf(c_0_1758,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1281]) ).
cnf(c_0_1759,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X1) = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1282]) ).
cnf(c_0_1760,plain,
( c_Set_Oinsert(X1,X2,X3) = X2
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1283]) ).
cnf(c_0_1761,plain,
( c_HOL_Oord__class_Oless(X3,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ouminus__class_Ouminus(X3,X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1284]) ).
cnf(c_0_1762,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_1285]) ).
cnf(c_0_1763,plain,
( hAPP(c_Complete__Lattice_OSup__class_OSup(X1),c_Set_Oinsert(X2,X3,X1)) = c_Lattices_Oupper__semilattice__class_Osup(X2,hAPP(c_Complete__Lattice_OSup__class_OSup(X1),X3),X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1286]) ).
cnf(c_0_1764,plain,
c_Set_Ocontents(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_1287]) ).
cnf(c_0_1765,plain,
c_The(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_1288]) ).
cnf(c_0_1766,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1289]) ).
cnf(c_0_1767,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3)
| ~ class_Lattices_Olattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1290]) ).
cnf(c_0_1768,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1291]) ).
cnf(c_0_1769,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1292]) ).
cnf(c_0_1770,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1293]) ).
cnf(c_0_1771,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1294]) ).
cnf(c_0_1772,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_1295]) ).
cnf(c_0_1773,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_1296]) ).
cnf(c_0_1774,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1297]) ).
cnf(c_0_1775,plain,
c_Set_Oinsert(X1,c_Set_Oinsert(X1,X2,X3),X3) = c_Set_Oinsert(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_1298]) ).
cnf(c_0_1776,plain,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1299]) ).
cnf(c_0_1777,plain,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1300]) ).
cnf(c_0_1778,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X2),X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1301]) ).
cnf(c_0_1779,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X2),X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1302]) ).
cnf(c_0_1780,plain,
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1303]) ).
cnf(c_0_1781,plain,
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1304]) ).
cnf(c_0_1782,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_1305]) ).
cnf(c_0_1783,plain,
( hBOOL(c_in(X2,c_Collect(X1,X3),X3))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1306]) ).
cnf(c_0_1784,plain,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
inference(split_conjunct,[status(thm)],[c_0_1307]) ).
cnf(c_0_1785,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1308]) ).
cnf(c_0_1786,plain,
( hBOOL(hAPP(X2,X1))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1309]) ).
cnf(c_0_1787,plain,
( c_Finite__Set_Ofinite(X2,X3)
| ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_1310]) ).
cnf(c_0_1788,plain,
~ c_HOL_Oord__class_Oless(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1311]) ).
cnf(c_0_1789,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) != X3
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1312]) ).
cnf(c_0_1790,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X3),c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1313]) ).
cnf(c_0_1791,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1314]) ).
cnf(c_0_1792,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1315]) ).
cnf(c_0_1793,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1316]) ).
cnf(c_0_1794,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| 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_1317]) ).
cnf(c_0_1795,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1318]) ).
cnf(c_0_1796,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1319]) ).
cnf(c_0_1797,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_1320]) ).
cnf(c_0_1798,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3) = c_HOL_Ominus__class_Ominus(X2,X1,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1321]) ).
cnf(c_0_1799,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_1322]) ).
cnf(c_0_1800,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_1323]) ).
cnf(c_0_1801,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1324]) ).
cnf(c_0_1802,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1325]) ).
cnf(c_0_1803,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1326]) ).
cnf(c_0_1804,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1327]) ).
cnf(c_0_1805,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_1328]) ).
cnf(c_0_1806,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(X2,X1,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1329]) ).
cnf(c_0_1807,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_fequal(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1330]) ).
cnf(c_0_1808,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1331]) ).
cnf(c_0_1809,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1))
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1332]) ).
cnf(c_0_1810,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X2))
| c_HOL_Oord__class_Oless(X2,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1333]) ).
cnf(c_0_1811,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1334]) ).
cnf(c_0_1812,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(X1,X1,X2) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
| ~ class_Orderings_Oorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1335]) ).
cnf(c_0_1813,plain,
( hBOOL(c_in(X2,X1,X3))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1336]) ).
cnf(c_0_1814,plain,
c_Collect(hAPP(c_fequal(X1),X2),X1) = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
inference(split_conjunct,[status(thm)],[c_0_1337]) ).
cnf(c_0_1815,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_1338]) ).
cnf(c_0_1816,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_1339]) ).
cnf(c_0_1817,plain,
c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1340]) ).
cnf(c_0_1818,plain,
( c_Finite__Set_Ofinite(c_Set_Oinsert(X3,X1,X2),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1341]) ).
cnf(c_0_1819,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1342]) ).
cnf(c_0_1820,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1343]) ).
cnf(c_0_1821,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1344]) ).
cnf(c_0_1822,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1345]) ).
cnf(c_0_1823,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_Orderings_Obot__class_Obot(X1)),X2))
| ~ class_Orderings_Obot(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1346]) ).
cnf(c_0_1824,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_1347]) ).
cnf(c_0_1825,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_1348]) ).
cnf(c_0_1826,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = X2,
inference(split_conjunct,[status(thm)],[c_0_1349]) ).
cnf(c_0_1827,plain,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
inference(split_conjunct,[status(thm)],[c_0_1350]) ).
cnf(c_0_1828,plain,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1,tc_fun(t_a,X2)),v_x) = c_HOL_Ouminus__class_Ouminus(hAPP(X1,v_x),X2)
| ~ class_HOL_Ouminus(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1351]) ).
cnf(c_0_1829,plain,
c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1352]) ).
cnf(c_0_1830,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Set_Oinsert(X2,X3,X1),
inference(split_conjunct,[status(thm)],[c_0_1353]) ).
cnf(c_0_1831,plain,
~ c_HOL_Oord__class_Oless(X1,X1,tc_fun(X2,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1354]) ).
cnf(c_0_1832,plain,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
inference(split_conjunct,[status(thm)],[c_0_1355]) ).
cnf(c_0_1833,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X2 = X1
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1356]) ).
cnf(c_0_1834,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1357]) ).
cnf(c_0_1835,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1358]) ).
cnf(c_0_1836,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1359]) ).
cnf(c_0_1837,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1360]) ).
cnf(c_0_1838,plain,
( X1 = X2
| c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X3,tc_bool)) != c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1361]) ).
cnf(c_0_1839,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1362]) ).
cnf(c_0_1840,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3)
| ~ class_Lattices_Olattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1363]) ).
cnf(c_0_1841,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X2))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1364]) ).
cnf(c_0_1842,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X2))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1365]) ).
cnf(c_0_1843,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_1366]) ).
cnf(c_0_1844,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_1367]) ).
cnf(c_0_1845,plain,
( hAPP(c_HOL_Ouminus__class_Ouminus(v_A,tc_fun(t_a,t_b)),v_x) = c_HOL_Ouminus__class_Ouminus(hAPP(v_A,v_x),t_b)
| ~ class_HOL_Ouminus(t_b) ),
inference(split_conjunct,[status(thm)],[c_0_1368]) ).
cnf(c_0_1846,plain,
hAPP(c_COMBK(v_P,t_a,t_b),v_Q) = v_P,
inference(split_conjunct,[status(thm)],[c_0_1369]) ).
cnf(c_0_1847,plain,
c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
inference(split_conjunct,[status(thm)],[c_0_1370]) ).
cnf(c_0_1848,plain,
hBOOL(hAPP(hAPP(c_fequal(X1),X2),X2)),
inference(split_conjunct,[status(thm)],[c_0_1371]) ).
cnf(c_0_1849,plain,
( X1 = c_Orderings_Obot__class_Obot(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X2) != c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1372]) ).
cnf(c_0_1850,plain,
( X1 = c_Orderings_Obot__class_Obot(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2) != c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1373]) ).
cnf(c_0_1851,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_1374]) ).
cnf(c_0_1852,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1375]) ).
cnf(c_0_1853,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1376]) ).
cnf(c_0_1854,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1377]) ).
cnf(c_0_1855,plain,
( hAPP(c_Complete__Lattice_OSup__class_OSup(X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1378]) ).
cnf(c_0_1856,plain,
c_Lattices_Oupper__semilattice__class_Osup(X1,X1,tc_fun(X2,tc_bool)) = X1,
inference(split_conjunct,[status(thm)],[c_0_1379]) ).
cnf(c_0_1857,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_1380]) ).
cnf(c_0_1858,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(X2),X2) = X1
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1381]) ).
cnf(c_0_1859,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X1),X2,X1) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1382]) ).
cnf(c_0_1860,plain,
c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
inference(split_conjunct,[status(thm)],[c_0_1383]) ).
cnf(c_0_1861,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X1,X2) = X1
| ~ class_Lattices_Oupper__semilattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1384]) ).
cnf(c_0_1862,plain,
( X1 = X2
| c_HOL_Ouminus__class_Ouminus(X1,X3) != c_HOL_Ouminus__class_Ouminus(X2,X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1385]) ).
cnf(c_0_1863,plain,
( X1 = X2
| c_HOL_Ouminus__class_Ouminus(X1,X3) != c_HOL_Ouminus__class_Ouminus(X2,X3)
| ~ class_Lattices_Oboolean__algebra(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1386]) ).
cnf(c_0_1864,plain,
c_The(hAPP(c_fequal(X1),X2),X1) = X2,
inference(split_conjunct,[status(thm)],[c_0_1387]) ).
cnf(c_0_1865,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1388]) ).
cnf(c_0_1866,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1
| ~ class_Lattices_Oboolean__algebra(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1389]) ).
cnf(c_0_1867,plain,
( X1 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1390]) ).
cnf(c_0_1868,plain,
( X1 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1391]) ).
cnf(c_0_1869,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1392]) ).
cnf(c_0_1870,plain,
( X1 = X2
| c_Com_Ocom_OSemi(X1,X3) != c_Com_Ocom_OSemi(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_1393]) ).
cnf(c_0_1871,plain,
( X1 = X2
| c_Com_Ocom_OSemi(X3,X1) != c_Com_Ocom_OSemi(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1394]) ).
cnf(c_0_1872,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_1395]) ).
cnf(c_0_1873,plain,
( class_HOL_Oord(tc_fun(X2,X1))
| ~ class_HOL_Oord(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1396]) ).
cnf(c_0_1874,plain,
( class_HOL_Ominus(tc_fun(X2,X1))
| ~ class_HOL_Ominus(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1397]) ).
cnf(c_0_1875,plain,
( class_HOL_Ouminus(tc_fun(X2,X1))
| ~ class_HOL_Ouminus(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1398]) ).
cnf(c_0_1876,plain,
( class_Orderings_Obot(tc_fun(X2,X1))
| ~ class_Orderings_Obot(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1399]) ).
cnf(c_0_1877,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1400]) ).
cnf(c_0_1878,plain,
( class_Lattices_Olattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1401]) ).
cnf(c_0_1879,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1402]) ).
cnf(c_0_1880,plain,
( class_Lattices_Oboolean__algebra(tc_fun(X2,X1))
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1403]) ).
cnf(c_0_1881,plain,
( class_Lattices_Obounded__lattice(tc_fun(X2,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1404]) ).
cnf(c_0_1882,plain,
( class_Lattices_Oupper__semilattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1405]) ).
cnf(c_0_1883,plain,
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1406]) ).
cnf(c_0_1884,plain,
c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_1407]) ).
cnf(c_0_1885,plain,
c_Com_Ocom_OSemi(X1,X2) != c_Com_Ocom_OSKIP,
inference(split_conjunct,[status(thm)],[c_0_1408]) ).
cnf(c_0_1886,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ class_Finite__Set_Ofinite_Ofinite(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1409]) ).
cnf(c_0_1887,plain,
c_Collect(X1,X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_1410]) ).
cnf(c_0_1888,plain,
class_HOL_Oord(tc_bool),
inference(split_conjunct,[status(thm)],[c_0_1411]) ).
cnf(c_0_1889,plain,
class_HOL_Ominus(tc_bool),
inference(split_conjunct,[status(thm)],[c_0_1412]) ).
cnf(c_0_1890,plain,
class_HOL_Ouminus(tc_bool),
inference(split_conjunct,[status(thm)],[c_0_1413]) ).
cnf(c_0_1891,plain,
class_Orderings_Obot(tc_bool),
inference(split_conjunct,[status(thm)],[c_0_1414]) ).
cnf(c_0_1892,plain,
class_Orderings_Oorder(tc_bool),
inference(split_conjunct,[status(thm)],[c_0_1415]) ).
cnf(c_0_1893,plain,
class_Lattices_Olattice(tc_bool),
inference(split_conjunct,[status(thm)],[c_0_1416]) ).
cnf(c_0_1894,plain,
class_Orderings_Opreorder(tc_bool),
inference(split_conjunct,[status(thm)],[c_0_1417]) ).
cnf(c_0_1895,plain,
class_Finite__Set_Ofinite_Ofinite(tc_bool),
inference(split_conjunct,[status(thm)],[c_0_1418]) ).
cnf(c_0_1896,plain,
class_Lattices_Oboolean__algebra(tc_bool),
inference(split_conjunct,[status(thm)],[c_0_1419]) ).
cnf(c_0_1897,plain,
class_Lattices_Obounded__lattice(tc_bool),
inference(split_conjunct,[status(thm)],[c_0_1420]) ).
cnf(c_0_1898,plain,
class_Lattices_Oupper__semilattice(tc_bool),
inference(split_conjunct,[status(thm)],[c_0_1421]) ).
cnf(c_0_1899,plain,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
inference(split_conjunct,[status(thm)],[c_0_1422]) ).
cnf(c_0_1900,plain,
class_HOL_Oord(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1423]) ).
cnf(c_0_1901,plain,
class_HOL_Ominus(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1424]) ).
cnf(c_0_1902,plain,
class_Orderings_Obot(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1425]) ).
cnf(c_0_1903,plain,
class_Orderings_Oorder(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1426]) ).
cnf(c_0_1904,plain,
class_Lattices_Olattice(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1427]) ).
cnf(c_0_1905,plain,
class_Orderings_Olinorder(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1428]) ).
cnf(c_0_1906,plain,
class_Orderings_Opreorder(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1429]) ).
cnf(c_0_1907,plain,
class_Lattices_Oupper__semilattice(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1430]) ).
cnf(c_0_1908,plain,
( c_Complete__Lattice_Ocomplete__lattice(X2,X1,c_COMBC(X3,X9,X9,tc_bool),c_COMBC(X4,X9,X9,tc_bool),X6,X5,X8,X7,X9)
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
c_0_1431,
[final] ).
cnf(c_0_1909,plain,
( hBOOL(hAPP(hAPP(X3,c_Complete__Lattice_Ocomplete__lattice_OINFI(X1,X11,X13,X9,X12)),hAPP(X13,X10)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| ~ hBOOL(c_in(X10,X11,X12)) ),
c_0_1432,
[final] ).
cnf(c_0_1910,plain,
( hBOOL(hAPP(hAPP(X3,hAPP(X13,X10)),c_Complete__Lattice_Ocomplete__lattice_OSUPR(X2,X11,X13,X9,X12)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| ~ hBOOL(c_in(X10,X11,X12)) ),
c_0_1433,
[final] ).
cnf(c_0_1911,plain,
( X10 = c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool))
| c_Complete__Lattice_Ocomplete__lattice_OINFI(X1,X10,c_COMBK(X12,X9,X11),X9,X11) = X12
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
c_0_1434,
[final] ).
cnf(c_0_1912,plain,
( X10 = c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool))
| c_Complete__Lattice_Ocomplete__lattice_OSUPR(X2,X10,c_COMBK(X12,X9,X11),X9,X11) = X12
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
c_0_1435,
[final] ).
cnf(c_0_1913,plain,
( hAPP(X2,c_Set_Oinsert(X10,c_Set_Oinsert(X11,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),X9),X9)) = hAPP(hAPP(X6,X10),X11)
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
c_0_1436,
[final] ).
cnf(c_0_1914,plain,
( hAPP(X1,c_Set_Oinsert(X10,c_Set_Oinsert(X11,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),X9),X9)) = hAPP(hAPP(X5,X10),X11)
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
c_0_1437,
[final] ).
cnf(c_0_1915,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_1438,
[final] ).
cnf(c_0_1916,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_1439,
[final] ).
cnf(c_0_1917,plain,
( hAPP(X2,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),X9)) = X10
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
c_0_1440,
[final] ).
cnf(c_0_1918,plain,
( hAPP(X1,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),X9)) = X10
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
c_0_1441,
[final] ).
cnf(c_0_1919,plain,
( hAPP(X2,c_Set_Oinsert(X10,X11,X9)) = hAPP(hAPP(X6,X10),hAPP(X2,X11))
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
c_0_1442,
[final] ).
cnf(c_0_1920,plain,
( hAPP(X1,c_Set_Oinsert(X10,X11,X9)) = hAPP(hAPP(X5,X10),hAPP(X1,X11))
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
c_0_1443,
[final] ).
cnf(c_0_1921,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_1444,
[final] ).
cnf(c_0_1922,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_1445,
[final] ).
cnf(c_0_1923,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),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_1446,
[final] ).
cnf(c_0_1924,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),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_1447,
[final] ).
cnf(c_0_1925,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,X4,X3,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(hAPP(c_COMBC(c_fequal(tc_Com_Ostate),tc_Com_Ostate,tc_Com_Ostate,tc_bool),v_sko__Hoare__Mirabelle__Xescape__2(X1,X2,X3,X4)),tc_fun(tc_Com_Ostate,tc_bool),t_a),X4,c_COMBK(hAPP(X3,v_sko__Hoare__Mirabelle__Xescape__1(X1,X2,X3,X4)),tc_fun(tc_Com_Ostate,tc_bool),t_a),t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
c_0_1448,
[final] ).
cnf(c_0_1926,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,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X2,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X1,X6,X7,X3))) ),
c_0_1449,
[final] ).
cnf(c_0_1927,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,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X2,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X1,X6,X7,X3))) ),
c_0_1450,
[final] ).
cnf(c_0_1928,plain,
( c_Nitpick_Ofold__graph_H(X4,X5,X2,hAPP(hAPP(X4,X1),X6),X3,X7)
| ~ hBOOL(c_in(X1,X2,X3))
| ~ c_Nitpick_Ofold__graph_H(X4,X5,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X6,X3,X7) ),
c_0_1451,
[final] ).
cnf(c_0_1929,plain,
( c_Finite__Set_Ofold__graph(X1,X2,X3,hAPP(hAPP(X1,X4),X6),X5,X7)
| ~ c_Finite__Set_Ofold__graph(X1,X2,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),tc_fun(X5,tc_bool)),X6,X5,X7)
| ~ hBOOL(c_in(X4,X3,X5)) ),
c_0_1452,
[final] ).
cnf(c_0_1930,plain,
( hBOOL(c_in(X1,X2,X3))
| c_Finite__Set_Ofold__graph(X4,X5,c_Set_Oinsert(X1,X2,X3),hAPP(hAPP(X4,X1),X6),X3,X7)
| ~ c_Finite__Set_Ofold__graph(X4,X5,X2,X6,X3,X7) ),
c_0_1453,
[final] ).
cnf(c_0_1931,plain,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(c_Set_Oimage(X2,X3,X4,X1),c_Set_Oimage(X2,X5,X4,X1),tc_fun(X1,tc_bool))),c_Set_Oimage(X2,c_HOL_Ominus__class_Ominus(X3,X5,tc_fun(X4,tc_bool)),X4,X1))),
c_0_1454,
[final] ).
cnf(c_0_1932,plain,
( hBOOL(c_in(X2,X3,X5))
| hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,c_Set_Oinsert(X2,X3,X5),X5),X4))
| ~ c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5,X5) ),
c_0_1455,
[final] ).
cnf(c_0_1933,plain,
( X4 = X2
| ~ c_Finite__Set_Ofold__graph(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X4,X3,X5) ),
c_0_1456,
[final] ).
cnf(c_0_1934,plain,
( c_Finite__Set_Ofinite(X3,X5)
| ~ c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5,X6) ),
c_0_1457,
[final] ).
cnf(c_0_1935,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xconseq12__1(X6,X2,X5,X4)),v_sko__Hoare__Mirabelle__Xconseq12__3(X6,X2,X5,X4))) ),
c_0_1458,
[final] ).
cnf(c_0_1936,plain,
( hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xconseq12__1(X5,X2,X6,X4)),v_sko__Hoare__Mirabelle__Xconseq12__2(X5,X2,X6,X4)))
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X5,X3,X6,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
c_0_1459,
[final] ).
cnf(c_0_1937,plain,
c_Nitpick_Ofold__graph_H(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X2,X3,X4),
c_0_1460,
[final] ).
cnf(c_0_1938,plain,
c_Finite__Set_Ofold__graph(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X2,X3,X4),
c_0_1461,
[final] ).
cnf(c_0_1939,plain,
( hBOOL(hAPP(hAPP(X4,X5),v_sko__Hoare__Mirabelle__Xconseq12__3(X6,X2,X7,X4)))
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X2,X5),v_sko__Hoare__Mirabelle__Xconseq12__2(X6,X2,X7,X4))) ),
c_0_1462,
[final] ).
cnf(c_0_1940,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,c_Com_Ocom_OSemi(X3,X6),X7,X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_bool)),tc_Hoare__Mirabelle_Otriple(X5)),X5)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_bool)),tc_Hoare__Mirabelle_Otriple(X5)),X5)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X4,X6,X7,X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_bool)),tc_Hoare__Mirabelle_Otriple(X5)),X5) ),
c_0_1463,
[final] ).
cnf(c_0_1941,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool))),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4)) ),
c_0_1464,
[final] ).
cnf(c_0_1942,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool))),X4))
| ~ hBOOL(c_in(X3,X2,X1)) ),
c_0_1465,
[final] ).
cnf(c_0_1943,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool))),X4))
| ~ hBOOL(c_in(X3,X2,X1)) ),
c_0_1466,
[final] ).
cnf(c_0_1944,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(X3,X6)),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X3,X4,tc_fun(X1,tc_bool))),X5))
| ~ hBOOL(c_in(X6,X2,X4)) ),
c_0_1467,
[final] ).
cnf(c_0_1945,plain,
( hBOOL(hAPP(hAPP(X1,v_sko__Hoare__Mirabelle__Xescape__1(X2,X1,X3,X4)),v_sko__Hoare__Mirabelle__Xescape__2(X2,X1,X3,X4)))
| c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
c_0_1468,
[final] ).
cnf(c_0_1946,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,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
c_0_1469,
[final] ).
cnf(c_0_1947,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,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
c_0_1470,
[final] ).
cnf(c_0_1948,plain,
( hBOOL(c_in(hAPP(X2,X6),X5,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Set_Oimage(X2,X3,X4,X1)),X5))
| ~ hBOOL(c_in(X6,X3,X4)) ),
c_0_1471,
[final] ).
cnf(c_0_1949,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,tc_bool)),c_Set_Oimage(X5,X2,X1,X4)),c_Set_Oimage(X5,X3,X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
c_0_1472,
[final] ).
cnf(c_0_1950,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Set_Oimage(X2,X3,X4,X1)),c_Set_Oimage(X2,X5,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,tc_bool)),X3),X5)) ),
c_0_1473,
[final] ).
cnf(c_0_1951,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X5,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xconseq2__1(X5,X4)),v_sko__Hoare__Mirabelle__Xconseq2__2(X5,X4))) ),
c_0_1474,
[final] ).
cnf(c_0_1952,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X5,X3,X4,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X2,v_sko__Hoare__Mirabelle__Xconseq1__1(X5,X2)),v_sko__Hoare__Mirabelle__Xconseq1__2(X5,X2))) ),
c_0_1475,
[final] ).
cnf(c_0_1953,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool))),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)))
| ~ hBOOL(c_in(X3,X2,X1)) ),
c_0_1476,
[final] ).
cnf(c_0_1954,plain,
( hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xconseq1__1(X5,X2)),v_sko__Hoare__Mirabelle__Xconseq1__2(X5,X2)))
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X5,X3,X4,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
c_0_1477,
[final] ).
cnf(c_0_1955,plain,
( hBOOL(hAPP(hAPP(X4,v_sko__Hoare__Mirabelle__Xconseq2__1(X5,X4)),v_sko__Hoare__Mirabelle__Xconseq2__2(X5,X4)))
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X5,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
c_0_1478,
[final] ).
cnf(c_0_1956,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X3),X3,X3,tc_bool),X1),X3),X2,tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,X2,X3),
c_0_1479,
[final] ).
cnf(c_0_1957,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X1,tc_bool))),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X5)) ),
c_0_1480,
[final] ).
cnf(c_0_1958,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X1,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(X3,X5,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X5)) ),
c_0_1481,
[final] ).
cnf(c_0_1959,plain,
( c_Finite__Set_Ofinite(X4,X3)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X4),c_Set_Oimage(X5,X1,X2,X3))) ),
c_0_1482,
[final] ).
cnf(c_0_1960,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X1,tc_bool))),X4)) ),
c_0_1483,
[final] ).
cnf(c_0_1961,plain,
( c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X4,X1,X2,X5),c_Finite__Set_Osetsum(X4,X3,X2,X5),X5) = c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),X2,X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X3),X1))
| ~ class_OrderedGroup_Oab__group__add(X5) ),
c_0_1484,
[final] ).
cnf(c_0_1962,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X1,tc_bool))),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,tc_fun(X1,tc_bool)))) ),
c_0_1485,
[final] ).
cnf(c_0_1963,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X1,tc_bool))),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X3)) ),
c_0_1486,
[final] ).
cnf(c_0_1964,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X1,tc_bool))),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X3)) ),
c_0_1487,
[final] ).
cnf(c_0_1965,plain,
( c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X1),X2)) ),
c_0_1488,
[final] ).
cnf(c_0_1966,plain,
( hBOOL(c_in(X1,X2,X3))
| c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X4),X2)) ),
c_0_1489,
[final] ).
cnf(c_0_1967,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
c_0_1490,
[final] ).
cnf(c_0_1968,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
c_0_1491,
[final] ).
cnf(c_0_1969,plain,
( X2 = X4
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),X4)) ),
c_0_1492,
[final] ).
cnf(c_0_1970,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X1,tc_bool))),X4)) ),
c_0_1493,
[final] ).
cnf(c_0_1971,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X1,tc_bool))),X4)) ),
c_0_1494,
[final] ).
cnf(c_0_1972,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastLessThan(X4,X5,X1)))
| ~ class_Orderings_Olinorder(X1) ),
c_0_1495,
[final] ).
cnf(c_0_1973,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastLessThan(X4,X5,X1)))
| ~ class_Orderings_Olinorder(X1) ),
c_0_1496,
[final] ).
cnf(c_0_1974,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,tc_bool)),hAPP(X5,X1)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X5,X3,tc_fun(X4,tc_bool))))
| ~ hBOOL(c_in(X1,X2,X3)) ),
c_0_1497,
[final] ).
cnf(c_0_1975,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_1498,
[final] ).
cnf(c_0_1976,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_1499,
[final] ).
cnf(c_0_1977,plain,
( c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2,X5) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X4,X1,X2,X5),hAPP(X4,X3),X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(c_in(X3,X1,X2))
| ~ class_OrderedGroup_Oab__group__add(X5) ),
c_0_1500,
[final] ).
cnf(c_0_1978,plain,
( c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2,X5) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X4,X1,X2,X5),hAPP(X4,X3),X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(c_in(X3,X1,X2))
| ~ class_Ring__and__Field_Oring(X5) ),
c_0_1501,
[final] ).
cnf(c_0_1979,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4,X3,tc_fun(X5,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,X3,tc_fun(X5,tc_bool)),
c_0_1502,
[final] ).
cnf(c_0_1980,plain,
( c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X4,X1,X3)) ),
c_0_1503,
[final] ).
cnf(c_0_1981,plain,
( hBOOL(c_in(X1,X2,X3))
| c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X1,X4,X3)) ),
c_0_1504,
[final] ).
cnf(c_0_1982,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(X1,X2,X4,X5),c_Set_Oimage(X1,X3,X4,X5),tc_fun(X5,tc_bool)) = c_Set_Oimage(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4,X5),
c_0_1505,
[final] ).
cnf(c_0_1983,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X1,tc_bool))),c_HOL_Ouminus__class_Ouminus(X3,tc_fun(X1,tc_bool)))) ),
c_0_1506,
[final] ).
cnf(c_0_1984,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Set_Oinsert(X2,X3,X1)),X4)) ),
c_0_1507,
[final] ).
cnf(c_0_1985,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_1508,
[final] ).
cnf(c_0_1986,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_1509,
[final] ).
cnf(c_0_1987,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Set_Oinsert(X4,X2,X1)),c_Set_Oinsert(X4,X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
c_0_1510,
[final] ).
cnf(c_0_1988,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X4),hAPP(X5,X1)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X5,X3,X4)))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) ),
c_0_1511,
[final] ).
cnf(c_0_1989,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_Set_Oinsert(X1,X4,X3)),X2))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X4),X2)) ),
c_0_1512,
[final] ).
cnf(c_0_1990,plain,
hBOOL(hAPP(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2))),
c_0_1513,
[final] ).
cnf(c_0_1991,plain,
( hBOOL(c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5))
| ~ hBOOL(c_in(X2,X3,X4)) ),
c_0_1514,
[final] ).
cnf(c_0_1992,plain,
( hBOOL(c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5))
| ~ hBOOL(c_in(X2,X3,X4)) ),
c_0_1515,
[final] ).
cnf(c_0_1993,plain,
( hBOOL(c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5))
| ~ hBOOL(c_in(X1,X2,X3)) ),
c_0_1516,
[final] ).
cnf(c_0_1994,plain,
( hBOOL(c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5))
| ~ hBOOL(c_in(X1,X2,X3)) ),
c_0_1517,
[final] ).
cnf(c_0_1995,plain,
c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,c_Com_Ocom_OSKIP,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3),
c_0_1518,
[final] ).
cnf(c_0_1996,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ class_Orderings_Oorder(X1) ),
c_0_1519,
[final] ).
cnf(c_0_1997,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| X2 = c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1))) ),
c_0_1520,
[final] ).
cnf(c_0_1998,plain,
( hBOOL(c_in(X2,X4,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Set_Oinsert(X2,X3,X1)),X4)) ),
c_0_1521,
[final] ).
cnf(c_0_1999,plain,
( hBOOL(c_in(X2,X3,X4))
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| ~ hBOOL(c_in(X2,X1,X4)) ),
c_0_1522,
[final] ).
cnf(c_0_2000,plain,
( hBOOL(c_in(X3,X1,X2))
| c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2,X5) = c_Finite__Set_Osetsum(X4,X1,X2,X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Oab__group__add(X5) ),
c_0_1523,
[final] ).
cnf(c_0_2001,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4)) ),
c_0_1524,
[final] ).
cnf(c_0_2002,plain,
( hBOOL(c_in(X1,X2,X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X2),c_Set_Oinsert(X1,X4,X3))) ),
c_0_1525,
[final] ).
cnf(c_0_2003,plain,
( hBOOL(c_in(X3,X2,X1))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1))) ),
c_0_1526,
[final] ).
cnf(c_0_2004,plain,
( hBOOL(c_in(X1,X2,X3))
| c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3,tc_nat) = c_Finite__Set_Osetsum(X4,X2,X3,tc_nat) ),
c_0_1527,
[final] ).
cnf(c_0_2005,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ouminus__class_Ouminus(X3,tc_fun(X1,tc_bool))),c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
c_0_1528,
[final] ).
cnf(c_0_2006,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ouminus__class_Ouminus(X3,tc_fun(X1,tc_bool))),c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
c_0_1529,
[final] ).
cnf(c_0_2007,plain,
c_Collect(hAPP(c_COMBC(c_fequal(X1),X1,X1,tc_bool),X2),X1) = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
c_0_1530,
[final] ).
cnf(c_0_2008,plain,
( c_HOL_Ominus__class_Ominus(X3,c_HOL_Ominus__class_Ominus(X4,X2,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4)) ),
c_0_1531,
[final] ).
cnf(c_0_2009,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_1532,
[final] ).
cnf(c_0_2010,plain,
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(X4,X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool))
| ~ hBOOL(c_in(X1,X2,X3)) ),
c_0_1533,
[final] ).
cnf(c_0_2011,plain,
hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),X2)),
c_0_1534,
[final] ).
cnf(c_0_2012,plain,
( hBOOL(c_in(X1,X2,X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X2),c_Set_Oinsert(X1,X4,X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X2),X4)) ),
c_0_1535,
[final] ).
cnf(c_0_2013,plain,
( hBOOL(c_in(X1,X2,X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X2),c_Set_Oinsert(X1,X4,X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X2),X4)) ),
c_0_1536,
[final] ).
cnf(c_0_2014,plain,
hAPP(hAPP(c_COMBC(X1,X2,X3,X4),X5),X6) = hAPP(hAPP(X1,X6),X5),
c_0_1537,
[final] ).
cnf(c_0_2015,plain,
c_The(hAPP(c_COMBC(c_fequal(X1),X1,X1,tc_bool),X2),X1) = X2,
c_0_1538,
[final] ).
cnf(c_0_2016,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| ~ class_Orderings_Oorder(X1) ),
c_0_1539,
[final] ).
cnf(c_0_2017,plain,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oinsert(X1,X2,X3),X4,X3,tc_fun(X5,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(X4,X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),
c_0_1540,
[final] ).
cnf(c_0_2018,plain,
( c_Set_Oinsert(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5) = c_Set_Oimage(X4,X2,X3,X5)
| ~ hBOOL(c_in(X1,X2,X3)) ),
c_0_1541,
[final] ).
cnf(c_0_2019,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X4,X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
c_0_1542,
[final] ).
cnf(c_0_2020,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)),X4))
| ~ class_Lattices_Oupper__semilattice(X1) ),
c_0_1543,
[final] ).
cnf(c_0_2021,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)),X4))
| ~ class_Lattices_Oupper__semilattice(X1) ),
c_0_1544,
[final] ).
cnf(c_0_2022,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)),X4))
| ~ class_Lattices_Oupper__semilattice(X1) ),
c_0_1545,
[final] ).
cnf(c_0_2023,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)),X4))
| ~ class_Lattices_Oupper__semilattice(X1) ),
c_0_1546,
[final] ).
cnf(c_0_2024,plain,
( X3 = c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2)
| ~ hBOOL(hAPP(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X3)) ),
c_0_1547,
[final] ).
cnf(c_0_2025,plain,
c_Set_Oimage(X1,c_Set_Oinsert(X2,X3,X4),X4,X5) = c_Set_Oinsert(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5),
c_0_1548,
[final] ).
cnf(c_0_2026,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X2)) ),
c_0_1549,
[final] ).
cnf(c_0_2027,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X2)) ),
c_0_1550,
[final] ).
cnf(c_0_2028,plain,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X1,tc_bool))),X2)),
c_0_1551,
[final] ).
cnf(c_0_2029,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,X2)),X4),X3))
| c_HOL_Oord__class_Oless(X3,X4,tc_fun(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,X2)),X3),X4))
| ~ class_HOL_Oord(X2) ),
c_0_1552,
[final] ).
cnf(c_0_2030,plain,
( c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1),c_SetInterval_Oord__class_OatLeastAtMost(X2,X5,X1),tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X5))
| ~ class_Orderings_Oorder(X1) ),
c_0_1553,
[final] ).
cnf(c_0_2031,plain,
( c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1),c_SetInterval_Oord__class_OatLeastAtMost(X2,X5,X1),tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ c_HOL_Oord__class_Oless(X4,X5,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X5))
| ~ class_Orderings_Oorder(X1) ),
c_0_1554,
[final] ).
cnf(c_0_2032,plain,
( hBOOL(c_in(X1,X2,X4))
| hBOOL(c_in(X1,X3,X4))
| ~ hBOOL(c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4)) ),
c_0_1555,
[final] ).
cnf(c_0_2033,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
c_0_1556,
[final] ).
cnf(c_0_2034,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
c_0_1557,
[final] ).
cnf(c_0_2035,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
c_0_1558,
[final] ).
cnf(c_0_2036,plain,
( hBOOL(c_in(X4,X1,X3))
| c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X1),X2)) ),
c_0_1559,
[final] ).
cnf(c_0_2037,plain,
( hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(X1,X4,X3))
| c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X4),X2)) ),
c_0_1560,
[final] ).
cnf(c_0_2038,plain,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)))),
c_0_1561,
[final] ).
cnf(c_0_2039,plain,
( X1 = X2
| ~ hBOOL(c_in(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)) ),
c_0_1562,
[final] ).
cnf(c_0_2040,plain,
( X1 = X2
| X1 = X3
| c_Set_Oinsert(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) ),
c_0_1563,
[final] ).
cnf(c_0_2041,plain,
( X1 = X2
| X3 = X2
| c_Set_Oinsert(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) ),
c_0_1564,
[final] ).
cnf(c_0_2042,plain,
( X1 = X2
| X3 = X2
| c_Set_Oinsert(X3,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) ),
c_0_1565,
[final] ).
cnf(c_0_2043,plain,
( X1 = X2
| X1 = X3
| c_Set_Oinsert(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) ),
c_0_1566,
[final] ).
cnf(c_0_2044,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)),
c_0_1567,
[final] ).
cnf(c_0_2045,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_1568,
[final] ).
cnf(c_0_2046,plain,
( c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3) = X2
| ~ hBOOL(c_in(X1,X2,X3)) ),
c_0_1569,
[final] ).
cnf(c_0_2047,plain,
c_Set_Oinsert(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)),X4) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),
c_0_1570,
[final] ).
cnf(c_0_2048,plain,
( hBOOL(c_in(X2,X3,X4))
| hBOOL(c_in(X2,X1,X4))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,tc_bool)),X1),X3))
| ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) ),
c_0_1571,
[final] ).
cnf(c_0_2049,plain,
( X1 = X2
| c_Hoare__Mirabelle_Otriple_Otriple(X1,X3,X4,X5) != c_Hoare__Mirabelle_Otriple_Otriple(X2,X6,X7,X5) ),
c_0_1572,
[final] ).
cnf(c_0_2050,plain,
( X1 = X2
| c_Hoare__Mirabelle_Otriple_Otriple(X3,X1,X4,X5) != c_Hoare__Mirabelle_Otriple_Otriple(X6,X2,X7,X5) ),
c_0_1573,
[final] ).
cnf(c_0_2051,plain,
( X1 = X2
| c_Hoare__Mirabelle_Otriple_Otriple(X3,X4,X1,X5) != c_Hoare__Mirabelle_Otriple_Otriple(X6,X7,X2,X5) ),
c_0_1574,
[final] ).
cnf(c_0_2052,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_Finite__Set_Olinorder__class_OMax(X2,X1)),c_Finite__Set_Olinorder__class_OMax(X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ c_Finite__Set_Ofinite(X3,X1)
| ~ class_Orderings_Olinorder(X1) ),
c_0_1575,
[final] ).
cnf(c_0_2053,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_Finite__Set_Olinorder__class_OMin(X3,X1)),c_Finite__Set_Olinorder__class_OMin(X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ c_Finite__Set_Ofinite(X3,X1)
| ~ class_Orderings_Olinorder(X1) ),
c_0_1576,
[final] ).
cnf(c_0_2054,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,X4,tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X3) ),
c_0_1577,
[final] ).
cnf(c_0_2055,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_1578,
[final] ).
cnf(c_0_2056,plain,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X4,tc_bool)),X4)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)),X4) ),
c_0_1579,
[final] ).
cnf(c_0_2057,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X2),hAPP(X3,X5)),hAPP(X4,X5)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,X2)),X3),X4))
| ~ class_HOL_Oord(X2) ),
c_0_1580,
[final] ).
cnf(c_0_2058,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),X4),X2)) ),
c_0_1581,
[final] ).
cnf(c_0_2059,plain,
( c_HOL_Oord__class_Oless(X4,X1,X3)
| c_HOL_Oord__class_Oless(X2,X5,X3)
| ~ c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| ~ class_Orderings_Oorder(X3) ),
c_0_1582,
[final] ).
cnf(c_0_2060,plain,
( hBOOL(c_in(X4,X3,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(c_in(X4,X2,X1)) ),
c_0_1583,
[final] ).
cnf(c_0_2061,plain,
( hBOOL(c_in(X4,X3,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(c_in(X4,X2,X1)) ),
c_0_1584,
[final] ).
cnf(c_0_2062,plain,
( hBOOL(c_in(X1,X4,X3))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X2),X4)) ),
c_0_1585,
[final] ).
cnf(c_0_2063,plain,
( hBOOL(c_in(X4,X3,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(c_in(X4,X2,X1)) ),
c_0_1586,
[final] ).
cnf(c_0_2064,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X3),X4),X1))
| ~ c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| ~ class_Orderings_Oorder(X3) ),
c_0_1587,
[final] ).
cnf(c_0_2065,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X5))
| ~ c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| ~ class_Orderings_Oorder(X3) ),
c_0_1588,
[final] ).
cnf(c_0_2066,plain,
c_Lattices_Oupper__semilattice__class_Osup(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_1589,
[final] ).
cnf(c_0_2067,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X1,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = X4,
c_0_1590,
[final] ).
cnf(c_0_2068,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_1591,
[final] ).
cnf(c_0_2069,plain,
~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X3)),
c_0_1592,
[final] ).
cnf(c_0_2070,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X1,tc_bool)))) ),
c_0_1593,
[final] ).
cnf(c_0_2071,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_1594,
[final] ).
cnf(c_0_2072,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_1595,
[final] ).
cnf(c_0_2073,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1),c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X2,X4,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_Orderings_Olinorder(X1) ),
c_0_1596,
[final] ).
cnf(c_0_2074,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X1),c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X4,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_Orderings_Olinorder(X1) ),
c_0_1597,
[final] ).
cnf(c_0_2075,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1),c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X4,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_Orderings_Olinorder(X1) ),
c_0_1598,
[final] ).
cnf(c_0_2076,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X4,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_Orderings_Olinorder(X1) ),
c_0_1599,
[final] ).
cnf(c_0_2077,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X2,c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
c_0_1600,
[final] ).
cnf(c_0_2078,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_1601,
[final] ).
cnf(c_0_2079,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_1602,
[final] ).
cnf(c_0_2080,plain,
c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3) = c_Set_Oinsert(X1,X2,X3),
c_0_1603,
[final] ).
cnf(c_0_2081,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool)),X2),X3)) ),
c_0_1604,
[final] ).
cnf(c_0_2082,plain,
( c_HOL_Oord__class_Oless(X1,X4,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X2),X4)) ),
c_0_1605,
[final] ).
cnf(c_0_2083,plain,
( c_HOL_Oord__class_Oless(X2,X4,tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_fun(X1,tc_bool)) ),
c_0_1606,
[final] ).
cnf(c_0_2084,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))) ),
c_0_1607,
[final] ).
cnf(c_0_2085,plain,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X4,X2,X3),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_1608,
[final] ).
cnf(c_0_2086,plain,
( c_Set_Oimage(c_COMBK(X4,X5,X3),X2,X3,X5) = c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5)
| ~ hBOOL(c_in(X1,X2,X3)) ),
c_0_1609,
[final] ).
cnf(c_0_2087,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,X4)),X2),X1))
| ~ class_HOL_Oord(X4) ),
c_0_1610,
[final] ).
cnf(c_0_2088,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X4,tc_bool)),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)),
c_0_1611,
[final] ).
cnf(c_0_2089,plain,
( X1 = X2
| hBOOL(c_in(X1,X3,X4))
| ~ hBOOL(c_in(X1,c_Set_Oinsert(X2,X3,X4),X4)) ),
c_0_1612,
[final] ).
cnf(c_0_2090,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
c_0_1613,
[final] ).
cnf(c_0_2091,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
c_0_1614,
[final] ).
cnf(c_0_2092,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X1,X4,tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)),
c_0_1615,
[final] ).
cnf(c_0_2093,plain,
( hAPP(c_Complete__Lattice_OSup__class_OSup(X1),c_Set_Oinsert(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1)) = c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
c_0_1616,
[final] ).
cnf(c_0_2094,plain,
hBOOL(hAPP(hAPP(c_lessequals(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_1617,
[final] ).
cnf(c_0_2095,plain,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X1,tc_bool)))),
c_0_1618,
[final] ).
cnf(c_0_2096,plain,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X1,tc_bool)))),
c_0_1619,
[final] ).
cnf(c_0_2097,plain,
( hBOOL(c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
c_0_1620,
[final] ).
cnf(c_0_2098,plain,
( hBOOL(c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X4,X2,tc_fun(X3,tc_bool)),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
c_0_1621,
[final] ).
cnf(c_0_2099,plain,
( hBOOL(hAPP(X1,X4))
| hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4)) ),
c_0_1622,
[final] ).
cnf(c_0_2100,plain,
( ~ hBOOL(c_in(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
c_0_1623,
[final] ).
cnf(c_0_2101,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1),tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ class_Orderings_Oorder(X1) ),
c_0_1624,
[final] ).
cnf(c_0_2102,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X3),X4),X5))
| ~ c_HOL_Oord__class_Oless(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_1625,
[final] ).
cnf(c_0_2103,plain,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBK(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool),X3),X3,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
c_0_1626,
[final] ).
cnf(c_0_2104,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ouminus__class_Ouminus(X3,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),X3))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
c_0_1627,
[final] ).
cnf(c_0_2105,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ouminus__class_Ouminus(X3,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),X3))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
c_0_1628,
[final] ).
cnf(c_0_2106,plain,
( c_HOL_Oord__class_Oless(X1,X3,tc_fun(X4,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| ~ hBOOL(c_in(X2,X3,X4)) ),
c_0_1629,
[final] ).
cnf(c_0_2107,plain,
( X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
c_0_1630,
[final] ).
cnf(c_0_2108,plain,
( c_HOL_Oord__class_Oless(X2,X3,tc_fun(X1,tc_bool))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
c_0_1631,
[final] ).
cnf(c_0_2109,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X1,tc_bool)) = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
c_0_1632,
[final] ).
cnf(c_0_2110,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X1,tc_bool)) = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
c_0_1633,
[final] ).
cnf(c_0_2111,plain,
( hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(X2,X4)) ),
c_0_1634,
[final] ).
cnf(c_0_2112,plain,
( hBOOL(hAPP(X4,X2))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X1),X4)) ),
c_0_1635,
[final] ).
cnf(c_0_2113,plain,
hBOOL(c_in(X1,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2)),
c_0_1636,
[final] ).
cnf(c_0_2114,plain,
c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = c_Set_Oinsert(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),
c_0_1637,
[final] ).
cnf(c_0_2115,plain,
( c_Finite__Set_Ofinite(c_Set_Oimage(X3,X1,X2,X4),X4)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
c_0_1638,
[final] ).
cnf(c_0_2116,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),c_HOL_Ouminus__class_Ouminus(X3,X1)))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
c_0_1639,
[final] ).
cnf(c_0_2117,plain,
( c_HOL_Ominus__class_Ominus(c_SetInterval_Oord__class_OatLeastLessThan(X2,X4,X1),c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
c_0_1640,
[final] ).
cnf(c_0_2118,plain,
( hBOOL(c_in(X1,X2,X3))
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X2,X3),c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) = X2 ),
c_0_1641,
[final] ).
cnf(c_0_2119,plain,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X2,X1))),
c_0_1642,
[final] ).
cnf(c_0_2120,plain,
( hBOOL(c_in(X1,X2,X3))
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X4,X2,tc_fun(X3,tc_bool)),X3) ),
c_0_1643,
[final] ).
cnf(c_0_2121,plain,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_COMBK(X2,tc_fun(X3,tc_bool),X1),X1,tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
c_0_1644,
[final] ).
cnf(c_0_2122,plain,
( hBOOL(c_in(X1,c_Set_Oinsert(X4,X2,X3),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
c_0_1645,
[final] ).
cnf(c_0_2123,plain,
( hBOOL(c_in(X1,c_Set_Oinsert(X4,X2,X3),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
c_0_1646,
[final] ).
cnf(c_0_2124,plain,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X2)),
c_0_1647,
[final] ).
cnf(c_0_2125,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
c_0_1648,
[final] ).
cnf(c_0_2126,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X4,X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
c_0_1649,
[final] ).
cnf(c_0_2127,plain,
( c_Finite__Set_Ofinite(X2,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ c_Finite__Set_Ofinite(X3,X1) ),
c_0_1650,
[final] ).
cnf(c_0_2128,plain,
( c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X3),X1)) ),
c_0_1651,
[final] ).
cnf(c_0_2129,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Set_Oimage(c_COMBK(X3,X4,X2),X1,X2,X4) = c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4) ),
c_0_1652,
[final] ).
cnf(c_0_2130,plain,
( c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X4,X2,X3)) ),
c_0_1653,
[final] ).
cnf(c_0_2131,plain,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
c_0_1654,
[final] ).
cnf(c_0_2132,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
c_0_1655,
[final] ).
cnf(c_0_2133,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Set_Oimage(X4,X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
c_0_1656,
[final] ).
cnf(c_0_2134,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Set_Oimage(X3,X1,X2,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
c_0_1657,
[final] ).
cnf(c_0_2135,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_HOL_Ominus__class_Ominus(X5,X4,X1) != c_HOL_Ominus__class_Ominus(X3,X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
c_0_1658,
[final] ).
cnf(c_0_2136,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_HOL_Ominus__class_Ominus(X3,X2,X1) != c_HOL_Ominus__class_Ominus(X5,X4,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
c_0_1659,
[final] ).
cnf(c_0_2137,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBK(X3,tc_fun(X4,tc_bool),X2),X2,tc_fun(X4,tc_bool)) = X3 ),
c_0_1660,
[final] ).
cnf(c_0_2138,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X2))
| ~ class_Orderings_Oorder(X1) ),
c_0_1661,
[final] ).
cnf(c_0_2139,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_Orderings_Opreorder(X1) ),
c_0_1662,
[final] ).
cnf(c_0_2140,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,X4)),X1),X2))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,X4))
| ~ class_HOL_Oord(X4) ),
c_0_1663,
[final] ).
cnf(c_0_2141,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(c_Complete__Lattice_OInf__class_OInf(X3),X2)),X1))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
c_0_1664,
[final] ).
cnf(c_0_2142,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ouminus__class_Ouminus(X3,X1)),c_HOL_Ouminus__class_Ouminus(X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
c_0_1665,
[final] ).
cnf(c_0_2143,plain,
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X4,X3),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_1666,
[final] ).
cnf(c_0_2144,plain,
c_Set_Oimage(c_COMBK(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
c_0_1667,
[final] ).
cnf(c_0_2145,plain,
( X1 = X4
| hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4)) ),
c_0_1668,
[final] ).
cnf(c_0_2146,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X2),c_Finite__Set_Olinorder__class_OMin(X1,X2)),X3))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(c_in(X3,X1,X2))
| ~ class_Orderings_Olinorder(X2) ),
c_0_1669,
[final] ).
cnf(c_0_2147,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ouminus__class_Ouminus(X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ouminus__class_Ouminus(X3,X1)))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
c_0_1670,
[final] ).
cnf(c_0_2148,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ouminus__class_Ouminus(X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ouminus__class_Ouminus(X3,X1)))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
c_0_1671,
[final] ).
cnf(c_0_2149,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X1,tc_bool)) != X3 ),
c_0_1672,
[final] ).
cnf(c_0_2150,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X1),X2))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_1673,
[final] ).
cnf(c_0_2151,plain,
( hBOOL(c_in(X4,X2,X3))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X4,X1,X3)) ),
c_0_1674,
[final] ).
cnf(c_0_2152,plain,
( X1 = X2
| hBOOL(c_in(X3,X1,X4))
| hBOOL(c_in(X3,X2,X4))
| c_Set_Oinsert(X3,X1,X4) != c_Set_Oinsert(X3,X2,X4) ),
c_0_1675,
[final] ).
cnf(c_0_2153,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),X3),
c_0_1676,
[final] ).
cnf(c_0_2154,plain,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) = c_Set_Oinsert(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),X4),
c_0_1677,
[final] ).
cnf(c_0_2155,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_1678,
[final] ).
cnf(c_0_2156,plain,
( ~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2))
| ~ hBOOL(hAPP(X3,X1)) ),
c_0_1679,
[final] ).
cnf(c_0_2157,plain,
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
c_0_1680,
[final] ).
cnf(c_0_2158,plain,
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X4,tc_bool)),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
c_0_1681,
[final] ).
cnf(c_0_2159,plain,
( hBOOL(hAPP(X3,X1))
| ~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)) ),
c_0_1682,
[final] ).
cnf(c_0_2160,plain,
( hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),X3)) ),
c_0_1683,
[final] ).
cnf(c_0_2161,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X3),X1),hAPP(c_Complete__Lattice_OSup__class_OSup(X3),X2)))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
c_0_1684,
[final] ).
cnf(c_0_2162,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X2),X3),c_Finite__Set_Olinorder__class_OMax(X1,X2)))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(c_in(X3,X1,X2))
| ~ class_Orderings_Olinorder(X2) ),
c_0_1685,
[final] ).
cnf(c_0_2163,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Oorder(X1) ),
c_0_1686,
[final] ).
cnf(c_0_2164,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Oorder(X1) ),
c_0_1687,
[final] ).
cnf(c_0_2165,plain,
( X3 = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Oorder(X1) ),
c_0_1688,
[final] ).
cnf(c_0_2166,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X2,tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,X2,X3),
c_0_1689,
[final] ).
cnf(c_0_2167,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
c_0_1690,
[final] ).
cnf(c_0_2168,plain,
~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
c_0_1691,
[final] ).
cnf(c_0_2169,plain,
~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
c_0_1692,
[final] ).
cnf(c_0_2170,plain,
~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
c_0_1693,
[final] ).
cnf(c_0_2171,plain,
( X1 = X2
| c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) != c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) ),
c_0_1694,
[final] ).
cnf(c_0_2172,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Opreorder(X1) ),
c_0_1695,
[final] ).
cnf(c_0_2173,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1696,
[final] ).
cnf(c_0_2174,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4),X4) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4),X4)
| ~ class_Lattices_Oupper__semilattice(X4) ),
c_0_1697,
[final] ).
cnf(c_0_2175,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4),X4) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4),X4)
| ~ class_Lattices_Olattice(X4) ),
c_0_1698,
[final] ).
cnf(c_0_2176,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3)
| ~ class_Lattices_Olattice(X3) ),
c_0_1699,
[final] ).
cnf(c_0_2177,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)))
| ~ class_Lattices_Oupper__semilattice(X1) ),
c_0_1700,
[final] ).
cnf(c_0_2178,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)))
| ~ class_Lattices_Olattice(X1) ),
c_0_1701,
[final] ).
cnf(c_0_2179,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X1)))
| ~ class_Lattices_Olattice(X1) ),
c_0_1702,
[final] ).
cnf(c_0_2180,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X1)))
| ~ class_Lattices_Oupper__semilattice(X1) ),
c_0_1703,
[final] ).
cnf(c_0_2181,plain,
c_Set_Oimage(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
c_0_1704,
[final] ).
cnf(c_0_2182,plain,
c_Set_Oimage(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
c_0_1705,
[final] ).
cnf(c_0_2183,plain,
hBOOL(c_in(X1,c_Set_Oinsert(X1,X2,X3),X3)),
c_0_1706,
[final] ).
cnf(c_0_2184,plain,
hBOOL(c_in(X1,c_Set_Oinsert(X1,X2,X3),X3)),
c_0_1707,
[final] ).
cnf(c_0_2185,plain,
hBOOL(c_in(X1,c_Set_Oinsert(X1,X2,X3),X3)),
c_0_1708,
[final] ).
cnf(c_0_2186,plain,
c_Set_Oinsert(X1,c_Set_Oinsert(X2,X3,X4),X4) = c_Set_Oinsert(X2,c_Set_Oinsert(X1,X3,X4),X4),
c_0_1709,
[final] ).
cnf(c_0_2187,plain,
( c_HOL_Oord__class_Oless(X1,X4,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X2,X4,tc_fun(X3,tc_bool)) ),
c_0_1710,
[final] ).
cnf(c_0_2188,plain,
( c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X4,X5,X3) != c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_1711,
[final] ).
cnf(c_0_2189,plain,
( c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_1712,
[final] ).
cnf(c_0_2190,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X4))
| ~ class_Orderings_Opreorder(X3) ),
c_0_1713,
[final] ).
cnf(c_0_2191,plain,
( c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Orderings_Opreorder(X1) ),
c_0_1714,
[final] ).
cnf(c_0_2192,plain,
( c_HOL_Oord__class_Oless(X4,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ c_HOL_Oord__class_Oless(X4,X2,X1)
| ~ class_Orderings_Oorder(X1) ),
c_0_1715,
[final] ).
cnf(c_0_2193,plain,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X4),X1))
| ~ class_Orderings_Oorder(X3) ),
c_0_1716,
[final] ).
cnf(c_0_2194,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_1717,
[final] ).
cnf(c_0_2195,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),
c_0_1718,
[final] ).
cnf(c_0_2196,plain,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),
c_0_1719,
[final] ).
cnf(c_0_2197,plain,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),
c_0_1720,
[final] ).
cnf(c_0_2198,plain,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)
| ~ class_Orderings_Oorder(X1) ),
c_0_1721,
[final] ).
cnf(c_0_2199,plain,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Oorder(X1) ),
c_0_1722,
[final] ).
cnf(c_0_2200,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_1723,
[final] ).
cnf(c_0_2201,plain,
( hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
c_0_1724,
[final] ).
cnf(c_0_2202,plain,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X2)),
c_0_1725,
[final] ).
cnf(c_0_2203,plain,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X2)),
c_0_1726,
[final] ).
cnf(c_0_2204,plain,
( hBOOL(hAPP(X2,X1))
| ~ hBOOL(c_in(X1,c_Collect(X2,X3),X3)) ),
c_0_1727,
[final] ).
cnf(c_0_2205,plain,
( c_Finite__Set_Ofinite(X2,X3)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X3) ),
c_0_1728,
[final] ).
cnf(c_0_2206,plain,
( c_Finite__Set_Ofinite(X1,X3)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X3) ),
c_0_1729,
[final] ).
cnf(c_0_2207,plain,
( c_Complete__Lattice_Ocomplete__lattice__axioms(c_Complete__Lattice_OInf__class_OInf(X1),c_Complete__Lattice_OSup__class_OSup(X1),c_lessequals(X1),X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
c_0_1730,
[final] ).
cnf(c_0_2208,plain,
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(X1,v_x),hAPP(X2,v_x),X3) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(t_a,X3)),v_x)
| ~ class_Lattices_Olattice(X3) ),
c_0_1731,
[final] ).
cnf(c_0_2209,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_1732,
[final] ).
cnf(c_0_2210,plain,
c_Finite__Set_Ofold1(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = X2,
c_0_1733,
[final] ).
cnf(c_0_2211,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1))
| ~ class_Orderings_Opreorder(X3) ),
c_0_1734,
[final] ).
cnf(c_0_2212,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1))
| ~ class_Orderings_Olinorder(X3) ),
c_0_1735,
[final] ).
cnf(c_0_2213,plain,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
c_0_1736,
[final] ).
cnf(c_0_2214,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),X1),X1))
| ~ class_Orderings_Olinorder(X2) ),
c_0_1737,
[final] ).
cnf(c_0_2215,plain,
( c_SetInterval_Oord__class_OatLeastLessThan(X3,X2,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
c_0_1738,
[final] ).
cnf(c_0_2216,plain,
( c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X2,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
c_0_1739,
[final] ).
cnf(c_0_2217,plain,
( c_HOL_Oord__class_Oless(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1740,
[final] ).
cnf(c_0_2218,plain,
( c_HOL_Oord__class_Oless(X1,c_Lattices_Oupper__semilattice__class_Osup(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1741,
[final] ).
cnf(c_0_2219,plain,
hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X1)),
c_0_1742,
[final] ).
cnf(c_0_2220,plain,
( hBOOL(c_in(X1,X2,X3))
| c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
c_0_1743,
[final] ).
cnf(c_0_2221,plain,
( hAPP(c_Complete__Lattice_OInf__class_OInf(X1),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)) = X2
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
c_0_1744,
[final] ).
cnf(c_0_2222,plain,
( hAPP(c_Complete__Lattice_OSup__class_OSup(X1),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)) = X2
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
c_0_1745,
[final] ).
cnf(c_0_2223,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_1746,
[final] ).
cnf(c_0_2224,plain,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1747,
[final] ).
cnf(c_0_2225,plain,
( c_Finite__Set_Olinorder__class_OMax(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = X1
| ~ class_Orderings_Olinorder(X2) ),
c_0_1748,
[final] ).
cnf(c_0_2226,plain,
( c_Finite__Set_Olinorder__class_OMin(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = X1
| ~ class_Orderings_Olinorder(X2) ),
c_0_1749,
[final] ).
cnf(c_0_2227,plain,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
c_0_1750,
[final] ).
cnf(c_0_2228,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| ~ class_Orderings_Olinorder(X3) ),
c_0_1751,
[final] ).
cnf(c_0_2229,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| ~ class_Orderings_Oorder(X3) ),
c_0_1752,
[final] ).
cnf(c_0_2230,plain,
( X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
c_0_1753,
[final] ).
cnf(c_0_2231,plain,
( X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
c_0_1754,
[final] ).
cnf(c_0_2232,plain,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
c_0_1755,
[final] ).
cnf(c_0_2233,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1))
| ~ class_Orderings_Oorder(X3) ),
c_0_1756,
[final] ).
cnf(c_0_2234,plain,
( X3 = X2
| c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
c_0_1757,
[final] ).
cnf(c_0_2235,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
c_0_1758,
[final] ).
cnf(c_0_2236,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X1) = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
c_0_1759,
[final] ).
cnf(c_0_2237,plain,
( c_Set_Oinsert(X1,X2,X3) = X2
| ~ hBOOL(c_in(X1,X2,X3)) ),
c_0_1760,
[final] ).
cnf(c_0_2238,plain,
( c_HOL_Oord__class_Oless(X3,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ouminus__class_Ouminus(X3,X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
c_0_1761,
[final] ).
cnf(c_0_2239,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_1762,
[final] ).
cnf(c_0_2240,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X2,hAPP(c_Complete__Lattice_OSup__class_OSup(X1),X3),X1) = hAPP(c_Complete__Lattice_OSup__class_OSup(X1),c_Set_Oinsert(X2,X3,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
c_0_1763,
[final] ).
cnf(c_0_2241,plain,
c_Set_Ocontents(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = X1,
c_0_1764,
[final] ).
cnf(c_0_2242,plain,
c_The(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = X1,
c_0_1765,
[final] ).
cnf(c_0_2243,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1766,
[final] ).
cnf(c_0_2244,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3)
| ~ class_Lattices_Olattice(X3) ),
c_0_1767,
[final] ).
cnf(c_0_2245,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1768,
[final] ).
cnf(c_0_2246,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ class_Orderings_Oorder(X3) ),
c_0_1769,
[final] ).
cnf(c_0_2247,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ class_Orderings_Oorder(X3) ),
c_0_1770,
[final] ).
cnf(c_0_2248,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1771,
[final] ).
cnf(c_0_2249,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_1772,
[final] ).
cnf(c_0_2250,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_1773,
[final] ).
cnf(c_0_2251,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
c_0_1774,
[final] ).
cnf(c_0_2252,plain,
c_Set_Oinsert(X1,c_Set_Oinsert(X1,X2,X3),X3) = c_Set_Oinsert(X1,X2,X3),
c_0_1775,
[final] ).
cnf(c_0_2253,plain,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_1776,
[final] ).
cnf(c_0_2254,plain,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_1777,
[final] ).
cnf(c_0_2255,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X2),X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
c_0_1778,
[final] ).
cnf(c_0_2256,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X2),X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
c_0_1779,
[final] ).
cnf(c_0_2257,plain,
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
c_0_1780,
[final] ).
cnf(c_0_2258,plain,
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
c_0_1781,
[final] ).
cnf(c_0_2259,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_1782,
[final] ).
cnf(c_0_2260,plain,
( hBOOL(c_in(X2,c_Collect(X1,X3),X3))
| ~ hBOOL(hAPP(X1,X2)) ),
c_0_1783,
[final] ).
cnf(c_0_2261,plain,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
c_0_1784,
[final] ).
cnf(c_0_2262,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
c_0_1785,
[final] ).
cnf(c_0_2263,plain,
( hBOOL(hAPP(X2,X1))
| ~ hBOOL(c_in(X1,X2,X3)) ),
c_0_1786,
[final] ).
cnf(c_0_2264,plain,
( c_Finite__Set_Ofinite(X2,X3)
| ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X1,X2,X3),X3) ),
c_0_1787,
[final] ).
cnf(c_0_2265,plain,
~ c_HOL_Oord__class_Oless(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
c_0_1788,
[final] ).
cnf(c_0_2266,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) != X3
| ~ class_Lattices_Oupper__semilattice(X1) ),
c_0_1789,
[final] ).
cnf(c_0_2267,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X3),c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_1790,
[final] ).
cnf(c_0_2268,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_1791,
[final] ).
cnf(c_0_2269,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1792,
[final] ).
cnf(c_0_2270,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)
| ~ class_Orderings_Oorder(X1) ),
c_0_1793,
[final] ).
cnf(c_0_2271,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Oorder(X1) ),
c_0_1794,
[final] ).
cnf(c_0_2272,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
c_0_1795,
[final] ).
cnf(c_0_2273,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
c_0_1796,
[final] ).
cnf(c_0_2274,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_1797,
[final] ).
cnf(c_0_2275,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3) = c_HOL_Ominus__class_Ominus(X2,X1,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
c_0_1798,
[final] ).
cnf(c_0_2276,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_1799,
[final] ).
cnf(c_0_2277,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_1800,
[final] ).
cnf(c_0_2278,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_1801,
[final] ).
cnf(c_0_2279,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_1802,
[final] ).
cnf(c_0_2280,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1803,
[final] ).
cnf(c_0_2281,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1804,
[final] ).
cnf(c_0_2282,plain,
c_The(c_Finite__Set_Ofold1Set(X1,X2,X3),X3) = c_Finite__Set_Ofold1(X1,X2,X3),
c_0_1805,
[final] ).
cnf(c_0_2283,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(X2,X1,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1806,
[final] ).
cnf(c_0_2284,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_fequal(X1),X2),X3)) ),
c_0_1807,
[final] ).
cnf(c_0_2285,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
c_0_1808,
[final] ).
cnf(c_0_2286,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1))
| ~ class_Orderings_Olinorder(X3) ),
c_0_1809,
[final] ).
cnf(c_0_2287,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X2))
| c_HOL_Oord__class_Oless(X2,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
c_0_1810,
[final] ).
cnf(c_0_2288,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
c_0_1811,
[final] ).
cnf(c_0_2289,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(X1,X1,X2) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
| ~ class_Orderings_Oorder(X2) ),
c_0_1812,
[final] ).
cnf(c_0_2290,plain,
( hBOOL(c_in(X2,X1,X3))
| ~ hBOOL(hAPP(X1,X2)) ),
c_0_1813,
[final] ).
cnf(c_0_2291,plain,
c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) = c_Collect(hAPP(c_fequal(X1),X2),X1),
c_0_1814,
[final] ).
cnf(c_0_2292,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_1815,
[final] ).
cnf(c_0_2293,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_1816,
[final] ).
cnf(c_0_2294,plain,
c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X3,tc_bool)),
c_0_1817,
[final] ).
cnf(c_0_2295,plain,
( c_Finite__Set_Ofinite(c_Set_Oinsert(X3,X1,X2),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
c_0_1818,
[final] ).
cnf(c_0_2296,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1819,
[final] ).
cnf(c_0_2297,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ class_Orderings_Oorder(X3) ),
c_0_1820,
[final] ).
cnf(c_0_2298,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ class_Orderings_Oorder(X3) ),
c_0_1821,
[final] ).
cnf(c_0_2299,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1822,
[final] ).
cnf(c_0_2300,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_Orderings_Obot__class_Obot(X1)),X2))
| ~ class_Orderings_Obot(X1) ),
c_0_1823,
[final] ).
cnf(c_0_2301,plain,
c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X2),
c_0_1824,
[final] ).
cnf(c_0_2302,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_1825,
[final] ).
cnf(c_0_2303,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = X2,
c_0_1826,
[final] ).
cnf(c_0_2304,plain,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
c_0_1827,
[final] ).
cnf(c_0_2305,plain,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1,tc_fun(t_a,X2)),v_x) = c_HOL_Ouminus__class_Ouminus(hAPP(X1,v_x),X2)
| ~ class_HOL_Ouminus(X2) ),
c_0_1828,
[final] ).
cnf(c_0_2306,plain,
c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
c_0_1829,
[final] ).
cnf(c_0_2307,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Set_Oinsert(X2,X3,X1),
c_0_1830,
[final] ).
cnf(c_0_2308,plain,
~ c_HOL_Oord__class_Oless(X1,X1,tc_fun(X2,tc_bool)),
c_0_1831,
[final] ).
cnf(c_0_2309,plain,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
c_0_1832,
[final] ).
cnf(c_0_2310,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X2 = X1
| ~ class_Orderings_Olinorder(X3) ),
c_0_1833,
[final] ).
cnf(c_0_2311,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1834,
[final] ).
cnf(c_0_2312,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1835,
[final] ).
cnf(c_0_2313,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2
| ~ class_Orderings_Olinorder(X3) ),
c_0_1836,
[final] ).
cnf(c_0_2314,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
c_0_1837,
[final] ).
cnf(c_0_2315,plain,
( X1 = X2
| c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X3,tc_bool)) != c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)) ),
c_0_1838,
[final] ).
cnf(c_0_2316,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1839,
[final] ).
cnf(c_0_2317,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3)
| ~ class_Lattices_Olattice(X3) ),
c_0_1840,
[final] ).
cnf(c_0_2318,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X2))
| ~ class_Orderings_Oorder(X1) ),
c_0_1841,
[final] ).
cnf(c_0_2319,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X2))
| ~ class_Orderings_Opreorder(X1) ),
c_0_1842,
[final] ).
cnf(c_0_2320,plain,
( ~ hBOOL(hAPP(X1,X2))
| c_Collect(X1,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
c_0_1843,
[final] ).
cnf(c_0_2321,plain,
( ~ hBOOL(hAPP(X1,X2))
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_Collect(X1,X3) ),
c_0_1844,
[final] ).
cnf(c_0_2322,plain,
( hAPP(c_HOL_Ouminus__class_Ouminus(v_A,tc_fun(t_a,t_b)),v_x) = c_HOL_Ouminus__class_Ouminus(hAPP(v_A,v_x),t_b)
| ~ class_HOL_Ouminus(t_b) ),
c_0_1845,
[final] ).
cnf(c_0_2323,plain,
hAPP(c_COMBK(v_P,t_a,t_b),v_Q) = v_P,
c_0_1846,
[final] ).
cnf(c_0_2324,plain,
c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
c_0_1847,
[final] ).
cnf(c_0_2325,plain,
hBOOL(hAPP(hAPP(c_fequal(X1),X2),X2)),
c_0_1848,
[final] ).
cnf(c_0_2326,plain,
( X1 = c_Orderings_Obot__class_Obot(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X2) != c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
c_0_1849,
[final] ).
cnf(c_0_2327,plain,
( X1 = c_Orderings_Obot__class_Obot(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2) != c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
c_0_1850,
[final] ).
cnf(c_0_2328,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_1851,
[final] ).
cnf(c_0_2329,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
c_0_1852,
[final] ).
cnf(c_0_2330,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
c_0_1853,
[final] ).
cnf(c_0_2331,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
c_0_1854,
[final] ).
cnf(c_0_2332,plain,
( hAPP(c_Complete__Lattice_OSup__class_OSup(X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
c_0_1855,
[final] ).
cnf(c_0_2333,plain,
c_Lattices_Oupper__semilattice__class_Osup(X1,X1,tc_fun(X2,tc_bool)) = X1,
c_0_1856,
[final] ).
cnf(c_0_2334,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_1857,
[final] ).
cnf(c_0_2335,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(X2),X2) = X1
| ~ class_Lattices_Obounded__lattice(X2) ),
c_0_1858,
[final] ).
cnf(c_0_2336,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X1),X2,X1) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
c_0_1859,
[final] ).
cnf(c_0_2337,plain,
c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
c_0_1860,
[final] ).
cnf(c_0_2338,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X1,X2) = X1
| ~ class_Lattices_Oupper__semilattice(X2) ),
c_0_1861,
[final] ).
cnf(c_0_2339,plain,
( X1 = X2
| c_HOL_Ouminus__class_Ouminus(X1,X3) != c_HOL_Ouminus__class_Ouminus(X2,X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
c_0_1862,
[final] ).
cnf(c_0_2340,plain,
( X1 = X2
| c_HOL_Ouminus__class_Ouminus(X1,X3) != c_HOL_Ouminus__class_Ouminus(X2,X3)
| ~ class_Lattices_Oboolean__algebra(X3) ),
c_0_1863,
[final] ).
cnf(c_0_2341,plain,
c_The(hAPP(c_fequal(X1),X2),X1) = X2,
c_0_1864,
[final] ).
cnf(c_0_2342,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_1865,
[final] ).
cnf(c_0_2343,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1
| ~ class_Lattices_Oboolean__algebra(X2) ),
c_0_1866,
[final] ).
cnf(c_0_2344,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_1867,
[final] ).
cnf(c_0_2345,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_1868,
[final] ).
cnf(c_0_2346,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_1869,
[final] ).
cnf(c_0_2347,plain,
( X1 = X2
| c_Com_Ocom_OSemi(X1,X3) != c_Com_Ocom_OSemi(X2,X4) ),
c_0_1870,
[final] ).
cnf(c_0_2348,plain,
( X1 = X2
| c_Com_Ocom_OSemi(X3,X1) != c_Com_Ocom_OSemi(X4,X2) ),
c_0_1871,
[final] ).
cnf(c_0_2349,plain,
( class_Finite__Set_Ofinite_Ofinite(tc_fun(X1,X2))
| ~ class_Finite__Set_Ofinite_Ofinite(X1)
| ~ class_Finite__Set_Ofinite_Ofinite(X2) ),
c_0_1872,
[final] ).
cnf(c_0_2350,plain,
( class_HOL_Oord(tc_fun(X2,X1))
| ~ class_HOL_Oord(X1) ),
c_0_1873,
[final] ).
cnf(c_0_2351,plain,
( class_HOL_Ominus(tc_fun(X2,X1))
| ~ class_HOL_Ominus(X1) ),
c_0_1874,
[final] ).
cnf(c_0_2352,plain,
( class_HOL_Ouminus(tc_fun(X2,X1))
| ~ class_HOL_Ouminus(X1) ),
c_0_1875,
[final] ).
cnf(c_0_2353,plain,
( class_Orderings_Obot(tc_fun(X2,X1))
| ~ class_Orderings_Obot(X1) ),
c_0_1876,
[final] ).
cnf(c_0_2354,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
c_0_1877,
[final] ).
cnf(c_0_2355,plain,
( class_Lattices_Olattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
c_0_1878,
[final] ).
cnf(c_0_2356,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
c_0_1879,
[final] ).
cnf(c_0_2357,plain,
( class_Lattices_Oboolean__algebra(tc_fun(X2,X1))
| ~ class_Lattices_Oboolean__algebra(X1) ),
c_0_1880,
[final] ).
cnf(c_0_2358,plain,
( class_Lattices_Obounded__lattice(tc_fun(X2,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
c_0_1881,
[final] ).
cnf(c_0_2359,plain,
( class_Lattices_Oupper__semilattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
c_0_1882,
[final] ).
cnf(c_0_2360,plain,
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
c_0_1883,
[final] ).
cnf(c_0_2361,plain,
c_Com_Ocom_OSemi(X1,X2) != c_Com_Ocom_OSKIP,
c_0_1884,
[final] ).
cnf(c_0_2362,plain,
c_Com_Ocom_OSemi(X1,X2) != c_Com_Ocom_OSKIP,
c_0_1885,
[final] ).
cnf(c_0_2363,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ class_Finite__Set_Ofinite_Ofinite(X2) ),
c_0_1886,
[final] ).
cnf(c_0_2364,plain,
c_Collect(X1,X2) = X1,
c_0_1887,
[final] ).
cnf(c_0_2365,plain,
class_HOL_Oord(tc_bool),
c_0_1888,
[final] ).
cnf(c_0_2366,plain,
class_HOL_Ominus(tc_bool),
c_0_1889,
[final] ).
cnf(c_0_2367,plain,
class_HOL_Ouminus(tc_bool),
c_0_1890,
[final] ).
cnf(c_0_2368,plain,
class_Orderings_Obot(tc_bool),
c_0_1891,
[final] ).
cnf(c_0_2369,plain,
class_Orderings_Oorder(tc_bool),
c_0_1892,
[final] ).
cnf(c_0_2370,plain,
class_Lattices_Olattice(tc_bool),
c_0_1893,
[final] ).
cnf(c_0_2371,plain,
class_Orderings_Opreorder(tc_bool),
c_0_1894,
[final] ).
cnf(c_0_2372,plain,
class_Finite__Set_Ofinite_Ofinite(tc_bool),
c_0_1895,
[final] ).
cnf(c_0_2373,plain,
class_Lattices_Oboolean__algebra(tc_bool),
c_0_1896,
[final] ).
cnf(c_0_2374,plain,
class_Lattices_Obounded__lattice(tc_bool),
c_0_1897,
[final] ).
cnf(c_0_2375,plain,
class_Lattices_Oupper__semilattice(tc_bool),
c_0_1898,
[final] ).
cnf(c_0_2376,plain,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
c_0_1899,
[final] ).
cnf(c_0_2377,plain,
class_HOL_Oord(tc_nat),
c_0_1900,
[final] ).
cnf(c_0_2378,plain,
class_HOL_Ominus(tc_nat),
c_0_1901,
[final] ).
cnf(c_0_2379,plain,
class_Orderings_Obot(tc_nat),
c_0_1902,
[final] ).
cnf(c_0_2380,plain,
class_Orderings_Oorder(tc_nat),
c_0_1903,
[final] ).
cnf(c_0_2381,plain,
class_Lattices_Olattice(tc_nat),
c_0_1904,
[final] ).
cnf(c_0_2382,plain,
class_Orderings_Olinorder(tc_nat),
c_0_1905,
[final] ).
cnf(c_0_2383,plain,
class_Orderings_Opreorder(tc_nat),
c_0_1906,
[final] ).
cnf(c_0_2384,plain,
class_Lattices_Oupper__semilattice(tc_nat),
c_0_1907,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_1908_0,axiom,
( c_Complete__Lattice_Ocomplete__lattice(X2,X1,c_COMBC(X3,X9,X9,tc_bool),c_COMBC(X4,X9,X9,tc_bool),X6,X5,X8,X7,X9)
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_1908]) ).
cnf(c_0_1908_1,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| c_Complete__Lattice_Ocomplete__lattice(X2,X1,c_COMBC(X3,X9,X9,tc_bool),c_COMBC(X4,X9,X9,tc_bool),X6,X5,X8,X7,X9) ),
inference(literals_permutation,[status(thm)],[c_0_1908]) ).
cnf(c_0_1909_0,axiom,
( hBOOL(hAPP(hAPP(X3,c_Complete__Lattice_Ocomplete__lattice_OINFI(X1,X11,X13,X9,X12)),hAPP(X13,X10)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| ~ hBOOL(c_in(X10,X11,X12)) ),
inference(literals_permutation,[status(thm)],[c_0_1909]) ).
cnf(c_0_1909_1,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| hBOOL(hAPP(hAPP(X3,c_Complete__Lattice_Ocomplete__lattice_OINFI(X1,X11,X13,X9,X12)),hAPP(X13,X10)))
| ~ hBOOL(c_in(X10,X11,X12)) ),
inference(literals_permutation,[status(thm)],[c_0_1909]) ).
cnf(c_0_1909_2,axiom,
( ~ hBOOL(c_in(X10,X11,X12))
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| hBOOL(hAPP(hAPP(X3,c_Complete__Lattice_Ocomplete__lattice_OINFI(X1,X11,X13,X9,X12)),hAPP(X13,X10))) ),
inference(literals_permutation,[status(thm)],[c_0_1909]) ).
cnf(c_0_1910_0,axiom,
( hBOOL(hAPP(hAPP(X3,hAPP(X13,X10)),c_Complete__Lattice_Ocomplete__lattice_OSUPR(X2,X11,X13,X9,X12)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| ~ hBOOL(c_in(X10,X11,X12)) ),
inference(literals_permutation,[status(thm)],[c_0_1910]) ).
cnf(c_0_1910_1,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| hBOOL(hAPP(hAPP(X3,hAPP(X13,X10)),c_Complete__Lattice_Ocomplete__lattice_OSUPR(X2,X11,X13,X9,X12)))
| ~ hBOOL(c_in(X10,X11,X12)) ),
inference(literals_permutation,[status(thm)],[c_0_1910]) ).
cnf(c_0_1910_2,axiom,
( ~ hBOOL(c_in(X10,X11,X12))
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| hBOOL(hAPP(hAPP(X3,hAPP(X13,X10)),c_Complete__Lattice_Ocomplete__lattice_OSUPR(X2,X11,X13,X9,X12))) ),
inference(literals_permutation,[status(thm)],[c_0_1910]) ).
cnf(c_0_1911_0,axiom,
( X10 = c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool))
| c_Complete__Lattice_Ocomplete__lattice_OINFI(X1,X10,c_COMBK(X12,X9,X11),X9,X11) = X12
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_1911]) ).
cnf(c_0_1911_1,axiom,
( c_Complete__Lattice_Ocomplete__lattice_OINFI(X1,X10,c_COMBK(X12,X9,X11),X9,X11) = X12
| X10 = c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool))
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_1911]) ).
cnf(c_0_1911_2,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| c_Complete__Lattice_Ocomplete__lattice_OINFI(X1,X10,c_COMBK(X12,X9,X11),X9,X11) = X12
| X10 = c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1911]) ).
cnf(c_0_1912_0,axiom,
( X10 = c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool))
| c_Complete__Lattice_Ocomplete__lattice_OSUPR(X2,X10,c_COMBK(X12,X9,X11),X9,X11) = X12
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_1912]) ).
cnf(c_0_1912_1,axiom,
( c_Complete__Lattice_Ocomplete__lattice_OSUPR(X2,X10,c_COMBK(X12,X9,X11),X9,X11) = X12
| X10 = c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool))
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_1912]) ).
cnf(c_0_1912_2,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| c_Complete__Lattice_Ocomplete__lattice_OSUPR(X2,X10,c_COMBK(X12,X9,X11),X9,X11) = X12
| X10 = c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1912]) ).
cnf(c_0_1913_0,axiom,
( hAPP(X2,c_Set_Oinsert(X10,c_Set_Oinsert(X11,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),X9),X9)) = 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_1913]) ).
cnf(c_0_1913_1,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| hAPP(X2,c_Set_Oinsert(X10,c_Set_Oinsert(X11,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),X9),X9)) = hAPP(hAPP(X6,X10),X11) ),
inference(literals_permutation,[status(thm)],[c_0_1913]) ).
cnf(c_0_1914_0,axiom,
( hAPP(X1,c_Set_Oinsert(X10,c_Set_Oinsert(X11,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),X9),X9)) = 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_1914]) ).
cnf(c_0_1914_1,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| hAPP(X1,c_Set_Oinsert(X10,c_Set_Oinsert(X11,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),X9),X9)) = hAPP(hAPP(X5,X10),X11) ),
inference(literals_permutation,[status(thm)],[c_0_1914]) ).
cnf(c_0_1915_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_1915]) ).
cnf(c_0_1915_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_1915]) ).
cnf(c_0_1915_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_1915]) ).
cnf(c_0_1916_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_1916]) ).
cnf(c_0_1916_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_1916]) ).
cnf(c_0_1916_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_1916]) ).
cnf(c_0_1917_0,axiom,
( hAPP(X2,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),X9)) = X10
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_1917]) ).
cnf(c_0_1917_1,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| hAPP(X2,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),X9)) = X10 ),
inference(literals_permutation,[status(thm)],[c_0_1917]) ).
cnf(c_0_1918_0,axiom,
( hAPP(X1,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),X9)) = X10
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_1918]) ).
cnf(c_0_1918_1,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| hAPP(X1,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),X9)) = X10 ),
inference(literals_permutation,[status(thm)],[c_0_1918]) ).
cnf(c_0_1919_0,axiom,
( hAPP(X2,c_Set_Oinsert(X10,X11,X9)) = 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_1919]) ).
cnf(c_0_1919_1,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| hAPP(X2,c_Set_Oinsert(X10,X11,X9)) = hAPP(hAPP(X6,X10),hAPP(X2,X11)) ),
inference(literals_permutation,[status(thm)],[c_0_1919]) ).
cnf(c_0_1920_0,axiom,
( hAPP(X1,c_Set_Oinsert(X10,X11,X9)) = 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_1920]) ).
cnf(c_0_1920_1,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| hAPP(X1,c_Set_Oinsert(X10,X11,X9)) = hAPP(hAPP(X5,X10),hAPP(X1,X11)) ),
inference(literals_permutation,[status(thm)],[c_0_1920]) ).
cnf(c_0_1921_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_1921]) ).
cnf(c_0_1921_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_1921]) ).
cnf(c_0_1922_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_1922]) ).
cnf(c_0_1922_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_1922]) ).
cnf(c_0_1923_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),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_1923]) ).
cnf(c_0_1923_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),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_1923]) ).
cnf(c_0_1923_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,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(literals_permutation,[status(thm)],[c_0_1923]) ).
cnf(c_0_1924_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),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_1924]) ).
cnf(c_0_1924_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),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_1924]) ).
cnf(c_0_1924_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,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(literals_permutation,[status(thm)],[c_0_1924]) ).
cnf(c_0_1925_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,X4,X3,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(hAPP(c_COMBC(c_fequal(tc_Com_Ostate),tc_Com_Ostate,tc_Com_Ostate,tc_bool),v_sko__Hoare__Mirabelle__Xescape__2(X1,X2,X3,X4)),tc_fun(tc_Com_Ostate,tc_bool),t_a),X4,c_COMBK(hAPP(X3,v_sko__Hoare__Mirabelle__Xescape__1(X1,X2,X3,X4)),tc_fun(tc_Com_Ostate,tc_bool),t_a),t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(literals_permutation,[status(thm)],[c_0_1925]) ).
cnf(c_0_1925_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(hAPP(c_COMBC(c_fequal(tc_Com_Ostate),tc_Com_Ostate,tc_Com_Ostate,tc_bool),v_sko__Hoare__Mirabelle__Xescape__2(X1,X2,X3,X4)),tc_fun(tc_Com_Ostate,tc_bool),t_a),X4,c_COMBK(hAPP(X3,v_sko__Hoare__Mirabelle__Xescape__1(X1,X2,X3,X4)),tc_fun(tc_Com_Ostate,tc_bool),t_a),t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,X4,X3,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(literals_permutation,[status(thm)],[c_0_1925]) ).
cnf(c_0_1926_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,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),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_1926]) ).
cnf(c_0_1926_1,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),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,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),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_1926]) ).
cnf(c_0_1926_2,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),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_1926]) ).
cnf(c_0_1926_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,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),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_1926]) ).
cnf(c_0_1927_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,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),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_1927]) ).
cnf(c_0_1927_1,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),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,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),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_1927]) ).
cnf(c_0_1927_2,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),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_1927]) ).
cnf(c_0_1927_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,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),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_1927]) ).
cnf(c_0_1928_0,axiom,
( c_Nitpick_Ofold__graph_H(X4,X5,X2,hAPP(hAPP(X4,X1),X6),X3,X7)
| ~ hBOOL(c_in(X1,X2,X3))
| ~ c_Nitpick_Ofold__graph_H(X4,X5,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X6,X3,X7) ),
inference(literals_permutation,[status(thm)],[c_0_1928]) ).
cnf(c_0_1928_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| c_Nitpick_Ofold__graph_H(X4,X5,X2,hAPP(hAPP(X4,X1),X6),X3,X7)
| ~ c_Nitpick_Ofold__graph_H(X4,X5,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X6,X3,X7) ),
inference(literals_permutation,[status(thm)],[c_0_1928]) ).
cnf(c_0_1928_2,axiom,
( ~ c_Nitpick_Ofold__graph_H(X4,X5,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X6,X3,X7)
| ~ hBOOL(c_in(X1,X2,X3))
| c_Nitpick_Ofold__graph_H(X4,X5,X2,hAPP(hAPP(X4,X1),X6),X3,X7) ),
inference(literals_permutation,[status(thm)],[c_0_1928]) ).
cnf(c_0_1929_0,axiom,
( c_Finite__Set_Ofold__graph(X1,X2,X3,hAPP(hAPP(X1,X4),X6),X5,X7)
| ~ c_Finite__Set_Ofold__graph(X1,X2,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),tc_fun(X5,tc_bool)),X6,X5,X7)
| ~ hBOOL(c_in(X4,X3,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1929]) ).
cnf(c_0_1929_1,axiom,
( ~ c_Finite__Set_Ofold__graph(X1,X2,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),tc_fun(X5,tc_bool)),X6,X5,X7)
| c_Finite__Set_Ofold__graph(X1,X2,X3,hAPP(hAPP(X1,X4),X6),X5,X7)
| ~ hBOOL(c_in(X4,X3,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1929]) ).
cnf(c_0_1929_2,axiom,
( ~ hBOOL(c_in(X4,X3,X5))
| ~ c_Finite__Set_Ofold__graph(X1,X2,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),tc_fun(X5,tc_bool)),X6,X5,X7)
| c_Finite__Set_Ofold__graph(X1,X2,X3,hAPP(hAPP(X1,X4),X6),X5,X7) ),
inference(literals_permutation,[status(thm)],[c_0_1929]) ).
cnf(c_0_1930_0,axiom,
( hBOOL(c_in(X1,X2,X3))
| c_Finite__Set_Ofold__graph(X4,X5,c_Set_Oinsert(X1,X2,X3),hAPP(hAPP(X4,X1),X6),X3,X7)
| ~ c_Finite__Set_Ofold__graph(X4,X5,X2,X6,X3,X7) ),
inference(literals_permutation,[status(thm)],[c_0_1930]) ).
cnf(c_0_1930_1,axiom,
( c_Finite__Set_Ofold__graph(X4,X5,c_Set_Oinsert(X1,X2,X3),hAPP(hAPP(X4,X1),X6),X3,X7)
| hBOOL(c_in(X1,X2,X3))
| ~ c_Finite__Set_Ofold__graph(X4,X5,X2,X6,X3,X7) ),
inference(literals_permutation,[status(thm)],[c_0_1930]) ).
cnf(c_0_1930_2,axiom,
( ~ c_Finite__Set_Ofold__graph(X4,X5,X2,X6,X3,X7)
| c_Finite__Set_Ofold__graph(X4,X5,c_Set_Oinsert(X1,X2,X3),hAPP(hAPP(X4,X1),X6),X3,X7)
| hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1930]) ).
cnf(c_0_1932_0,axiom,
( hBOOL(c_in(X2,X3,X5))
| hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,c_Set_Oinsert(X2,X3,X5),X5),X4))
| ~ c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1932]) ).
cnf(c_0_1932_1,axiom,
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,c_Set_Oinsert(X2,X3,X5),X5),X4))
| hBOOL(c_in(X2,X3,X5))
| ~ c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1932]) ).
cnf(c_0_1932_2,axiom,
( ~ c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5,X5)
| hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,c_Set_Oinsert(X2,X3,X5),X5),X4))
| hBOOL(c_in(X2,X3,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1932]) ).
cnf(c_0_1933_0,axiom,
( X4 = X2
| ~ c_Finite__Set_Ofold__graph(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X4,X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1933]) ).
cnf(c_0_1933_1,axiom,
( ~ c_Finite__Set_Ofold__graph(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X4,X3,X5)
| X4 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1933]) ).
cnf(c_0_1934_0,axiom,
( c_Finite__Set_Ofinite(X3,X5)
| ~ c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1934]) ).
cnf(c_0_1934_1,axiom,
( ~ c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5,X6)
| c_Finite__Set_Ofinite(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1934]) ).
cnf(c_0_1935_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xconseq12__1(X6,X2,X5,X4)),v_sko__Hoare__Mirabelle__Xconseq12__3(X6,X2,X5,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_1935]) ).
cnf(c_0_1935_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xconseq12__1(X6,X2,X5,X4)),v_sko__Hoare__Mirabelle__Xconseq12__3(X6,X2,X5,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_1935]) ).
cnf(c_0_1935_2,axiom,
( ~ hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xconseq12__1(X6,X2,X5,X4)),v_sko__Hoare__Mirabelle__Xconseq12__3(X6,X2,X5,X4)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(literals_permutation,[status(thm)],[c_0_1935]) ).
cnf(c_0_1936_0,axiom,
( hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xconseq12__1(X5,X2,X6,X4)),v_sko__Hoare__Mirabelle__Xconseq12__2(X5,X2,X6,X4)))
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X5,X3,X6,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(literals_permutation,[status(thm)],[c_0_1936]) ).
cnf(c_0_1936_1,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X5,X3,X6,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xconseq12__1(X5,X2,X6,X4)),v_sko__Hoare__Mirabelle__Xconseq12__2(X5,X2,X6,X4)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(literals_permutation,[status(thm)],[c_0_1936]) ).
cnf(c_0_1936_2,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X5,X3,X6,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xconseq12__1(X5,X2,X6,X4)),v_sko__Hoare__Mirabelle__Xconseq12__2(X5,X2,X6,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_1936]) ).
cnf(c_0_1939_0,axiom,
( hBOOL(hAPP(hAPP(X4,X5),v_sko__Hoare__Mirabelle__Xconseq12__3(X6,X2,X7,X4)))
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X2,X5),v_sko__Hoare__Mirabelle__Xconseq12__2(X6,X2,X7,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_1939]) ).
cnf(c_0_1939_1,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X4,X5),v_sko__Hoare__Mirabelle__Xconseq12__3(X6,X2,X7,X4)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X2,X5),v_sko__Hoare__Mirabelle__Xconseq12__2(X6,X2,X7,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_1939]) ).
cnf(c_0_1939_2,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X4,X5),v_sko__Hoare__Mirabelle__Xconseq12__3(X6,X2,X7,X4)))
| ~ hBOOL(hAPP(hAPP(X2,X5),v_sko__Hoare__Mirabelle__Xconseq12__2(X6,X2,X7,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_1939]) ).
cnf(c_0_1939_3,axiom,
( ~ hBOOL(hAPP(hAPP(X2,X5),v_sko__Hoare__Mirabelle__Xconseq12__2(X6,X2,X7,X4)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X4,X5),v_sko__Hoare__Mirabelle__Xconseq12__3(X6,X2,X7,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_1939]) ).
cnf(c_0_1940_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,c_Com_Ocom_OSemi(X3,X6),X7,X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_bool)),tc_Hoare__Mirabelle_Otriple(X5)),X5)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_bool)),tc_Hoare__Mirabelle_Otriple(X5)),X5)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X4,X6,X7,X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_bool)),tc_Hoare__Mirabelle_Otriple(X5)),X5) ),
inference(literals_permutation,[status(thm)],[c_0_1940]) ).
cnf(c_0_1940_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_bool)),tc_Hoare__Mirabelle_Otriple(X5)),X5)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,c_Com_Ocom_OSemi(X3,X6),X7,X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_bool)),tc_Hoare__Mirabelle_Otriple(X5)),X5)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X4,X6,X7,X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_bool)),tc_Hoare__Mirabelle_Otriple(X5)),X5) ),
inference(literals_permutation,[status(thm)],[c_0_1940]) ).
cnf(c_0_1940_2,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X4,X6,X7,X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_bool)),tc_Hoare__Mirabelle_Otriple(X5)),X5)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_bool)),tc_Hoare__Mirabelle_Otriple(X5)),X5)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,c_Com_Ocom_OSemi(X3,X6),X7,X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_bool)),tc_Hoare__Mirabelle_Otriple(X5)),X5) ),
inference(literals_permutation,[status(thm)],[c_0_1940]) ).
cnf(c_0_1941_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool))),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1941]) ).
cnf(c_0_1941_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool))),X4))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1941]) ).
cnf(c_0_1941_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool))),X4))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1941]) ).
cnf(c_0_1942_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool))),X4))
| ~ hBOOL(c_in(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1942]) ).
cnf(c_0_1942_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool))),X4))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)))
| ~ hBOOL(c_in(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1942]) ).
cnf(c_0_1942_2,axiom,
( ~ hBOOL(c_in(X3,X2,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool))),X4))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1942]) ).
cnf(c_0_1943_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool))),X4))
| ~ hBOOL(c_in(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1943]) ).
cnf(c_0_1943_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool))),X4))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)))
| ~ hBOOL(c_in(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1943]) ).
cnf(c_0_1943_2,axiom,
( ~ hBOOL(c_in(X3,X2,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool))),X4))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1943]) ).
cnf(c_0_1944_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(X3,X6)),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X3,X4,tc_fun(X1,tc_bool))),X5))
| ~ hBOOL(c_in(X6,X2,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1944]) ).
cnf(c_0_1944_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X3,X4,tc_fun(X1,tc_bool))),X5))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(X3,X6)),X5))
| ~ hBOOL(c_in(X6,X2,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1944]) ).
cnf(c_0_1944_2,axiom,
( ~ hBOOL(c_in(X6,X2,X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X3,X4,tc_fun(X1,tc_bool))),X5))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(X3,X6)),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1944]) ).
cnf(c_0_1945_0,axiom,
( hBOOL(hAPP(hAPP(X1,v_sko__Hoare__Mirabelle__Xescape__1(X2,X1,X3,X4)),v_sko__Hoare__Mirabelle__Xescape__2(X2,X1,X3,X4)))
| c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(literals_permutation,[status(thm)],[c_0_1945]) ).
cnf(c_0_1945_1,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X1,v_sko__Hoare__Mirabelle__Xescape__1(X2,X1,X3,X4)),v_sko__Hoare__Mirabelle__Xescape__2(X2,X1,X3,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_1945]) ).
cnf(c_0_1946_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,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(literals_permutation,[status(thm)],[c_0_1946]) ).
cnf(c_0_1946_1,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),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_1946]) ).
cnf(c_0_1947_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,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(literals_permutation,[status(thm)],[c_0_1947]) ).
cnf(c_0_1947_1,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),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_1947]) ).
cnf(c_0_1948_0,axiom,
( hBOOL(c_in(hAPP(X2,X6),X5,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Set_Oimage(X2,X3,X4,X1)),X5))
| ~ hBOOL(c_in(X6,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1948]) ).
cnf(c_0_1948_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Set_Oimage(X2,X3,X4,X1)),X5))
| hBOOL(c_in(hAPP(X2,X6),X5,X1))
| ~ hBOOL(c_in(X6,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1948]) ).
cnf(c_0_1948_2,axiom,
( ~ hBOOL(c_in(X6,X3,X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Set_Oimage(X2,X3,X4,X1)),X5))
| hBOOL(c_in(hAPP(X2,X6),X5,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1948]) ).
cnf(c_0_1949_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,tc_bool)),c_Set_Oimage(X5,X2,X1,X4)),c_Set_Oimage(X5,X3,X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1949]) ).
cnf(c_0_1949_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,tc_bool)),c_Set_Oimage(X5,X2,X1,X4)),c_Set_Oimage(X5,X3,X1,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_1949]) ).
cnf(c_0_1950_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Set_Oimage(X2,X3,X4,X1)),c_Set_Oimage(X2,X5,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,tc_bool)),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1950]) ).
cnf(c_0_1950_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,tc_bool)),X3),X5))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Set_Oimage(X2,X3,X4,X1)),c_Set_Oimage(X2,X5,X4,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1950]) ).
cnf(c_0_1951_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X5,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xconseq2__1(X5,X4)),v_sko__Hoare__Mirabelle__Xconseq2__2(X5,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_1951]) ).
cnf(c_0_1951_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X5,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xconseq2__1(X5,X4)),v_sko__Hoare__Mirabelle__Xconseq2__2(X5,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_1951]) ).
cnf(c_0_1951_2,axiom,
( ~ hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xconseq2__1(X5,X4)),v_sko__Hoare__Mirabelle__Xconseq2__2(X5,X4)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X5,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(literals_permutation,[status(thm)],[c_0_1951]) ).
cnf(c_0_1952_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X5,X3,X4,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X2,v_sko__Hoare__Mirabelle__Xconseq1__1(X5,X2)),v_sko__Hoare__Mirabelle__Xconseq1__2(X5,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1952]) ).
cnf(c_0_1952_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X5,X3,X4,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X2,v_sko__Hoare__Mirabelle__Xconseq1__1(X5,X2)),v_sko__Hoare__Mirabelle__Xconseq1__2(X5,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1952]) ).
cnf(c_0_1952_2,axiom,
( ~ hBOOL(hAPP(hAPP(X2,v_sko__Hoare__Mirabelle__Xconseq1__1(X5,X2)),v_sko__Hoare__Mirabelle__Xconseq1__2(X5,X2)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X5,X3,X4,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(literals_permutation,[status(thm)],[c_0_1952]) ).
cnf(c_0_1953_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool))),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)))
| ~ hBOOL(c_in(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1953]) ).
cnf(c_0_1953_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool))),X4))
| ~ hBOOL(c_in(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1953]) ).
cnf(c_0_1953_2,axiom,
( ~ hBOOL(c_in(X3,X2,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool))),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1953]) ).
cnf(c_0_1954_0,axiom,
( hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xconseq1__1(X5,X2)),v_sko__Hoare__Mirabelle__Xconseq1__2(X5,X2)))
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X5,X3,X4,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(literals_permutation,[status(thm)],[c_0_1954]) ).
cnf(c_0_1954_1,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X5,X3,X4,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xconseq1__1(X5,X2)),v_sko__Hoare__Mirabelle__Xconseq1__2(X5,X2)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(literals_permutation,[status(thm)],[c_0_1954]) ).
cnf(c_0_1954_2,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X5,X3,X4,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xconseq1__1(X5,X2)),v_sko__Hoare__Mirabelle__Xconseq1__2(X5,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1954]) ).
cnf(c_0_1955_0,axiom,
( hBOOL(hAPP(hAPP(X4,v_sko__Hoare__Mirabelle__Xconseq2__1(X5,X4)),v_sko__Hoare__Mirabelle__Xconseq2__2(X5,X4)))
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X5,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(literals_permutation,[status(thm)],[c_0_1955]) ).
cnf(c_0_1955_1,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X5,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X4,v_sko__Hoare__Mirabelle__Xconseq2__1(X5,X4)),v_sko__Hoare__Mirabelle__Xconseq2__2(X5,X4)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(literals_permutation,[status(thm)],[c_0_1955]) ).
cnf(c_0_1955_2,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X5,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X4,v_sko__Hoare__Mirabelle__Xconseq2__1(X5,X4)),v_sko__Hoare__Mirabelle__Xconseq2__2(X5,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_1955]) ).
cnf(c_0_1957_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X1,tc_bool))),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1957]) ).
cnf(c_0_1957_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X1,tc_bool))),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1957]) ).
cnf(c_0_1957_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X1,tc_bool))),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X1,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_1957]) ).
cnf(c_0_1958_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X1,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(X3,X5,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1958]) ).
cnf(c_0_1958_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X1,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(X3,X5,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1958]) ).
cnf(c_0_1958_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X1,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(X3,X5,tc_fun(X1,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_1958]) ).
cnf(c_0_1959_0,axiom,
( c_Finite__Set_Ofinite(X4,X3)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X4),c_Set_Oimage(X5,X1,X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1959]) ).
cnf(c_0_1959_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(X4,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X4),c_Set_Oimage(X5,X1,X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1959]) ).
cnf(c_0_1959_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X4),c_Set_Oimage(X5,X1,X2,X3)))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1959]) ).
cnf(c_0_1960_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_lessequals(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_1960]) ).
cnf(c_0_1960_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X1,tc_bool))),X4))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,tc_fun(X1,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_1960]) ).
cnf(c_0_1961_0,axiom,
( c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X4,X1,X2,X5),c_Finite__Set_Osetsum(X4,X3,X2,X5),X5) = c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),X2,X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X3),X1))
| ~ class_OrderedGroup_Oab__group__add(X5) ),
inference(literals_permutation,[status(thm)],[c_0_1961]) ).
cnf(c_0_1961_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X4,X1,X2,X5),c_Finite__Set_Osetsum(X4,X3,X2,X5),X5) = c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),X2,X5)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X3),X1))
| ~ class_OrderedGroup_Oab__group__add(X5) ),
inference(literals_permutation,[status(thm)],[c_0_1961]) ).
cnf(c_0_1961_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X4,X1,X2,X5),c_Finite__Set_Osetsum(X4,X3,X2,X5),X5) = c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),X2,X5)
| ~ class_OrderedGroup_Oab__group__add(X5) ),
inference(literals_permutation,[status(thm)],[c_0_1961]) ).
cnf(c_0_1961_3,axiom,
( ~ class_OrderedGroup_Oab__group__add(X5)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X4,X1,X2,X5),c_Finite__Set_Osetsum(X4,X3,X2,X5),X5) = c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),X2,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1961]) ).
cnf(c_0_1962_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X1,tc_bool))),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,tc_fun(X1,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_1962]) ).
cnf(c_0_1962_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,tc_fun(X1,tc_bool))))
| hBOOL(hAPP(hAPP(c_lessequals(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_1962]) ).
cnf(c_0_1963_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X1,tc_bool))),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1963]) ).
cnf(c_0_1963_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X1,tc_bool))),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1963]) ).
cnf(c_0_1963_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X1,tc_bool))),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1963]) ).
cnf(c_0_1964_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X1,tc_bool))),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1964]) ).
cnf(c_0_1964_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X1,tc_bool))),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1964]) ).
cnf(c_0_1964_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X1,tc_bool))),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1964]) ).
cnf(c_0_1965_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1965]) ).
cnf(c_0_1965_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1965]) ).
cnf(c_0_1965_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1965]) ).
cnf(c_0_1965_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X1),X2))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1965]) ).
cnf(c_0_1966_0,axiom,
( hBOOL(c_in(X1,X2,X3))
| c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1966]) ).
cnf(c_0_1966_1,axiom,
( c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool))
| hBOOL(c_in(X1,X2,X3))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1966]) ).
cnf(c_0_1966_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool))
| hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1966]) ).
cnf(c_0_1966_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X4),X2))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool))
| hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1966]) ).
cnf(c_0_1967_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1967]) ).
cnf(c_0_1967_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1967]) ).
cnf(c_0_1967_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X5))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1967]) ).
cnf(c_0_1967_3,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1967]) ).
cnf(c_0_1968_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1968]) ).
cnf(c_0_1968_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1968]) ).
cnf(c_0_1968_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X2))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1968]) ).
cnf(c_0_1968_3,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1968]) ).
cnf(c_0_1969_0,axiom,
( X2 = X4
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1969]) ).
cnf(c_0_1969_1,axiom,
( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),X4))
| X2 = X4 ),
inference(literals_permutation,[status(thm)],[c_0_1969]) ).
cnf(c_0_1970_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X1,tc_bool))),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1970]) ).
cnf(c_0_1970_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X1,tc_bool))),X4))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1970]) ).
cnf(c_0_1971_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X1,tc_bool))),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1971]) ).
cnf(c_0_1971_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X1,tc_bool))),X4))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1971]) ).
cnf(c_0_1972_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastLessThan(X4,X5,X1)))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1972]) ).
cnf(c_0_1972_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastLessThan(X4,X5,X1)))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1972]) ).
cnf(c_0_1972_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastLessThan(X4,X5,X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1972]) ).
cnf(c_0_1972_3,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastLessThan(X4,X5,X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1972]) ).
cnf(c_0_1973_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastLessThan(X4,X5,X1)))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1973]) ).
cnf(c_0_1973_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X5))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastLessThan(X4,X5,X1)))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1973]) ).
cnf(c_0_1973_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastLessThan(X4,X5,X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X5))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1973]) ).
cnf(c_0_1973_3,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastLessThan(X4,X5,X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X5))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1973]) ).
cnf(c_0_1974_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,tc_bool)),hAPP(X5,X1)),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_1974]) ).
cnf(c_0_1974_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,tc_bool)),hAPP(X5,X1)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X5,X3,tc_fun(X4,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_1974]) ).
cnf(c_0_1975_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_1975]) ).
cnf(c_0_1975_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_1975]) ).
cnf(c_0_1975_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_1975]) ).
cnf(c_0_1976_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_1976]) ).
cnf(c_0_1976_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_1976]) ).
cnf(c_0_1976_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_1976]) ).
cnf(c_0_1977_0,axiom,
( c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2,X5) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X4,X1,X2,X5),hAPP(X4,X3),X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(c_in(X3,X1,X2))
| ~ class_OrderedGroup_Oab__group__add(X5) ),
inference(literals_permutation,[status(thm)],[c_0_1977]) ).
cnf(c_0_1977_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2,X5) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X4,X1,X2,X5),hAPP(X4,X3),X5)
| ~ hBOOL(c_in(X3,X1,X2))
| ~ class_OrderedGroup_Oab__group__add(X5) ),
inference(literals_permutation,[status(thm)],[c_0_1977]) ).
cnf(c_0_1977_2,axiom,
( ~ hBOOL(c_in(X3,X1,X2))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2,X5) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X4,X1,X2,X5),hAPP(X4,X3),X5)
| ~ class_OrderedGroup_Oab__group__add(X5) ),
inference(literals_permutation,[status(thm)],[c_0_1977]) ).
cnf(c_0_1977_3,axiom,
( ~ class_OrderedGroup_Oab__group__add(X5)
| ~ hBOOL(c_in(X3,X1,X2))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2,X5) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X4,X1,X2,X5),hAPP(X4,X3),X5) ),
inference(literals_permutation,[status(thm)],[c_0_1977]) ).
cnf(c_0_1978_0,axiom,
( c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2,X5) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X4,X1,X2,X5),hAPP(X4,X3),X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(c_in(X3,X1,X2))
| ~ class_Ring__and__Field_Oring(X5) ),
inference(literals_permutation,[status(thm)],[c_0_1978]) ).
cnf(c_0_1978_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2,X5) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X4,X1,X2,X5),hAPP(X4,X3),X5)
| ~ hBOOL(c_in(X3,X1,X2))
| ~ class_Ring__and__Field_Oring(X5) ),
inference(literals_permutation,[status(thm)],[c_0_1978]) ).
cnf(c_0_1978_2,axiom,
( ~ hBOOL(c_in(X3,X1,X2))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2,X5) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X4,X1,X2,X5),hAPP(X4,X3),X5)
| ~ class_Ring__and__Field_Oring(X5) ),
inference(literals_permutation,[status(thm)],[c_0_1978]) ).
cnf(c_0_1978_3,axiom,
( ~ class_Ring__and__Field_Oring(X5)
| ~ hBOOL(c_in(X3,X1,X2))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2,X5) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X4,X1,X2,X5),hAPP(X4,X3),X5) ),
inference(literals_permutation,[status(thm)],[c_0_1978]) ).
cnf(c_0_1980_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X4,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1980]) ).
cnf(c_0_1980_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X4,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1980]) ).
cnf(c_0_1980_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X4,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1980]) ).
cnf(c_0_1980_3,axiom,
( ~ hBOOL(c_in(X4,X1,X3))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1980]) ).
cnf(c_0_1981_0,axiom,
( hBOOL(c_in(X1,X2,X3))
| c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1981]) ).
cnf(c_0_1981_1,axiom,
( c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool))
| hBOOL(c_in(X1,X2,X3))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1981]) ).
cnf(c_0_1981_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool))
| hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1981]) ).
cnf(c_0_1981_3,axiom,
( ~ hBOOL(c_in(X1,X4,X3))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool))
| hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1981]) ).
cnf(c_0_1983_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X1,tc_bool))),c_HOL_Ouminus__class_Ouminus(X3,tc_fun(X1,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_1983]) ).
cnf(c_0_1983_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X1,tc_bool))),c_HOL_Ouminus__class_Ouminus(X3,tc_fun(X1,tc_bool))))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1983]) ).
cnf(c_0_1984_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Set_Oinsert(X2,X3,X1)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1984]) ).
cnf(c_0_1984_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Set_Oinsert(X2,X3,X1)),X4))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1984]) ).
cnf(c_0_1985_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_1985]) ).
cnf(c_0_1985_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_1985]) ).
cnf(c_0_1985_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_1985]) ).
cnf(c_0_1986_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_1986]) ).
cnf(c_0_1986_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_1986]) ).
cnf(c_0_1986_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_1986]) ).
cnf(c_0_1987_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Set_Oinsert(X4,X2,X1)),c_Set_Oinsert(X4,X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1987]) ).
cnf(c_0_1987_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Set_Oinsert(X4,X2,X1)),c_Set_Oinsert(X4,X3,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1987]) ).
cnf(c_0_1988_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X4),hAPP(X5,X1)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X5,X3,X4)))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1988]) ).
cnf(c_0_1988_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(hAPP(hAPP(c_lessequals(X4),hAPP(X5,X1)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X5,X3,X4)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1988]) ).
cnf(c_0_1988_2,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X4)
| ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(hAPP(hAPP(c_lessequals(X4),hAPP(X5,X1)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X5,X3,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_1988]) ).
cnf(c_0_1989_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_Set_Oinsert(X1,X4,X3)),X2))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1989]) ).
cnf(c_0_1989_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_Set_Oinsert(X1,X4,X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1989]) ).
cnf(c_0_1989_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X4),X2))
| ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_Set_Oinsert(X1,X4,X3)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1989]) ).
cnf(c_0_1991_0,axiom,
( hBOOL(c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5))
| ~ hBOOL(c_in(X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1991]) ).
cnf(c_0_1991_1,axiom,
( ~ hBOOL(c_in(X2,X3,X4))
| hBOOL(c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1991]) ).
cnf(c_0_1992_0,axiom,
( hBOOL(c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5))
| ~ hBOOL(c_in(X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1992]) ).
cnf(c_0_1992_1,axiom,
( ~ hBOOL(c_in(X2,X3,X4))
| hBOOL(c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1992]) ).
cnf(c_0_1993_0,axiom,
( hBOOL(c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1993]) ).
cnf(c_0_1993_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1993]) ).
cnf(c_0_1994_0,axiom,
( hBOOL(c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1994]) ).
cnf(c_0_1994_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1994]) ).
cnf(c_0_1996_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1996]) ).
cnf(c_0_1996_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1996]) ).
cnf(c_0_1996_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X5,X1)))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1996]) ).
cnf(c_0_1996_3,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X5,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1996]) ).
cnf(c_0_1997_0,axiom,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| X2 = c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1997]) ).
cnf(c_0_1997_1,axiom,
( X2 = c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1997]) ).
cnf(c_0_1997_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)))
| X2 = c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1997]) ).
cnf(c_0_1998_0,axiom,
( hBOOL(c_in(X2,X4,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Set_Oinsert(X2,X3,X1)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1998]) ).
cnf(c_0_1998_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Set_Oinsert(X2,X3,X1)),X4))
| hBOOL(c_in(X2,X4,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1998]) ).
cnf(c_0_1999_0,axiom,
( hBOOL(c_in(X2,X3,X4))
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| ~ hBOOL(c_in(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1999]) ).
cnf(c_0_1999_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool))
| hBOOL(c_in(X2,X3,X4))
| ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| ~ hBOOL(c_in(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1999]) ).
cnf(c_0_1999_2,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool))
| hBOOL(c_in(X2,X3,X4))
| ~ hBOOL(c_in(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1999]) ).
cnf(c_0_1999_3,axiom,
( ~ hBOOL(c_in(X2,X1,X4))
| ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool))
| hBOOL(c_in(X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1999]) ).
cnf(c_0_2000_0,axiom,
( hBOOL(c_in(X3,X1,X2))
| c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2,X5) = c_Finite__Set_Osetsum(X4,X1,X2,X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Oab__group__add(X5) ),
inference(literals_permutation,[status(thm)],[c_0_2000]) ).
cnf(c_0_2000_1,axiom,
( c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2,X5) = c_Finite__Set_Osetsum(X4,X1,X2,X5)
| hBOOL(c_in(X3,X1,X2))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Oab__group__add(X5) ),
inference(literals_permutation,[status(thm)],[c_0_2000]) ).
cnf(c_0_2000_2,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2,X5) = c_Finite__Set_Osetsum(X4,X1,X2,X5)
| hBOOL(c_in(X3,X1,X2))
| ~ class_OrderedGroup_Oab__group__add(X5) ),
inference(literals_permutation,[status(thm)],[c_0_2000]) ).
cnf(c_0_2000_3,axiom,
( ~ class_OrderedGroup_Oab__group__add(X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2,X5) = c_Finite__Set_Osetsum(X4,X1,X2,X5)
| hBOOL(c_in(X3,X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2000]) ).
cnf(c_0_2001_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2001]) ).
cnf(c_0_2001_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2001]) ).
cnf(c_0_2001_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2001]) ).
cnf(c_0_2002_0,axiom,
( hBOOL(c_in(X1,X2,X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X2),c_Set_Oinsert(X1,X4,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2002]) ).
cnf(c_0_2002_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X2),X4))
| hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X2),c_Set_Oinsert(X1,X4,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2002]) ).
cnf(c_0_2002_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X2),c_Set_Oinsert(X1,X4,X3)))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X2),X4))
| hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2002]) ).
cnf(c_0_2003_0,axiom,
( hBOOL(c_in(X3,X2,X1))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2003]) ).
cnf(c_0_2003_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4))
| hBOOL(c_in(X3,X2,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2003]) ).
cnf(c_0_2003_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4))
| hBOOL(c_in(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2003]) ).
cnf(c_0_2004_0,axiom,
( hBOOL(c_in(X1,X2,X3))
| c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3,tc_nat) = c_Finite__Set_Osetsum(X4,X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2004]) ).
cnf(c_0_2004_1,axiom,
( c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3,tc_nat) = c_Finite__Set_Osetsum(X4,X2,X3,tc_nat)
| hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2004]) ).
cnf(c_0_2005_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ouminus__class_Ouminus(X3,tc_fun(X1,tc_bool))),c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2005]) ).
cnf(c_0_2005_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ouminus__class_Ouminus(X3,tc_fun(X1,tc_bool))),c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X1,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_2005]) ).
cnf(c_0_2006_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ouminus__class_Ouminus(X3,tc_fun(X1,tc_bool))),c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2006]) ).
cnf(c_0_2006_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ouminus__class_Ouminus(X3,tc_fun(X1,tc_bool))),c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X1,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_2006]) ).
cnf(c_0_2008_0,axiom,
( c_HOL_Ominus__class_Ominus(X3,c_HOL_Ominus__class_Ominus(X4,X2,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2008]) ).
cnf(c_0_2008_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| c_HOL_Ominus__class_Ominus(X3,c_HOL_Ominus__class_Ominus(X4,X2,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2008]) ).
cnf(c_0_2008_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| c_HOL_Ominus__class_Ominus(X3,c_HOL_Ominus__class_Ominus(X4,X2,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2008]) ).
cnf(c_0_2009_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_2009]) ).
cnf(c_0_2009_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_2009]) ).
cnf(c_0_2009_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_2009]) ).
cnf(c_0_2009_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_2009]) ).
cnf(c_0_2010_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(X4,X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2010]) ).
cnf(c_0_2010_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| c_Lattices_Oupper__semilattice__class_Osup(hAPP(X4,X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2010]) ).
cnf(c_0_2012_0,axiom,
( hBOOL(c_in(X1,X2,X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X2),c_Set_Oinsert(X1,X4,X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2012]) ).
cnf(c_0_2012_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X2),c_Set_Oinsert(X1,X4,X3)))
| hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2012]) ).
cnf(c_0_2012_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X2),X4))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X2),c_Set_Oinsert(X1,X4,X3)))
| hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2012]) ).
cnf(c_0_2013_0,axiom,
( hBOOL(c_in(X1,X2,X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X2),c_Set_Oinsert(X1,X4,X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2013]) ).
cnf(c_0_2013_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X2),c_Set_Oinsert(X1,X4,X3)))
| hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2013]) ).
cnf(c_0_2013_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X2),X4))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X2),c_Set_Oinsert(X1,X4,X3)))
| hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2013]) ).
cnf(c_0_2016_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2016]) ).
cnf(c_0_2016_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2016]) ).
cnf(c_0_2016_2,axiom,
( ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2016]) ).
cnf(c_0_2018_0,axiom,
( c_Set_Oinsert(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5) = c_Set_Oimage(X4,X2,X3,X5)
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2018]) ).
cnf(c_0_2018_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| c_Set_Oinsert(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5) = c_Set_Oimage(X4,X2,X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2018]) ).
cnf(c_0_2019_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X4,X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2019]) ).
cnf(c_0_2019_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X4,X3,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2019]) ).
cnf(c_0_2020_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)),X4))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2020]) ).
cnf(c_0_2020_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2020]) ).
cnf(c_0_2020_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2020]) ).
cnf(c_0_2021_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)),X4))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2021]) ).
cnf(c_0_2021_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2021]) ).
cnf(c_0_2021_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2021]) ).
cnf(c_0_2022_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)),X4))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2022]) ).
cnf(c_0_2022_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2022]) ).
cnf(c_0_2022_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2022]) ).
cnf(c_0_2023_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)),X4))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2023]) ).
cnf(c_0_2023_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2023]) ).
cnf(c_0_2023_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2023]) ).
cnf(c_0_2024_0,axiom,
( X3 = c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2)
| ~ hBOOL(hAPP(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2024]) ).
cnf(c_0_2024_1,axiom,
( ~ hBOOL(hAPP(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X3))
| X3 = c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2024]) ).
cnf(c_0_2026_0,axiom,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2026]) ).
cnf(c_0_2026_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2026]) ).
cnf(c_0_2026_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_2026]) ).
cnf(c_0_2027_0,axiom,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2027]) ).
cnf(c_0_2027_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2027]) ).
cnf(c_0_2027_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_2027]) ).
cnf(c_0_2029_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,X2)),X4),X3))
| c_HOL_Oord__class_Oless(X3,X4,tc_fun(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,X2)),X3),X4))
| ~ class_HOL_Oord(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2029]) ).
cnf(c_0_2029_1,axiom,
( c_HOL_Oord__class_Oless(X3,X4,tc_fun(X1,X2))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,X2)),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,X2)),X3),X4))
| ~ class_HOL_Oord(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2029]) ).
cnf(c_0_2029_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,X2)),X3),X4))
| c_HOL_Oord__class_Oless(X3,X4,tc_fun(X1,X2))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,X2)),X4),X3))
| ~ class_HOL_Oord(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2029]) ).
cnf(c_0_2029_3,axiom,
( ~ class_HOL_Oord(X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,X2)),X3),X4))
| c_HOL_Oord__class_Oless(X3,X4,tc_fun(X1,X2))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,X2)),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2029]) ).
cnf(c_0_2030_0,axiom,
( c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1),c_SetInterval_Oord__class_OatLeastAtMost(X2,X5,X1),tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X5))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2030]) ).
cnf(c_0_2030_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1),c_SetInterval_Oord__class_OatLeastAtMost(X2,X5,X1),tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X5))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2030]) ).
cnf(c_0_2030_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1),c_SetInterval_Oord__class_OatLeastAtMost(X2,X5,X1),tc_fun(X1,tc_bool))
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X5))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2030]) ).
cnf(c_0_2030_3,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1),c_SetInterval_Oord__class_OatLeastAtMost(X2,X5,X1),tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X5))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2030]) ).
cnf(c_0_2030_4,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X5))
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1),c_SetInterval_Oord__class_OatLeastAtMost(X2,X5,X1),tc_fun(X1,tc_bool))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2030]) ).
cnf(c_0_2030_5,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X5))
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1),c_SetInterval_Oord__class_OatLeastAtMost(X2,X5,X1),tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2030]) ).
cnf(c_0_2031_0,axiom,
( c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1),c_SetInterval_Oord__class_OatLeastAtMost(X2,X5,X1),tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ c_HOL_Oord__class_Oless(X4,X5,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X5))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2031]) ).
cnf(c_0_2031_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1),c_SetInterval_Oord__class_OatLeastAtMost(X2,X5,X1),tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ c_HOL_Oord__class_Oless(X4,X5,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X5))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2031]) ).
cnf(c_0_2031_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1),c_SetInterval_Oord__class_OatLeastAtMost(X2,X5,X1),tc_fun(X1,tc_bool))
| ~ c_HOL_Oord__class_Oless(X4,X5,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X5))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2031]) ).
cnf(c_0_2031_3,axiom,
( ~ c_HOL_Oord__class_Oless(X4,X5,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1),c_SetInterval_Oord__class_OatLeastAtMost(X2,X5,X1),tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X5))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2031]) ).
cnf(c_0_2031_4,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X5))
| ~ c_HOL_Oord__class_Oless(X4,X5,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1),c_SetInterval_Oord__class_OatLeastAtMost(X2,X5,X1),tc_fun(X1,tc_bool))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2031]) ).
cnf(c_0_2031_5,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X5))
| ~ c_HOL_Oord__class_Oless(X4,X5,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1),c_SetInterval_Oord__class_OatLeastAtMost(X2,X5,X1),tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2031]) ).
cnf(c_0_2032_0,axiom,
( hBOOL(c_in(X1,X2,X4))
| hBOOL(c_in(X1,X3,X4))
| ~ hBOOL(c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2032]) ).
cnf(c_0_2032_1,axiom,
( hBOOL(c_in(X1,X3,X4))
| hBOOL(c_in(X1,X2,X4))
| ~ hBOOL(c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2032]) ).
cnf(c_0_2032_2,axiom,
( ~ hBOOL(c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4))
| hBOOL(c_in(X1,X3,X4))
| hBOOL(c_in(X1,X2,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2032]) ).
cnf(c_0_2033_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2033]) ).
cnf(c_0_2033_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2033]) ).
cnf(c_0_2033_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1)),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2033]) ).
cnf(c_0_2033_3,axiom,
( ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2033]) ).
cnf(c_0_2034_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2034]) ).
cnf(c_0_2034_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2034]) ).
cnf(c_0_2034_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1)),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2034]) ).
cnf(c_0_2034_3,axiom,
( ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2034]) ).
cnf(c_0_2035_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2035]) ).
cnf(c_0_2035_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2035]) ).
cnf(c_0_2035_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1)),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2035]) ).
cnf(c_0_2035_3,axiom,
( ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2035]) ).
cnf(c_0_2036_0,axiom,
( hBOOL(c_in(X4,X1,X3))
| c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2036]) ).
cnf(c_0_2036_1,axiom,
( c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| hBOOL(c_in(X4,X1,X3))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2036]) ).
cnf(c_0_2036_2,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| hBOOL(c_in(X4,X1,X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2036]) ).
cnf(c_0_2036_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X1),X2))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| hBOOL(c_in(X4,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2036]) ).
cnf(c_0_2037_0,axiom,
( hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(X1,X4,X3))
| c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2037]) ).
cnf(c_0_2037_1,axiom,
( hBOOL(c_in(X1,X4,X3))
| hBOOL(c_in(X1,X2,X3))
| c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2037]) ).
cnf(c_0_2037_2,axiom,
( c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool))
| hBOOL(c_in(X1,X4,X3))
| hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2037]) ).
cnf(c_0_2037_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X4),X2))
| c_HOL_Oord__class_Oless(X4,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool))
| hBOOL(c_in(X1,X4,X3))
| hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2037]) ).
cnf(c_0_2039_0,axiom,
( X1 = X2
| ~ hBOOL(c_in(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2039]) ).
cnf(c_0_2039_1,axiom,
( ~ hBOOL(c_in(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2039]) ).
cnf(c_0_2040_0,axiom,
( X1 = X2
| X1 = X3
| c_Set_Oinsert(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) ),
inference(literals_permutation,[status(thm)],[c_0_2040]) ).
cnf(c_0_2040_1,axiom,
( X1 = X3
| X1 = X2
| c_Set_Oinsert(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) ),
inference(literals_permutation,[status(thm)],[c_0_2040]) ).
cnf(c_0_2040_2,axiom,
( c_Set_Oinsert(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5)
| X1 = X3
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2040]) ).
cnf(c_0_2041_0,axiom,
( X1 = X2
| X3 = X2
| c_Set_Oinsert(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2041]) ).
cnf(c_0_2041_1,axiom,
( X3 = X2
| X1 = X2
| c_Set_Oinsert(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2041]) ).
cnf(c_0_2041_2,axiom,
( c_Set_Oinsert(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4)
| X3 = X2
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2041]) ).
cnf(c_0_2042_0,axiom,
( X1 = X2
| X3 = X2
| c_Set_Oinsert(X3,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2042]) ).
cnf(c_0_2042_1,axiom,
( X3 = X2
| X1 = X2
| c_Set_Oinsert(X3,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2042]) ).
cnf(c_0_2042_2,axiom,
( c_Set_Oinsert(X3,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4)
| X3 = X2
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2042]) ).
cnf(c_0_2043_0,axiom,
( X1 = X2
| X1 = X3
| c_Set_Oinsert(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) ),
inference(literals_permutation,[status(thm)],[c_0_2043]) ).
cnf(c_0_2043_1,axiom,
( X1 = X3
| X1 = X2
| c_Set_Oinsert(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) ),
inference(literals_permutation,[status(thm)],[c_0_2043]) ).
cnf(c_0_2043_2,axiom,
( c_Set_Oinsert(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5)
| X1 = X3
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2043]) ).
cnf(c_0_2045_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_2045]) ).
cnf(c_0_2045_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_2045]) ).
cnf(c_0_2046_0,axiom,
( c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3) = X2
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2046]) ).
cnf(c_0_2046_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2046]) ).
cnf(c_0_2048_0,axiom,
( hBOOL(c_in(X2,X3,X4))
| hBOOL(c_in(X2,X1,X4))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,tc_bool)),X1),X3))
| ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2048]) ).
cnf(c_0_2048_1,axiom,
( hBOOL(c_in(X2,X1,X4))
| hBOOL(c_in(X2,X3,X4))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,tc_bool)),X1),X3))
| ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2048]) ).
cnf(c_0_2048_2,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,tc_bool)),X1),X3))
| hBOOL(c_in(X2,X1,X4))
| hBOOL(c_in(X2,X3,X4))
| ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2048]) ).
cnf(c_0_2048_3,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,tc_bool)),X1),X3))
| hBOOL(c_in(X2,X1,X4))
| hBOOL(c_in(X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2048]) ).
cnf(c_0_2049_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_2049]) ).
cnf(c_0_2049_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_2049]) ).
cnf(c_0_2050_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_2050]) ).
cnf(c_0_2050_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_2050]) ).
cnf(c_0_2051_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_2051]) ).
cnf(c_0_2051_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_2051]) ).
cnf(c_0_2052_0,axiom,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_Finite__Set_Olinorder__class_OMax(X2,X1)),c_Finite__Set_Olinorder__class_OMax(X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ c_Finite__Set_Ofinite(X3,X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2052]) ).
cnf(c_0_2052_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_Finite__Set_Olinorder__class_OMax(X2,X1)),c_Finite__Set_Olinorder__class_OMax(X3,X1)))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ c_Finite__Set_Ofinite(X3,X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2052]) ).
cnf(c_0_2052_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_Finite__Set_Olinorder__class_OMax(X2,X1)),c_Finite__Set_Olinorder__class_OMax(X3,X1)))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ c_Finite__Set_Ofinite(X3,X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2052]) ).
cnf(c_0_2052_3,axiom,
( ~ c_Finite__Set_Ofinite(X3,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_Finite__Set_Olinorder__class_OMax(X2,X1)),c_Finite__Set_Olinorder__class_OMax(X3,X1)))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2052]) ).
cnf(c_0_2052_4,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_Finite__Set_Ofinite(X3,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_Finite__Set_Olinorder__class_OMax(X2,X1)),c_Finite__Set_Olinorder__class_OMax(X3,X1)))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2052]) ).
cnf(c_0_2053_0,axiom,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_Finite__Set_Olinorder__class_OMin(X3,X1)),c_Finite__Set_Olinorder__class_OMin(X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ c_Finite__Set_Ofinite(X3,X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2053]) ).
cnf(c_0_2053_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_Finite__Set_Olinorder__class_OMin(X3,X1)),c_Finite__Set_Olinorder__class_OMin(X2,X1)))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ c_Finite__Set_Ofinite(X3,X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2053]) ).
cnf(c_0_2053_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_Finite__Set_Olinorder__class_OMin(X3,X1)),c_Finite__Set_Olinorder__class_OMin(X2,X1)))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ c_Finite__Set_Ofinite(X3,X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2053]) ).
cnf(c_0_2053_3,axiom,
( ~ c_Finite__Set_Ofinite(X3,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_Finite__Set_Olinorder__class_OMin(X3,X1)),c_Finite__Set_Olinorder__class_OMin(X2,X1)))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2053]) ).
cnf(c_0_2053_4,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_Finite__Set_Ofinite(X3,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_Finite__Set_Olinorder__class_OMin(X3,X1)),c_Finite__Set_Olinorder__class_OMin(X2,X1)))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2053]) ).
cnf(c_0_2054_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,X4,tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2054]) ).
cnf(c_0_2054_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,X4,tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2054]) ).
cnf(c_0_2054_2,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,X4,tc_Hoare__Mirabelle_Otriple(X3)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2054]) ).
cnf(c_0_2055_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_2055]) ).
cnf(c_0_2055_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_2055]) ).
cnf(c_0_2056_0,axiom,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X4,tc_bool)),X4)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2056]) ).
cnf(c_0_2056_1,axiom,
( ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)),X4)
| c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X4,tc_bool)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2056]) ).
cnf(c_0_2057_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X2),hAPP(X3,X5)),hAPP(X4,X5)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,X2)),X3),X4))
| ~ class_HOL_Oord(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2057]) ).
cnf(c_0_2057_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,X2)),X3),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X2),hAPP(X3,X5)),hAPP(X4,X5)))
| ~ class_HOL_Oord(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2057]) ).
cnf(c_0_2057_2,axiom,
( ~ class_HOL_Oord(X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,X2)),X3),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X2),hAPP(X3,X5)),hAPP(X4,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_2057]) ).
cnf(c_0_2058_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2058]) ).
cnf(c_0_2058_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2058]) ).
cnf(c_0_2058_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),X4),X2))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2058]) ).
cnf(c_0_2059_0,axiom,
( c_HOL_Oord__class_Oless(X4,X1,X3)
| c_HOL_Oord__class_Oless(X2,X5,X3)
| ~ c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2059]) ).
cnf(c_0_2059_1,axiom,
( c_HOL_Oord__class_Oless(X2,X5,X3)
| c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2059]) ).
cnf(c_0_2059_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X2,X5,X3)
| c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2059]) ).
cnf(c_0_2059_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| ~ c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X2,X5,X3)
| c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2059]) ).
cnf(c_0_2059_4,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| ~ c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X2,X5,X3)
| c_HOL_Oord__class_Oless(X4,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2059]) ).
cnf(c_0_2060_0,axiom,
( hBOOL(c_in(X4,X3,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(c_in(X4,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2060]) ).
cnf(c_0_2060_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(c_in(X4,X3,X1))
| ~ hBOOL(c_in(X4,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2060]) ).
cnf(c_0_2060_2,axiom,
( ~ hBOOL(c_in(X4,X2,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(c_in(X4,X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2060]) ).
cnf(c_0_2061_0,axiom,
( hBOOL(c_in(X4,X3,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(c_in(X4,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2061]) ).
cnf(c_0_2061_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(c_in(X4,X3,X1))
| ~ hBOOL(c_in(X4,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2061]) ).
cnf(c_0_2061_2,axiom,
( ~ hBOOL(c_in(X4,X2,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(c_in(X4,X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2061]) ).
cnf(c_0_2062_0,axiom,
( hBOOL(c_in(X1,X4,X3))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2062]) ).
cnf(c_0_2062_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(X1,X4,X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2062]) ).
cnf(c_0_2062_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X2),X4))
| ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2062]) ).
cnf(c_0_2063_0,axiom,
( hBOOL(c_in(X4,X3,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(c_in(X4,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2063]) ).
cnf(c_0_2063_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(c_in(X4,X3,X1))
| ~ hBOOL(c_in(X4,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2063]) ).
cnf(c_0_2063_2,axiom,
( ~ hBOOL(c_in(X4,X2,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(c_in(X4,X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2063]) ).
cnf(c_0_2064_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X3),X4),X1))
| ~ c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2064]) ).
cnf(c_0_2064_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_lessequals(X3),X4),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2064]) ).
cnf(c_0_2064_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| ~ c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_lessequals(X3),X4),X1))
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2064]) ).
cnf(c_0_2064_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| ~ c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_lessequals(X3),X4),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2064]) ).
cnf(c_0_2065_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X5))
| ~ c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2065]) ).
cnf(c_0_2065_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2065]) ).
cnf(c_0_2065_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| ~ c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X5))
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2065]) ).
cnf(c_0_2065_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| ~ c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2065]) ).
cnf(c_0_2070_0,axiom,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X1,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_2070]) ).
cnf(c_0_2070_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X1,tc_bool))))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2070]) ).
cnf(c_0_2071_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_2071]) ).
cnf(c_0_2071_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_2071]) ).
cnf(c_0_2071_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_2071]) ).
cnf(c_0_2072_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_2072]) ).
cnf(c_0_2072_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_2072]) ).
cnf(c_0_2072_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_2072]) ).
cnf(c_0_2073_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1),c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X2,X4,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2073]) ).
cnf(c_0_2073_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1),c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X2,X4,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2073]) ).
cnf(c_0_2073_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1),c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X2,X4,X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2073]) ).
cnf(c_0_2073_3,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1),c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X2,X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2073]) ).
cnf(c_0_2074_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X1),c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X4,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2074]) ).
cnf(c_0_2074_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X1),c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X4,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2074]) ).
cnf(c_0_2074_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X1),c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X4,X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2074]) ).
cnf(c_0_2074_3,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X1),c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2074]) ).
cnf(c_0_2075_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1),c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X4,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2075]) ).
cnf(c_0_2075_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1),c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X4,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2075]) ).
cnf(c_0_2075_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1),c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X4,X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2075]) ).
cnf(c_0_2075_3,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1),c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2075]) ).
cnf(c_0_2076_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X4,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2076]) ).
cnf(c_0_2076_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X4,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2076]) ).
cnf(c_0_2076_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X4,X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2076]) ).
cnf(c_0_2076_3,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2076]) ).
cnf(c_0_2077_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2077]) ).
cnf(c_0_2077_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| c_Lattices_Oupper__semilattice__class_Osup(X2,c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_2077]) ).
cnf(c_0_2078_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_2078]) ).
cnf(c_0_2078_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_2078]) ).
cnf(c_0_2078_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_2078]) ).
cnf(c_0_2079_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_2079]) ).
cnf(c_0_2079_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_2079]) ).
cnf(c_0_2079_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_2079]) ).
cnf(c_0_2081_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2081]) ).
cnf(c_0_2081_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool)),X2),X3))
| c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2081]) ).
cnf(c_0_2082_0,axiom,
( c_HOL_Oord__class_Oless(X1,X4,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2082]) ).
cnf(c_0_2082_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X1,X4,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2082]) ).
cnf(c_0_2082_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X2),X4))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X1,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2082]) ).
cnf(c_0_2083_0,axiom,
( c_HOL_Oord__class_Oless(X2,X4,tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2083]) ).
cnf(c_0_2083_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| c_HOL_Oord__class_Oless(X2,X4,tc_fun(X1,tc_bool))
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2083]) ).
cnf(c_0_2083_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| c_HOL_Oord__class_Oless(X2,X4,tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2083]) ).
cnf(c_0_2084_0,axiom,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_2084]) ).
cnf(c_0_2084_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),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_2084]) ).
cnf(c_0_2085_0,axiom,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X4,X2,X3),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_2085]) ).
cnf(c_0_2085_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,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2085]) ).
cnf(c_0_2086_0,axiom,
( c_Set_Oimage(c_COMBK(X4,X5,X3),X2,X3,X5) = c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5)
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2086]) ).
cnf(c_0_2086_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| c_Set_Oimage(c_COMBK(X4,X5,X3),X2,X3,X5) = c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5) ),
inference(literals_permutation,[status(thm)],[c_0_2086]) ).
cnf(c_0_2087_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,X4)),X2),X1))
| ~ class_HOL_Oord(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2087]) ).
cnf(c_0_2087_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,X4)),X2),X1))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,X4))
| ~ class_HOL_Oord(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2087]) ).
cnf(c_0_2087_2,axiom,
( ~ class_HOL_Oord(X4)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,X4)),X2),X1))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2087]) ).
cnf(c_0_2089_0,axiom,
( X1 = X2
| hBOOL(c_in(X1,X3,X4))
| ~ hBOOL(c_in(X1,c_Set_Oinsert(X2,X3,X4),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2089]) ).
cnf(c_0_2089_1,axiom,
( hBOOL(c_in(X1,X3,X4))
| X1 = X2
| ~ hBOOL(c_in(X1,c_Set_Oinsert(X2,X3,X4),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2089]) ).
cnf(c_0_2089_2,axiom,
( ~ hBOOL(c_in(X1,c_Set_Oinsert(X2,X3,X4),X4))
| hBOOL(c_in(X1,X3,X4))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2089]) ).
cnf(c_0_2090_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2090]) ).
cnf(c_0_2090_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2090]) ).
cnf(c_0_2090_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2090]) ).
cnf(c_0_2091_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2091]) ).
cnf(c_0_2091_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2091]) ).
cnf(c_0_2091_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2091]) ).
cnf(c_0_2093_0,axiom,
( hAPP(c_Complete__Lattice_OSup__class_OSup(X1),c_Set_Oinsert(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1)) = c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2093]) ).
cnf(c_0_2093_1,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| hAPP(c_Complete__Lattice_OSup__class_OSup(X1),c_Set_Oinsert(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1)) = c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2093]) ).
cnf(c_0_2097_0,axiom,
( hBOOL(c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2097]) ).
cnf(c_0_2097_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2097]) ).
cnf(c_0_2098_0,axiom,
( hBOOL(c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X4,X2,tc_fun(X3,tc_bool)),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2098]) ).
cnf(c_0_2098_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X4,X2,tc_fun(X3,tc_bool)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2098]) ).
cnf(c_0_2099_0,axiom,
( hBOOL(hAPP(X1,X4))
| hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2099]) ).
cnf(c_0_2099_1,axiom,
( hBOOL(hAPP(X2,X4))
| hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2099]) ).
cnf(c_0_2099_2,axiom,
( ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4))
| hBOOL(hAPP(X2,X4))
| hBOOL(hAPP(X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2099]) ).
cnf(c_0_2100_0,axiom,
( ~ hBOOL(c_in(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2100]) ).
cnf(c_0_2100_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2100]) ).
cnf(c_0_2101_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1),tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2101]) ).
cnf(c_0_2101_1,axiom,
( c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1),tc_fun(X1,tc_bool))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2101]) ).
cnf(c_0_2101_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1),tc_fun(X1,tc_bool))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2101]) ).
cnf(c_0_2101_3,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1),tc_fun(X1,tc_bool))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2101]) ).
cnf(c_0_2102_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X3),X4),X5))
| ~ c_HOL_Oord__class_Oless(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_2102]) ).
cnf(c_0_2102_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_lessequals(X3),X4),X5))
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2102]) ).
cnf(c_0_2102_2,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_lessequals(X3),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2102]) ).
cnf(c_0_2104_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ouminus__class_Ouminus(X3,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),X3))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2104]) ).
cnf(c_0_2104_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ouminus__class_Ouminus(X3,X1)),X2))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2104]) ).
cnf(c_0_2104_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ouminus__class_Ouminus(X3,X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2104]) ).
cnf(c_0_2105_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ouminus__class_Ouminus(X3,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),X3))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2105]) ).
cnf(c_0_2105_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ouminus__class_Ouminus(X3,X1)),X2))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2105]) ).
cnf(c_0_2105_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ouminus__class_Ouminus(X3,X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2105]) ).
cnf(c_0_2106_0,axiom,
( c_HOL_Oord__class_Oless(X1,X3,tc_fun(X4,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| ~ hBOOL(c_in(X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2106]) ).
cnf(c_0_2106_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| c_HOL_Oord__class_Oless(X1,X3,tc_fun(X4,tc_bool))
| ~ hBOOL(c_in(X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2106]) ).
cnf(c_0_2106_2,axiom,
( ~ hBOOL(c_in(X2,X3,X4))
| ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| c_HOL_Oord__class_Oless(X1,X3,tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2106]) ).
cnf(c_0_2107_0,axiom,
( X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2107]) ).
cnf(c_0_2107_1,axiom,
( c_HOL_Oord__class_Oless(X2,X3,tc_fun(X1,tc_bool))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2107]) ).
cnf(c_0_2107_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| c_HOL_Oord__class_Oless(X2,X3,tc_fun(X1,tc_bool))
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_2107]) ).
cnf(c_0_2108_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,tc_fun(X1,tc_bool))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2108]) ).
cnf(c_0_2108_1,axiom,
( X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2108]) ).
cnf(c_0_2108_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2108]) ).
cnf(c_0_2109_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X1,tc_bool)) = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2109]) ).
cnf(c_0_2109_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X1,tc_bool)) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_2109]) ).
cnf(c_0_2110_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X1,tc_bool)) = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2110]) ).
cnf(c_0_2110_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X1,tc_bool)) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_2110]) ).
cnf(c_0_2111_0,axiom,
( hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(X2,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2111]) ).
cnf(c_0_2111_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(X2,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2111]) ).
cnf(c_0_2111_2,axiom,
( ~ hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2111]) ).
cnf(c_0_2112_0,axiom,
( hBOOL(hAPP(X4,X2))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X1),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2112]) ).
cnf(c_0_2112_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X4,X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X1),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2112]) ).
cnf(c_0_2112_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X1),X4))
| ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X4,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2112]) ).
cnf(c_0_2115_0,axiom,
( c_Finite__Set_Ofinite(c_Set_Oimage(X3,X1,X2,X4),X4)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2115]) ).
cnf(c_0_2115_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(c_Set_Oimage(X3,X1,X2,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2115]) ).
cnf(c_0_2116_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),c_HOL_Ouminus__class_Ouminus(X3,X1)))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2116]) ).
cnf(c_0_2116_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),c_HOL_Ouminus__class_Ouminus(X3,X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2116]) ).
cnf(c_0_2116_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),c_HOL_Ouminus__class_Ouminus(X3,X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2116]) ).
cnf(c_0_2117_0,axiom,
( c_HOL_Ominus__class_Ominus(c_SetInterval_Oord__class_OatLeastLessThan(X2,X4,X1),c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2117]) ).
cnf(c_0_2117_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_HOL_Ominus__class_Ominus(c_SetInterval_Oord__class_OatLeastLessThan(X2,X4,X1),c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2117]) ).
cnf(c_0_2117_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_HOL_Ominus__class_Ominus(c_SetInterval_Oord__class_OatLeastLessThan(X2,X4,X1),c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2117]) ).
cnf(c_0_2118_0,axiom,
( hBOOL(c_in(X1,X2,X3))
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X2,X3),c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2118]) ).
cnf(c_0_2118_1,axiom,
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X2,X3),c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) = X2
| hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2118]) ).
cnf(c_0_2120_0,axiom,
( hBOOL(c_in(X1,X2,X3))
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X4,X2,tc_fun(X3,tc_bool)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2120]) ).
cnf(c_0_2120_1,axiom,
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X4,X2,tc_fun(X3,tc_bool)),X3)
| hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2120]) ).
cnf(c_0_2122_0,axiom,
( hBOOL(c_in(X1,c_Set_Oinsert(X4,X2,X3),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2122]) ).
cnf(c_0_2122_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(X1,c_Set_Oinsert(X4,X2,X3),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2122]) ).
cnf(c_0_2123_0,axiom,
( hBOOL(c_in(X1,c_Set_Oinsert(X4,X2,X3),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2123]) ).
cnf(c_0_2123_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(X1,c_Set_Oinsert(X4,X2,X3),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2123]) ).
cnf(c_0_2125_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2125]) ).
cnf(c_0_2125_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1)))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2125]) ).
cnf(c_0_2125_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2125]) ).
cnf(c_0_2126_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X4,X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2126]) ).
cnf(c_0_2126_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X4,X3,X1)))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2126]) ).
cnf(c_0_2126_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X4,X3,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2126]) ).
cnf(c_0_2127_0,axiom,
( c_Finite__Set_Ofinite(X2,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ c_Finite__Set_Ofinite(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2127]) ).
cnf(c_0_2127_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| c_Finite__Set_Ofinite(X2,X1)
| ~ c_Finite__Set_Ofinite(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2127]) ).
cnf(c_0_2127_2,axiom,
( ~ c_Finite__Set_Ofinite(X3,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| c_Finite__Set_Ofinite(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2127]) ).
cnf(c_0_2128_0,axiom,
( c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X3),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2128]) ).
cnf(c_0_2128_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(X3,X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X3),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2128]) ).
cnf(c_0_2128_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2128]) ).
cnf(c_0_2129_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Set_Oimage(c_COMBK(X3,X4,X2),X1,X2,X4) = c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2129]) ).
cnf(c_0_2129_1,axiom,
( c_Set_Oimage(c_COMBK(X3,X4,X2),X1,X2,X4) = c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2129]) ).
cnf(c_0_2130_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X4,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2130]) ).
cnf(c_0_2130_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X4,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2130]) ).
cnf(c_0_2130_2,axiom,
( ~ hBOOL(c_in(X4,X2,X3))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2130]) ).
cnf(c_0_2133_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Set_Oimage(X4,X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2133]) ).
cnf(c_0_2133_1,axiom,
( c_Set_Oimage(X4,X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2133]) ).
cnf(c_0_2134_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Set_Oimage(X3,X1,X2,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2134]) ).
cnf(c_0_2134_1,axiom,
( c_Set_Oimage(X3,X1,X2,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2134]) ).
cnf(c_0_2135_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_HOL_Ominus__class_Ominus(X5,X4,X1) != c_HOL_Ominus__class_Ominus(X3,X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2135]) ).
cnf(c_0_2135_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| c_HOL_Ominus__class_Ominus(X5,X4,X1) != c_HOL_Ominus__class_Ominus(X3,X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2135]) ).
cnf(c_0_2135_2,axiom,
( c_HOL_Ominus__class_Ominus(X5,X4,X1) != c_HOL_Ominus__class_Ominus(X3,X2,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2135]) ).
cnf(c_0_2135_3,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X5,X4,X1) != c_HOL_Ominus__class_Ominus(X3,X2,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2135]) ).
cnf(c_0_2136_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_HOL_Ominus__class_Ominus(X3,X2,X1) != c_HOL_Ominus__class_Ominus(X5,X4,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2136]) ).
cnf(c_0_2136_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| c_HOL_Ominus__class_Ominus(X3,X2,X1) != c_HOL_Ominus__class_Ominus(X5,X4,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2136]) ).
cnf(c_0_2136_2,axiom,
( c_HOL_Ominus__class_Ominus(X3,X2,X1) != c_HOL_Ominus__class_Ominus(X5,X4,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2136]) ).
cnf(c_0_2136_3,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X3,X2,X1) != c_HOL_Ominus__class_Ominus(X5,X4,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2136]) ).
cnf(c_0_2137_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBK(X3,tc_fun(X4,tc_bool),X2),X2,tc_fun(X4,tc_bool)) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_2137]) ).
cnf(c_0_2137_1,axiom,
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBK(X3,tc_fun(X4,tc_bool),X2),X2,tc_fun(X4,tc_bool)) = X3
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2137]) ).
cnf(c_0_2138_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X2))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2138]) ).
cnf(c_0_2138_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X2))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2138]) ).
cnf(c_0_2138_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2138]) ).
cnf(c_0_2138_3,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2138]) ).
cnf(c_0_2139_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2139]) ).
cnf(c_0_2139_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2139]) ).
cnf(c_0_2139_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2139]) ).
cnf(c_0_2139_3,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2139]) ).
cnf(c_0_2140_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,X4)),X1),X2))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,X4))
| ~ class_HOL_Oord(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2140]) ).
cnf(c_0_2140_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,X4))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,X4)),X1),X2))
| ~ class_HOL_Oord(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2140]) ).
cnf(c_0_2140_2,axiom,
( ~ class_HOL_Oord(X4)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,X4))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,X4)),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2140]) ).
cnf(c_0_2141_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(c_Complete__Lattice_OInf__class_OInf(X3),X2)),X1))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2141]) ).
cnf(c_0_2141_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(c_Complete__Lattice_OInf__class_OInf(X3),X2)),X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2141]) ).
cnf(c_0_2141_2,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(c_Complete__Lattice_OInf__class_OInf(X3),X2)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2141]) ).
cnf(c_0_2142_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ouminus__class_Ouminus(X3,X1)),c_HOL_Ouminus__class_Ouminus(X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2142]) ).
cnf(c_0_2142_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ouminus__class_Ouminus(X3,X1)),c_HOL_Ouminus__class_Ouminus(X2,X1)))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2142]) ).
cnf(c_0_2142_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ouminus__class_Ouminus(X3,X1)),c_HOL_Ouminus__class_Ouminus(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2142]) ).
cnf(c_0_2143_0,axiom,
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X4,X3),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_2143]) ).
cnf(c_0_2143_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X4,X3),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_2143]) ).
cnf(c_0_2145_0,axiom,
( X1 = X4
| hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2145]) ).
cnf(c_0_2145_1,axiom,
( hBOOL(hAPP(X2,X4))
| X1 = X4
| ~ hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2145]) ).
cnf(c_0_2145_2,axiom,
( ~ hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4))
| hBOOL(hAPP(X2,X4))
| X1 = X4 ),
inference(literals_permutation,[status(thm)],[c_0_2145]) ).
cnf(c_0_2146_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X2),c_Finite__Set_Olinorder__class_OMin(X1,X2)),X3))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(c_in(X3,X1,X2))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2146]) ).
cnf(c_0_2146_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(hAPP(hAPP(c_lessequals(X2),c_Finite__Set_Olinorder__class_OMin(X1,X2)),X3))
| ~ hBOOL(c_in(X3,X1,X2))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2146]) ).
cnf(c_0_2146_2,axiom,
( ~ hBOOL(c_in(X3,X1,X2))
| ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(hAPP(hAPP(c_lessequals(X2),c_Finite__Set_Olinorder__class_OMin(X1,X2)),X3))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2146]) ).
cnf(c_0_2146_3,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ hBOOL(c_in(X3,X1,X2))
| ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(hAPP(hAPP(c_lessequals(X2),c_Finite__Set_Olinorder__class_OMin(X1,X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2146]) ).
cnf(c_0_2147_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ouminus__class_Ouminus(X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ouminus__class_Ouminus(X3,X1)))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2147]) ).
cnf(c_0_2147_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ouminus__class_Ouminus(X3,X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ouminus__class_Ouminus(X2,X1)))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2147]) ).
cnf(c_0_2147_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ouminus__class_Ouminus(X3,X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ouminus__class_Ouminus(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2147]) ).
cnf(c_0_2148_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ouminus__class_Ouminus(X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ouminus__class_Ouminus(X3,X1)))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2148]) ).
cnf(c_0_2148_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ouminus__class_Ouminus(X3,X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ouminus__class_Ouminus(X2,X1)))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2148]) ).
cnf(c_0_2148_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ouminus__class_Ouminus(X3,X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ouminus__class_Ouminus(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2148]) ).
cnf(c_0_2149_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X1,tc_bool)) != X3 ),
inference(literals_permutation,[status(thm)],[c_0_2149]) ).
cnf(c_0_2149_1,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X1,tc_bool)) != X3
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2149]) ).
cnf(c_0_2150_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X1),X2))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2150]) ).
cnf(c_0_2150_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2150]) ).
cnf(c_0_2151_0,axiom,
( hBOOL(c_in(X4,X2,X3))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X4,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2151]) ).
cnf(c_0_2151_1,axiom,
( ~ c_HOL_Oord__class_Oless(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_2151]) ).
cnf(c_0_2151_2,axiom,
( ~ hBOOL(c_in(X4,X1,X3))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| hBOOL(c_in(X4,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2151]) ).
cnf(c_0_2152_0,axiom,
( X1 = X2
| hBOOL(c_in(X3,X1,X4))
| hBOOL(c_in(X3,X2,X4))
| c_Set_Oinsert(X3,X1,X4) != c_Set_Oinsert(X3,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2152]) ).
cnf(c_0_2152_1,axiom,
( hBOOL(c_in(X3,X1,X4))
| X1 = X2
| hBOOL(c_in(X3,X2,X4))
| c_Set_Oinsert(X3,X1,X4) != c_Set_Oinsert(X3,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2152]) ).
cnf(c_0_2152_2,axiom,
( hBOOL(c_in(X3,X2,X4))
| hBOOL(c_in(X3,X1,X4))
| X1 = X2
| c_Set_Oinsert(X3,X1,X4) != c_Set_Oinsert(X3,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2152]) ).
cnf(c_0_2152_3,axiom,
( c_Set_Oinsert(X3,X1,X4) != c_Set_Oinsert(X3,X2,X4)
| hBOOL(c_in(X3,X2,X4))
| hBOOL(c_in(X3,X1,X4))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2152]) ).
cnf(c_0_2155_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_2155]) ).
cnf(c_0_2155_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_2155]) ).
cnf(c_0_2155_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_2155]) ).
cnf(c_0_2156_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_2156]) ).
cnf(c_0_2156_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_2156]) ).
cnf(c_0_2157_0,axiom,
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2157]) ).
cnf(c_0_2157_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2157]) ).
cnf(c_0_2158_0,axiom,
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X4,tc_bool)),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2158]) ).
cnf(c_0_2158_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X4,tc_bool)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2158]) ).
cnf(c_0_2159_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_2159]) ).
cnf(c_0_2159_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_2159]) ).
cnf(c_0_2160_0,axiom,
( hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2160]) ).
cnf(c_0_2160_1,axiom,
( hBOOL(c_in(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),X3))
| hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2160]) ).
cnf(c_0_2161_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X3),X1),hAPP(c_Complete__Lattice_OSup__class_OSup(X3),X2)))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2161]) ).
cnf(c_0_2161_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(hAPP(hAPP(c_lessequals(X3),X1),hAPP(c_Complete__Lattice_OSup__class_OSup(X3),X2)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2161]) ).
cnf(c_0_2161_2,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(hAPP(hAPP(c_lessequals(X3),X1),hAPP(c_Complete__Lattice_OSup__class_OSup(X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2161]) ).
cnf(c_0_2162_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X2),X3),c_Finite__Set_Olinorder__class_OMax(X1,X2)))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(c_in(X3,X1,X2))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2162]) ).
cnf(c_0_2162_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(hAPP(hAPP(c_lessequals(X2),X3),c_Finite__Set_Olinorder__class_OMax(X1,X2)))
| ~ hBOOL(c_in(X3,X1,X2))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2162]) ).
cnf(c_0_2162_2,axiom,
( ~ hBOOL(c_in(X3,X1,X2))
| ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(hAPP(hAPP(c_lessequals(X2),X3),c_Finite__Set_Olinorder__class_OMax(X1,X2)))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2162]) ).
cnf(c_0_2162_3,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ hBOOL(c_in(X3,X1,X2))
| ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(hAPP(hAPP(c_lessequals(X2),X3),c_Finite__Set_Olinorder__class_OMax(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2162]) ).
cnf(c_0_2163_0,axiom,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2163]) ).
cnf(c_0_2163_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2163]) ).
cnf(c_0_2163_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| X2 = X3
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2163]) ).
cnf(c_0_2163_3,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_2163]) ).
cnf(c_0_2164_0,axiom,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2164]) ).
cnf(c_0_2164_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2164]) ).
cnf(c_0_2164_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| X2 = X3
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2164]) ).
cnf(c_0_2164_3,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_2164]) ).
cnf(c_0_2165_0,axiom,
( X3 = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2165]) ).
cnf(c_0_2165_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| X3 = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2165]) ).
cnf(c_0_2165_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| X3 = X2
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2165]) ).
cnf(c_0_2165_3,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| X3 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2165]) ).
cnf(c_0_2171_0,axiom,
( X1 = X2
| c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) != c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2171]) ).
cnf(c_0_2171_1,axiom,
( c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) != c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2171]) ).
cnf(c_0_2172_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2172]) ).
cnf(c_0_2172_1,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2172]) ).
cnf(c_0_2172_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_HOL_Oord__class_Oless(X2,X3,X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2172]) ).
cnf(c_0_2172_3,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_HOL_Oord__class_Oless(X2,X3,X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2172]) ).
cnf(c_0_2173_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2173]) ).
cnf(c_0_2173_1,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2173]) ).
cnf(c_0_2174_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4),X4) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4),X4)
| ~ class_Lattices_Oupper__semilattice(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2174]) ).
cnf(c_0_2174_1,axiom,
( ~ class_Lattices_Oupper__semilattice(X4)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4),X4) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2174]) ).
cnf(c_0_2175_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4),X4) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4),X4)
| ~ class_Lattices_Olattice(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2175]) ).
cnf(c_0_2175_1,axiom,
( ~ class_Lattices_Olattice(X4)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4),X4) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2175]) ).
cnf(c_0_2176_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3)
| ~ class_Lattices_Olattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2176]) ).
cnf(c_0_2176_1,axiom,
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2176]) ).
cnf(c_0_2177_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2177]) ).
cnf(c_0_2177_1,axiom,
( ~ class_Lattices_Oupper__semilattice(X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2177]) ).
cnf(c_0_2178_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)))
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2178]) ).
cnf(c_0_2178_1,axiom,
( ~ class_Lattices_Olattice(X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2178]) ).
cnf(c_0_2179_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X1)))
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2179]) ).
cnf(c_0_2179_1,axiom,
( ~ class_Lattices_Olattice(X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2179]) ).
cnf(c_0_2180_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X1)))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2180]) ).
cnf(c_0_2180_1,axiom,
( ~ class_Lattices_Oupper__semilattice(X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2180]) ).
cnf(c_0_2187_0,axiom,
( c_HOL_Oord__class_Oless(X1,X4,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2187]) ).
cnf(c_0_2187_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X1,X4,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2187]) ).
cnf(c_0_2187_2,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X4,tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X1,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2187]) ).
cnf(c_0_2188_0,axiom,
( c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X4,X5,X3) != c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2188]) ).
cnf(c_0_2188_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X5,X3)
| c_HOL_Ominus__class_Ominus(X4,X5,X3) != c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2188]) ).
cnf(c_0_2188_2,axiom,
( c_HOL_Ominus__class_Ominus(X4,X5,X3) != c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2188]) ).
cnf(c_0_2188_3,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X4,X5,X3) != c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2188]) ).
cnf(c_0_2189_0,axiom,
( c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2189]) ).
cnf(c_0_2189_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X5,X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2189]) ).
cnf(c_0_2189_2,axiom,
( c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2189]) ).
cnf(c_0_2189_3,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2189]) ).
cnf(c_0_2190_0,axiom,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X4))
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2190]) ).
cnf(c_0_2190_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X4))
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2190]) ).
cnf(c_0_2190_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X4))
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2190]) ).
cnf(c_0_2190_3,axiom,
( ~ class_Orderings_Opreorder(X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X4))
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2190]) ).
cnf(c_0_2191_0,axiom,
( c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2191]) ).
cnf(c_0_2191_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2191]) ).
cnf(c_0_2191_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2191]) ).
cnf(c_0_2191_3,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_HOL_Oord__class_Oless(X2,X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2191]) ).
cnf(c_0_2192_0,axiom,
( c_HOL_Oord__class_Oless(X4,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ c_HOL_Oord__class_Oless(X4,X2,X1)
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2192]) ).
cnf(c_0_2192_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_HOL_Oord__class_Oless(X4,X3,X1)
| ~ c_HOL_Oord__class_Oless(X4,X2,X1)
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2192]) ).
cnf(c_0_2192_2,axiom,
( ~ c_HOL_Oord__class_Oless(X4,X2,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_HOL_Oord__class_Oless(X4,X3,X1)
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2192]) ).
cnf(c_0_2192_3,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X4,X2,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_HOL_Oord__class_Oless(X4,X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2192]) ).
cnf(c_0_2193_0,axiom,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X4),X1))
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2193]) ).
cnf(c_0_2193_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X4),X1))
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2193]) ).
cnf(c_0_2193_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X4),X1))
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2193]) ).
cnf(c_0_2193_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X4),X1))
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2193]) ).
cnf(c_0_2198_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2198]) ).
cnf(c_0_2198_1,axiom,
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2198]) ).
cnf(c_0_2198_2,axiom,
( ~ class_Orderings_Oorder(X1)
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2198]) ).
cnf(c_0_2199_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| 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_2199]) ).
cnf(c_0_2199_1,axiom,
( c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2199]) ).
cnf(c_0_2199_2,axiom,
( ~ class_Orderings_Oorder(X1)
| c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2199]) ).
cnf(c_0_2200_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_2200]) ).
cnf(c_0_2200_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_2200]) ).
cnf(c_0_2200_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_2200]) ).
cnf(c_0_2201_0,axiom,
( hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2201]) ).
cnf(c_0_2201_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2201]) ).
cnf(c_0_2204_0,axiom,
( hBOOL(hAPP(X2,X1))
| ~ hBOOL(c_in(X1,c_Collect(X2,X3),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2204]) ).
cnf(c_0_2204_1,axiom,
( ~ hBOOL(c_in(X1,c_Collect(X2,X3),X3))
| hBOOL(hAPP(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2204]) ).
cnf(c_0_2205_0,axiom,
( c_Finite__Set_Ofinite(X2,X3)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2205]) ).
cnf(c_0_2205_1,axiom,
( ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X3)
| c_Finite__Set_Ofinite(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2205]) ).
cnf(c_0_2206_0,axiom,
( c_Finite__Set_Ofinite(X1,X3)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2206]) ).
cnf(c_0_2206_1,axiom,
( ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X3)
| c_Finite__Set_Ofinite(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2206]) ).
cnf(c_0_2207_0,axiom,
( c_Complete__Lattice_Ocomplete__lattice__axioms(c_Complete__Lattice_OInf__class_OInf(X1),c_Complete__Lattice_OSup__class_OSup(X1),c_lessequals(X1),X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2207]) ).
cnf(c_0_2207_1,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| c_Complete__Lattice_Ocomplete__lattice__axioms(c_Complete__Lattice_OInf__class_OInf(X1),c_Complete__Lattice_OSup__class_OSup(X1),c_lessequals(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2207]) ).
cnf(c_0_2208_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(X1,v_x),hAPP(X2,v_x),X3) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(t_a,X3)),v_x)
| ~ class_Lattices_Olattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2208]) ).
cnf(c_0_2208_1,axiom,
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(hAPP(X1,v_x),hAPP(X2,v_x),X3) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(t_a,X3)),v_x) ),
inference(literals_permutation,[status(thm)],[c_0_2208]) ).
cnf(c_0_2209_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_2209]) ).
cnf(c_0_2209_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_2209]) ).
cnf(c_0_2211_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1))
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2211]) ).
cnf(c_0_2211_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1))
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2211]) ).
cnf(c_0_2211_2,axiom,
( ~ class_Orderings_Opreorder(X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1))
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2211]) ).
cnf(c_0_2212_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1))
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2212]) ).
cnf(c_0_2212_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1))
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2212]) ).
cnf(c_0_2212_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1))
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2212]) ).
cnf(c_0_2213_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2213]) ).
cnf(c_0_2213_1,axiom,
( ~ c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2213]) ).
cnf(c_0_2213_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2213]) ).
cnf(c_0_2214_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),X1),X1))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2214]) ).
cnf(c_0_2214_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X2),X1),X1))
| ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2214]) ).
cnf(c_0_2214_2,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),X1),X1))
| ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2214]) ).
cnf(c_0_2215_0,axiom,
( c_SetInterval_Oord__class_OatLeastLessThan(X3,X2,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2215]) ).
cnf(c_0_2215_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_SetInterval_Oord__class_OatLeastLessThan(X3,X2,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2215]) ).
cnf(c_0_2215_2,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_SetInterval_Oord__class_OatLeastLessThan(X3,X2,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2215]) ).
cnf(c_0_2216_0,axiom,
( c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X2,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2216]) ).
cnf(c_0_2216_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X2,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2216]) ).
cnf(c_0_2216_2,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X2,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2216]) ).
cnf(c_0_2217_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2217]) ).
cnf(c_0_2217_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2217]) ).
cnf(c_0_2217_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2217]) ).
cnf(c_0_2218_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_Lattices_Oupper__semilattice__class_Osup(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2218]) ).
cnf(c_0_2218_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,c_Lattices_Oupper__semilattice__class_Osup(X4,X2,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2218]) ).
cnf(c_0_2218_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,c_Lattices_Oupper__semilattice__class_Osup(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2218]) ).
cnf(c_0_2220_0,axiom,
( hBOOL(c_in(X1,X2,X3))
| c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2220]) ).
cnf(c_0_2220_1,axiom,
( c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2220]) ).
cnf(c_0_2221_0,axiom,
( hAPP(c_Complete__Lattice_OInf__class_OInf(X1),c_Set_Oinsert(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_2221]) ).
cnf(c_0_2221_1,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| hAPP(c_Complete__Lattice_OInf__class_OInf(X1),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2221]) ).
cnf(c_0_2222_0,axiom,
( hAPP(c_Complete__Lattice_OSup__class_OSup(X1),c_Set_Oinsert(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_2222]) ).
cnf(c_0_2222_1,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| hAPP(c_Complete__Lattice_OSup__class_OSup(X1),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2222]) ).
cnf(c_0_2223_0,axiom,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2223]) ).
cnf(c_0_2223_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2223]) ).
cnf(c_0_2223_2,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2223]) ).
cnf(c_0_2223_3,axiom,
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2223]) ).
cnf(c_0_2224_0,axiom,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2224]) ).
cnf(c_0_2224_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2224]) ).
cnf(c_0_2224_2,axiom,
( ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2224]) ).
cnf(c_0_2224_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2224]) ).
cnf(c_0_2225_0,axiom,
( c_Finite__Set_Olinorder__class_OMax(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = X1
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2225]) ).
cnf(c_0_2225_1,axiom,
( ~ class_Orderings_Olinorder(X2)
| c_Finite__Set_Olinorder__class_OMax(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2225]) ).
cnf(c_0_2226_0,axiom,
( c_Finite__Set_Olinorder__class_OMin(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = X1
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2226]) ).
cnf(c_0_2226_1,axiom,
( ~ class_Orderings_Olinorder(X2)
| c_Finite__Set_Olinorder__class_OMin(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2226]) ).
cnf(c_0_2227_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2227]) ).
cnf(c_0_2227_1,axiom,
( X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2227]) ).
cnf(c_0_2227_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2227]) ).
cnf(c_0_2227_3,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2227]) ).
cnf(c_0_2228_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2228]) ).
cnf(c_0_2228_1,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2228]) ).
cnf(c_0_2228_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2228]) ).
cnf(c_0_2228_3,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2228]) ).
cnf(c_0_2229_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2229]) ).
cnf(c_0_2229_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2229]) ).
cnf(c_0_2229_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2229]) ).
cnf(c_0_2229_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2229]) ).
cnf(c_0_2230_0,axiom,
( X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2230]) ).
cnf(c_0_2230_1,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2230]) ).
cnf(c_0_2230_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_HOL_Oord__class_Oless(X2,X3,X1)
| X2 = X3
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2230]) ).
cnf(c_0_2230_3,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_HOL_Oord__class_Oless(X2,X3,X1)
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_2230]) ).
cnf(c_0_2231_0,axiom,
( X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2231]) ).
cnf(c_0_2231_1,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2231]) ).
cnf(c_0_2231_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_HOL_Oord__class_Oless(X2,X3,X1)
| X2 = X3
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2231]) ).
cnf(c_0_2231_3,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_HOL_Oord__class_Oless(X2,X3,X1)
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_2231]) ).
cnf(c_0_2232_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2232]) ).
cnf(c_0_2232_1,axiom,
( X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2232]) ).
cnf(c_0_2232_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2232]) ).
cnf(c_0_2232_3,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2232]) ).
cnf(c_0_2233_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1))
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2233]) ).
cnf(c_0_2233_1,axiom,
( c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1))
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2233]) ).
cnf(c_0_2233_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1))
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2233]) ).
cnf(c_0_2233_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1))
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2233]) ).
cnf(c_0_2234_0,axiom,
( X3 = X2
| c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2234]) ).
cnf(c_0_2234_1,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X3 = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2234]) ).
cnf(c_0_2234_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_HOL_Oord__class_Oless(X2,X3,X1)
| X3 = X2
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2234]) ).
cnf(c_0_2234_3,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_HOL_Oord__class_Oless(X2,X3,X1)
| X3 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2234]) ).
cnf(c_0_2235_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2235]) ).
cnf(c_0_2235_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = X3
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2235]) ).
cnf(c_0_2235_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_2235]) ).
cnf(c_0_2236_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X1) = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2236]) ).
cnf(c_0_2236_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X1) = X3
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2236]) ).
cnf(c_0_2236_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X1) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_2236]) ).
cnf(c_0_2237_0,axiom,
( c_Set_Oinsert(X1,X2,X3) = X2
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2237]) ).
cnf(c_0_2237_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| c_Set_Oinsert(X1,X2,X3) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2237]) ).
cnf(c_0_2238_0,axiom,
( c_HOL_Oord__class_Oless(X3,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ouminus__class_Ouminus(X3,X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2238]) ).
cnf(c_0_2238_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ouminus__class_Ouminus(X3,X2),X2)
| c_HOL_Oord__class_Oless(X3,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2238]) ).
cnf(c_0_2238_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ouminus__class_Ouminus(X3,X2),X2)
| c_HOL_Oord__class_Oless(X3,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2238]) ).
cnf(c_0_2239_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_2239]) ).
cnf(c_0_2239_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_2239]) ).
cnf(c_0_2239_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_2239]) ).
cnf(c_0_2240_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,hAPP(c_Complete__Lattice_OSup__class_OSup(X1),X3),X1) = hAPP(c_Complete__Lattice_OSup__class_OSup(X1),c_Set_Oinsert(X2,X3,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2240]) ).
cnf(c_0_2240_1,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(X2,hAPP(c_Complete__Lattice_OSup__class_OSup(X1),X3),X1) = hAPP(c_Complete__Lattice_OSup__class_OSup(X1),c_Set_Oinsert(X2,X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2240]) ).
cnf(c_0_2243_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2243]) ).
cnf(c_0_2243_1,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2243]) ).
cnf(c_0_2244_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3)
| ~ class_Lattices_Olattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2244]) ).
cnf(c_0_2244_1,axiom,
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2244]) ).
cnf(c_0_2245_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2245]) ).
cnf(c_0_2245_1,axiom,
( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2245]) ).
cnf(c_0_2245_2,axiom,
( ~ class_Orderings_Oorder(X3)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2245]) ).
cnf(c_0_2246_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2246]) ).
cnf(c_0_2246_1,axiom,
( c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2246]) ).
cnf(c_0_2246_2,axiom,
( ~ class_Orderings_Oorder(X3)
| c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2246]) ).
cnf(c_0_2247_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2247]) ).
cnf(c_0_2247_1,axiom,
( c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2247]) ).
cnf(c_0_2247_2,axiom,
( ~ class_Orderings_Oorder(X3)
| c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2247]) ).
cnf(c_0_2248_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2248]) ).
cnf(c_0_2248_1,axiom,
( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2248]) ).
cnf(c_0_2248_2,axiom,
( ~ class_Orderings_Oorder(X3)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2248]) ).
cnf(c_0_2249_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_2249]) ).
cnf(c_0_2249_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_2249]) ).
cnf(c_0_2249_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_2249]) ).
cnf(c_0_2249_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_2249]) ).
cnf(c_0_2250_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_2250]) ).
cnf(c_0_2250_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_2250]) ).
cnf(c_0_2250_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_2250]) ).
cnf(c_0_2250_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_2250]) ).
cnf(c_0_2251_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2251]) ).
cnf(c_0_2251_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2251]) ).
cnf(c_0_2251_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2251]) ).
cnf(c_0_2253_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2253]) ).
cnf(c_0_2253_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2253]) ).
cnf(c_0_2253_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2253]) ).
cnf(c_0_2254_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2254]) ).
cnf(c_0_2254_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2254]) ).
cnf(c_0_2254_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2254]) ).
cnf(c_0_2255_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X2),X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2255]) ).
cnf(c_0_2255_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X2),X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2255]) ).
cnf(c_0_2255_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X2),X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2255]) ).
cnf(c_0_2256_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X2),X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2256]) ).
cnf(c_0_2256_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X2),X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2256]) ).
cnf(c_0_2256_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X2),X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2256]) ).
cnf(c_0_2257_0,axiom,
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2257]) ).
cnf(c_0_2257_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2257]) ).
cnf(c_0_2257_2,axiom,
( ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2257]) ).
cnf(c_0_2258_0,axiom,
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2258]) ).
cnf(c_0_2258_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2258]) ).
cnf(c_0_2258_2,axiom,
( ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2258]) ).
cnf(c_0_2259_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_2259]) ).
cnf(c_0_2259_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_2259]) ).
cnf(c_0_2259_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_2259]) ).
cnf(c_0_2260_0,axiom,
( hBOOL(c_in(X2,c_Collect(X1,X3),X3))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2260]) ).
cnf(c_0_2260_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(c_in(X2,c_Collect(X1,X3),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2260]) ).
cnf(c_0_2263_0,axiom,
( hBOOL(hAPP(X2,X1))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2263]) ).
cnf(c_0_2263_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(hAPP(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2263]) ).
cnf(c_0_2264_0,axiom,
( c_Finite__Set_Ofinite(X2,X3)
| ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X1,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2264]) ).
cnf(c_0_2264_1,axiom,
( ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X1,X2,X3),X3)
| c_Finite__Set_Ofinite(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2264]) ).
cnf(c_0_2266_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) != X3
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2266]) ).
cnf(c_0_2266_1,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) != X3
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2266]) ).
cnf(c_0_2266_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) != X3
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2266]) ).
cnf(c_0_2267_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X3),c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2267]) ).
cnf(c_0_2267_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X3),c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2267]) ).
cnf(c_0_2267_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X3),c_HOL_Ouminus__class_Ouminus(X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2267]) ).
cnf(c_0_2268_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2268]) ).
cnf(c_0_2268_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2268]) ).
cnf(c_0_2268_2,axiom,
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2268]) ).
cnf(c_0_2269_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2269]) ).
cnf(c_0_2269_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2269]) ).
cnf(c_0_2269_2,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2269]) ).
cnf(c_0_2270_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2270]) ).
cnf(c_0_2270_1,axiom,
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2270]) ).
cnf(c_0_2270_2,axiom,
( ~ class_Orderings_Oorder(X1)
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2270]) ).
cnf(c_0_2271_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| 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_2271]) ).
cnf(c_0_2271_1,axiom,
( c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2271]) ).
cnf(c_0_2271_2,axiom,
( ~ class_Orderings_Oorder(X1)
| c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2271]) ).
cnf(c_0_2272_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2272]) ).
cnf(c_0_2272_1,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2272]) ).
cnf(c_0_2273_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2273]) ).
cnf(c_0_2273_1,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2273]) ).
cnf(c_0_2274_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_2274]) ).
cnf(c_0_2274_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_2274]) ).
cnf(c_0_2275_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3) = c_HOL_Ominus__class_Ominus(X2,X1,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2275]) ).
cnf(c_0_2275_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3) = c_HOL_Ominus__class_Ominus(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2275]) ).
cnf(c_0_2276_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_2276]) ).
cnf(c_0_2276_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_2276]) ).
cnf(c_0_2276_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_2276]) ).
cnf(c_0_2277_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_2277]) ).
cnf(c_0_2277_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_2277]) ).
cnf(c_0_2277_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_2277]) ).
cnf(c_0_2278_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2278]) ).
cnf(c_0_2278_1,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2278]) ).
cnf(c_0_2278_2,axiom,
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2278]) ).
cnf(c_0_2279_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2279]) ).
cnf(c_0_2279_1,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2279]) ).
cnf(c_0_2279_2,axiom,
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2279]) ).
cnf(c_0_2280_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2280]) ).
cnf(c_0_2280_1,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2280]) ).
cnf(c_0_2280_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2280]) ).
cnf(c_0_2281_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2281]) ).
cnf(c_0_2281_1,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2281]) ).
cnf(c_0_2281_2,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2281]) ).
cnf(c_0_2283_0,axiom,
( c_SetInterval_Oord__class_OatLeastAtMost(X2,X1,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2283]) ).
cnf(c_0_2283_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_SetInterval_Oord__class_OatLeastAtMost(X2,X1,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2283]) ).
cnf(c_0_2283_2,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_SetInterval_Oord__class_OatLeastAtMost(X2,X1,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2283]) ).
cnf(c_0_2284_0,axiom,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_fequal(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2284]) ).
cnf(c_0_2284_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_fequal(X1),X2),X3))
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_2284]) ).
cnf(c_0_2285_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2285]) ).
cnf(c_0_2285_1,axiom,
( c_HOL_Oord__class_Oless(X3,X2,X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2285]) ).
cnf(c_0_2285_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2285]) ).
cnf(c_0_2286_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1))
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2286]) ).
cnf(c_0_2286_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1))
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2286]) ).
cnf(c_0_2286_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1))
| c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2286]) ).
cnf(c_0_2287_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X2))
| c_HOL_Oord__class_Oless(X2,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2287]) ).
cnf(c_0_2287_1,axiom,
( c_HOL_Oord__class_Oless(X2,X2,X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2287]) ).
cnf(c_0_2287_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| c_HOL_Oord__class_Oless(X2,X2,X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2287]) ).
cnf(c_0_2288_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2288]) ).
cnf(c_0_2288_1,axiom,
( c_HOL_Oord__class_Oless(X3,X2,X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2288]) ).
cnf(c_0_2288_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2288]) ).
cnf(c_0_2289_0,axiom,
( c_SetInterval_Oord__class_OatLeastAtMost(X1,X1,X2) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
| ~ class_Orderings_Oorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2289]) ).
cnf(c_0_2289_1,axiom,
( ~ class_Orderings_Oorder(X2)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X1,X2) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2289]) ).
cnf(c_0_2290_0,axiom,
( hBOOL(c_in(X2,X1,X3))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2290]) ).
cnf(c_0_2290_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(c_in(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2290]) ).
cnf(c_0_2295_0,axiom,
( c_Finite__Set_Ofinite(c_Set_Oinsert(X3,X1,X2),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2295]) ).
cnf(c_0_2295_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(c_Set_Oinsert(X3,X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2295]) ).
cnf(c_0_2296_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2296]) ).
cnf(c_0_2296_1,axiom,
( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2296]) ).
cnf(c_0_2296_2,axiom,
( ~ class_Orderings_Oorder(X3)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2296]) ).
cnf(c_0_2297_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2297]) ).
cnf(c_0_2297_1,axiom,
( c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2297]) ).
cnf(c_0_2297_2,axiom,
( ~ class_Orderings_Oorder(X3)
| c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2297]) ).
cnf(c_0_2298_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2298]) ).
cnf(c_0_2298_1,axiom,
( c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2298]) ).
cnf(c_0_2298_2,axiom,
( ~ class_Orderings_Oorder(X3)
| c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2298]) ).
cnf(c_0_2299_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2299]) ).
cnf(c_0_2299_1,axiom,
( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2299]) ).
cnf(c_0_2299_2,axiom,
( ~ class_Orderings_Oorder(X3)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2299]) ).
cnf(c_0_2300_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_Orderings_Obot__class_Obot(X1)),X2))
| ~ class_Orderings_Obot(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2300]) ).
cnf(c_0_2300_1,axiom,
( ~ class_Orderings_Obot(X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_Orderings_Obot__class_Obot(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2300]) ).
cnf(c_0_2305_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1,tc_fun(t_a,X2)),v_x) = c_HOL_Ouminus__class_Ouminus(hAPP(X1,v_x),X2)
| ~ class_HOL_Ouminus(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2305]) ).
cnf(c_0_2305_1,axiom,
( ~ class_HOL_Ouminus(X2)
| hAPP(c_HOL_Ouminus__class_Ouminus(X1,tc_fun(t_a,X2)),v_x) = c_HOL_Ouminus__class_Ouminus(hAPP(X1,v_x),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2305]) ).
cnf(c_0_2310_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X2 = X1
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2310]) ).
cnf(c_0_2310_1,axiom,
( c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X2 = X1
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2310]) ).
cnf(c_0_2310_2,axiom,
( X2 = X1
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2310]) ).
cnf(c_0_2310_3,axiom,
( ~ class_Orderings_Olinorder(X3)
| X2 = X1
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2310]) ).
cnf(c_0_2311_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2311]) ).
cnf(c_0_2311_1,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2311]) ).
cnf(c_0_2311_2,axiom,
( c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2311]) ).
cnf(c_0_2311_3,axiom,
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2311]) ).
cnf(c_0_2312_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2312]) ).
cnf(c_0_2312_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2312]) ).
cnf(c_0_2312_2,axiom,
( c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2312]) ).
cnf(c_0_2312_3,axiom,
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2312]) ).
cnf(c_0_2313_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2313]) ).
cnf(c_0_2313_1,axiom,
( c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2313]) ).
cnf(c_0_2313_2,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2313]) ).
cnf(c_0_2313_3,axiom,
( ~ class_Orderings_Olinorder(X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2313]) ).
cnf(c_0_2314_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2314]) ).
cnf(c_0_2314_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2314]) ).
cnf(c_0_2314_2,axiom,
( c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2314]) ).
cnf(c_0_2314_3,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2314]) ).
cnf(c_0_2315_0,axiom,
( X1 = X2
| c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X3,tc_bool)) != c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2315]) ).
cnf(c_0_2315_1,axiom,
( c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X3,tc_bool)) != c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2315]) ).
cnf(c_0_2316_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2316]) ).
cnf(c_0_2316_1,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2316]) ).
cnf(c_0_2317_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3)
| ~ class_Lattices_Olattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2317]) ).
cnf(c_0_2317_1,axiom,
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2317]) ).
cnf(c_0_2318_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X2))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2318]) ).
cnf(c_0_2318_1,axiom,
( ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2318]) ).
cnf(c_0_2319_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X2))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2319]) ).
cnf(c_0_2319_1,axiom,
( ~ class_Orderings_Opreorder(X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2319]) ).
cnf(c_0_2320_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_2320]) ).
cnf(c_0_2320_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_2320]) ).
cnf(c_0_2321_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_2321]) ).
cnf(c_0_2321_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_2321]) ).
cnf(c_0_2322_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(v_A,tc_fun(t_a,t_b)),v_x) = c_HOL_Ouminus__class_Ouminus(hAPP(v_A,v_x),t_b)
| ~ class_HOL_Ouminus(t_b) ),
inference(literals_permutation,[status(thm)],[c_0_2322]) ).
cnf(c_0_2322_1,axiom,
( ~ class_HOL_Ouminus(t_b)
| hAPP(c_HOL_Ouminus__class_Ouminus(v_A,tc_fun(t_a,t_b)),v_x) = c_HOL_Ouminus__class_Ouminus(hAPP(v_A,v_x),t_b) ),
inference(literals_permutation,[status(thm)],[c_0_2322]) ).
cnf(c_0_2326_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X2) != c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2326]) ).
cnf(c_0_2326_1,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X2) != c_Orderings_Obot__class_Obot(X2)
| X1 = c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2326]) ).
cnf(c_0_2326_2,axiom,
( ~ class_Lattices_Obounded__lattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X2) != c_Orderings_Obot__class_Obot(X2)
| X1 = c_Orderings_Obot__class_Obot(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2326]) ).
cnf(c_0_2327_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2) != c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2327]) ).
cnf(c_0_2327_1,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2) != c_Orderings_Obot__class_Obot(X2)
| X1 = c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2327]) ).
cnf(c_0_2327_2,axiom,
( ~ class_Lattices_Obounded__lattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2) != c_Orderings_Obot__class_Obot(X2)
| X1 = c_Orderings_Obot__class_Obot(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2327]) ).
cnf(c_0_2329_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2329]) ).
cnf(c_0_2329_1,axiom,
( ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2329]) ).
cnf(c_0_2330_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2330]) ).
cnf(c_0_2330_1,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2330]) ).
cnf(c_0_2331_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2331]) ).
cnf(c_0_2331_1,axiom,
( ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2331]) ).
cnf(c_0_2332_0,axiom,
( hAPP(c_Complete__Lattice_OSup__class_OSup(X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2332]) ).
cnf(c_0_2332_1,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| hAPP(c_Complete__Lattice_OSup__class_OSup(X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = c_Orderings_Obot__class_Obot(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2332]) ).
cnf(c_0_2334_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_2334]) ).
cnf(c_0_2334_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_2334]) ).
cnf(c_0_2335_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(X2),X2) = X1
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2335]) ).
cnf(c_0_2335_1,axiom,
( ~ class_Lattices_Obounded__lattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2335]) ).
cnf(c_0_2336_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X1),X2,X1) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2336]) ).
cnf(c_0_2336_1,axiom,
( ~ class_Lattices_Obounded__lattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X1),X2,X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2336]) ).
cnf(c_0_2338_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X1,X2) = X1
| ~ class_Lattices_Oupper__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2338]) ).
cnf(c_0_2338_1,axiom,
( ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X1,X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2338]) ).
cnf(c_0_2339_0,axiom,
( X1 = X2
| c_HOL_Ouminus__class_Ouminus(X1,X3) != c_HOL_Ouminus__class_Ouminus(X2,X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2339]) ).
cnf(c_0_2339_1,axiom,
( c_HOL_Ouminus__class_Ouminus(X1,X3) != c_HOL_Ouminus__class_Ouminus(X2,X3)
| X1 = X2
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2339]) ).
cnf(c_0_2339_2,axiom,
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(X1,X3) != c_HOL_Ouminus__class_Ouminus(X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2339]) ).
cnf(c_0_2340_0,axiom,
( X1 = X2
| c_HOL_Ouminus__class_Ouminus(X1,X3) != c_HOL_Ouminus__class_Ouminus(X2,X3)
| ~ class_Lattices_Oboolean__algebra(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2340]) ).
cnf(c_0_2340_1,axiom,
( c_HOL_Ouminus__class_Ouminus(X1,X3) != c_HOL_Ouminus__class_Ouminus(X2,X3)
| X1 = X2
| ~ class_Lattices_Oboolean__algebra(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2340]) ).
cnf(c_0_2340_2,axiom,
( ~ class_Lattices_Oboolean__algebra(X3)
| c_HOL_Ouminus__class_Ouminus(X1,X3) != c_HOL_Ouminus__class_Ouminus(X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2340]) ).
cnf(c_0_2342_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2342]) ).
cnf(c_0_2342_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2342]) ).
cnf(c_0_2343_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1
| ~ class_Lattices_Oboolean__algebra(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2343]) ).
cnf(c_0_2343_1,axiom,
( ~ class_Lattices_Oboolean__algebra(X2)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2343]) ).
cnf(c_0_2344_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2344]) ).
cnf(c_0_2344_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2344]) ).
cnf(c_0_2345_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2345]) ).
cnf(c_0_2345_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2345]) ).
cnf(c_0_2346_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2346]) ).
cnf(c_0_2346_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2346]) ).
cnf(c_0_2347_0,axiom,
( X1 = X2
| c_Com_Ocom_OSemi(X1,X3) != c_Com_Ocom_OSemi(X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2347]) ).
cnf(c_0_2347_1,axiom,
( c_Com_Ocom_OSemi(X1,X3) != c_Com_Ocom_OSemi(X2,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2347]) ).
cnf(c_0_2348_0,axiom,
( X1 = X2
| c_Com_Ocom_OSemi(X3,X1) != c_Com_Ocom_OSemi(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2348]) ).
cnf(c_0_2348_1,axiom,
( c_Com_Ocom_OSemi(X3,X1) != c_Com_Ocom_OSemi(X4,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2348]) ).
cnf(c_0_2349_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_2349]) ).
cnf(c_0_2349_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_2349]) ).
cnf(c_0_2349_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_2349]) ).
cnf(c_0_2350_0,axiom,
( class_HOL_Oord(tc_fun(X2,X1))
| ~ class_HOL_Oord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2350]) ).
cnf(c_0_2350_1,axiom,
( ~ class_HOL_Oord(X1)
| class_HOL_Oord(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2350]) ).
cnf(c_0_2351_0,axiom,
( class_HOL_Ominus(tc_fun(X2,X1))
| ~ class_HOL_Ominus(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2351]) ).
cnf(c_0_2351_1,axiom,
( ~ class_HOL_Ominus(X1)
| class_HOL_Ominus(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2351]) ).
cnf(c_0_2352_0,axiom,
( class_HOL_Ouminus(tc_fun(X2,X1))
| ~ class_HOL_Ouminus(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2352]) ).
cnf(c_0_2352_1,axiom,
( ~ class_HOL_Ouminus(X1)
| class_HOL_Ouminus(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2352]) ).
cnf(c_0_2353_0,axiom,
( class_Orderings_Obot(tc_fun(X2,X1))
| ~ class_Orderings_Obot(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2353]) ).
cnf(c_0_2353_1,axiom,
( ~ class_Orderings_Obot(X1)
| class_Orderings_Obot(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2353]) ).
cnf(c_0_2354_0,axiom,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2354]) ).
cnf(c_0_2354_1,axiom,
( ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2354]) ).
cnf(c_0_2355_0,axiom,
( class_Lattices_Olattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2355]) ).
cnf(c_0_2355_1,axiom,
( ~ class_Lattices_Olattice(X1)
| class_Lattices_Olattice(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2355]) ).
cnf(c_0_2356_0,axiom,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2356]) ).
cnf(c_0_2356_1,axiom,
( ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2356]) ).
cnf(c_0_2357_0,axiom,
( class_Lattices_Oboolean__algebra(tc_fun(X2,X1))
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2357]) ).
cnf(c_0_2357_1,axiom,
( ~ class_Lattices_Oboolean__algebra(X1)
| class_Lattices_Oboolean__algebra(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2357]) ).
cnf(c_0_2358_0,axiom,
( class_Lattices_Obounded__lattice(tc_fun(X2,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2358]) ).
cnf(c_0_2358_1,axiom,
( ~ class_Lattices_Obounded__lattice(X1)
| class_Lattices_Obounded__lattice(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2358]) ).
cnf(c_0_2359_0,axiom,
( class_Lattices_Oupper__semilattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2359]) ).
cnf(c_0_2359_1,axiom,
( ~ class_Lattices_Olattice(X1)
| class_Lattices_Oupper__semilattice(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2359]) ).
cnf(c_0_2360_0,axiom,
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2360]) ).
cnf(c_0_2360_1,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2360]) ).
cnf(c_0_2363_0,axiom,
( c_Finite__Set_Ofinite(X1,X2)
| ~ class_Finite__Set_Ofinite_Ofinite(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2363]) ).
cnf(c_0_2363_1,axiom,
( ~ class_Finite__Set_Ofinite_Ofinite(X2)
| c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2363]) ).
cnf(c_0_2069_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_2069]) ).
cnf(c_0_2168_0,axiom,
~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
inference(literals_permutation,[status(thm)],[c_0_2168]) ).
cnf(c_0_2169_0,axiom,
~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
inference(literals_permutation,[status(thm)],[c_0_2169]) ).
cnf(c_0_2170_0,axiom,
~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
inference(literals_permutation,[status(thm)],[c_0_2170]) ).
cnf(c_0_2261_0,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
inference(literals_permutation,[status(thm)],[c_0_2261]) ).
cnf(c_0_2265_0,axiom,
~ c_HOL_Oord__class_Oless(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2265]) ).
cnf(c_0_2306_0,axiom,
c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2306]) ).
cnf(c_0_2307_0,axiom,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Set_Oinsert(X2,X3,X1),
inference(literals_permutation,[status(thm)],[c_0_2307]) ).
cnf(c_0_2308_0,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_fun(X2,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2308]) ).
cnf(c_0_2361_0,axiom,
c_Com_Ocom_OSemi(X1,X2) != c_Com_Ocom_OSKIP,
inference(literals_permutation,[status(thm)],[c_0_2361]) ).
cnf(c_0_2362_0,axiom,
c_Com_Ocom_OSemi(X1,X2) != c_Com_Ocom_OSKIP,
inference(literals_permutation,[status(thm)],[c_0_2362]) ).
cnf(c_0_1931_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(c_Set_Oimage(X2,X3,X4,X1),c_Set_Oimage(X2,X5,X4,X1),tc_fun(X1,tc_bool))),c_Set_Oimage(X2,c_HOL_Ominus__class_Ominus(X3,X5,tc_fun(X4,tc_bool)),X4,X1))),
inference(literals_permutation,[status(thm)],[c_0_1931]) ).
cnf(c_0_1937_0,axiom,
c_Nitpick_Ofold__graph_H(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X2,X3,X4),
inference(literals_permutation,[status(thm)],[c_0_1937]) ).
cnf(c_0_1938_0,axiom,
c_Finite__Set_Ofold__graph(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X2,X3,X4),
inference(literals_permutation,[status(thm)],[c_0_1938]) ).
cnf(c_0_1956_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X3),X3,X3,tc_bool),X1),X3),X2,tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,X2,X3),
inference(literals_permutation,[status(thm)],[c_0_1956]) ).
cnf(c_0_1979_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4,X3,tc_fun(X5,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,X3,tc_fun(X5,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_1979]) ).
cnf(c_0_1982_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(X1,X2,X4,X5),c_Set_Oimage(X1,X3,X4,X5),tc_fun(X5,tc_bool)) = c_Set_Oimage(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4,X5),
inference(literals_permutation,[status(thm)],[c_0_1982]) ).
cnf(c_0_1990_0,axiom,
hBOOL(hAPP(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2))),
inference(literals_permutation,[status(thm)],[c_0_1990]) ).
cnf(c_0_1995_0,axiom,
c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,c_Com_Ocom_OSKIP,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3),
inference(literals_permutation,[status(thm)],[c_0_1995]) ).
cnf(c_0_2007_0,axiom,
c_Collect(hAPP(c_COMBC(c_fequal(X1),X1,X1,tc_bool),X2),X1) = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
inference(literals_permutation,[status(thm)],[c_0_2007]) ).
cnf(c_0_2011_0,axiom,
hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),X2)),
inference(literals_permutation,[status(thm)],[c_0_2011]) ).
cnf(c_0_2014_0,axiom,
hAPP(hAPP(c_COMBC(X1,X2,X3,X4),X5),X6) = hAPP(hAPP(X1,X6),X5),
inference(literals_permutation,[status(thm)],[c_0_2014]) ).
cnf(c_0_2015_0,axiom,
c_The(hAPP(c_COMBC(c_fequal(X1),X1,X1,tc_bool),X2),X1) = X2,
inference(literals_permutation,[status(thm)],[c_0_2015]) ).
cnf(c_0_2017_0,axiom,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oinsert(X1,X2,X3),X4,X3,tc_fun(X5,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(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_2017]) ).
cnf(c_0_2025_0,axiom,
c_Set_Oimage(X1,c_Set_Oinsert(X2,X3,X4),X4,X5) = c_Set_Oinsert(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5),
inference(literals_permutation,[status(thm)],[c_0_2025]) ).
cnf(c_0_2028_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X1,tc_bool))),X2)),
inference(literals_permutation,[status(thm)],[c_0_2028]) ).
cnf(c_0_2038_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)))),
inference(literals_permutation,[status(thm)],[c_0_2038]) ).
cnf(c_0_2044_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2044]) ).
cnf(c_0_2047_0,axiom,
c_Set_Oinsert(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)),X4) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),
inference(literals_permutation,[status(thm)],[c_0_2047]) ).
cnf(c_0_2066_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(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_2066]) ).
cnf(c_0_2067_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X1,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = X4,
inference(literals_permutation,[status(thm)],[c_0_2067]) ).
cnf(c_0_2068_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_2068]) ).
cnf(c_0_2080_0,axiom,
c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3) = c_Set_Oinsert(X1,X2,X3),
inference(literals_permutation,[status(thm)],[c_0_2080]) ).
cnf(c_0_2088_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X4,tc_bool)),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2088]) ).
cnf(c_0_2092_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X1,X4,tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2092]) ).
cnf(c_0_2094_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(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_2094]) ).
cnf(c_0_2095_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X1,tc_bool)))),
inference(literals_permutation,[status(thm)],[c_0_2095]) ).
cnf(c_0_2096_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X1,tc_bool)))),
inference(literals_permutation,[status(thm)],[c_0_2096]) ).
cnf(c_0_2103_0,axiom,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBK(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool),X3),X3,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2103]) ).
cnf(c_0_2113_0,axiom,
hBOOL(c_in(X1,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2)),
inference(literals_permutation,[status(thm)],[c_0_2113]) ).
cnf(c_0_2114_0,axiom,
c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = c_Set_Oinsert(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),
inference(literals_permutation,[status(thm)],[c_0_2114]) ).
cnf(c_0_2119_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X2,X1))),
inference(literals_permutation,[status(thm)],[c_0_2119]) ).
cnf(c_0_2121_0,axiom,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_COMBK(X2,tc_fun(X3,tc_bool),X1),X1,tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2121]) ).
cnf(c_0_2124_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X2)),
inference(literals_permutation,[status(thm)],[c_0_2124]) ).
cnf(c_0_2131_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2131]) ).
cnf(c_0_2132_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2132]) ).
cnf(c_0_2144_0,axiom,
c_Set_Oimage(c_COMBK(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2144]) ).
cnf(c_0_2153_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),X3),
inference(literals_permutation,[status(thm)],[c_0_2153]) ).
cnf(c_0_2154_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) = c_Set_Oinsert(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),X4),
inference(literals_permutation,[status(thm)],[c_0_2154]) ).
cnf(c_0_2166_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X2,tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,X2,X3),
inference(literals_permutation,[status(thm)],[c_0_2166]) ).
cnf(c_0_2167_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2167]) ).
cnf(c_0_2181_0,axiom,
c_Set_Oimage(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2181]) ).
cnf(c_0_2182_0,axiom,
c_Set_Oimage(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2182]) ).
cnf(c_0_2183_0,axiom,
hBOOL(c_in(X1,c_Set_Oinsert(X1,X2,X3),X3)),
inference(literals_permutation,[status(thm)],[c_0_2183]) ).
cnf(c_0_2184_0,axiom,
hBOOL(c_in(X1,c_Set_Oinsert(X1,X2,X3),X3)),
inference(literals_permutation,[status(thm)],[c_0_2184]) ).
cnf(c_0_2185_0,axiom,
hBOOL(c_in(X1,c_Set_Oinsert(X1,X2,X3),X3)),
inference(literals_permutation,[status(thm)],[c_0_2185]) ).
cnf(c_0_2186_0,axiom,
c_Set_Oinsert(X1,c_Set_Oinsert(X2,X3,X4),X4) = c_Set_Oinsert(X2,c_Set_Oinsert(X1,X3,X4),X4),
inference(literals_permutation,[status(thm)],[c_0_2186]) ).
cnf(c_0_2194_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_2194]) ).
cnf(c_0_2195_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2195]) ).
cnf(c_0_2196_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2196]) ).
cnf(c_0_2197_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2197]) ).
cnf(c_0_2202_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X2)),
inference(literals_permutation,[status(thm)],[c_0_2202]) ).
cnf(c_0_2203_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X2)),
inference(literals_permutation,[status(thm)],[c_0_2203]) ).
cnf(c_0_2210_0,axiom,
c_Finite__Set_Ofold1(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = X2,
inference(literals_permutation,[status(thm)],[c_0_2210]) ).
cnf(c_0_2219_0,axiom,
hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X1)),
inference(literals_permutation,[status(thm)],[c_0_2219]) ).
cnf(c_0_2241_0,axiom,
c_Set_Ocontents(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = X1,
inference(literals_permutation,[status(thm)],[c_0_2241]) ).
cnf(c_0_2242_0,axiom,
c_The(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = X1,
inference(literals_permutation,[status(thm)],[c_0_2242]) ).
cnf(c_0_2252_0,axiom,
c_Set_Oinsert(X1,c_Set_Oinsert(X1,X2,X3),X3) = c_Set_Oinsert(X1,X2,X3),
inference(literals_permutation,[status(thm)],[c_0_2252]) ).
cnf(c_0_2262_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2262]) ).
cnf(c_0_2282_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_2282]) ).
cnf(c_0_2291_0,axiom,
c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) = c_Collect(hAPP(c_fequal(X1),X2),X1),
inference(literals_permutation,[status(thm)],[c_0_2291]) ).
cnf(c_0_2292_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_2292]) ).
cnf(c_0_2293_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_2293]) ).
cnf(c_0_2294_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X3,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2294]) ).
cnf(c_0_2301_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_2301]) ).
cnf(c_0_2302_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_2302]) ).
cnf(c_0_2303_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = X2,
inference(literals_permutation,[status(thm)],[c_0_2303]) ).
cnf(c_0_2304_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
inference(literals_permutation,[status(thm)],[c_0_2304]) ).
cnf(c_0_2309_0,axiom,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
inference(literals_permutation,[status(thm)],[c_0_2309]) ).
cnf(c_0_2323_0,axiom,
hAPP(c_COMBK(v_P,t_a,t_b),v_Q) = v_P,
inference(literals_permutation,[status(thm)],[c_0_2323]) ).
cnf(c_0_2324_0,axiom,
c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
inference(literals_permutation,[status(thm)],[c_0_2324]) ).
cnf(c_0_2325_0,axiom,
hBOOL(hAPP(hAPP(c_fequal(X1),X2),X2)),
inference(literals_permutation,[status(thm)],[c_0_2325]) ).
cnf(c_0_2328_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_2328]) ).
cnf(c_0_2333_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,X1,tc_fun(X2,tc_bool)) = X1,
inference(literals_permutation,[status(thm)],[c_0_2333]) ).
cnf(c_0_2337_0,axiom,
c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
inference(literals_permutation,[status(thm)],[c_0_2337]) ).
cnf(c_0_2341_0,axiom,
c_The(hAPP(c_fequal(X1),X2),X1) = X2,
inference(literals_permutation,[status(thm)],[c_0_2341]) ).
cnf(c_0_2364_0,axiom,
c_Collect(X1,X2) = X1,
inference(literals_permutation,[status(thm)],[c_0_2364]) ).
cnf(c_0_2365_0,axiom,
class_HOL_Oord(tc_bool),
inference(literals_permutation,[status(thm)],[c_0_2365]) ).
cnf(c_0_2366_0,axiom,
class_HOL_Ominus(tc_bool),
inference(literals_permutation,[status(thm)],[c_0_2366]) ).
cnf(c_0_2367_0,axiom,
class_HOL_Ouminus(tc_bool),
inference(literals_permutation,[status(thm)],[c_0_2367]) ).
cnf(c_0_2368_0,axiom,
class_Orderings_Obot(tc_bool),
inference(literals_permutation,[status(thm)],[c_0_2368]) ).
cnf(c_0_2369_0,axiom,
class_Orderings_Oorder(tc_bool),
inference(literals_permutation,[status(thm)],[c_0_2369]) ).
cnf(c_0_2370_0,axiom,
class_Lattices_Olattice(tc_bool),
inference(literals_permutation,[status(thm)],[c_0_2370]) ).
cnf(c_0_2371_0,axiom,
class_Orderings_Opreorder(tc_bool),
inference(literals_permutation,[status(thm)],[c_0_2371]) ).
cnf(c_0_2372_0,axiom,
class_Finite__Set_Ofinite_Ofinite(tc_bool),
inference(literals_permutation,[status(thm)],[c_0_2372]) ).
cnf(c_0_2373_0,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
inference(literals_permutation,[status(thm)],[c_0_2373]) ).
cnf(c_0_2374_0,axiom,
class_Lattices_Obounded__lattice(tc_bool),
inference(literals_permutation,[status(thm)],[c_0_2374]) ).
cnf(c_0_2375_0,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
inference(literals_permutation,[status(thm)],[c_0_2375]) ).
cnf(c_0_2376_0,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
inference(literals_permutation,[status(thm)],[c_0_2376]) ).
cnf(c_0_2377_0,axiom,
class_HOL_Oord(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2377]) ).
cnf(c_0_2378_0,axiom,
class_HOL_Ominus(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2378]) ).
cnf(c_0_2379_0,axiom,
class_Orderings_Obot(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2379]) ).
cnf(c_0_2380_0,axiom,
class_Orderings_Oorder(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2380]) ).
cnf(c_0_2381_0,axiom,
class_Lattices_Olattice(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2381]) ).
cnf(c_0_2382_0,axiom,
class_Orderings_Olinorder(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2382]) ).
cnf(c_0_2383_0,axiom,
class_Orderings_Opreorder(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2383]) ).
cnf(c_0_2384_0,axiom,
class_Lattices_Oupper__semilattice(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2384]) ).
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_001,negated_conjecture,
! [X1,X2,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X3,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(v_Z(X2,X1),v_c,v_s(X2,X1),t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),X3))
| ~ hBOOL(hAPP(hAPP(v_P,X2),X1)) ),
file('<stdin>',cls_conjecture_3) ).
fof(c_0_1_002,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a),
file('<stdin>',cls_conjecture_1) ).
fof(c_0_2_003,negated_conjecture,
! [X1,X2] :
( c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(v_Z(X2,X1),v_c,v_s(X2,X1),t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(v_P,X2),X1)) ),
file('<stdin>',cls_conjecture_2) ).
fof(c_0_3_004,negated_conjecture,
! [X1,X2,X4] :
( hBOOL(hAPP(hAPP(v_Q,X2),X4))
| ~ hBOOL(hAPP(hAPP(v_s(X2,X1),v_sa(X2,X1,X4)),X4))
| ~ hBOOL(hAPP(hAPP(v_P,X2),X1)) ),
file('<stdin>',cls_conjecture_5) ).
fof(c_0_4_005,negated_conjecture,
! [X1,X2,X4] :
( hBOOL(hAPP(hAPP(v_Q,X2),X4))
| hBOOL(hAPP(hAPP(v_Z(X2,X1),v_sa(X2,X1,X4)),X1))
| ~ hBOOL(hAPP(hAPP(v_P,X2),X1)) ),
file('<stdin>',cls_conjecture_4) ).
fof(c_0_5_006,negated_conjecture,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),v_Ga)),
file('<stdin>',cls_conjecture_0) ).
fof(c_0_6_007,negated_conjecture,
! [X1,X2,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X3,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(v_Z(X2,X1),v_c,v_s(X2,X1),t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),X3))
| ~ hBOOL(hAPP(hAPP(v_P,X2),X1)) ),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_7_008,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_8_009,negated_conjecture,
! [X1,X2] :
( c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(v_Z(X2,X1),v_c,v_s(X2,X1),t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(v_P,X2),X1)) ),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_9_010,negated_conjecture,
! [X1,X2,X4] :
( hBOOL(hAPP(hAPP(v_Q,X2),X4))
| ~ hBOOL(hAPP(hAPP(v_s(X2,X1),v_sa(X2,X1,X4)),X4))
| ~ hBOOL(hAPP(hAPP(v_P,X2),X1)) ),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_10_011,negated_conjecture,
! [X1,X2,X4] :
( hBOOL(hAPP(hAPP(v_Q,X2),X4))
| hBOOL(hAPP(hAPP(v_Z(X2,X1),v_sa(X2,X1,X4)),X1))
| ~ hBOOL(hAPP(hAPP(v_P,X2),X1)) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_11_012,negated_conjecture,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),v_Ga)),
c_0_5 ).
fof(c_0_12_013,negated_conjecture,
! [X4,X5,X6] :
( c_Hoare__Mirabelle_Ohoare__derivs(X6,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(v_Z(X5,X4),v_c,v_s(X5,X4),t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),X6))
| ~ hBOOL(hAPP(hAPP(v_P,X5),X4)) ),
inference(variable_rename,[status(thm)],[c_0_6]) ).
fof(c_0_13_014,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a),
c_0_7 ).
fof(c_0_14_015,negated_conjecture,
! [X3,X4] :
( c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(v_Z(X4,X3),v_c,v_s(X4,X3),t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(v_P,X4),X3)) ),
inference(variable_rename,[status(thm)],[c_0_8]) ).
fof(c_0_15_016,negated_conjecture,
! [X5,X6,X7] :
( hBOOL(hAPP(hAPP(v_Q,X6),X7))
| ~ hBOOL(hAPP(hAPP(v_s(X6,X5),v_sa(X6,X5,X7)),X7))
| ~ hBOOL(hAPP(hAPP(v_P,X6),X5)) ),
inference(variable_rename,[status(thm)],[c_0_9]) ).
fof(c_0_16_017,negated_conjecture,
! [X5,X6,X7] :
( hBOOL(hAPP(hAPP(v_Q,X6),X7))
| hBOOL(hAPP(hAPP(v_Z(X6,X5),v_sa(X6,X5,X7)),X5))
| ~ hBOOL(hAPP(hAPP(v_P,X6),X5)) ),
inference(variable_rename,[status(thm)],[c_0_10]) ).
fof(c_0_17_018,negated_conjecture,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),v_Ga)),
c_0_11 ).
cnf(c_0_18_019,negated_conjecture,
( c_Hoare__Mirabelle_Ohoare__derivs(X3,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(v_Z(X1,X2),v_c,v_s(X1,X2),t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(v_P,X1),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19_020,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20_021,negated_conjecture,
( c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(v_Z(X1,X2),v_c,v_s(X1,X2),t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(v_P,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21_022,negated_conjecture,
( hBOOL(hAPP(hAPP(v_Q,X1),X3))
| ~ hBOOL(hAPP(hAPP(v_P,X1),X2))
| ~ hBOOL(hAPP(hAPP(v_s(X1,X2),v_sa(X1,X2,X3)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22_023,negated_conjecture,
( hBOOL(hAPP(hAPP(v_Z(X1,X2),v_sa(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_16]) ).
cnf(c_0_23_024,negated_conjecture,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),v_Ga)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24_025,negated_conjecture,
( c_Hoare__Mirabelle_Ohoare__derivs(X3,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(v_Z(X1,X2),v_c,v_s(X1,X2),t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(v_P,X1),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),X3)) ),
c_0_18,
[final] ).
cnf(c_0_25_026,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a),
c_0_19,
[final] ).
cnf(c_0_26_027,negated_conjecture,
( c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(v_Z(X1,X2),v_c,v_s(X1,X2),t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(v_P,X1),X2)) ),
c_0_20,
[final] ).
cnf(c_0_27_028,negated_conjecture,
( hBOOL(hAPP(hAPP(v_Q,X1),X3))
| ~ hBOOL(hAPP(hAPP(v_P,X1),X2))
| ~ hBOOL(hAPP(hAPP(v_s(X1,X2),v_sa(X1,X2,X3)),X3)) ),
c_0_21,
[final] ).
cnf(c_0_28_029,negated_conjecture,
( hBOOL(hAPP(hAPP(v_Z(X1,X2),v_sa(X1,X2,X3)),X2))
| hBOOL(hAPP(hAPP(v_Q,X1),X3))
| ~ hBOOL(hAPP(hAPP(v_P,X1),X2)) ),
c_0_22,
[final] ).
cnf(c_0_29_030,negated_conjecture,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),v_Ga)),
c_0_23,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_1151,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a),
file('/export/starexec/sandbox/tmp/iprover_modulo_794ee3.p',c_0_25) ).
cnf(c_1477,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a),
inference(copy,[status(esa)],[c_1151]) ).
cnf(c_1497,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a),
inference(copy,[status(esa)],[c_1477]) ).
cnf(c_1500,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a),
inference(copy,[status(esa)],[c_1497]) ).
cnf(c_1509,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a),
inference(copy,[status(esa)],[c_1500]) ).
cnf(c_4917,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a),
inference(copy,[status(esa)],[c_1509]) ).
cnf(c_1097,plain,
( ~ hBOOL(hAPP(hAPP(X0,X1),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X2,X3,X4,X5)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),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,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_794ee3.p',c_0_1927_1) ).
cnf(c_4809,plain,
( ~ hBOOL(hAPP(hAPP(X0,X1),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X2,X3,X4,X5)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),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,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(copy,[status(esa)],[c_1097]) ).
cnf(c_4810,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,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(rewriting,[status(thm)],[c_4809]) ).
cnf(c_5052,plain,
( ~ hBOOL(hAPP(hAPP(X0,X1),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(v_Ga,v_P,v_Q,v_c)))
| hBOOL(hAPP(hAPP(X2,X1),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(v_Ga,v_P,v_Q,v_c,X0,X2)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(resolution,[status(thm)],[c_4917,c_4810]) ).
cnf(c_5053,plain,
( ~ hBOOL(hAPP(hAPP(X0,X1),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(v_Ga,v_P,v_Q,v_c)))
| hBOOL(hAPP(hAPP(X2,X1),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(v_Ga,v_P,v_Q,v_c,X0,X2)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(rewriting,[status(thm)],[c_5052]) ).
cnf(c_1147,negated_conjecture,
( ~ hBOOL(hAPP(hAPP(v_P,X0),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),X2))
| c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(v_Z(X0,X1),v_c,v_s(X0,X1),t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_794ee3.p',c_0_24) ).
cnf(c_1469,negated_conjecture,
( ~ hBOOL(hAPP(hAPP(v_P,X0),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),X2))
| c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(v_Z(X0,X1),v_c,v_s(X0,X1),t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(copy,[status(esa)],[c_1147]) ).
cnf(c_1493,negated_conjecture,
( ~ hBOOL(hAPP(hAPP(v_P,X0),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),X2))
| c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(v_Z(X0,X1),v_c,v_s(X0,X1),t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(copy,[status(esa)],[c_1469]) ).
cnf(c_1504,negated_conjecture,
( ~ hBOOL(hAPP(hAPP(v_P,X0),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),X2))
| c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(v_Z(X0,X1),v_c,v_s(X0,X1),t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(copy,[status(esa)],[c_1493]) ).
cnf(c_1505,negated_conjecture,
( ~ hBOOL(hAPP(hAPP(v_P,X0),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),X2))
| c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(v_Z(X0,X1),v_c,v_s(X0,X1),t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(copy,[status(esa)],[c_1504]) ).
cnf(c_4909,plain,
( ~ hBOOL(hAPP(hAPP(v_P,X0),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),X2))
| c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(v_Z(X0,X1),v_c,v_s(X0,X1),t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(copy,[status(esa)],[c_1505]) ).
cnf(c_7160,plain,
( ~ hBOOL(hAPP(hAPP(v_P,X0),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),v_Ga))
| ~ hBOOL(hAPP(hAPP(v_Z(X0,X1),X2),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(v_Ga,v_P,v_Q,v_c)))
| hBOOL(hAPP(hAPP(v_s(X0,X1),X2),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(v_Ga,v_P,v_Q,v_c,v_Z(X0,X1),v_s(X0,X1)))) ),
inference(resolution,[status(thm)],[c_5053,c_4909]) ).
cnf(c_7161,plain,
( ~ hBOOL(hAPP(hAPP(v_P,X0),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),v_Ga))
| ~ hBOOL(hAPP(hAPP(v_Z(X0,X1),X2),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(v_Ga,v_P,v_Q,v_c)))
| hBOOL(hAPP(hAPP(v_s(X0,X1),X2),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(v_Ga,v_P,v_Q,v_c,v_Z(X0,X1),v_s(X0,X1)))) ),
inference(rewriting,[status(thm)],[c_7160]) ).
cnf(c_1152,negated_conjecture,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),v_Ga)),
file('/export/starexec/sandbox/tmp/iprover_modulo_794ee3.p',c_0_29) ).
cnf(c_1479,negated_conjecture,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),v_Ga)),
inference(copy,[status(esa)],[c_1152]) ).
cnf(c_1498,negated_conjecture,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),v_Ga)),
inference(copy,[status(esa)],[c_1479]) ).
cnf(c_1499,negated_conjecture,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),v_Ga)),
inference(copy,[status(esa)],[c_1498]) ).
cnf(c_1510,negated_conjecture,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),v_Ga)),
inference(copy,[status(esa)],[c_1499]) ).
cnf(c_4919,plain,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),v_Ga)),
inference(copy,[status(esa)],[c_1510]) ).
cnf(c_7911,plain,
( ~ hBOOL(hAPP(hAPP(v_P,X0),X1))
| ~ hBOOL(hAPP(hAPP(v_Z(X0,X1),X2),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(v_Ga,v_P,v_Q,v_c)))
| hBOOL(hAPP(hAPP(v_s(X0,X1),X2),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(v_Ga,v_P,v_Q,v_c,v_Z(X0,X1),v_s(X0,X1)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7161,c_4919]) ).
cnf(c_7912,plain,
( ~ hBOOL(hAPP(hAPP(v_P,X0),X1))
| ~ hBOOL(hAPP(hAPP(v_Z(X0,X1),X2),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(v_Ga,v_P,v_Q,v_c)))
| hBOOL(hAPP(hAPP(v_s(X0,X1),X2),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(v_Ga,v_P,v_Q,v_c,v_Z(X0,X1),v_s(X0,X1)))) ),
inference(rewriting,[status(thm)],[c_7911]) ).
cnf(c_1149,negated_conjecture,
( ~ hBOOL(hAPP(hAPP(v_P,X0),X1))
| hBOOL(hAPP(hAPP(v_Q,X0),X2))
| ~ hBOOL(hAPP(hAPP(v_s(X0,X1),v_sa(X0,X1,X2)),X2)) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_794ee3.p',c_0_27) ).
cnf(c_1473,negated_conjecture,
( ~ hBOOL(hAPP(hAPP(v_P,X0),X1))
| hBOOL(hAPP(hAPP(v_Q,X0),X2))
| ~ hBOOL(hAPP(hAPP(v_s(X0,X1),v_sa(X0,X1,X2)),X2)) ),
inference(copy,[status(esa)],[c_1149]) ).
cnf(c_1495,negated_conjecture,
( ~ hBOOL(hAPP(hAPP(v_P,X0),X1))
| hBOOL(hAPP(hAPP(v_Q,X0),X2))
| ~ hBOOL(hAPP(hAPP(v_s(X0,X1),v_sa(X0,X1,X2)),X2)) ),
inference(copy,[status(esa)],[c_1473]) ).
cnf(c_1502,negated_conjecture,
( ~ hBOOL(hAPP(hAPP(v_P,X0),X1))
| hBOOL(hAPP(hAPP(v_Q,X0),X2))
| ~ hBOOL(hAPP(hAPP(v_s(X0,X1),v_sa(X0,X1,X2)),X2)) ),
inference(copy,[status(esa)],[c_1495]) ).
cnf(c_1507,negated_conjecture,
( ~ hBOOL(hAPP(hAPP(v_P,X0),X1))
| hBOOL(hAPP(hAPP(v_Q,X0),X2))
| ~ hBOOL(hAPP(hAPP(v_s(X0,X1),v_sa(X0,X1,X2)),X2)) ),
inference(copy,[status(esa)],[c_1502]) ).
cnf(c_4913,negated_conjecture,
( ~ hBOOL(hAPP(hAPP(v_P,X0),X1))
| hBOOL(hAPP(hAPP(v_Q,X0),X2))
| ~ hBOOL(hAPP(hAPP(v_s(X0,X1),v_sa(X0,X1,X2)),X2)) ),
inference(copy,[status(esa)],[c_1507]) ).
cnf(c_7928,plain,
( ~ hBOOL(hAPP(hAPP(v_P,X0),X1))
| hBOOL(hAPP(hAPP(v_Q,X0),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(v_Ga,v_P,v_Q,v_c,v_Z(X0,X1),v_s(X0,X1))))
| ~ hBOOL(hAPP(hAPP(v_Z(X0,X1),v_sa(X0,X1,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(v_Ga,v_P,v_Q,v_c,v_Z(X0,X1),v_s(X0,X1)))),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(v_Ga,v_P,v_Q,v_c))) ),
inference(resolution,[status(thm)],[c_7912,c_4913]) ).
cnf(c_7929,plain,
( ~ hBOOL(hAPP(hAPP(v_P,X0),X1))
| hBOOL(hAPP(hAPP(v_Q,X0),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(v_Ga,v_P,v_Q,v_c,v_Z(X0,X1),v_s(X0,X1))))
| ~ hBOOL(hAPP(hAPP(v_Z(X0,X1),v_sa(X0,X1,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(v_Ga,v_P,v_Q,v_c,v_Z(X0,X1),v_s(X0,X1)))),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(v_Ga,v_P,v_Q,v_c))) ),
inference(rewriting,[status(thm)],[c_7928]) ).
cnf(c_1150,negated_conjecture,
( ~ hBOOL(hAPP(hAPP(v_P,X0),X1))
| hBOOL(hAPP(hAPP(v_Q,X0),X2))
| hBOOL(hAPP(hAPP(v_Z(X0,X1),v_sa(X0,X1,X2)),X1)) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_794ee3.p',c_0_28) ).
cnf(c_1475,negated_conjecture,
( ~ hBOOL(hAPP(hAPP(v_P,X0),X1))
| hBOOL(hAPP(hAPP(v_Q,X0),X2))
| hBOOL(hAPP(hAPP(v_Z(X0,X1),v_sa(X0,X1,X2)),X1)) ),
inference(copy,[status(esa)],[c_1150]) ).
cnf(c_1496,negated_conjecture,
( ~ hBOOL(hAPP(hAPP(v_P,X0),X1))
| hBOOL(hAPP(hAPP(v_Q,X0),X2))
| hBOOL(hAPP(hAPP(v_Z(X0,X1),v_sa(X0,X1,X2)),X1)) ),
inference(copy,[status(esa)],[c_1475]) ).
cnf(c_1501,negated_conjecture,
( ~ hBOOL(hAPP(hAPP(v_P,X0),X1))
| hBOOL(hAPP(hAPP(v_Q,X0),X2))
| hBOOL(hAPP(hAPP(v_Z(X0,X1),v_sa(X0,X1,X2)),X1)) ),
inference(copy,[status(esa)],[c_1496]) ).
cnf(c_1508,negated_conjecture,
( ~ hBOOL(hAPP(hAPP(v_P,X0),X1))
| hBOOL(hAPP(hAPP(v_Q,X0),X2))
| hBOOL(hAPP(hAPP(v_Z(X0,X1),v_sa(X0,X1,X2)),X1)) ),
inference(copy,[status(esa)],[c_1501]) ).
cnf(c_4915,negated_conjecture,
( ~ hBOOL(hAPP(hAPP(v_P,X0),X1))
| hBOOL(hAPP(hAPP(v_Q,X0),X2))
| hBOOL(hAPP(hAPP(v_Z(X0,X1),v_sa(X0,X1,X2)),X1)) ),
inference(copy,[status(esa)],[c_1508]) ).
cnf(c_7963,plain,
( ~ hBOOL(hAPP(hAPP(v_P,X0),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(v_Ga,v_P,v_Q,v_c)))
| hBOOL(hAPP(hAPP(v_Q,X0),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(v_Ga,v_P,v_Q,v_c,v_Z(X0,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(v_Ga,v_P,v_Q,v_c)),v_s(X0,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(v_Ga,v_P,v_Q,v_c))))) ),
inference(resolution,[status(thm)],[c_7929,c_4915]) ).
cnf(c_7964,plain,
( ~ hBOOL(hAPP(hAPP(v_P,X0),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(v_Ga,v_P,v_Q,v_c)))
| hBOOL(hAPP(hAPP(v_Q,X0),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(v_Ga,v_P,v_Q,v_c,v_Z(X0,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(v_Ga,v_P,v_Q,v_c)),v_s(X0,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(v_Ga,v_P,v_Q,v_c))))) ),
inference(rewriting,[status(thm)],[c_7963]) ).
cnf(c_1110,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,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_794ee3.p',c_0_1923_0) ).
cnf(c_4835,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,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(copy,[status(esa)],[c_1110]) ).
cnf(c_5055,plain,
( ~ hBOOL(hAPP(hAPP(v_Q,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(v_Ga,v_P,v_Q,v_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(v_Ga,v_P,v_Q,v_c,X0,X1)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(resolution,[status(thm)],[c_4917,c_4835]) ).
cnf(c_5058,plain,
( ~ hBOOL(hAPP(hAPP(v_Q,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(v_Ga,v_P,v_Q,v_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(v_Ga,v_P,v_Q,v_c,X0,X1)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(rewriting,[status(thm)],[c_5055]) ).
cnf(c_6758,plain,
( ~ hBOOL(hAPP(hAPP(v_P,X0),X1))
| ~ hBOOL(hAPP(hAPP(v_Q,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(v_Ga,v_P,v_Q,v_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(v_Ga,v_P,v_Q,v_c,v_Z(X0,X1),v_s(X0,X1))))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),v_Ga)) ),
inference(resolution,[status(thm)],[c_5058,c_4909]) ).
cnf(c_6759,plain,
( ~ hBOOL(hAPP(hAPP(v_P,X0),X1))
| ~ hBOOL(hAPP(hAPP(v_Q,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(v_Ga,v_P,v_Q,v_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(v_Ga,v_P,v_Q,v_c,v_Z(X0,X1),v_s(X0,X1))))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),v_Ga)) ),
inference(rewriting,[status(thm)],[c_6758]) ).
cnf(c_7113,plain,
( ~ hBOOL(hAPP(hAPP(v_P,X0),X1))
| ~ hBOOL(hAPP(hAPP(v_Q,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(v_Ga,v_P,v_Q,v_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(v_Ga,v_P,v_Q,v_c,v_Z(X0,X1),v_s(X0,X1)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6759,c_4919]) ).
cnf(c_7114,plain,
( ~ hBOOL(hAPP(hAPP(v_P,X0),X1))
| ~ hBOOL(hAPP(hAPP(v_Q,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(v_Ga,v_P,v_Q,v_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(v_Ga,v_P,v_Q,v_c,v_Z(X0,X1),v_s(X0,X1)))) ),
inference(rewriting,[status(thm)],[c_7113]) ).
cnf(c_7983,plain,
~ hBOOL(hAPP(hAPP(v_P,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(v_Ga,v_P,v_Q,v_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(v_Ga,v_P,v_Q,v_c))),
inference(resolution,[status(thm)],[c_7964,c_7114]) ).
cnf(c_7984,plain,
~ hBOOL(hAPP(hAPP(v_P,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(v_Ga,v_P,v_Q,v_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(v_Ga,v_P,v_Q,v_c))),
inference(rewriting,[status(thm)],[c_7983]) ).
cnf(c_1050,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,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_794ee3.p',c_0_1946_1) ).
cnf(c_4715,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,c_Set_Oinsert(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)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(copy,[status(esa)],[c_1050]) ).
cnf(c_5040,plain,
hBOOL(hAPP(hAPP(v_P,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(v_Ga,v_P,v_Q,v_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(v_Ga,v_P,v_Q,v_c))),
inference(resolution,[status(thm)],[c_4917,c_4715]) ).
cnf(c_5043,plain,
hBOOL(hAPP(hAPP(v_P,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(v_Ga,v_P,v_Q,v_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(v_Ga,v_P,v_Q,v_c))),
inference(rewriting,[status(thm)],[c_5040]) ).
cnf(c_8907,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_7984,c_5043]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SWV838-1 : TPTP v8.1.0. Released v4.1.0.
% 0.08/0.15 % Command : iprover_modulo %s %d
% 0.15/0.37 % Computer : n022.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 600
% 0.15/0.37 % DateTime : Wed Jun 15 04:13:18 EDT 2022
% 0.15/0.37 % CPUTime :
% 0.15/0.37 % Running in mono-core mode
% 0.23/0.55 % Orienting using strategy Equiv(ClausalAll)
% 0.23/0.55 % Orientation found
% 0.23/0.55 % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format " --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_e1f9e8.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_794ee3.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_0c69da | grep -v "SZS"
% 0.23/0.58
% 0.23/0.58 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.23/0.58
% 0.23/0.58 %
% 0.23/0.58 % ------ iProver source info
% 0.23/0.58
% 0.23/0.58 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.23/0.58 % git: non_committed_changes: true
% 0.23/0.58 % git: last_make_outside_of_git: true
% 0.23/0.58
% 0.23/0.58 %
% 0.23/0.58 % ------ Input Options
% 0.23/0.58
% 0.23/0.58 % --out_options all
% 0.23/0.58 % --tptp_safe_out true
% 0.23/0.58 % --problem_path ""
% 0.23/0.58 % --include_path ""
% 0.23/0.58 % --clausifier .//eprover
% 0.23/0.58 % --clausifier_options --tstp-format
% 0.23/0.58 % --stdin false
% 0.23/0.58 % --dbg_backtrace false
% 0.23/0.58 % --dbg_dump_prop_clauses false
% 0.23/0.58 % --dbg_dump_prop_clauses_file -
% 0.23/0.58 % --dbg_out_stat false
% 0.23/0.58
% 0.23/0.58 % ------ General Options
% 0.23/0.58
% 0.23/0.58 % --fof false
% 0.23/0.58 % --time_out_real 150.
% 0.23/0.58 % --time_out_prep_mult 0.2
% 0.23/0.58 % --time_out_virtual -1.
% 0.23/0.58 % --schedule none
% 0.23/0.58 % --ground_splitting input
% 0.23/0.58 % --splitting_nvd 16
% 0.23/0.58 % --non_eq_to_eq false
% 0.23/0.58 % --prep_gs_sim true
% 0.23/0.58 % --prep_unflatten false
% 0.23/0.58 % --prep_res_sim true
% 0.23/0.58 % --prep_upred true
% 0.23/0.58 % --res_sim_input true
% 0.23/0.58 % --clause_weak_htbl true
% 0.23/0.58 % --gc_record_bc_elim false
% 0.23/0.58 % --symbol_type_check false
% 0.23/0.58 % --clausify_out false
% 0.23/0.58 % --large_theory_mode false
% 0.23/0.58 % --prep_sem_filter none
% 0.23/0.58 % --prep_sem_filter_out false
% 0.23/0.58 % --preprocessed_out false
% 0.23/0.58 % --sub_typing false
% 0.23/0.58 % --brand_transform false
% 0.23/0.58 % --pure_diseq_elim true
% 0.23/0.58 % --min_unsat_core false
% 0.23/0.58 % --pred_elim true
% 0.23/0.58 % --add_important_lit false
% 0.23/0.58 % --soft_assumptions false
% 0.23/0.58 % --reset_solvers false
% 0.23/0.58 % --bc_imp_inh []
% 0.23/0.58 % --conj_cone_tolerance 1.5
% 0.23/0.58 % --prolific_symb_bound 500
% 0.23/0.58 % --lt_threshold 2000
% 0.23/0.58
% 0.23/0.58 % ------ SAT Options
% 0.23/0.58
% 0.23/0.58 % --sat_mode false
% 0.23/0.58 % --sat_fm_restart_options ""
% 0.23/0.58 % --sat_gr_def false
% 0.23/0.58 % --sat_epr_types true
% 0.23/0.58 % --sat_non_cyclic_types false
% 0.23/0.58 % --sat_finite_models false
% 0.23/0.58 % --sat_fm_lemmas false
% 0.23/0.58 % --sat_fm_prep false
% 0.23/0.58 % --sat_fm_uc_incr true
% 0.23/0.58 % --sat_out_model small
% 0.23/0.58 % --sat_out_clauses false
% 0.23/0.58
% 0.23/0.58 % ------ QBF Options
% 0.23/0.58
% 0.23/0.58 % --qbf_mode false
% 0.23/0.58 % --qbf_elim_univ true
% 0.23/0.58 % --qbf_sk_in true
% 0.23/0.58 % --qbf_pred_elim true
% 0.23/0.58 % --qbf_split 32
% 0.23/0.58
% 0.23/0.58 % ------ BMC1 Options
% 0.23/0.58
% 0.23/0.58 % --bmc1_incremental false
% 0.23/0.58 % --bmc1_axioms reachable_all
% 0.23/0.58 % --bmc1_min_bound 0
% 0.23/0.58 % --bmc1_max_bound -1
% 0.23/0.58 % --bmc1_max_bound_default -1
% 0.23/0.58 % --bmc1_symbol_reachability true
% 0.23/0.58 % --bmc1_property_lemmas false
% 0.23/0.58 % --bmc1_k_induction false
% 0.23/0.58 % --bmc1_non_equiv_states false
% 0.23/0.58 % --bmc1_deadlock false
% 0.23/0.58 % --bmc1_ucm false
% 0.23/0.58 % --bmc1_add_unsat_core none
% 0.23/0.58 % --bmc1_unsat_core_children false
% 0.23/0.58 % --bmc1_unsat_core_extrapolate_axioms false
% 0.23/0.58 % --bmc1_out_stat full
% 0.23/0.58 % --bmc1_ground_init false
% 0.23/0.58 % --bmc1_pre_inst_next_state false
% 0.23/0.58 % --bmc1_pre_inst_state false
% 0.23/0.58 % --bmc1_pre_inst_reach_state false
% 0.23/0.58 % --bmc1_out_unsat_core false
% 0.23/0.58 % --bmc1_aig_witness_out false
% 0.23/0.58 % --bmc1_verbose false
% 0.23/0.58 % --bmc1_dump_clauses_tptp false
% 3.88/4.11 % --bmc1_dump_unsat_core_tptp false
% 3.88/4.11 % --bmc1_dump_file -
% 3.88/4.11 % --bmc1_ucm_expand_uc_limit 128
% 3.88/4.11 % --bmc1_ucm_n_expand_iterations 6
% 3.88/4.11 % --bmc1_ucm_extend_mode 1
% 3.88/4.11 % --bmc1_ucm_init_mode 2
% 3.88/4.11 % --bmc1_ucm_cone_mode none
% 3.88/4.11 % --bmc1_ucm_reduced_relation_type 0
% 3.88/4.11 % --bmc1_ucm_relax_model 4
% 3.88/4.11 % --bmc1_ucm_full_tr_after_sat true
% 3.88/4.11 % --bmc1_ucm_expand_neg_assumptions false
% 3.88/4.11 % --bmc1_ucm_layered_model none
% 3.88/4.11 % --bmc1_ucm_max_lemma_size 10
% 3.88/4.11
% 3.88/4.11 % ------ AIG Options
% 3.88/4.11
% 3.88/4.11 % --aig_mode false
% 3.88/4.11
% 3.88/4.11 % ------ Instantiation Options
% 3.88/4.11
% 3.88/4.11 % --instantiation_flag true
% 3.88/4.11 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 3.88/4.11 % --inst_solver_per_active 750
% 3.88/4.11 % --inst_solver_calls_frac 0.5
% 3.88/4.11 % --inst_passive_queue_type priority_queues
% 3.88/4.11 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 3.88/4.11 % --inst_passive_queues_freq [25;2]
% 3.88/4.11 % --inst_dismatching true
% 3.88/4.11 % --inst_eager_unprocessed_to_passive true
% 3.88/4.11 % --inst_prop_sim_given true
% 3.88/4.11 % --inst_prop_sim_new false
% 3.88/4.11 % --inst_orphan_elimination true
% 3.88/4.11 % --inst_learning_loop_flag true
% 3.88/4.11 % --inst_learning_start 3000
% 3.88/4.11 % --inst_learning_factor 2
% 3.88/4.11 % --inst_start_prop_sim_after_learn 3
% 3.88/4.11 % --inst_sel_renew solver
% 3.88/4.11 % --inst_lit_activity_flag true
% 3.88/4.11 % --inst_out_proof true
% 3.88/4.11
% 3.88/4.11 % ------ Resolution Options
% 3.88/4.11
% 3.88/4.11 % --resolution_flag true
% 3.88/4.11 % --res_lit_sel kbo_max
% 3.88/4.11 % --res_to_prop_solver none
% 3.88/4.11 % --res_prop_simpl_new false
% 3.88/4.11 % --res_prop_simpl_given false
% 3.88/4.11 % --res_passive_queue_type priority_queues
% 3.88/4.11 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 3.88/4.11 % --res_passive_queues_freq [15;5]
% 3.88/4.11 % --res_forward_subs full
% 3.88/4.11 % --res_backward_subs full
% 3.88/4.11 % --res_forward_subs_resolution true
% 3.88/4.11 % --res_backward_subs_resolution true
% 3.88/4.11 % --res_orphan_elimination false
% 3.88/4.11 % --res_time_limit 1000.
% 3.88/4.11 % --res_out_proof true
% 3.88/4.11 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_e1f9e8.s
% 3.88/4.11 % --modulo true
% 3.88/4.11
% 3.88/4.11 % ------ Combination Options
% 3.88/4.11
% 3.88/4.11 % --comb_res_mult 1000
% 3.88/4.11 % --comb_inst_mult 300
% 3.88/4.11 % ------
% 3.88/4.11
% 3.88/4.11 % ------ Parsing...% successful
% 3.88/4.11
% 3.88/4.11 % ------ 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 %
% 3.88/4.11
% 3.88/4.11 % ------ Proving...
% 3.88/4.11 % ------ Problem Properties
% 3.88/4.11
% 3.88/4.11 %
% 3.88/4.11 % EPR false
% 3.88/4.11 % Horn false
% 3.88/4.11 % Has equality true
% 3.88/4.11
% 3.88/4.11 % % ------ Input Options Time Limit: Unbounded
% 3.88/4.11
% 3.88/4.11
% 3.88/4.11 Compiling...
% 3.88/4.11 Loading plugin: done.
% 3.88/4.11 Compiling...
% 3.88/4.11 Loading plugin: done.
% 3.88/4.11 Compiling...
% 3.88/4.11 Loading plugin: done.
% 3.88/4.11 Compiling...
% 3.88/4.11 Loading plugin: done.
% 3.88/4.11 Compiling...
% 3.88/4.11 Loading plugin: done.
% 3.88/4.11 Compiling...
% 3.88/4.11 Loading plugin: done.
% 3.88/4.11 Compiling...
% 3.88/4.11 Loading plugin: done.
% 3.88/4.11 Compiling...
% 3.88/4.11 Loading plugin: done.
% 3.88/4.11 Compiling...
% 3.88/4.11 Loading plugin: done.
% 3.88/4.11 Compiling...
% 3.88/4.11 Loading plugin: done.
% 3.88/4.11 Compiling...
% 3.88/4.11 Loading plugin: done.
% 3.88/4.11 Compiling...
% 3.88/4.11 Loading plugin: done.
% 3.88/4.11 Compiling...
% 3.88/4.11 Loading plugin: done.
% 3.88/4.11 Compiling...
% 3.88/4.11 Loading plugin: done.
% 3.88/4.11 Compiling...
% 3.88/4.11 Loading plugin: done.
% 3.88/4.11 Compiling...
% 3.88/4.11 Loading plugin: done.
% 3.88/4.11 % % ------ Current options:
% 3.88/4.11
% 3.88/4.11 % ------ Input Options
% 3.88/4.11
% 3.88/4.11 % --out_options all
% 3.88/4.11 % --tptp_safe_out true
% 3.88/4.11 % --problem_path ""
% 3.88/4.11 % --include_path ""
% 3.88/4.11 % --clausifier .//eprover
% 3.88/4.11 % --clausifier_options --tstp-format
% 3.88/4.11 % --stdin false
% 3.88/4.11 % --dbg_backtrace false
% 3.88/4.11 % --dbg_dump_prop_clauses false
% 3.88/4.11 % --dbg_dump_prop_clauses_file -
% 3.88/4.11 % --dbg_out_stat false
% 3.88/4.11
% 3.88/4.11 % ------ General Options
% 3.88/4.11
% 3.88/4.11 % --fof false
% 3.88/4.11 % --time_out_real 150.
% 3.88/4.11 % --time_out_prep_mult 0.2
% 3.88/4.11 % --time_out_virtual -1.
% 3.88/4.11 % --schedule none
% 3.88/4.11 % --ground_splitting input
% 3.88/4.11 % --splitting_nvd 16
% 3.88/4.11 % --non_eq_to_eq false
% 3.88/4.11 % --prep_gs_sim true
% 3.88/4.11 % --prep_unflatten false
% 3.88/4.11 % --prep_res_sim true
% 3.88/4.11 % --prep_upred true
% 3.88/4.11 % --res_sim_input true
% 3.88/4.11 % --clause_weak_htbl true
% 3.88/4.11 % --gc_record_bc_elim false
% 3.88/4.11 % --symbol_type_check false
% 3.88/4.11 % --clausify_out false
% 3.88/4.11 % --large_theory_mode false
% 3.88/4.11 % --prep_sem_filter none
% 3.88/4.11 % --prep_sem_filter_out false
% 3.88/4.11 % --preprocessed_out false
% 3.88/4.11 % --sub_typing false
% 3.88/4.11 % --brand_transform false
% 3.88/4.11 % --pure_diseq_elim true
% 3.88/4.11 % --min_unsat_core false
% 3.88/4.11 % --pred_elim true
% 3.88/4.11 % --add_important_lit false
% 3.88/4.11 % --soft_assumptions false
% 3.88/4.11 % --reset_solvers false
% 3.88/4.11 % --bc_imp_inh []
% 3.88/4.11 % --conj_cone_tolerance 1.5
% 3.88/4.11 % --prolific_symb_bound 500
% 3.88/4.11 % --lt_threshold 2000
% 3.88/4.11
% 3.88/4.11 % ------ SAT Options
% 3.88/4.11
% 3.88/4.11 % --sat_mode false
% 3.88/4.11 % --sat_fm_restart_options ""
% 3.88/4.11 % --sat_gr_def false
% 3.88/4.11 % --sat_epr_types true
% 3.88/4.11 % --sat_non_cyclic_types false
% 3.88/4.11 % --sat_finite_models false
% 3.88/4.11 % --sat_fm_lemmas false
% 3.88/4.11 % --sat_fm_prep false
% 3.88/4.11 % --sat_fm_uc_incr true
% 3.88/4.11 % --sat_out_model small
% 3.88/4.11 % --sat_out_clauses false
% 3.88/4.11
% 3.88/4.11 % ------ QBF Options
% 3.88/4.11
% 3.88/4.11 % --qbf_mode false
% 3.88/4.11 % --qbf_elim_univ true
% 3.88/4.11 % --qbf_sk_in true
% 3.88/4.11 % --qbf_pred_elim true
% 3.88/4.11 % --qbf_split 32
% 3.88/4.11
% 3.88/4.11 % ------ BMC1 Options
% 3.88/4.11
% 3.88/4.11 % --bmc1_incremental false
% 3.88/4.11 % --bmc1_axioms reachable_all
% 3.88/4.11 % --bmc1_min_bound 0
% 3.88/4.11 % --bmc1_max_bound -1
% 3.88/4.11 % --bmc1_max_bound_default -1
% 3.88/4.11 % --bmc1_symbol_reachability true
% 3.88/4.11 % --bmc1_property_lemmas false
% 3.88/4.11 % --bmc1_k_induction false
% 3.88/4.11 % --bmc1_non_equiv_states false
% 3.88/4.11 % --bmc1_deadlock false
% 3.88/4.11 % --bmc1_ucm false
% 3.88/4.11 % --bmc1_add_unsat_core none
% 3.88/4.11 % --bmc1_unsat_core_children false
% 3.88/4.11 % --bmc1_unsat_core_extrapolate_axioms false
% 3.88/4.11 % --bmc1_out_stat full
% 3.88/4.11 % --bmc1_ground_init false
% 3.88/4.11 % --bmc1_pre_inst_next_state false
% 3.88/4.11 % --bmc1_pre_inst_state false
% 3.88/4.11 % --bmc1_pre_inst_reach_state false
% 3.88/4.11 % --bmc1_out_unsat_core false
% 3.88/4.11 % --bmc1_aig_witness_out false
% 3.88/4.11 % --bmc1_verbose false
% 3.88/4.11 % --bmc1_dump_clauses_tptp false
% 3.88/4.11 % --bmc1_dump_unsat_core_tptp false
% 3.88/4.11 % --bmc1_dump_file -
% 3.88/4.11 % --bmc1_ucm_expand_uc_limit 128
% 3.88/4.11 % --bmc1_ucm_n_expand_iterations 6
% 3.88/4.11 % --bmc1_ucm_extend_mode 1
% 3.88/4.11 % --bmc1_ucm_init_mode 2
% 3.88/4.11 % --bmc1_ucm_cone_mode none
% 3.88/4.11 % --bmc1_ucm_reduced_relation_type 0
% 3.88/4.11 % --bmc1_ucm_relax_model 4
% 3.88/4.11 % --bmc1_ucm_full_tr_after_sat true
% 3.88/4.11 % --bmc1_ucm_expand_neg_assumptions false
% 3.88/4.11 % --bmc1_ucm_layered_model none
% 3.88/4.11 % --bmc1_ucm_max_lemma_size 10
% 3.88/4.11
% 3.88/4.11 % ------ AIG Options
% 3.88/4.11
% 3.88/4.11 % --aig_mode false
% 150.30/150.58
% 150.30/150.58 % ------ Instantiation Options
% 150.30/150.58
% 150.30/150.58 % --instantiation_flag true
% 150.30/150.58 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 150.30/150.58 % --inst_solver_per_active 750
% 150.30/150.58 % --inst_solver_calls_frac 0.5
% 150.30/150.58 % --inst_passive_queue_type priority_queues
% 150.30/150.58 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 150.30/150.58 % --inst_passive_queues_freq [25;2]
% 150.30/150.58 % --inst_dismatching true
% 150.30/150.58 % --inst_eager_unprocessed_to_passive true
% 150.30/150.58 % --inst_prop_sim_given true
% 150.30/150.58 % --inst_prop_sim_new false
% 150.30/150.58 % --inst_orphan_elimination true
% 150.30/150.58 % --inst_learning_loop_flag true
% 150.30/150.58 % --inst_learning_start 3000
% 150.30/150.58 % --inst_learning_factor 2
% 150.30/150.58 % --inst_start_prop_sim_after_learn 3
% 150.30/150.58 % --inst_sel_renew solver
% 150.30/150.58 % --inst_lit_activity_flag true
% 150.30/150.58 % --inst_out_proof true
% 150.30/150.58
% 150.30/150.58 % ------ Resolution Options
% 150.30/150.58
% 150.30/150.58 % --resolution_flag true
% 150.30/150.58 % --res_lit_sel kbo_max
% 150.30/150.58 % --res_to_prop_solver none
% 150.30/150.58 % --res_prop_simpl_new false
% 150.30/150.58 % --res_prop_simpl_given false
% 150.30/150.58 % --res_passive_queue_type priority_queues
% 150.30/150.58 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 150.30/150.58 % --res_passive_queues_freq [15;5]
% 150.30/150.58 % --res_forward_subs full
% 150.30/150.58 % --res_backward_subs full
% 150.30/150.58 % --res_forward_subs_resolution true
% 150.30/150.58 % --res_backward_subs_resolution true
% 150.30/150.58 % --res_orphan_elimination false
% 150.30/150.58 % --res_time_limit 1000.
% 150.30/150.58 % --res_out_proof true
% 150.30/150.58 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_e1f9e8.s
% 150.30/150.58 % --modulo true
% 150.30/150.58
% 150.30/150.58 % ------ Combination Options
% 150.30/150.58
% 150.30/150.58 % --comb_res_mult 1000
% 150.30/150.58 % --comb_inst_mult 300
% 150.30/150.58 % ------
% 150.30/150.58
% 150.30/150.58
% 150.30/150.58
% 150.30/150.58 % ------ Proving...
% 150.30/150.58 %
% 150.30/150.58
% 150.30/150.58
% 150.30/150.58 % Time Out Real
% 150.30/150.58
% 150.30/150.58 % ------ Statistics
% 150.30/150.58
% 150.30/150.58 % ------ General
% 150.30/150.58
% 150.30/150.58 % num_of_input_clauses: 1153
% 150.30/150.58 % num_of_input_neg_conjectures: 6
% 150.30/150.58 % num_of_splits: 0
% 150.30/150.58 % num_of_split_atoms: 0
% 150.30/150.58 % num_of_sem_filtered_clauses: 0
% 150.30/150.58 % num_of_subtypes: 0
% 150.30/150.58 % monotx_restored_types: 0
% 150.30/150.58 % sat_num_of_epr_types: 0
% 150.30/150.58 % sat_num_of_non_cyclic_types: 0
% 150.30/150.58 % sat_guarded_non_collapsed_types: 0
% 150.30/150.58 % is_epr: 0
% 150.30/150.58 % is_horn: 0
% 150.30/150.58 % has_eq: 1
% 150.30/150.58 % num_pure_diseq_elim: 0
% 150.30/150.58 % simp_replaced_by: 0
% 150.30/150.58 % res_preprocessed: 12
% 150.30/150.58 % prep_upred: 0
% 150.30/150.58 % prep_unflattend: 0
% 150.30/150.58 % pred_elim_cands: 0
% 150.30/150.58 % pred_elim: 0
% 150.30/150.58 % pred_elim_cl: 0
% 150.30/150.58 % pred_elim_cycles: 0
% 150.30/150.58 % forced_gc_time: 0
% 150.30/150.58 % gc_basic_clause_elim: 0
% 150.30/150.58 % parsing_time: 0.068
% 150.30/150.58 % sem_filter_time: 0.
% 150.30/150.58 % pred_elim_time: 0.
% 150.30/150.58 % out_proof_time: 0.
% 150.30/150.58 % monotx_time: 0.
% 150.30/150.58 % subtype_inf_time: 0.
% 150.30/150.58 % unif_index_cands_time: 0.669
% 150.30/150.58 % unif_index_add_time: 0.101
% 150.30/150.58 % total_time: 150.017
% 150.30/150.58 % num_of_symbols: 115
% 150.30/150.58 % num_of_terms: 1613271
% 150.30/150.58
% 150.30/150.58 % ------ Propositional Solver
% 150.30/150.58
% 150.30/150.58 % prop_solver_calls: 17
% 150.30/150.58 % prop_fast_solver_calls: 39
% 150.30/150.58 % prop_num_of_clauses: 20061
% 150.30/150.58 % prop_preprocess_simplified: 35241
% 150.30/150.58 % prop_fo_subsumed: 0
% 150.30/150.58 % prop_solver_time: 0.01
% 150.30/150.58 % prop_fast_solver_time: 0.
% 150.30/150.58 % prop_unsat_core_time: 0.
% 150.30/150.58
% 150.30/150.58 % ------ QBF
% 150.30/150.58
% 150.30/150.58 % qbf_q_res: 0
% 150.30/150.58 % qbf_num_tautologies: 0
% 150.30/150.59 % qbf_prep_cycles: 0
% 150.30/150.59
% 150.30/150.59 % ------ BMC1
% 150.30/150.59
% 150.30/150.59 % bmc1_current_bound: -1
% 150.30/150.59 % bmc1_last_solved_bound: -1
% 150.30/150.59 % bmc1_unsat_core_size: -1
% 150.30/150.59 % bmc1_unsat_core_parents_size: -1
% 150.30/150.59 % bmc1_merge_next_fun: 0
% 150.30/150.59 % bmc1_unsat_core_clauses_time: 0.
% 150.30/150.59
% 150.30/150.59 % ------ Instantiation
% 150.30/150.59
% 150.30/150.59 % inst_num_of_clauses: 3518
% 150.30/150.59 % inst_num_in_passive: 2213
% 150.30/150.59 % inst_num_in_active: 1096
% 150.30/150.59 % inst_num_in_unprocessed: 205
% 150.30/150.59 % inst_num_of_loops: 1199
% 150.30/150.59 % inst_num_of_learning_restarts: 1
% 150.30/150.59 % inst_num_moves_active_passive: 98
% 150.30/150.59 % inst_lit_activity: 664
% 150.30/150.59 % inst_lit_activity_moves: 0
% 150.30/150.59 % inst_num_tautologies: 4
% 150.30/150.59 % inst_num_prop_implied: 0
% 150.30/150.59 % inst_num_existing_simplified: 0
% 150.30/150.59 % inst_num_eq_res_simplified: 0
% 150.30/150.59 % inst_num_child_elim: 0
% 150.30/150.59 % inst_num_of_dismatching_blockings: 4447
% 150.30/150.59 % inst_num_of_non_proper_insts: 4144
% 150.30/150.59 % inst_num_of_duplicates: 5673
% 150.30/150.59 % inst_inst_num_from_inst_to_res: 0
% 150.30/150.59 % inst_dismatching_checking_time: 0.272
% 150.30/150.59
% 150.30/150.59 % ------ Resolution
% 150.30/150.59
% 150.30/150.59 % res_num_of_clauses: 840583
% 150.30/150.59 % res_num_in_passive: 844213
% 150.30/150.59 % res_num_in_active: 11190
% 150.30/150.59 % res_num_of_loops: 14808
% 150.30/150.59 % res_forward_subset_subsumed: 89411
% 150.30/150.59 % res_backward_subset_subsumed: 16135
% 150.30/150.59 % res_forward_subsumed: 3787
% 150.30/150.59 % res_backward_subsumed: 142
% 150.30/150.59 % res_forward_subsumption_resolution: 527
% 150.30/150.59 % res_backward_subsumption_resolution: 15
% 150.30/150.59 % res_clause_to_clause_subsumption: 274999
% 150.30/150.59 % res_orphan_elimination: 0
% 150.30/150.59 % res_tautology_del: 5775
% 150.30/150.59 % res_num_eq_res_simplified: 0
% 150.30/150.59 % res_num_sel_changes: 0
% 150.30/150.59 % res_moves_from_active_to_pass: 0
% 150.30/150.59
% 150.30/150.59 % Status Unknown
% 150.39/150.74 % Orienting using strategy ClausalAll
% 150.39/150.74 % Orientation found
% 150.39/150.74 % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format " --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_e1f9e8.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_794ee3.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_728d6d | grep -v "SZS"
% 150.55/150.76
% 150.55/150.76 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 150.55/150.76
% 150.55/150.76 %
% 150.55/150.76 % ------ iProver source info
% 150.55/150.76
% 150.55/150.76 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 150.55/150.76 % git: non_committed_changes: true
% 150.55/150.76 % git: last_make_outside_of_git: true
% 150.55/150.76
% 150.55/150.76 %
% 150.55/150.76 % ------ Input Options
% 150.55/150.76
% 150.55/150.76 % --out_options all
% 150.55/150.76 % --tptp_safe_out true
% 150.55/150.76 % --problem_path ""
% 150.55/150.76 % --include_path ""
% 150.55/150.76 % --clausifier .//eprover
% 150.55/150.76 % --clausifier_options --tstp-format
% 150.55/150.76 % --stdin false
% 150.55/150.76 % --dbg_backtrace false
% 150.55/150.76 % --dbg_dump_prop_clauses false
% 150.55/150.76 % --dbg_dump_prop_clauses_file -
% 150.55/150.76 % --dbg_out_stat false
% 150.55/150.76
% 150.55/150.76 % ------ General Options
% 150.55/150.76
% 150.55/150.76 % --fof false
% 150.55/150.76 % --time_out_real 150.
% 150.55/150.76 % --time_out_prep_mult 0.2
% 150.55/150.76 % --time_out_virtual -1.
% 150.55/150.76 % --schedule none
% 150.55/150.76 % --ground_splitting input
% 150.55/150.76 % --splitting_nvd 16
% 150.55/150.76 % --non_eq_to_eq false
% 150.55/150.76 % --prep_gs_sim true
% 150.55/150.76 % --prep_unflatten false
% 150.55/150.76 % --prep_res_sim true
% 150.55/150.76 % --prep_upred true
% 150.55/150.76 % --res_sim_input true
% 150.55/150.76 % --clause_weak_htbl true
% 150.55/150.76 % --gc_record_bc_elim false
% 150.55/150.76 % --symbol_type_check false
% 150.55/150.76 % --clausify_out false
% 150.55/150.76 % --large_theory_mode false
% 150.55/150.76 % --prep_sem_filter none
% 150.55/150.76 % --prep_sem_filter_out false
% 150.55/150.76 % --preprocessed_out false
% 150.55/150.76 % --sub_typing false
% 150.55/150.76 % --brand_transform false
% 150.55/150.76 % --pure_diseq_elim true
% 150.55/150.76 % --min_unsat_core false
% 150.55/150.76 % --pred_elim true
% 150.55/150.76 % --add_important_lit false
% 150.55/150.76 % --soft_assumptions false
% 150.55/150.76 % --reset_solvers false
% 150.55/150.76 % --bc_imp_inh []
% 150.55/150.76 % --conj_cone_tolerance 1.5
% 150.55/150.76 % --prolific_symb_bound 500
% 150.55/150.76 % --lt_threshold 2000
% 150.55/150.76
% 150.55/150.76 % ------ SAT Options
% 150.55/150.76
% 150.55/150.76 % --sat_mode false
% 150.55/150.76 % --sat_fm_restart_options ""
% 150.55/150.76 % --sat_gr_def false
% 150.55/150.76 % --sat_epr_types true
% 150.55/150.76 % --sat_non_cyclic_types false
% 150.55/150.76 % --sat_finite_models false
% 150.55/150.76 % --sat_fm_lemmas false
% 150.55/150.76 % --sat_fm_prep false
% 150.55/150.76 % --sat_fm_uc_incr true
% 150.55/150.76 % --sat_out_model small
% 150.55/150.76 % --sat_out_clauses false
% 150.55/150.76
% 150.55/150.76 % ------ QBF Options
% 150.55/150.76
% 150.55/150.76 % --qbf_mode false
% 150.55/150.76 % --qbf_elim_univ true
% 150.55/150.76 % --qbf_sk_in true
% 150.55/150.76 % --qbf_pred_elim true
% 150.55/150.76 % --qbf_split 32
% 150.55/150.76
% 150.55/150.76 % ------ BMC1 Options
% 150.55/150.76
% 150.55/150.76 % --bmc1_incremental false
% 150.55/150.76 % --bmc1_axioms reachable_all
% 150.55/150.76 % --bmc1_min_bound 0
% 150.55/150.76 % --bmc1_max_bound -1
% 150.55/150.76 % --bmc1_max_bound_default -1
% 150.55/150.76 % --bmc1_symbol_reachability true
% 150.55/150.76 % --bmc1_property_lemmas false
% 150.55/150.76 % --bmc1_k_induction false
% 150.55/150.76 % --bmc1_non_equiv_states false
% 150.55/150.76 % --bmc1_deadlock false
% 150.55/150.76 % --bmc1_ucm false
% 150.55/150.76 % --bmc1_add_unsat_core none
% 150.55/150.76 % --bmc1_unsat_core_children false
% 150.55/150.76 % --bmc1_unsat_core_extrapolate_axioms false
% 150.55/150.76 % --bmc1_out_stat full
% 150.55/150.76 % --bmc1_ground_init false
% 150.55/150.76 % --bmc1_pre_inst_next_state false
% 150.55/150.76 % --bmc1_pre_inst_state false
% 150.55/150.76 % --bmc1_pre_inst_reach_state false
% 150.55/150.76 % --bmc1_out_unsat_core false
% 150.55/150.76 % --bmc1_aig_witness_out false
% 150.55/150.76 % --bmc1_verbose false
% 150.55/150.76 % --bmc1_dump_clauses_tptp false
% 153.40/153.63 % --bmc1_dump_unsat_core_tptp false
% 153.40/153.63 % --bmc1_dump_file -
% 153.40/153.63 % --bmc1_ucm_expand_uc_limit 128
% 153.40/153.63 % --bmc1_ucm_n_expand_iterations 6
% 153.40/153.63 % --bmc1_ucm_extend_mode 1
% 153.40/153.63 % --bmc1_ucm_init_mode 2
% 153.40/153.63 % --bmc1_ucm_cone_mode none
% 153.40/153.63 % --bmc1_ucm_reduced_relation_type 0
% 153.40/153.63 % --bmc1_ucm_relax_model 4
% 153.40/153.63 % --bmc1_ucm_full_tr_after_sat true
% 153.40/153.63 % --bmc1_ucm_expand_neg_assumptions false
% 153.40/153.63 % --bmc1_ucm_layered_model none
% 153.40/153.63 % --bmc1_ucm_max_lemma_size 10
% 153.40/153.63
% 153.40/153.63 % ------ AIG Options
% 153.40/153.63
% 153.40/153.63 % --aig_mode false
% 153.40/153.63
% 153.40/153.63 % ------ Instantiation Options
% 153.40/153.63
% 153.40/153.63 % --instantiation_flag true
% 153.40/153.63 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 153.40/153.63 % --inst_solver_per_active 750
% 153.40/153.63 % --inst_solver_calls_frac 0.5
% 153.40/153.63 % --inst_passive_queue_type priority_queues
% 153.40/153.63 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 153.40/153.63 % --inst_passive_queues_freq [25;2]
% 153.40/153.63 % --inst_dismatching true
% 153.40/153.63 % --inst_eager_unprocessed_to_passive true
% 153.40/153.63 % --inst_prop_sim_given true
% 153.40/153.63 % --inst_prop_sim_new false
% 153.40/153.63 % --inst_orphan_elimination true
% 153.40/153.63 % --inst_learning_loop_flag true
% 153.40/153.63 % --inst_learning_start 3000
% 153.40/153.63 % --inst_learning_factor 2
% 153.40/153.63 % --inst_start_prop_sim_after_learn 3
% 153.40/153.63 % --inst_sel_renew solver
% 153.40/153.63 % --inst_lit_activity_flag true
% 153.40/153.63 % --inst_out_proof true
% 153.40/153.63
% 153.40/153.63 % ------ Resolution Options
% 153.40/153.63
% 153.40/153.63 % --resolution_flag true
% 153.40/153.63 % --res_lit_sel kbo_max
% 153.40/153.63 % --res_to_prop_solver none
% 153.40/153.63 % --res_prop_simpl_new false
% 153.40/153.63 % --res_prop_simpl_given false
% 153.40/153.63 % --res_passive_queue_type priority_queues
% 153.40/153.63 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 153.40/153.63 % --res_passive_queues_freq [15;5]
% 153.40/153.63 % --res_forward_subs full
% 153.40/153.63 % --res_backward_subs full
% 153.40/153.63 % --res_forward_subs_resolution true
% 153.40/153.63 % --res_backward_subs_resolution true
% 153.40/153.63 % --res_orphan_elimination false
% 153.40/153.63 % --res_time_limit 1000.
% 153.40/153.63 % --res_out_proof true
% 153.40/153.63 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_e1f9e8.s
% 153.40/153.63 % --modulo true
% 153.40/153.63
% 153.40/153.63 % ------ Combination Options
% 153.40/153.63
% 153.40/153.63 % --comb_res_mult 1000
% 153.40/153.63 % --comb_inst_mult 300
% 153.40/153.63 % ------
% 153.40/153.63
% 153.40/153.63 % ------ Parsing...% successful
% 153.40/153.63
% 153.40/153.63 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e pe_s pe_e snvd_s sp: 0 0s snvd_e %
% 153.40/153.63
% 153.40/153.63 % ------ Proving...
% 153.40/153.63 % ------ Problem Properties
% 153.40/153.63
% 153.40/153.63 %
% 153.40/153.63 % EPR false
% 153.40/153.63 % Horn false
% 153.40/153.63 % Has equality true
% 153.40/153.63
% 153.40/153.63 % % ------ Input Options Time Limit: Unbounded
% 153.40/153.63
% 153.40/153.63
% 153.40/153.63 Compiling...
% 153.40/153.63 Loading plugin: done.
% 153.40/153.63 Compiling...
% 153.40/153.63 Loading plugin: done.
% 153.40/153.63 Compiling...
% 153.40/153.63 Loading plugin: done.
% 153.40/153.63 Compiling...
% 153.40/153.63 Loading plugin: done.
% 153.40/153.63 Compiling...
% 153.40/153.63 Loading plugin: done.
% 153.40/153.63 Compiling...
% 153.40/153.63 Loading plugin: done.
% 153.40/153.63 Compiling...
% 153.40/153.63 Loading plugin: done.
% 153.40/153.63 Compiling...
% 153.40/153.63 Loading plugin: done.
% 153.40/153.63 Compiling...
% 153.40/153.63 Loading plugin: done.
% 153.40/153.63 Compiling...
% 153.40/153.63 Loading plugin: done.
% 153.40/153.63 Compiling...
% 153.40/153.63 Loading plugin: done.
% 153.40/153.63 Compiling...
% 153.40/153.63 Loading plugin: done.
% 153.40/153.63 Compiling...
% 153.40/153.63 Loading plugin: done.
% 153.40/153.63 % % ------ Current options:
% 153.40/153.63
% 153.40/153.63 % ------ Input Options
% 153.40/153.63
% 153.40/153.63 % --out_options all
% 153.40/153.63 % --tptp_safe_out true
% 153.40/153.63 % --problem_path ""
% 153.40/153.63 % --include_path ""
% 153.40/153.63 % --clausifier .//eprover
% 153.40/153.63 % --clausifier_options --tstp-format
% 153.40/153.63 % --stdin false
% 153.40/153.63 % --dbg_backtrace false
% 153.40/153.63 % --dbg_dump_prop_clauses false
% 153.40/153.63 % --dbg_dump_prop_clauses_file -
% 153.40/153.63 % --dbg_out_stat false
% 153.40/153.63
% 153.40/153.63 % ------ General Options
% 153.40/153.63
% 153.40/153.63 % --fof false
% 153.40/153.63 % --time_out_real 150.
% 153.40/153.63 % --time_out_prep_mult 0.2
% 153.40/153.63 % --time_out_virtual -1.
% 153.40/153.63 % --schedule none
% 153.40/153.63 % --ground_splitting input
% 153.40/153.63 % --splitting_nvd 16
% 153.40/153.63 % --non_eq_to_eq false
% 153.40/153.63 % --prep_gs_sim true
% 153.40/153.63 % --prep_unflatten false
% 153.40/153.63 % --prep_res_sim true
% 153.40/153.63 % --prep_upred true
% 153.40/153.63 % --res_sim_input true
% 153.40/153.63 % --clause_weak_htbl true
% 153.40/153.63 % --gc_record_bc_elim false
% 153.40/153.63 % --symbol_type_check false
% 153.40/153.63 % --clausify_out false
% 153.40/153.63 % --large_theory_mode false
% 153.40/153.63 % --prep_sem_filter none
% 153.40/153.63 % --prep_sem_filter_out false
% 153.40/153.63 % --preprocessed_out false
% 153.40/153.63 % --sub_typing false
% 153.40/153.63 % --brand_transform false
% 153.40/153.63 % --pure_diseq_elim true
% 153.40/153.63 % --min_unsat_core false
% 153.40/153.63 % --pred_elim true
% 153.40/153.63 % --add_important_lit false
% 153.40/153.63 % --soft_assumptions false
% 153.40/153.63 % --reset_solvers false
% 153.40/153.63 % --bc_imp_inh []
% 153.40/153.63 % --conj_cone_tolerance 1.5
% 153.40/153.63 % --prolific_symb_bound 500
% 153.40/153.63 % --lt_threshold 2000
% 153.40/153.63
% 153.40/153.63 % ------ SAT Options
% 153.40/153.63
% 153.40/153.63 % --sat_mode false
% 153.40/153.63 % --sat_fm_restart_options ""
% 153.40/153.63 % --sat_gr_def false
% 153.40/153.63 % --sat_epr_types true
% 153.40/153.63 % --sat_non_cyclic_types false
% 153.40/153.63 % --sat_finite_models false
% 153.40/153.63 % --sat_fm_lemmas false
% 153.40/153.63 % --sat_fm_prep false
% 153.40/153.63 % --sat_fm_uc_incr true
% 153.40/153.63 % --sat_out_model small
% 153.40/153.63 % --sat_out_clauses false
% 153.40/153.63
% 153.40/153.63 % ------ QBF Options
% 153.40/153.63
% 153.40/153.63 % --qbf_mode false
% 153.40/153.63 % --qbf_elim_univ true
% 153.40/153.63 % --qbf_sk_in true
% 153.40/153.63 % --qbf_pred_elim true
% 153.40/153.63 % --qbf_split 32
% 153.40/153.63
% 153.40/153.63 % ------ BMC1 Options
% 153.40/153.63
% 153.40/153.63 % --bmc1_incremental false
% 153.40/153.63 % --bmc1_axioms reachable_all
% 153.40/153.63 % --bmc1_min_bound 0
% 153.40/153.63 % --bmc1_max_bound -1
% 153.40/153.63 % --bmc1_max_bound_default -1
% 153.40/153.63 % --bmc1_symbol_reachability true
% 153.40/153.63 % --bmc1_property_lemmas false
% 153.40/153.63 % --bmc1_k_induction false
% 153.40/153.63 % --bmc1_non_equiv_states false
% 153.40/153.63 % --bmc1_deadlock false
% 153.40/153.63 % --bmc1_ucm false
% 153.40/153.63 % --bmc1_add_unsat_core none
% 153.40/153.63 % --bmc1_unsat_core_children false
% 153.40/153.63 % --bmc1_unsat_core_extrapolate_axioms false
% 153.40/153.63 % --bmc1_out_stat full
% 153.40/153.63 % --bmc1_ground_init false
% 153.40/153.63 % --bmc1_pre_inst_next_state false
% 153.40/153.63 % --bmc1_pre_inst_state false
% 153.40/153.63 % --bmc1_pre_inst_reach_state false
% 153.40/153.63 % --bmc1_out_unsat_core false
% 153.40/153.63 % --bmc1_aig_witness_out false
% 153.40/153.63 % --bmc1_verbose false
% 153.40/153.63 % --bmc1_dump_clauses_tptp false
% 153.40/153.63 % --bmc1_dump_unsat_core_tptp false
% 153.40/153.63 % --bmc1_dump_file -
% 153.40/153.63 % --bmc1_ucm_expand_uc_limit 128
% 153.40/153.63 % --bmc1_ucm_n_expand_iterations 6
% 153.40/153.63 % --bmc1_ucm_extend_mode 1
% 153.40/153.63 % --bmc1_ucm_init_mode 2
% 153.40/153.63 % --bmc1_ucm_cone_mode none
% 153.40/153.63 % --bmc1_ucm_reduced_relation_type 0
% 153.40/153.63 % --bmc1_ucm_relax_model 4
% 153.40/153.63 % --bmc1_ucm_full_tr_after_sat true
% 153.40/153.63 % --bmc1_ucm_expand_neg_assumptions false
% 153.40/153.63 % --bmc1_ucm_layered_model none
% 153.40/153.63 % --bmc1_ucm_max_lemma_size 10
% 153.40/153.63
% 153.40/153.63 % ------ AIG Options
% 153.40/153.63
% 153.40/153.63 % --aig_mode false
% 153.40/153.63
% 153.40/153.63 % ------ Instantiation Options
% 153.40/153.63
% 153.40/153.63 % --instantiation_flag true
% 153.40/153.63 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 153.61/153.85 % --inst_solver_per_active 750
% 153.61/153.85 % --inst_solver_calls_frac 0.5
% 153.61/153.85 % --inst_passive_queue_type priority_queues
% 153.61/153.85 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 153.61/153.85 % --inst_passive_queues_freq [25;2]
% 153.61/153.85 % --inst_dismatching true
% 153.61/153.85 % --inst_eager_unprocessed_to_passive true
% 153.61/153.85 % --inst_prop_sim_given true
% 153.61/153.85 % --inst_prop_sim_new false
% 153.61/153.85 % --inst_orphan_elimination true
% 153.61/153.85 % --inst_learning_loop_flag true
% 153.61/153.85 % --inst_learning_start 3000
% 153.61/153.85 % --inst_learning_factor 2
% 153.61/153.85 % --inst_start_prop_sim_after_learn 3
% 153.61/153.85 % --inst_sel_renew solver
% 153.61/153.85 % --inst_lit_activity_flag true
% 153.61/153.85 % --inst_out_proof true
% 153.61/153.85
% 153.61/153.85 % ------ Resolution Options
% 153.61/153.85
% 153.61/153.85 % --resolution_flag true
% 153.61/153.85 % --res_lit_sel kbo_max
% 153.61/153.85 % --res_to_prop_solver none
% 153.61/153.85 % --res_prop_simpl_new false
% 153.61/153.85 % --res_prop_simpl_given false
% 153.61/153.85 % --res_passive_queue_type priority_queues
% 153.61/153.85 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 153.61/153.85 % --res_passive_queues_freq [15;5]
% 153.61/153.85 % --res_forward_subs full
% 153.61/153.85 % --res_backward_subs full
% 153.61/153.85 % --res_forward_subs_resolution true
% 153.61/153.85 % --res_backward_subs_resolution true
% 153.61/153.85 % --res_orphan_elimination false
% 153.61/153.85 % --res_time_limit 1000.
% 153.61/153.85 % --res_out_proof true
% 153.61/153.85 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_e1f9e8.s
% 153.61/153.85 % --modulo true
% 153.61/153.85
% 153.61/153.85 % ------ Combination Options
% 153.61/153.85
% 153.61/153.85 % --comb_res_mult 1000
% 153.61/153.85 % --comb_inst_mult 300
% 153.61/153.85 % ------
% 153.61/153.85
% 153.61/153.85
% 153.61/153.85
% 153.61/153.85 % ------ Proving...
% 153.61/153.85 %
% 153.61/153.85
% 153.61/153.85
% 153.61/153.85 % Resolution empty clause
% 153.61/153.85
% 153.61/153.85 % ------ Statistics
% 153.61/153.85
% 153.61/153.85 % ------ General
% 153.61/153.85
% 153.61/153.85 % num_of_input_clauses: 1153
% 153.61/153.85 % num_of_input_neg_conjectures: 6
% 153.61/153.85 % num_of_splits: 0
% 153.61/153.85 % num_of_split_atoms: 0
% 153.61/153.85 % num_of_sem_filtered_clauses: 0
% 153.61/153.85 % num_of_subtypes: 0
% 153.61/153.85 % monotx_restored_types: 0
% 153.61/153.85 % sat_num_of_epr_types: 0
% 153.61/153.85 % sat_num_of_non_cyclic_types: 0
% 153.61/153.85 % sat_guarded_non_collapsed_types: 0
% 153.61/153.85 % is_epr: 0
% 153.61/153.85 % is_horn: 0
% 153.61/153.85 % has_eq: 1
% 153.61/153.85 % num_pure_diseq_elim: 0
% 153.61/153.85 % simp_replaced_by: 0
% 153.61/153.85 % res_preprocessed: 12
% 153.61/153.85 % prep_upred: 0
% 153.61/153.85 % prep_unflattend: 0
% 153.61/153.85 % pred_elim_cands: 0
% 153.61/153.85 % pred_elim: 0
% 153.61/153.85 % pred_elim_cl: 0
% 153.61/153.85 % pred_elim_cycles: 0
% 153.61/153.85 % forced_gc_time: 0
% 153.61/153.85 % gc_basic_clause_elim: 0
% 153.61/153.85 % parsing_time: 0.078
% 153.61/153.85 % sem_filter_time: 0.
% 153.61/153.85 % pred_elim_time: 0.
% 153.61/153.85 % out_proof_time: 0.002
% 153.61/153.85 % monotx_time: 0.
% 153.61/153.85 % subtype_inf_time: 0.
% 153.61/153.85 % unif_index_cands_time: 0.
% 153.61/153.85 % unif_index_add_time: 0.001
% 153.61/153.85 % total_time: 3.103
% 153.61/153.85 % num_of_symbols: 115
% 153.61/153.85 % num_of_terms: 11867
% 153.61/153.85
% 153.61/153.85 % ------ Propositional Solver
% 153.61/153.85
% 153.61/153.85 % prop_solver_calls: 1
% 153.61/153.85 % prop_fast_solver_calls: 39
% 153.61/153.85 % prop_num_of_clauses: 1089
% 153.61/153.85 % prop_preprocess_simplified: 3551
% 153.61/153.85 % prop_fo_subsumed: 0
% 153.61/153.85 % prop_solver_time: 0.
% 153.61/153.85 % prop_fast_solver_time: 0.
% 153.61/153.85 % prop_unsat_core_time: 0.
% 153.61/153.85
% 153.61/153.85 % ------ QBF
% 153.61/153.85
% 153.61/153.85 % qbf_q_res: 0
% 153.61/153.85 % qbf_num_tautologies: 0
% 153.61/153.85 % qbf_prep_cycles: 0
% 153.61/153.85
% 153.61/153.85 % ------ BMC1
% 153.61/153.85
% 153.61/153.85 % bmc1_current_bound: -1
% 153.61/153.85 % bmc1_last_solved_bound: -1
% 153.61/153.85 % bmc1_unsat_core_size: -1
% 153.61/153.85 % bmc1_unsat_core_parents_size: -1
% 153.61/153.85 % bmc1_merge_next_fun: 0
% 153.61/153.85 % bmc1_unsat_core_clauses_time: 0.
% 153.61/153.85
% 153.61/153.85 % ------ Instantiation
% 153.61/153.85
% 153.61/153.85 % inst_num_of_clauses: 1020
% 153.61/153.85 % inst_num_in_passive: 0
% 153.61/153.85 % inst_num_in_active: 0
% 153.61/153.85 % inst_num_in_unprocessed: 1153
% 153.61/153.85 % inst_num_of_loops: 0
% 153.61/153.85 % inst_num_of_learning_restarts: 0
% 153.61/153.85 % inst_num_moves_active_passive: 0
% 153.61/153.85 % inst_lit_activity: 0
% 153.61/153.85 % inst_lit_activity_moves: 0
% 153.61/153.85 % inst_num_tautologies: 0
% 153.61/153.85 % inst_num_prop_implied: 0
% 153.61/153.85 % inst_num_existing_simplified: 0
% 153.61/153.85 % inst_num_eq_res_simplified: 0
% 153.61/153.85 % inst_num_child_elim: 0
% 153.61/153.85 % inst_num_of_dismatching_blockings: 0
% 153.61/153.85 % inst_num_of_non_proper_insts: 0
% 153.61/153.85 % inst_num_of_duplicates: 0
% 153.61/153.85 % inst_inst_num_from_inst_to_res: 0
% 153.61/153.85 % inst_dismatching_checking_time: 0.
% 153.61/153.85
% 153.61/153.85 % ------ Resolution
% 153.61/153.85
% 153.61/153.85 % res_num_of_clauses: 2767
% 153.61/153.85 % res_num_in_passive: 1577
% 153.61/153.85 % res_num_in_active: 552
% 153.61/153.85 % res_num_of_loops: 121
% 153.61/153.85 % res_forward_subset_subsumed: 665
% 153.61/153.85 % res_backward_subset_subsumed: 9
% 153.61/153.85 % res_forward_subsumed: 26
% 153.61/153.85 % res_backward_subsumed: 0
% 153.61/153.85 % res_forward_subsumption_resolution: 14
% 153.61/153.85 % res_backward_subsumption_resolution: 0
% 153.61/153.85 % res_clause_to_clause_subsumption: 620
% 153.61/153.85 % res_orphan_elimination: 0
% 153.61/153.85 % res_tautology_del: 3
% 153.61/153.85 % res_num_eq_res_simplified: 0
% 153.61/153.85 % res_num_sel_changes: 0
% 153.61/153.85 % res_moves_from_active_to_pass: 0
% 153.61/153.85
% 153.61/153.85 % Status Unsatisfiable
% 153.61/153.85 % SZS status Unsatisfiable
% 153.61/153.85 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------