ITP001 Axioms: ITP045+4.ax
%------------------------------------------------------------------------------
% File : ITP045+4 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 syntactic export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : bag.ax [Gau19]
% : HL4045+4.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 396 ( 190 unt; 0 def)
% Number of atoms : 900 ( 368 equ)
% Maximal formula atoms : 66 ( 2 avg)
% Number of connectives : 549 ( 45 ~; 21 |; 179 &)
% ( 95 <=>; 209 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 6 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 170 ( 170 usr; 83 con; 0-3 aty)
% Number of variables : 1478 (1446 !; 32 ?)
% SPC : FOF_SAT_RFO_SEQ
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
fof(reserved_2Eho_2Eboolext,axiom,
! [V0_2E0,V1_2E0] :
( ( p(s(tyop_2Emin_2Ebool,V0_2E0))
<=> p(s(tyop_2Emin_2Ebool,V1_2E0)) )
=> s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0) ) ).
fof(reserved_2Eho_2Etruth,axiom,
p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ).
fof(reserved_2Eho_2Enotfalse,axiom,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) ).
fof(reserved_2Eho_2Ebool__cases__ax,axiom,
! [V0t_2E0] :
( s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
| s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ).
fof(reserved_2Eho_2Ei__thm,axiom,
! [A_27a,V0x_2E0] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0))) = s(A_27a,V0x_2E0) ).
fof(reserved_2Eho_2Ek__thm,axiom,
! [A_27a,A_27b,V0x_2E0,V1y_2E0] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0))) = s(A_27a,V0x_2E0) ).
fof(reserved_2Eho_2Es__thm,axiom,
! [A_27a,A_27b,A_27c,V0f_2E0,V1g_2E0,V2x_2E0] : s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))))) ).
fof(reserved_2Elogic_2E_2F_5C,axiom,
! [V0_2E0,V1_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,V0_2E0))
& p(s(tyop_2Emin_2Ebool,V1_2E0)) ) ) ).
fof(reserved_2Elogic_2E_5C_2F,axiom,
! [V0_2E0,V1_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,V0_2E0))
| p(s(tyop_2Emin_2Ebool,V1_2E0)) ) ) ).
fof(reserved_2Elogic_2E_7E,axiom,
! [V0_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0))))
<=> ~ p(s(tyop_2Emin_2Ebool,V0_2E0)) ) ).
fof(reserved_2Elogic_2E_3D_3D_3E,axiom,
! [V0_2E0,V1_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,V0_2E0))
=> p(s(tyop_2Emin_2Ebool,V1_2E0)) ) ) ).
fof(reserved_2Elogic_2E_3D,axiom,
! [A_27a,V0_2E0,V1_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0))))
<=> s(A_27a,V0_2E0) = s(A_27a,V1_2E0) ) ).
fof(reserved_2Equant_2E_21,axiom,
! [A_27a,V0f_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0))))
<=> ! [V1x_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0)))) ) ).
fof(reserved_2Equant_2E_3F,axiom,
! [A_27a,V0f_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0))))
<=> ? [V1x_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0)))) ) ).
fof(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
! [X0_2E0,X1_2E0] :
( ( p(s(tyop_2Emin_2Ebool,X0_2E0))
& p(s(tyop_2Emin_2Ebool,X1_2E0)) )
<=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) ) ).
fof(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,
! [X0_2E0,X1_2E0] :
( ( p(s(tyop_2Emin_2Ebool,X0_2E0))
| p(s(tyop_2Emin_2Ebool,X1_2E0)) )
<=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) ) ).
fof(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,
! [X0_2E0] :
( ~ p(s(tyop_2Emin_2Ebool,X0_2E0))
<=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))) ) ).
fof(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
! [X0_2E0,X1_2E0] :
( ( p(s(tyop_2Emin_2Ebool,X0_2E0))
=> p(s(tyop_2Emin_2Ebool,X1_2E0)) )
<=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) ) ).
fof(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] :
( s(A_27a,X0_2E0) = s(A_27a,X1_2E0)
<=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))) ) ).
fof(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq1_2Ec_2Ebag_2EBAG__ALL__DISTINCT_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__ALL__DISTINCT_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Ebag_2EBAG__ALL__DISTINCT_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))) ).
fof(arityeq1_2Ec_2Ebag_2EBAG__OF__SET_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__OF__SET_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),c_2Ebag_2EBAG__OF__SET_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq2_2Ec_2Ebag_2EBAG__DIFF_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))),c_2Ebag_2EBAG__DIFF_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0))) ).
fof(arityeq2_2Ec_2Ebag_2EBAG__MERGE_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__MERGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))),c_2Ebag_2EBAG__MERGE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0))) ).
fof(arityeq2_2Ec_2Ebag_2EBAG__UNION_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))),c_2Ebag_2EBAG__UNION_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0))) ).
fof(arityeq1_2Ec_2Ebag_2EBAG__ALL__DISTINCT_2E1_2Emono_2EA_27b,axiom,
! [A_27b,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__ALL__DISTINCT_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Ebag_2EBAG__ALL__DISTINCT_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X0_2E0))) ).
fof(arityeq2_2Ec_2Ebag_2EBAG__INSERT_2E2_2Emono_2EA_27b,axiom,
! [A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27b,X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum))),c_2Ebag_2EBAG__INSERT_2E0),s(A_27b,X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X1_2E0))) ).
fof(arityeq1_2Ec_2Ebag_2EBAG__CARD_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__CARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Enum_2Enum),c_2Ebag_2EBAG__CARD_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))) ).
fof(arityeq2_2Ec_2Ebag_2EBAG__INSERT_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))),c_2Ebag_2EBAG__INSERT_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0))) ).
fof(arityeq1_2Ec_2Ebag_2EBAG__CHOICE_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(A_27a,c_2Ebag_2EBAG__CHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),A_27a),c_2Ebag_2EBAG__CHOICE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))) ).
fof(arityeq1_2Ec_2Ebag_2ESET__OF__BAG_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebag_2ESET__OF__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ebag_2ESET__OF__BAG_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))) ).
fof(arityeq1_2Ec_2Ebag_2EBAG__REST_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__REST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),c_2Ebag_2EBAG__REST_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))) ).
fof(arityeq1_2Ec_2Ebag_2EBIG__BAG__UNION_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBIG__BAG__UNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),c_2Ebag_2EBIG__BAG__UNION_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq2_2Ec_2Epred__set_2EDELETE_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Enum_2Enum_29,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool))),c_2Epred__set_2EDELETE_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0))) ).
fof(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Enum_2Enum_29,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool))),c_2Epred__set_2EINSERT_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Enum_2Enum_29,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool))),c_2Epred__set_2EUNION_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq1_2Ec_2Ebag_2EEL__BAG_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEL__BAG_2E1(s(A_27a,X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),c_2Ebag_2EEL__BAG_2E0),s(A_27a,X0_2E0))) ).
fof(arityeq1_2Ec_2Ebag_2EEMPTY__BAG_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Enum_2Enum,c_2Ebag_2EEMPTY__BAG_2E1(s(A_27a,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0),s(A_27a,X0_2E0))) ).
fof(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EFINITE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Enum_2Enum_29,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EFINITE_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq1_2Ec_2Ebag_2EFINITE__BAG_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Ebag_2EFINITE__BAG_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))) ).
fof(arityeq2_2Ec_2Ebag_2EBAG__FILTER_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__FILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))),c_2Ebag_2EBAG__FILTER_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0))) ).
fof(arityeq2_2Ec_2Ebag_2EBAG__INTER_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))),c_2Ebag_2EBAG__INTER_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0))) ).
fof(arityeq2_2Ec_2Ebag_2EBAG__IMAGE_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),c_2Ebag_2EBAG__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum))),c_2Ebag_2EBAG__IMAGE_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0))) ).
fof(arityeq1_2Ec_2Ebag_2EFINITE__BAG_2E1_2Emono_2EA_27b,axiom,
! [A_27b,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Ebag_2EFINITE__BAG_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X0_2E0))) ).
fof(arityeq1_2Ec_2Ebag_2EFINITE__BAG_2E1_2Emono_2EA_27c,axiom,
! [A_27c,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Ebag_2EFINITE__BAG_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),X0_2E0))) ).
fof(arityeq1_2Ec_2Ebag_2EFINITE__BAG_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Ebag_2EFINITE__BAG_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) ).
fof(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ecombin_2EK_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),c_2Ecombin_2EK_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).
fof(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1,axiom,
! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT1_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).
fof(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1,axiom,
! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2ENUMERAL_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).
fof(arityeq2_2Ec_2Ebag_2EBAG__IMAGE_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))),c_2Ebag_2EBAG__IMAGE_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X1_2E0))) ).
fof(arityeq1_2Ec_2Ebag_2ESING__BAG_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebag_2ESING__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Ebag_2ESING__BAG_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))) ).
fof(arityeq1_2Ec_2Enum_2ESUC_2E1,axiom,
! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enum_2ESUC_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).
fof(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWF_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) ).
fof(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Enum_2Enum_29,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWF_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),X0_2E0))) ).
fof(arityeq1_2Ec_2Ebag_2Emlt1_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Ebag_2Emlt1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool))),c_2Ebag_2Emlt1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) ).
fof(arityeq1_2Ec_2Erelation_2Etransitive_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Etransitive_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) ).
fof(arityeq3_2Ec_2Ebag_2EITBAG_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(A_27b,c_2Ebag_2EITBAG_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0),s(A_27b,X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27b,A_27b))),c_2Ebag_2EITBAG_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0))),s(A_27b,X2_2E0))) ).
fof(arityeq2_2Ec_2Earithmetic_2E_2A_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2A_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).
fof(arityeq2_2Ec_2Ebag_2EBAG__GEN__PROD_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__GEN__PROD_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebag_2EBAG__GEN__PROD_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).
fof(arityeq2_2Ec_2Earithmetic_2E_2B_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2B_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).
fof(arityeq2_2Ec_2Ebag_2EBAG__GEN__SUM_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__GEN__SUM_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebag_2EBAG__GEN__SUM_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).
fof(arityeq2_2Ec_2Ebag_2Ebag__size_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Enum_2Enum,c_2Ebag_2Ebag__size_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Enum_2Enum)),c_2Ebag_2Ebag__size_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))) ).
fof(arityeq2_2Ec_2Earithmetic_2E_2D_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).
fof(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Eprim__rec_2E_3C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).
fof(arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Earithmetic_2E_3C_3D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).
fof(arityeq2_2Ec_2Earithmetic_2E_3E_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Earithmetic_2E_3E_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).
fof(arityeq2_2Ec_2Earithmetic_2E_3E_3D_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_3D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Earithmetic_2E_3E_3D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).
fof(arityeq2_2Ec_2Ebag_2EBAG__CARD__RELn_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__CARD__RELn_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Ebag_2EBAG__CARD__RELn_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).
fof(arityeq2_2Ec_2Epred__set_2EINTER_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Enum_2Enum_29,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool))),c_2Epred__set_2EINTER_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Ebag_2EBAG__DIFF_2E2_2Emono_2EA_27b,axiom,
! [A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum))),c_2Ebag_2EBAG__DIFF_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X1_2E0))) ).
fof(arityeq2_2Ec_2Ebag_2EBAG__DIFF_2E2_2Emono_2EA_27c,axiom,
! [A_27c,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum))),c_2Ebag_2EBAG__DIFF_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),X1_2E0))) ).
fof(arityeq2_2Ec_2Ebag_2EBAG__DIFF_2E2_2Emono_2EA_27d,axiom,
! [A_27d,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27d,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Emin_2Efun(A_27d,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27d,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27d,tyop_2Enum_2Enum))),c_2Ebag_2EBAG__DIFF_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27d,tyop_2Enum_2Enum),X1_2E0))) ).
fof(arityeq2_2Ec_2Ebag_2EBAG__DISJOINT_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__DISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Ebag_2EBAG__DISJOINT_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0))) ).
fof(arityeq2_2Ec_2Ebag_2EBAG__DISJOINT_2E2_2Emono_2EA_27b,axiom,
! [A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__DISJOINT_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Ebag_2EBAG__DISJOINT_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X1_2E0))) ).
fof(arityeq2_2Ec_2Ebag_2EBAG__EVERY_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__EVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Ebag_2EBAG__EVERY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0))) ).
fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Ebag_2EBAG__EVERY_2E2_2Emono_2EA_27b,axiom,
! [A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__EVERY_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Ebag_2EBAG__EVERY_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X1_2E0))) ).
fof(arityeq2_2Ec_2Ebag_2EBAG__INSERT_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Ebag_2EBAG__INSERT_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0))) ).
fof(arityeq2_2Ec_2Ebag_2EBAG__UNION_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Ebag_2EBAG__UNION_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0))) ).
fof(arityeq2_2Ec_2Ebag_2EBAG__IMAGE_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))),c_2Ebag_2EBAG__IMAGE_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0))) ).
fof(arityeq2_2Ec_2Ebag_2EBAG__IMAGE_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a,A_27c,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))),c_2Ebag_2EBAG__IMAGE_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),X1_2E0))) ).
fof(arityeq2_2Ec_2Ebag_2EBAG__IMAGE_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),c_2Ebag_2EBAG__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum))),c_2Ebag_2EBAG__IMAGE_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),X1_2E0))) ).
fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27c,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0))) = s(tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0))) ).
fof(arityeq2_2Ec_2Ebag_2EBAG__IN_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Ebag_2EBAG__IN_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0))) ).
fof(arityeq2_2Ec_2Ebag_2EBAG__IN_2E2_2Emono_2EA_27b,axiom,
! [A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27b,X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Ebag_2EBAG__IN_2E0),s(A_27b,X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X1_2E0))) ).
fof(arityeq2_2Ec_2Ebag_2EBAG__IN_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Ebag_2EBAG__IN_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0))) ).
fof(arityeq2_2Ec_2Ebag_2EBAG__OF__SET_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__OF__SET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),c_2Ebag_2EBAG__OF__SET_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))) ).
fof(arityeq2_2Ec_2Ebag_2EBAG__UNION_2E2_2Emono_2EA_27b,axiom,
! [A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum))),c_2Ebag_2EBAG__UNION_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X1_2E0))) ).
fof(arityeq2_2Ec_2Ebag_2EBAG__UNION_2E2_2Emono_2EA_27c,axiom,
! [A_27c,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum))),c_2Ebag_2EBAG__UNION_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),X1_2E0))) ).
fof(arityeq2_2Ec_2Ebag_2EBIG__BAG__UNION_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Enum_2Enum,c_2Ebag_2EBIG__BAG__UNION_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),c_2Ebag_2EBIG__BAG__UNION_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))) ).
fof(arityeq2_2Ec_2Epred__set_2EDISJOINT_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EDISJOINT_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq1_2Ec_2Ebag_2ESET__OF__BAG_2E1_2Emono_2EA_27b,axiom,
! [A_27b,X0_2E0] : s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Ebag_2ESET__OF__BAG_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Ebag_2ESET__OF__BAG_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X0_2E0))) ).
fof(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27b,axiom,
! [A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(A_27b,X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Enum_2Enum_29,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EINSERT_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Ebag_2EBAG__FILTER_2E2_2Emono_2EA_27b,axiom,
! [A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),c_2Ebag_2EBAG__FILTER_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum))),c_2Ebag_2EBAG__FILTER_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X1_2E0))) ).
fof(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Enum_2Enum,axiom,
! [A_27b,X0_2E0,X1_2E0] : s(tyop_2Enum_2Enum,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Enum_2Enum)),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X1_2E0))) ).
fof(arityeq2_2Ec_2Ebag_2EPSUB__BAG_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebag_2EPSUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Ebag_2EPSUB__BAG_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0))) ).
fof(arityeq2_2Ec_2Ebag_2ESET__OF__BAG_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebag_2ESET__OF__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ebag_2ESET__OF__BAG_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(A_27a,X1_2E0))) ).
fof(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2ESUBSET_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) ).
fof(arityeq2_2Ec_2Epred__set_2EDIFF_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EDIFF_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Ebag_2ESUB__BAG_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Ebag_2ESUB__BAG_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0))) ).
fof(arityeq2_2Ec_2Ebag_2ESUB__BAG_2E2_2Emono_2EA_27d,axiom,
! [A_27d,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Ebag_2ESUB__BAG_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27d,tyop_2Enum_2Enum),X1_2E0))) ).
fof(arityeq2_2Ec_2Epred__set_2ESUM__IMAGE_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Enum_2Enum_29,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Enum_2Enum)),c_2Epred__set_2ESUM__IMAGE_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EUNION_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Erelation_2EWFP_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Enum_2Enum_29,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Erelation_2EWFP_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Erelation_2EWFP_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0))) ).
fof(arityeq2_2Ec_2Edivides_2Edivides_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Edivides_2Edivides_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).
fof(arityeq3_2Ec_2Ebag_2EBAG__DELETE_2E3_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__DELETE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(A_27a,X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool))),c_2Ebag_2EBAG__DELETE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X2_2E0))) ).
fof(arityeq3_2Ec_2Ebag_2EBAG__DIFF_2E3_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__DIFF_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))),c_2Ebag_2EBAG__DIFF_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0))),s(A_27a,X2_2E0))) ).
fof(arityeq3_2Ec_2Ebag_2EBAG__FILTER_2E3_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__FILTER_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))),c_2Ebag_2EBAG__FILTER_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0))),s(A_27a,X2_2E0))) ).
fof(arityeq3_2Ec_2Ebag_2EBAG__IMAGE_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__IMAGE_2E3(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))),c_2Ebag_2EBAG__IMAGE_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X1_2E0))),s(A_27a,X2_2E0))) ).
fof(arityeq3_2Ec_2Ebag_2EBAG__INN_2E3_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__INN_2E3(s(A_27a,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool))),c_2Ebag_2EBAG__INN_2E0),s(A_27a,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X2_2E0))) ).
fof(arityeq3_2Ec_2Ebag_2EBAG__INSERT_2E3_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__INSERT_2E3(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))),c_2Ebag_2EBAG__INSERT_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0))),s(A_27a,X2_2E0))) ).
fof(arityeq3_2Ec_2Ebag_2EBAG__INTER_2E3_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__INTER_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))),c_2Ebag_2EBAG__INTER_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0))),s(A_27a,X2_2E0))) ).
fof(arityeq3_2Ec_2Ebag_2EBAG__MERGE_2E3_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__MERGE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))),c_2Ebag_2EBAG__MERGE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0))),s(A_27a,X2_2E0))) ).
fof(arityeq3_2Ec_2Ebag_2EBAG__UNION_2E3_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__UNION_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))),c_2Ebag_2EBAG__UNION_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0))),s(A_27a,X2_2E0))) ).
fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27b,axiom,
! [A_27b,X0_2E0,X1_2E0,X2_2E0] : s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(A_27b,X1_2E0),s(A_27b,X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(A_27b,X1_2E0))),s(A_27b,X2_2E0))) ).
fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Enum_2Enum_29,axiom,
! [A_27a,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X2_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X2_2E0))) ).
fof(arityeq1_2Ec_2Ebag_2EBAG__CARD_2E1_2Emono_2EA_27b,axiom,
! [A_27b,X0_2E0] : s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__CARD_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Enum_2Enum),c_2Ebag_2EBAG__CARD_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X0_2E0))) ).
fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) ).
fof(arityeq3_2Ec_2Ebag_2EITBAG_2E3_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum,axiom,
! [A_27a,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Enum_2Enum,c_2Ebag_2EITBAG_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Ebag_2EITBAG_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) ).
fof(arityeq3_2Ec_2Ebag_2EITBAG_2E3_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Enum_2Enum,c_2Ebag_2EITBAG_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Ebag_2EITBAG_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) ).
fof(arityeq3_2Ec_2Epred__set_2EITSET_2E3_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Enum_2Enum_29,axiom,
! [A_27a,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Epred__set_2EITSET_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X2_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)))),c_2Epred__set_2EITSET_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X2_2E0))) ).
fof(arityeq3_2Ec_2Erelation_2ETC_2E3_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Enum_2Enum_29,axiom,
! [A_27a,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool))),c_2Erelation_2ETC_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X2_2E0))) ).
fof(arityeq3_2Ec_2Erelation_2ETC_2E3_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool))),c_2Erelation_2ETC_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X2_2E0))) ).
fof(arityeq1_2Ec_2Ebag_2Emlt1_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Ebag_2Emlt1_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool))),c_2Ebag_2Emlt1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0))) ).
fof(arityeq3_2Ec_2Ebag_2Edominates_2E3_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2Ebag_2Edominates_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Ebag_2Edominates_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0))) ).
fof(arityeq3_2Ec_2Ebag_2Edominates_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2Ebag_2Edominates_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Ebag_2Edominates_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0))) ).
fof(arityeq3_2Ec_2Ebag_2Emlt1_2E3_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2Ebag_2Emlt1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool))),c_2Ebag_2Emlt1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X2_2E0))) ).
fof(thm_2Ebag_2EEMPTY__BAG,axiom,
! [A_27a] : s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ecombin_2EK_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) ).
fof(thm_2Ebag_2EBAG__INN,axiom,
! [A_27a,V0e_2E0,V1n_2E0,V2b_2E0] : s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__INN_2E3(s(A_27a,V0e_2E0),s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_3D_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b_2E0),s(A_27a,V0e_2E0))),s(tyop_2Enum_2Enum,V1n_2E0))) ).
fof(thm_2Ebag_2ESUB__BAG,axiom,
! [A_27a,V0b1_2E0,V1b2_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))))
<=> ! [V2x_2E0,V3n_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__INN_2E3(s(A_27a,V2x_2E0),s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__INN_2E3(s(A_27a,V2x_2E0),s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0)))) ) ) ).
fof(thm_2Ebag_2EPSUB__BAG,axiom,
! [A_27a,V0b1_2E0,V1b2_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EPSUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))))
& s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0) ) ) ).
fof(thm_2Ebag_2EBAG__IN,axiom,
! [A_27a,V0e_2E0,V1b_2E0] : s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__INN_2E3(s(A_27a,V0e_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))) ).
fof(thm_2Ebag_2EBAG__UNION,axiom,
! [A_27a,V0b_2E0,V1c_2E0,V2x_2E0] : s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__UNION_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1c_2E0),s(A_27a,V2x_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0),s(A_27a,V2x_2E0))),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1c_2E0),s(A_27a,V2x_2E0))))) ).
fof(thm_2Ebag_2EBAG__DIFF,axiom,
! [A_27a,V0b1_2E0,V1b2_2E0,V2x_2E0] : s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__DIFF_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0),s(A_27a,V2x_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(A_27a,V2x_2E0))),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0),s(A_27a,V2x_2E0))))) ).
fof(thm_2Ebag_2EBAG__INSERT,axiom,
! [A_27a,F0_2E0] :
( ! [V2x_2E0,V0e_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(A_27a,V2x_2E0))),s(A_27a,V0e_2E0))))
<=> s(A_27a,V2x_2E0) = s(A_27a,V0e_2E0) )
=> ! [V0e_2E0,V1b_2E0,V2x_2E0] : s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__INSERT_2E3(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0),s(A_27a,V2x_2E0))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(A_27a,V2x_2E0))),s(A_27a,V0e_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0),s(A_27a,V0e_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0),s(A_27a,V2x_2E0))))) ) ).
fof(thm_2Ebag_2EBAG__INTER,axiom,
! [A_27a,V0b1_2E0,V1b2_2E0,V2x_2E0] : s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__INTER_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0),s(A_27a,V2x_2E0))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(A_27a,V2x_2E0))),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0),s(A_27a,V2x_2E0))))),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(A_27a,V2x_2E0))),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0),s(A_27a,V2x_2E0))))) ).
fof(thm_2Ebag_2EBAG__MERGE,axiom,
! [A_27a,V0b1_2E0,V1b2_2E0,V2x_2E0] : s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__MERGE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0),s(A_27a,V2x_2E0))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(A_27a,V2x_2E0))),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0),s(A_27a,V2x_2E0))))),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0),s(A_27a,V2x_2E0))),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(A_27a,V2x_2E0))))) ).
fof(thm_2Ebag_2EBAG__DELETE,axiom,
! [A_27a,V0b0_2E0,V1e_2E0,V2b_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__DELETE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b0_2E0),s(A_27a,V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b_2E0))))
<=> s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b0_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b_2E0))) ) ).
fof(thm_2Ebag_2ESING__BAG,axiom,
! [A_27a,V0b_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESING__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))))
<=> ? [V1x_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0))) ) ).
fof(thm_2Ebag_2EEL__BAG,axiom,
! [A_27a,V0e_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEL__BAG_2E1(s(A_27a,V0e_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0))) ).
fof(thm_2Ebag_2ESET__OF__BAG,axiom,
! [A_27a,V0b_2E0,V1x_2E0] : s(tyop_2Emin_2Ebool,c_2Ebag_2ESET__OF__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0),s(A_27a,V1x_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))) ).
fof(thm_2Ebag_2EBAG__OF__SET,axiom,
! [A_27a,V0P_2E0,V1x_2E0] : s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__OF__SET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V1x_2E0))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) ).
fof(thm_2Ebag_2EBAG__DISJOINT,axiom,
! [A_27a,V0b1_2E0,V1b2_2E0] : s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__DISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebag_2ESET__OF__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebag_2ESET__OF__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))))) ).
fof(thm_2Ebag_2EFINITE__BAG,axiom,
! [A_27a,V0b_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))))
<=> ! [V1P_2E0] :
( ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0))))
& ! [V2b_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b_2E0))))
=> ! [V3e_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V3e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b_2E0)))))) ) )
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0)))) ) ) ).
fof(thm_2Ebag_2EBAG__CARD__RELn,axiom,
! [A_27a,V0b_2E0,V1n_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__CARD__RELn_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))
<=> ! [V2P_2E0] :
( ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V2P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))
& ! [V3b_2E0,V4n_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V2P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3b_2E0))),s(tyop_2Enum_2Enum,V4n_2E0))))
=> ! [V5e_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V2P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V5e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3b_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V4n_2E0)))))) ) )
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V2P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))),s(tyop_2Enum_2Enum,V1n_2E0)))) ) ) ).
fof(thm_2Ebag_2EBAG__CARD,axiom,
! [A_27a,V0b_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__CARD__RELn_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0),s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__CARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0)))))) ) ).
fof(thm_2Ebag_2EBAG__FILTER__DEF,axiom,
! [A_27a,V0P_2E0,V1b_2E0,V2x_2E0] : s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__FILTER_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0),s(A_27a,V2x_2E0))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0))),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0),s(A_27a,V2x_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) ).
fof(thm_2Ebag_2EBAG__IMAGE__DEF,axiom,
! [A_27a,A_27b,F0_2E0,F1_2E0] :
( ! [V3sb_2E0] : s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Enum_2Enum),F0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V3sb_2E0))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V3sb_2E0))),s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__CARD_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V3sb_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))
=> ( ! [V0f_2E0,V2x_2E0,V4e0_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),F1_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V0f_2E0))),s(A_27a,V2x_2E0))),s(A_27b,V4e0_2E0))))
<=> s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V0f_2E0),s(A_27b,V4e0_2E0))) = s(A_27a,V2x_2E0) )
=> ! [V0f_2E0,V1b_2E0,V2x_2E0] : s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__IMAGE_2E3(s(tyop_2Emin_2Efun(A_27b,A_27a),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V1b_2E0),s(A_27a,V2x_2E0))) = s(tyop_2Enum_2Enum,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Enum_2Enum),F0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),c_2Ebag_2EBAG__FILTER_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),F1_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V0f_2E0))),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V1b_2E0))))) ) ) ).
fof(thm_2Ebag_2EBAG__CHOICE__DEF,axiom,
! [A_27a,V0b_2E0] :
( s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0)
=> p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,c_2Ebag_2EBAG__CHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0)))) ) ).
fof(thm_2Ebag_2EBAG__REST__DEF,axiom,
! [A_27a,V0b_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__REST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEL__BAG_2E1(s(A_27a,c_2Ebag_2EBAG__CHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))))))) ).
fof(thm_2Ebag_2EBAG__GEN__SUM__def,axiom,
! [V0bag_2E0,V1n_2E0] : s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__GEN__SUM_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0bag_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Ebag_2EITBAG_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2B_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0bag_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) ).
fof(thm_2Ebag_2EBAG__GEN__PROD__def,axiom,
! [V0bag_2E0,V1n_2E0] : s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__GEN__PROD_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0bag_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Ebag_2EITBAG_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2A_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0bag_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) ).
fof(thm_2Ebag_2EBAG__EVERY,axiom,
! [A_27a,V0P_2E0,V1b_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__EVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))))
<=> ! [V2e_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))))
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2e_2E0)))) ) ) ).
fof(thm_2Ebag_2EBAG__ALL__DISTINCT,axiom,
! [A_27a,V0b_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__ALL__DISTINCT_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))))
<=> ! [V1e_2E0] : p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0),s(A_27a,V1e_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))) ) ).
fof(thm_2Ebag_2EBIG__BAG__UNION__def,axiom,
! [A_27a,F0_2E0] :
( ! [V1x_2E0,V2b_2E0] : s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Enum_2Enum)),F0_2E0),s(A_27a,V1x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b_2E0),s(A_27a,V1x_2E0)))
=> ! [V0sob_2E0,V1x_2E0] : s(tyop_2Enum_2Enum,c_2Ebag_2EBIG__BAG__UNION_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V0sob_2E0),s(A_27a,V1x_2E0))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Enum_2Enum)),F0_2E0),s(A_27a,V1x_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V0sob_2E0))) ) ).
fof(thm_2Ebag_2Emlt1__def,axiom,
! [A_27a,V0r_2E0,V1b1_2E0,V2b2_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2Emlt1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b2_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b2_2E0))))
& ? [V3e_2E0,V4rep_2E0,V5res_2E0] :
( s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V4rep_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V5res_2E0)))
& s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b2_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V5res_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V3e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0)))))
& ! [V6e_27_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V6e_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V4rep_2E0))))
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0r_2E0),s(A_27a,V6e_27_2E0))),s(A_27a,V3e_2E0)))) ) ) ) ) ).
fof(thm_2Ebag_2Edominates__def,axiom,
! [A_27a,A_27b,V0R_2E0,V1s1_2E0,V2s2_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2Edominates_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s2_2E0))))
<=> ! [V3x_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s1_2E0))))
=> ? [V4y_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V4y_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s2_2E0))))
& p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3x_2E0))),s(A_27b,V4y_2E0)))) ) ) ) ).
fof(thm_2Ebag_2Ebag__size__def,axiom,
! [A_27a,F0_2E0] :
( ! [V0eltsize_2E0,V2e_2E0,V3acc_2E0] : s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0eltsize_2E0))),s(A_27a,V2e_2E0))),s(tyop_2Enum_2Enum,V3acc_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0eltsize_2E0),s(A_27a,V2e_2E0))))),s(tyop_2Enum_2Enum,V3acc_2E0)))
=> ! [V0eltsize_2E0,V1b_2E0] : s(tyop_2Enum_2Enum,c_2Ebag_2Ebag__size_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0eltsize_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))) = s(tyop_2Enum_2Enum,c_2Ebag_2EITBAG_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0eltsize_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) ) ).
fof(thm_2Ebag_2EEMPTY__BAG__alt,axiom,
! [A_27a,V0x_2E0] : s(tyop_2Enum_2Enum,c_2Ebag_2EEMPTY__BAG_2E1(s(A_27a,V0x_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) ).
fof(thm_2Ebag_2EBAG__cases,axiom,
! [A_27a,V0b_2E0] :
( s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0)
| ? [V1b0_2E0,V2e_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b0_2E0))) ) ).
fof(thm_2Ebag_2EBAG__MERGE__IDEM,axiom,
! [A_27a,V0b_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__MERGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0) ).
fof(thm_2Ebag_2EBAG__INN__0,axiom,
! [A_27a,V0b_2E0,V1e_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__INN_2E3(s(A_27a,V1e_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0)))) ).
fof(thm_2Ebag_2EBAG__INN__LESS,axiom,
! [A_27a,V0b_2E0,V1e_2E0,V2n_2E0,V3m_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__INN_2E3(s(A_27a,V1e_2E0),s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3m_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))) )
=> p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__INN_2E3(s(A_27a,V1e_2E0),s(tyop_2Enum_2Enum,V3m_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0)))) ) ).
fof(thm_2Ebag_2EBAG__IN__BAG__INSERT,axiom,
! [A_27a,V0b_2E0,V1e1_2E0,V2e2_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V1e1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V2e2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))))))
<=> ( s(A_27a,V1e1_2E0) = s(A_27a,V2e2_2E0)
| p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V1e1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0)))) ) ) ).
fof(thm_2Ebag_2EBAG__INN__BAG__INSERT,axiom,
! [A_27a,V0n_2E0,V1b_2E0,V2e1_2E0,V3e2_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__INN_2E3(s(A_27a,V2e1_2E0),s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V3e2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))))))
<=> ( ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__INN_2E3(s(A_27a,V2e1_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))))
& s(A_27a,V2e1_2E0) = s(A_27a,V3e2_2E0) )
| p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__INN_2E3(s(A_27a,V2e1_2E0),s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0)))) ) ) ).
fof(thm_2Ebag_2EBAG__INN__BAG__INSERT__STRONG,axiom,
! [A_27a,V0b_2E0,V1n_2E0,V2e1_2E0,V3e2_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__INN_2E3(s(A_27a,V2e1_2E0),s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V3e2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))))))
<=> ( ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__INN_2E3(s(A_27a,V2e1_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))))
& s(A_27a,V2e1_2E0) = s(A_27a,V3e2_2E0) )
| ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__INN_2E3(s(A_27a,V2e1_2E0),s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))))
& s(A_27a,V2e1_2E0) != s(A_27a,V3e2_2E0) ) ) ) ).
fof(thm_2Ebag_2EBAG__UNION__EQ__LCANCEL1,axiom,
! [A_27a,V0c_2E0,V1b_2E0] :
( s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0c_2E0)))
<=> s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0c_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0) ) ).
fof(thm_2Ebag_2EBAG__UNION__EQ__RCANCEL1,axiom,
! [A_27a,V0c_2E0,V1b_2E0] :
( s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0c_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0)))
<=> s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0c_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0) ) ).
fof(thm_2Ebag_2EBAG__IN__BAG__UNION,axiom,
! [A_27a,V0b1_2E0,V1b2_2E0,V2e_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0))))
| p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0)))) ) ) ).
fof(thm_2Ebag_2EBAG__INN__BAG__UNION,axiom,
! [A_27a,V0n_2E0,V1e_2E0,V2b1_2E0,V3b2_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__INN_2E3(s(A_27a,V1e_2E0),s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3b2_2E0))))))
<=> ? [V4m1_2E0,V5m2_2E0] :
( s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V4m1_2E0),s(tyop_2Enum_2Enum,V5m2_2E0)))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__INN_2E3(s(A_27a,V1e_2E0),s(tyop_2Enum_2Enum,V4m1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b1_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__INN_2E3(s(A_27a,V1e_2E0),s(tyop_2Enum_2Enum,V5m2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3b2_2E0)))) ) ) ).
fof(thm_2Ebag_2EBAG__INN__BAG__MERGE,axiom,
! [A_27a,V0n_2E0,V1e_2E0,V2b1_2E0,V3b2_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__INN_2E3(s(A_27a,V1e_2E0),s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__MERGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3b2_2E0))))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__INN_2E3(s(A_27a,V1e_2E0),s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b1_2E0))))
| p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__INN_2E3(s(A_27a,V1e_2E0),s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3b2_2E0)))) ) ) ).
fof(thm_2Ebag_2EBAG__IN__BAG__MERGE,axiom,
! [A_27a,V0e_2E0,V1b1_2E0,V2b2_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__MERGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b2_2E0))))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0))))
| p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b2_2E0)))) ) ) ).
fof(thm_2Ebag_2EBAG__EXTENSION,axiom,
! [A_27a,V0b1_2E0,V1b2_2E0] :
( s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0)
<=> ! [V2n_2E0,V3e_2E0] : s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__INN_2E3(s(A_27a,V3e_2E0),s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__INN_2E3(s(A_27a,V3e_2E0),s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))) ) ).
fof(thm_2Ebag_2EBAG__UNION__INSERT,axiom,
! [A_27a,V0e_2E0,V1b1_2E0,V2b2_2E0] :
( s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b2_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b2_2E0)))))
& s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b2_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b2_2E0))))) ) ).
fof(thm_2Ebag_2EBAG__INSERT__DIFF,axiom,
! [A_27a,V0x_2E0,V1b_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))) != s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0) ).
fof(thm_2Ebag_2EBAG__INSERT__NOT__EMPTY,axiom,
! [A_27a,V0x_2E0,V1b_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))) != s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0) ).
fof(thm_2Ebag_2EBAG__INSERT__ONE__ONE,axiom,
! [A_27a,V0b1_2E0,V1b2_2E0,V2x_2E0] :
( s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0)))
<=> s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0) ) ).
fof(thm_2Ebag_2EC__BAG__INSERT__ONE__ONE,axiom,
! [A_27a,V0x_2E0,V1y_2E0,V2b_2E0] :
( s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V1y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b_2E0)))
<=> s(A_27a,V0x_2E0) = s(A_27a,V1y_2E0) ) ).
fof(thm_2Ebag_2EBAG__INSERT__commutes,axiom,
! [A_27a,V0b_2E0,V1e1_2E0,V2e2_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V1e1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V2e2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V2e2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V1e1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))))) ).
fof(thm_2Ebag_2EBAG__DECOMPOSE,axiom,
! [A_27a,V0e_2E0,V1b_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))))
=> ? [V2b_27_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b_27_2E0))) ) ).
fof(thm_2Ebag_2EBAG__UNION__LEFT__CANCEL,axiom,
! [A_27a,V0b_2E0,V1b1_2E0,V2b2_2E0] :
( s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b2_2E0)))
<=> s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b2_2E0) ) ).
fof(thm_2Ebag_2ECOMM__BAG__UNION,axiom,
! [A_27a,V0b1_2E0,V1b2_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0))) ).
fof(thm_2Ebag_2EBAG__UNION__RIGHT__CANCEL,axiom,
! [A_27a,V0b_2E0,V1b1_2E0,V2b2_2E0] :
( s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0)))
<=> s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b2_2E0) ) ).
fof(thm_2Ebag_2EASSOC__BAG__UNION,axiom,
! [A_27a,V0b1_2E0,V1b2_2E0,V2b3_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b3_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b3_2E0))) ).
fof(thm_2Ebag_2EBAG__UNION__EMPTY,axiom,
! [A_27a,A_27b,A_27c] :
( ! [V0b_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0)
& ! [V1b_2E0] : s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V1b_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V1b_2E0)
& ! [V2b1_2E0,V3b2_2E0] :
( s(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),V2b1_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),V3b2_2E0))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0)
<=> ( s(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),V2b1_2E0) = s(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0)
& s(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),V3b2_2E0) = s(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0) ) ) ) ).
fof(thm_2Ebag_2EBAG__DELETE__EMPTY,axiom,
! [A_27a,V0e_2E0,V1b_2E0] : ~ p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__DELETE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0),s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0)))) ).
fof(thm_2Ebag_2EBAG__DELETE__commutes,axiom,
! [A_27a,V0b0_2E0,V1b1_2E0,V2b2_2E0,V3e1_2E0,V4e2_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__DELETE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b0_2E0),s(A_27a,V3e1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__DELETE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0),s(A_27a,V4e2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b2_2E0)))) )
=> ? [V5b_27_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__DELETE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b0_2E0),s(A_27a,V4e2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V5b_27_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__DELETE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V5b_27_2E0),s(A_27a,V3e1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b2_2E0)))) ) ) ).
fof(thm_2Ebag_2EBAG__DELETE__11,axiom,
! [A_27a,V0b0_2E0,V1e1_2E0,V2e2_2E0,V3b1_2E0,V4b2_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__DELETE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b0_2E0),s(A_27a,V1e1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3b1_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__DELETE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b0_2E0),s(A_27a,V2e2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V4b2_2E0)))) )
=> ( s(A_27a,V1e1_2E0) = s(A_27a,V2e2_2E0)
<=> s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3b1_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V4b2_2E0) ) ) ).
fof(thm_2Ebag_2EBAG__INN__BAG__DELETE,axiom,
! [A_27a,V0b_2E0,V1n_2E0,V2e_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__INN_2E3(s(A_27a,V2e_2E0),s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) )
=> ? [V3b_27_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__DELETE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0),s(A_27a,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3b_27_2E0)))) ) ).
fof(thm_2Ebag_2EBAG__IN__BAG__DELETE,axiom,
! [A_27a,V0b_2E0,V1e_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))))
=> ? [V2b_27_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__DELETE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0),s(A_27a,V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b_27_2E0)))) ) ).
fof(thm_2Ebag_2EBAG__DELETE__INSERT,axiom,
! [A_27a,V0x_2E0,V1y_2E0,V2b1_2E0,V3b2_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__DELETE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b1_2E0))),s(A_27a,V1y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3b2_2E0))))
=> ( ( s(A_27a,V0x_2E0) = s(A_27a,V1y_2E0)
& s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b1_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3b2_2E0) )
| ( ? [V4b3_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__DELETE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b1_2E0),s(A_27a,V1y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V4b3_2E0))))
& s(A_27a,V0x_2E0) != s(A_27a,V1y_2E0) ) ) ) ).
fof(thm_2Ebag_2EBAG__DELETE__BAG__IN__up,axiom,
! [A_27a,V0b0_2E0,V1b_2E0,V2e_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__DELETE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b0_2E0),s(A_27a,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))))
=> ! [V3e_27_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V3e_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V3e_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b0_2E0)))) ) ) ).
fof(thm_2Ebag_2EBAG__DELETE__BAG__IN__down,axiom,
! [A_27a,V0b0_2E0,V1b_2E0,V2e1_2E0,V3e2_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__DELETE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b0_2E0),s(A_27a,V2e1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))))
& s(A_27a,V2e1_2E0) != s(A_27a,V3e2_2E0)
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V3e2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b0_2E0)))) )
=> p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V3e2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0)))) ) ).
fof(thm_2Ebag_2EBAG__DELETE__BAG__IN,axiom,
! [A_27a,V0b0_2E0,V1b_2E0,V2e_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__DELETE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b0_2E0),s(A_27a,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b0_2E0)))) ) ).
fof(thm_2Ebag_2EBAG__DELETE__concrete,axiom,
! [A_27a,F0_2E0] :
( ! [V3x_2E0,V2e_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(A_27a,V3x_2E0))),s(A_27a,V2e_2E0))))
<=> s(A_27a,V3x_2E0) = s(A_27a,V2e_2E0) )
=> ! [V0b0_2E0,V1b_2E0,V2e_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__DELETE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b0_2E0),s(A_27a,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b0_2E0),s(A_27a,V2e_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))
& ! [V3x_2E0] : s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0),s(A_27a,V3x_2E0))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(A_27a,V3x_2E0))),s(A_27a,V2e_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b0_2E0),s(A_27a,V2e_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b0_2E0),s(A_27a,V3x_2E0))))) ) ) ) ).
fof(thm_2Ebag_2EBAG__UNION__DIFF__eliminate,axiom,
! [A_27a,V0c_2E0,V1b_2E0] :
( s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0c_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0c_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0)
& s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0c_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0c_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0) ) ).
fof(thm_2Ebag_2EBAG__INSERT__EQUAL,axiom,
! [A_27a,V0b_2E0,V1a_2E0,V2N_2E0,V3M_2E0] :
( s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V1a_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3M_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V0b_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2N_2E0)))
<=> ( ( s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3M_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2N_2E0)
& s(A_27a,V1a_2E0) = s(A_27a,V0b_2E0) )
| ? [V4k_2E0] :
( s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3M_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V0b_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V4k_2E0)))
& s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2N_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V1a_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V4k_2E0))) ) ) ) ).
fof(thm_2Ebag_2EBAG__DELETE__TWICE,axiom,
! [A_27a,V0b0_2E0,V1e1_2E0,V2e2_2E0,V3b1_2E0,V4b2_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__DELETE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b0_2E0),s(A_27a,V1e1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3b1_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__DELETE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b0_2E0),s(A_27a,V2e2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V4b2_2E0))))
& s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3b1_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V4b2_2E0) )
=> ? [V5b_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__DELETE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3b1_2E0),s(A_27a,V2e2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V5b_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__DELETE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V4b2_2E0),s(A_27a,V1e1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V5b_2E0)))) ) ) ).
fof(thm_2Ebag_2ESING__BAG__THM,axiom,
! [A_27a,V0e_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESING__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0)))))) ).
fof(thm_2Ebag_2EEL__BAG__11,axiom,
! [A_27a,V0x_2E0,V1y_2E0] :
( s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEL__BAG_2E1(s(A_27a,V0x_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEL__BAG_2E1(s(A_27a,V1y_2E0)))
=> s(A_27a,V0x_2E0) = s(A_27a,V1y_2E0) ) ).
fof(thm_2Ebag_2EEL__BAG__INSERT__squeeze,axiom,
! [A_27a,V0x_2E0,V1b_2E0,V2y_2E0] :
( s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEL__BAG_2E1(s(A_27a,V0x_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V2y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0)))
=> ( s(A_27a,V0x_2E0) = s(A_27a,V2y_2E0)
& s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0) ) ) ).
fof(thm_2Ebag_2ESING__EL__BAG,axiom,
! [A_27a,V0e_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESING__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEL__BAG_2E1(s(A_27a,V0e_2E0)))))) ).
fof(thm_2Ebag_2EBAG__INSERT__UNION,axiom,
! [A_27a,V0b_2E0,V1e_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEL__BAG_2E1(s(A_27a,V1e_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))) ).
fof(thm_2Ebag_2EBAG__INSERT__EQ__UNION,axiom,
! [A_27a,V0e_2E0,V1b1_2E0,V2b2_2E0,V3b_2E0] :
( s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3b_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b2_2E0)))
=> ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0))))
| p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b2_2E0)))) ) ) ).
fof(thm_2Ebag_2EBAG__DELETE__SING,axiom,
! [A_27a,V0b_2E0,V1e_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__DELETE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0),s(A_27a,V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESING__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0)))) ) ).
fof(thm_2Ebag_2ENOT__IN__EMPTY__BAG,axiom,
! [A_27a,V0x_2E0] : ~ p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0)))) ).
fof(thm_2Ebag_2EBAG__INN__EMPTY__BAG,axiom,
! [A_27a,V0e_2E0,V1n_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__INN_2E3(s(A_27a,V0e_2E0),s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0))))
<=> s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) ) ).
fof(thm_2Ebag_2EMEMBER__NOT__EMPTY,axiom,
! [A_27a,V0b_2E0] :
( ? [V1x_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))))
<=> s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0) ) ).
fof(thm_2Ebag_2ESUB__BAG__LEQ,axiom,
! [A_27a,V0b2_2E0,V1b1_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b2_2E0))))
<=> ! [V2x_2E0] : p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0),s(A_27a,V2x_2E0))),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b2_2E0),s(A_27a,V2x_2E0)))))) ) ).
fof(thm_2Ebag_2ESUB__BAG__EMPTY,axiom,
! [A_27a] :
( ! [V0b_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))))
& ! [V1b_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0))))
<=> s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0) ) ) ).
fof(thm_2Ebag_2ESUB__BAG__REFL,axiom,
! [A_27a,V0b_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0)))) ).
fof(thm_2Ebag_2EPSUB__BAG__IRREFL,axiom,
! [A_27a,V0b_2E0] : ~ p(s(tyop_2Emin_2Ebool,c_2Ebag_2EPSUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0)))) ).
fof(thm_2Ebag_2ESUB__BAG__ANTISYM,axiom,
! [A_27a,V0b1_2E0,V1b2_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0)))) )
=> s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0) ) ).
fof(thm_2Ebag_2EPSUB__BAG__ANTISYM,axiom,
! [A_27a,V0b1_2E0,V1b2_2E0] :
~ ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EPSUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2EPSUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0)))) ) ).
fof(thm_2Ebag_2ESUB__BAG__TRANS,axiom,
! [A_27a,V0b1_2E0,V1b2_2E0,V2b3_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b3_2E0)))) )
=> p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b3_2E0)))) ) ).
fof(thm_2Ebag_2EPSUB__BAG__TRANS,axiom,
! [A_27a,V0b1_2E0,V1b2_2E0,V2b3_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EPSUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2EPSUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b3_2E0)))) )
=> p(s(tyop_2Emin_2Ebool,c_2Ebag_2EPSUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b3_2E0)))) ) ).
fof(thm_2Ebag_2EPSUB__BAG__SUB__BAG,axiom,
! [A_27a,V0b1_2E0,V1b2_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EPSUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0)))) ) ).
fof(thm_2Ebag_2EPSUB__BAG__NOT__EQ,axiom,
! [A_27a,V0b1_2E0,V1b2_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EPSUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))))
=> s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0) ) ).
fof(thm_2Ebag_2EBAG__DIFF__EMPTY,axiom,
! [A_27a,A_27b,A_27c,A_27d] :
( ! [V0b_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0)
& ! [V1b_2E0] : s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V1b_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V1b_2E0)
& ! [V2b_2E0] : s(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),V2b_2E0))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0)
& ! [V3b1_2E0,V4b2_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Enum_2Enum),V3b1_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Enum_2Enum),V4b2_2E0))))
=> s(tyop_2Emin_2Efun(A_27d,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Enum_2Enum),V3b1_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Enum_2Enum),V4b2_2E0))) = s(tyop_2Emin_2Efun(A_27d,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0) ) ) ).
fof(thm_2Ebag_2EBAG__DIFF__EMPTY__simple,axiom,
! [A_27a,A_27b,A_27c] :
( ! [V0b_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0)
& ! [V1b_2E0] : s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V1b_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V1b_2E0)
& ! [V2b_2E0] : s(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),V2b_2E0))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0) ) ).
fof(thm_2Ebag_2EBAG__DIFF__EQ__EMPTY,axiom,
! [A_27a,V0c_2E0,V1b_2E0] :
( s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0c_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0)
<=> p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0c_2E0)))) ) ).
fof(thm_2Ebag_2EBAG__DIFF__INSERT__same,axiom,
! [A_27a,V0x_2E0,V1b1_2E0,V2b2_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b2_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b2_2E0))) ).
fof(thm_2Ebag_2EBAG__DIFF__INSERT,axiom,
! [A_27a,V0x_2E0,V1b1_2E0,V2b2_2E0] :
( ~ p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0))))
=> s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0))))) ) ).
fof(thm_2Ebag_2ENOT__IN__BAG__DIFF,axiom,
! [A_27a,V0x_2E0,V1b1_2E0,V2b2_2E0] :
( ~ p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0))))
=> s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b2_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b2_2E0))) ) ).
fof(thm_2Ebag_2EBAG__IN__DIFF__I,axiom,
! [A_27a,V0e_2E0,V1b2_2E0,V2b1_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b1_2E0))))
& ~ p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0)))) )
=> p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0)))))) ) ).
fof(thm_2Ebag_2EBAG__IN__DIFF__E,axiom,
! [A_27a,V0e_2E0,V1b2_2E0,V2b1_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))))))
=> p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b1_2E0)))) ) ).
fof(thm_2Ebag_2EBAG__UNION__DIFF,axiom,
! [A_27a,V0X_2E0,V1Y_2E0,V2Z_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2Z_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1Y_2E0))))
=> ( s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0X_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1Y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2Z_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0X_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1Y_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2Z_2E0)))
& s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1Y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2Z_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0X_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0X_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1Y_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2Z_2E0))) ) ) ).
fof(thm_2Ebag_2EBAG__DIFF__2L,axiom,
! [A_27a,V0X_2E0,V1Y_2E0,V2Z_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0X_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1Y_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2Z_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0X_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1Y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2Z_2E0))))) ).
fof(thm_2Ebag_2EBAG__DIFF__2R,axiom,
! [A_27a,V0A_2E0,V1B_2E0,V2C_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2C_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1B_2E0))))
=> s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0A_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1B_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2C_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0A_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2C_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1B_2E0))) ) ).
fof(thm_2Ebag_2ESUB__BAG__BAG__DIFF,axiom,
! [A_27a,V0X_2E0,V1Y_2E0,V2Y_27_2E0,V3Z_2E0,V4W_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0X_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1Y_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3Z_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V4W_2E0))))))
=> p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0X_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1Y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2Y_27_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3Z_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V4W_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2Y_27_2E0)))))))) ) ).
fof(thm_2Ebag_2EBAG__DIFF__UNION__eliminate,axiom,
! [A_27a,V0b1_2E0,V1b2_2E0,V2b3_2E0] :
( s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b3_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b3_2E0)))
& s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b3_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b3_2E0)))
& s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b3_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b3_2E0)))
& s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b3_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b3_2E0))) ) ).
fof(thm_2Ebag_2ESUB__BAG__UNION__eliminate,axiom,
! [A_27a,V0b1_2E0,V1b2_2E0,V2b3_2E0] :
( s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b3_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b3_2E0)))
& s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b3_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b3_2E0)))
& s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b3_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b3_2E0)))
& s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b3_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b3_2E0))) ) ).
fof(thm_2Ebag_2Emove__BAG__UNION__over__eq,axiom,
! [A_27a,V0X_2E0,V1Y_2E0,V2Z_2E0] :
( s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0X_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1Y_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2Z_2E0)
=> s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0X_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2Z_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1Y_2E0))) ) ).
fof(thm_2Ebag_2ESUB__BAG__UNION,axiom,
! [A_27a] :
( ! [V0b1_2E0,V1b2_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))))
=> ! [V2b_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b_2E0)))))) )
& ! [V3b1_2E0,V4b2_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V4b2_2E0))))
=> ! [V5b_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V5b_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V4b2_2E0)))))) )
& ! [V6b1_2E0,V7b2_2E0,V8b3_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V6b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V7b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V8b3_2E0))))))
=> ! [V9b_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V6b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V7b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V9b_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V8b3_2E0)))))) )
& ! [V10b1_2E0,V11b2_2E0,V12b3_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V10b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V11b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V12b3_2E0))))))
=> ! [V13b_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V10b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V13b_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V11b2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V12b3_2E0)))))) )
& ! [V14b1_2E0,V15b2_2E0,V16b3_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V14b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V16b3_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V15b2_2E0))))))
=> ! [V17b_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V14b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V16b3_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V15b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V17b_2E0)))))))) )
& ! [V18b1_2E0,V19b2_2E0,V20b3_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V18b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V20b3_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V19b2_2E0))))))
=> ! [V21b_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V18b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V20b3_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V21b_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V19b2_2E0)))))))) )
& ! [V22b1_2E0,V23b2_2E0,V24b3_2E0,V25b4_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V22b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V24b3_2E0))))
=> ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V23b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V25b4_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V22b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V23b2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V24b3_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V25b4_2E0)))))) ) )
& ! [V26b1_2E0,V27b2_2E0,V28b3_2E0,V29b4_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V26b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V29b4_2E0))))
=> ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V27b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V28b3_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V26b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V27b2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V28b3_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V29b4_2E0)))))) ) )
& ! [V30b1_2E0,V31b2_2E0,V32b3_2E0,V33b4_2E0,V34b5_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V30b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V32b3_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V34b5_2E0))))))
=> ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V31b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V33b4_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V30b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V31b2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V32b3_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V33b4_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V34b5_2E0)))))) ) )
& ! [V35b1_2E0,V36b2_2E0,V37b3_2E0,V38b4_2E0,V39b5_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V35b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V38b4_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V39b5_2E0))))))
=> ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V36b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V37b3_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V35b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V36b2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V37b3_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V38b4_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V39b5_2E0)))))) ) )
& ! [V40b1_2E0,V41b2_2E0,V42b3_2E0,V43b4_2E0,V44b5_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V41b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V42b3_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V44b5_2E0))))))
=> ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V40b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V43b4_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V40b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V41b2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V42b3_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V43b4_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V44b5_2E0)))))) ) )
& ! [V45b1_2E0,V46b2_2E0,V47b3_2E0,V48b4_2E0,V49b5_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V46b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V48b4_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V49b5_2E0))))))
=> ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V45b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V47b3_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V45b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V46b2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V47b3_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V48b4_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V49b5_2E0)))))) ) )
& ! [V50b1_2E0,V51b2_2E0,V52b3_2E0,V53b4_2E0,V54b5_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V50b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V54b5_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V52b3_2E0))))))
=> ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V51b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V53b4_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V51b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V50b1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V54b5_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V52b3_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V53b4_2E0)))))))) ) )
& ! [V55b1_2E0,V56b2_2E0,V57b3_2E0,V58b4_2E0,V59b5_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V55b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V59b5_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V58b4_2E0))))))
=> ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V56b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V57b3_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V56b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V55b1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V59b5_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V57b3_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V58b4_2E0)))))))) ) )
& ! [V60b1_2E0,V61b2_2E0,V62b3_2E0,V63b4_2E0,V64b5_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V61b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V64b5_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V62b3_2E0))))))
=> ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V60b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V63b4_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V61b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V60b1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V64b5_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V62b3_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V63b4_2E0)))))))) ) )
& ! [V65b1_2E0,V66b2_2E0,V67b3_2E0,V68b4_2E0,V69b5_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V66b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V69b5_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V68b4_2E0))))))
=> ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V65b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V67b3_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V66b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V65b1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V69b5_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V67b3_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V68b4_2E0)))))))) ) )
& ! [V70b1_2E0,V71b2_2E0,V72b3_2E0,V73b4_2E0,V74b5_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V70b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V71b2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V73b4_2E0))))
=> ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V72b3_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V74b5_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V70b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V72b3_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V71b2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V73b4_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V74b5_2E0)))))) ) )
& ! [V75b1_2E0,V76b2_2E0,V77b3_2E0,V78b4_2E0,V79b5_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V75b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V76b2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V79b5_2E0))))
=> ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V77b3_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V78b4_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V75b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V77b3_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V76b2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V78b4_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V79b5_2E0)))))) ) )
& ! [V80b1_2E0,V81b2_2E0,V82b3_2E0,V83b4_2E0,V84b5_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V82b3_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V81b2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V83b4_2E0))))
=> ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V80b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V84b5_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V80b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V82b3_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V81b2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V83b4_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V84b5_2E0)))))) ) )
& ! [V85b1_2E0,V86b2_2E0,V87b3_2E0,V88b4_2E0,V89b5_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V87b3_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V86b2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V89b5_2E0))))
=> ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V85b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V88b4_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V85b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V87b3_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V86b2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V88b4_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V89b5_2E0)))))) ) )
& ! [V90b1_2E0,V91b2_2E0,V92b3_2E0,V93b4_2E0,V94b5_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V91b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V90b1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V93b4_2E0))))
=> ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V92b3_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V94b5_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V91b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V90b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V92b3_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V94b5_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V93b4_2E0)))))) ) )
& ! [V95b1_2E0,V96b2_2E0,V97b3_2E0,V98b4_2E0,V99b5_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V96b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V95b1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V99b5_2E0))))
=> ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V97b3_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V98b4_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V96b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V95b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V97b3_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V99b5_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V98b4_2E0)))))) ) )
& ! [V100b1_2E0,V101b2_2E0,V102b3_2E0,V103b4_2E0,V104b5_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V101b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V102b3_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V103b4_2E0))))
=> ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V100b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V104b5_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V101b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V100b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V102b3_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V104b5_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V103b4_2E0)))))) ) )
& ! [V105b1_2E0,V106b2_2E0,V107b3_2E0,V108b4_2E0,V109b5_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V106b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V107b3_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V109b5_2E0))))
=> ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V105b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V108b4_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V106b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V105b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V107b3_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V109b5_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V108b4_2E0)))))) ) ) ) ).
fof(thm_2Ebag_2ESUB__BAG__EL__BAG,axiom,
! [A_27a,V0e_2E0,V1b_2E0] : s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEL__BAG_2E1(s(A_27a,V0e_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))) ).
fof(thm_2Ebag_2ESUB__BAG__INSERT,axiom,
! [A_27a,V0e_2E0,V1b1_2E0,V2b2_2E0] : s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b2_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b2_2E0))) ).
fof(thm_2Ebag_2ESUB__BAG__INSERT__I,axiom,
! [A_27a,V0b_2E0,V1c_2E0,V2e_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1c_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1c_2E0)))))) ) ).
fof(thm_2Ebag_2ENOT__IN__SUB__BAG__INSERT,axiom,
! [A_27a,V0b1_2E0,V1b2_2E0,V2e_2E0] :
( ~ p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0))))
=> s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))) ) ).
fof(thm_2Ebag_2ESUB__BAG__BAG__IN,axiom,
! [A_27a,V0x_2E0,V1b1_2E0,V2b2_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b2_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b2_2E0)))) ) ).
fof(thm_2Ebag_2ESUB__BAG__EXISTS,axiom,
! [A_27a,V0b1_2E0,V1b2_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))))
<=> ? [V2b_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b_2E0))) ) ).
fof(thm_2Ebag_2ESUB__BAG__UNION__DIFF,axiom,
! [A_27a,V0b1_2E0,V1b2_2E0,V2b3_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b3_2E0))))
=> s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b3_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b3_2E0))) ) ).
fof(thm_2Ebag_2ESUB__BAG__UNION__down,axiom,
! [A_27a,V0b1_2E0,V1b2_2E0,V2b3_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b3_2E0))))
=> ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b3_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b3_2E0)))) ) ) ).
fof(thm_2Ebag_2ESUB__BAG__DIFF,axiom,
! [A_27a] :
( ! [V0b1_2E0,V1b2_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))))
=> ! [V2b3_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b3_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0)))) )
& ! [V3b1_2E0,V4b2_2E0,V5b3_2E0,V6b4_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V4b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3b1_2E0))))
=> ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V6b4_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V5b3_2E0))))
=> s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V4b2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V5b3_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V6b4_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V6b4_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V4b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V5b3_2E0))))) ) ) ) ).
fof(thm_2Ebag_2ESUB__BAG__PSUB__BAG,axiom,
! [A_27a,V0b1_2E0,V1b2_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EPSUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))))
| s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0) ) ) ).
fof(thm_2Ebag_2EBAG__DELETE__PSUB__BAG,axiom,
! [A_27a,V0b0_2E0,V1e_2E0,V2b_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__DELETE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b0_2E0),s(A_27a,V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Ebag_2EPSUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b0_2E0)))) ) ).
fof(thm_2Ebag_2ESET__OF__EMPTY,axiom,
! [A_27a] : s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__OF__SET_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0) ).
fof(thm_2Ebag_2EBAG__IN__BAG__OF__SET,axiom,
! [A_27a,V0P_2E0,V1p_2E0] : s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V1p_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__OF__SET_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1p_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))) ).
fof(thm_2Ebag_2EBAG__OF__EMPTY,axiom,
! [A_27a] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebag_2ESET__OF__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) ).
fof(thm_2Ebag_2ESET__BAG__I,axiom,
! [A_27a,V0s_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebag_2ESET__OF__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__OF__SET_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) ).
fof(thm_2Ebag_2ESUB__BAG__SET,axiom,
! [A_27a,V0b1_2E0,V1b2_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebag_2ESET__OF__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebag_2ESET__OF__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0)))))) ) ).
fof(thm_2Ebag_2ESET__OF__BAG__UNION,axiom,
! [A_27a,V0b1_2E0,V1b2_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebag_2ESET__OF__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebag_2ESET__OF__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebag_2ESET__OF__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))))) ).
fof(thm_2Ebag_2ESET__OF__BAG__MERGE,axiom,
! [A_27a,V0b1_2E0,V1b2_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebag_2ESET__OF__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__MERGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebag_2ESET__OF__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebag_2ESET__OF__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))))) ).
fof(thm_2Ebag_2ESET__OF__BAG__INSERT,axiom,
! [A_27a,V0e_2E0,V1b_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebag_2ESET__OF__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebag_2ESET__OF__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))))) ).
fof(thm_2Ebag_2ESET__OF__EL__BAG,axiom,
! [A_27a,V0e_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebag_2ESET__OF__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEL__BAG_2E1(s(A_27a,V0e_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) ).
fof(thm_2Ebag_2ESET__OF__BAG__DIFF__SUBSET__down,axiom,
! [A_27a,V0b1_2E0,V1b2_2E0] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebag_2ESET__OF__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebag_2ESET__OF__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebag_2ESET__OF__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0)))))))) ).
fof(thm_2Ebag_2ESET__OF__BAG__DIFF__SUBSET__up,axiom,
! [A_27a,V0b1_2E0,V1b2_2E0] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebag_2ESET__OF__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebag_2ESET__OF__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0)))))) ).
fof(thm_2Ebag_2EIN__SET__OF__BAG,axiom,
! [A_27a,V0x_2E0,V1b_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebag_2ESET__OF__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))) ).
fof(thm_2Ebag_2ESET__OF__BAG__EQ__EMPTY,axiom,
! [A_27a,V0b_2E0] :
( ( s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebag_2ESET__OF__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0)))
<=> s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0) )
& ( s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebag_2ESET__OF__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)
<=> s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0) ) ) ).
fof(thm_2Ebag_2EBAG__DISJOINT__EMPTY,axiom,
! [A_27a,V0b_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__DISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__DISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0)))) ) ).
fof(thm_2Ebag_2EBAG__DISJOINT__DIFF,axiom,
! [A_27a,V0B1_2E0,V1B2_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__DISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0B1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1B2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1B2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0B1_2E0)))))) ).
fof(thm_2Ebag_2EBAG__DISJOINT__BAG__IN,axiom,
! [A_27a,V0b1_2E0,V1b2_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__DISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))))
<=> ! [V2e_2E0] :
( ~ p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0)))) ) ) ).
fof(thm_2Ebag_2EBAG__DISJOINT__BAG__INSERT,axiom,
! [A_27a,A_27b] :
( ! [V0b1_2E0,V1b2_2E0,V2e1_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__DISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V2e1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))))
<=> ( ~ p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V2e1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__DISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0)))) ) )
& ! [V3b1_2E0,V4b2_2E0,V5e2_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__DISJOINT_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V3b1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27b,V5e2_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V4b2_2E0))))))
<=> ( ~ p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27b,V5e2_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V3b1_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__DISJOINT_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V3b1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V4b2_2E0)))) ) ) ) ).
fof(thm_2Ebag_2EBAG__DISJOINT__BAG__UNION,axiom,
! [A_27a,V0b3_2E0,V1b2_2E0,V2b1_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__DISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b3_2E0))))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__DISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__DISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b3_2E0)))) ) )
& ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__DISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b3_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__DISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b3_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__DISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b3_2E0)))) ) ) ) ).
fof(thm_2Ebag_2EFINITE__EMPTY__BAG,axiom,
! [A_27a] : p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0)))) ).
fof(thm_2Ebag_2EFINITE__BAG__INSERT,axiom,
! [A_27a,V0b_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))))
=> ! [V1e_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0)))))) ) ).
fof(thm_2Ebag_2EFINITE__BAG__INDUCT,axiom,
! [A_27a,V0P_2E0] :
( ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0))))
& ! [V1b_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))))
=> ! [V2e_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0)))))) ) )
=> ! [V3b_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3b_2E0))))
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3b_2E0)))) ) ) ).
fof(thm_2Ebag_2ESTRONG__FINITE__BAG__INDUCT,axiom,
! [A_27a,V0P_2E0] :
( ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0))))
& ! [V1b_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))))
& p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0)))) )
=> ! [V2e_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0)))))) ) )
=> ! [V3b_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3b_2E0))))
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3b_2E0)))) ) ) ).
fof(thm_2Ebag_2EFINITE__BAG__THM,axiom,
! [A_27a] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0))))
& ! [V0e_2E0,V1b_2E0] : s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))) ) ).
fof(thm_2Ebag_2EFINITE__BAG__DIFF,axiom,
! [A_27a,V0b1_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0))))
=> ! [V1b2_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0)))))) ) ).
fof(thm_2Ebag_2EFINITE__BAG__DIFF__dual,axiom,
! [A_27a,V0b1_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0))))
=> ! [V1b2_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0))))))
=> p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0)))) ) ) ).
fof(thm_2Ebag_2EFINITE__BAG__UNION,axiom,
! [A_27a,V0b1_2E0,V1b2_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0)))) ) ) ).
fof(thm_2Ebag_2EFINITE__SUB__BAG,axiom,
! [A_27a,V0b1_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0))))
=> ! [V1b2_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0)))) ) ) ).
fof(thm_2Ebag_2EBAG__CARD__EMPTY,axiom,
! [A_27a] : s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__CARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) ).
fof(thm_2Ebag_2EBCARD__0,axiom,
! [A_27a,V0b_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))))
=> ( s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__CARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)
<=> s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0) ) ) ).
fof(thm_2Ebag_2EBAG__CARD__THM,axiom,
! [A_27a] :
( s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__CARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)
& ! [V0b_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))))
=> ! [V1e_2E0] : s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__CARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__CARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))) ) ) ).
fof(thm_2Ebag_2EBAG__CARD__UNION,axiom,
! [A_27a,V0b1_2E0,V1b2_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0)))) )
=> s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__CARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__CARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0))),s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__CARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))))) ) ).
fof(thm_2Ebag_2EBCARD__SUC,axiom,
! [A_27a,V0b_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))))
=> ! [V1n_2E0] :
( s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__CARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))
<=> ? [V2b0_2E0,V3e_2E0] :
( s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V3e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b0_2E0)))
& s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__CARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b0_2E0))) = s(tyop_2Enum_2Enum,V1n_2E0) ) ) ) ).
fof(thm_2Ebag_2EBAG__CARD__BAG__INN,axiom,
! [A_27a,V0b_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))))
=> ! [V1n_2E0,V2e_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__INN_2E3(s(A_27a,V2e_2E0),s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__CARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0)))))) ) ) ).
fof(thm_2Ebag_2ESUB__BAG__DIFF__EQ,axiom,
! [A_27a,V0b1_2E0,V1b2_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))))
=> s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0))))) ) ).
fof(thm_2Ebag_2ESUB__BAG__CARD,axiom,
! [A_27a,V0b1_2E0,V1b2_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0)))) )
=> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__CARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0))),s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__CARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0)))))) ) ).
fof(thm_2Ebag_2EBAG__CARD__DIFF,axiom,
! [A_27a,V0b_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))))
=> ! [V1c_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1c_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))))
=> s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__CARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1c_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__CARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))),s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__CARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1c_2E0))))) ) ) ).
fof(thm_2Ebag_2EBAG__FILTER__EMPTY,axiom,
! [A_27a,V0P_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__FILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0) ).
fof(thm_2Ebag_2EBAG__FILTER__BAG__INSERT,axiom,
! [A_27a,V0e_2E0,V1b_2E0,V2P_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__FILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(A_27a,V0e_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__FILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__FILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))))) ).
fof(thm_2Ebag_2EFINITE__BAG__FILTER,axiom,
! [A_27a,V0P_2E0,V1b_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__FILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0)))))) ) ).
fof(thm_2Ebag_2EBAG__INN__BAG__FILTER,axiom,
! [A_27a,V0n_2E0,V1e_2E0,V2b_2E0,V3P_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__INN_2E3(s(A_27a,V1e_2E0),s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__FILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b_2E0))))))
<=> ( s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)
| ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0),s(A_27a,V1e_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__INN_2E3(s(A_27a,V1e_2E0),s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b_2E0)))) ) ) ) ).
fof(thm_2Ebag_2EBAG__IN__BAG__FILTER,axiom,
! [A_27a,V0e_2E0,V1b_2E0,V2P_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__FILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))))))
<=> ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(A_27a,V0e_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0)))) ) ) ).
fof(thm_2Ebag_2EBAG__FILTER__FILTER,axiom,
! [A_27a,F0_2E0] :
( ! [V2P_2E0,V1Q_2E0,V3a_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0))),s(A_27a,V3a_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(A_27a,V3a_2E0))))
& p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V3a_2E0)))) ) )
=> ! [V0b_2E0,V1Q_2E0,V2P_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__FILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__FILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__FILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))) ) ).
fof(thm_2Ebag_2EBAG__FILTER__SUB__BAG,axiom,
! [A_27a,V0P_2E0,V1b_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__FILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0)))) ).
fof(thm_2Ebag_2ESET__OF__BAG__EQ__INSERT,axiom,
! [A_27a,V0b_2E0,V1e_2E0,V2s_2E0] :
( s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebag_2ESET__OF__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0)))
<=> ? [V3b0_2E0,V4eb_2E0] :
( s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V4eb_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3b0_2E0)))
& s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebag_2ESET__OF__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3b0_2E0)))
& ! [V5e_27_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V5e_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V4eb_2E0))))
=> s(A_27a,V5e_27_2E0) = s(A_27a,V1e_2E0) )
& ( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V4eb_2E0)))) ) ) ) ).
fof(thm_2Ebag_2EFINITE__SET__OF__BAG,axiom,
! [A_27a,V0b_2E0] : s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebag_2ESET__OF__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))) ).
fof(thm_2Ebag_2EBAG__IMAGE__EMPTY,axiom,
! [A_27a,A_27b,V0f_2E0] : s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),c_2Ebag_2EBAG__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0) ).
fof(thm_2Ebag_2EBAG__IMAGE__FINITE__INSERT,axiom,
! [A_27a,A_27b,V0b_2E0,V1f_2E0,V2e_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))))
=> s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),c_2Ebag_2EBAG__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(A_27a,V2e_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),c_2Ebag_2EBAG__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))))) ) ).
fof(thm_2Ebag_2EBAG__IMAGE__FINITE__UNION,axiom,
! [A_27a,A_27b,V0b1_2E0,V1b2_2E0,V2f_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0)))) )
=> s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),c_2Ebag_2EBAG__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),c_2Ebag_2EBAG__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),c_2Ebag_2EBAG__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))))) ) ).
fof(thm_2Ebag_2EBAG__IMAGE__FINITE,axiom,
! [A_27a,A_27b,V0f_2E0,V1b_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),c_2Ebag_2EBAG__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0)))))) ) ).
fof(thm_2Ebag_2EBAG__IMAGE__COMPOSE,axiom,
! [A_27a,A_27b,A_27c,V0f_2E0,V1g_2E0,V2b_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),V2b_2E0))))
=> s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),c_2Ebag_2EBAG__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),V1g_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),V2b_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),c_2Ebag_2EBAG__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),V1g_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),V2b_2E0))))) ) ).
fof(thm_2Ebag_2EBAG__IMAGE__FINITE__I,axiom,
! [A_27a,V0b_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))))
=> s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2EI_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0) ) ).
fof(thm_2Ebag_2EBAG__IN__FINITE__BAG__IMAGE,axiom,
! [A_27a,A_27b,V0x_2E0,V1f_2E0,V2b_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b_2E0))))
=> ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27b,V0x_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),c_2Ebag_2EBAG__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b_2E0))))))
<=> ? [V3y_2E0] :
( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(A_27a,V3y_2E0))) = s(A_27b,V0x_2E0)
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V3y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b_2E0)))) ) ) ) ).
fof(thm_2Ebag_2EBAG__IMAGE__EQ__EMPTY,axiom,
! [A_27a,A_27b,V0f_2E0,V1b_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))))
=> ( s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),c_2Ebag_2EBAG__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0)
<=> s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0) ) ) ).
fof(thm_2Ebag_2EBAG__INSERT__CHOICE__REST,axiom,
! [A_27a,V0b_2E0] :
( s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0)
=> s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,c_2Ebag_2EBAG__CHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__REST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))))) ) ).
fof(thm_2Ebag_2EBAG__CHOICE__SING,axiom,
! [A_27a,V0x_2E0] : s(A_27a,c_2Ebag_2EBAG__CHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0))))) = s(A_27a,V0x_2E0) ).
fof(thm_2Ebag_2EBAG__REST__SING,axiom,
! [A_27a,V0x_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__REST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0) ).
fof(thm_2Ebag_2ESUB__BAG__REST,axiom,
! [A_27a,V0b_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__REST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0)))) ).
fof(thm_2Ebag_2EPSUB__BAG__REST,axiom,
! [A_27a,V0b_2E0] :
( s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0)
=> p(s(tyop_2Emin_2Ebool,c_2Ebag_2EPSUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__REST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0)))) ) ).
fof(thm_2Ebag_2ESUB__BAG__UNION__MONO,axiom,
! [A_27a] :
( ! [V0x_2E0,V1y_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1y_2E0))))))
& ! [V2x_2E0,V3y_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2x_2E0)))))) ) ).
fof(thm_2Ebag_2EPSUB__BAG__CARD,axiom,
! [A_27a,V0b1_2E0,V1b2_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2EPSUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0)))) )
=> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__CARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0))),s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__CARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0)))))) ) ).
fof(thm_2Ebag_2EEL__BAG__BAG__INSERT,axiom,
! [A_27a,V0y_2E0,V1x_2E0,V2b_2E0] :
( s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V0y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b_2E0)))
<=> ( s(A_27a,V1x_2E0) = s(A_27a,V0y_2E0)
& s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0) ) ) ).
fof(thm_2Ebag_2EEL__BAG__SUB__BAG,axiom,
! [A_27a,V0x_2E0,V1b_2E0] : s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))) ).
fof(thm_2Ebag_2EITBAG__IND,axiom,
! [A_27a,A_27b,V0f_2E0,V1P_2E0] :
( ! [V2b_2E0,V3acc_2E0] :
( ( ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b_2E0))))
& s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0) )
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__REST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b_2E0))))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V0f_2E0),s(A_27a,c_2Ebag_2EBAG__CHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b_2E0))))),s(A_27b,V3acc_2E0)))))) )
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b_2E0))),s(A_27b,V3acc_2E0)))) )
=> ! [V4v_2E0,V5v1_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V4v_2E0))),s(A_27b,V5v1_2E0)))) ) ).
fof(thm_2Ebag_2EITBAG__THM,axiom,
! [A_27a,A_27b,F0_2E0] :
( ! [V0b_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))))
<=> s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0) )
=> ! [V0b_2E0,V1f_2E0,V2acc_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))))
=> s(A_27b,c_2Ebag_2EITBAG_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0),s(A_27b,V2acc_2E0))) = s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))),s(A_27b,V2acc_2E0),s(A_27b,c_2Ebag_2EITBAG_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__REST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V1f_2E0),s(A_27a,c_2Ebag_2EBAG__CHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))))),s(A_27b,V2acc_2E0))))))) ) ) ).
fof(thm_2Ebag_2EITBAG__EMPTY,axiom,
! [A_27a,A_27b,V0f_2E0,V1acc_2E0] : s(A_27b,c_2Ebag_2EITBAG_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0),s(A_27b,V1acc_2E0))) = s(A_27b,V1acc_2E0) ).
fof(thm_2Ebag_2EITBAG__INSERT,axiom,
! [A_27a,A_27b,V0x_2E0,V1b_2E0,V2f_2E0,V3acc_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))))
=> s(A_27b,c_2Ebag_2EITBAG_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))),s(A_27b,V3acc_2E0))) = s(A_27b,c_2Ebag_2EITBAG_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__REST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V2f_2E0),s(A_27a,c_2Ebag_2EBAG__CHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))))))),s(A_27b,V3acc_2E0))))) ) ).
fof(thm_2Ebag_2ECOMMUTING__ITBAG__INSERT,axiom,
! [A_27a,A_27b,V0f_2E0,V1b_2E0] :
( ( ! [V2x_2E0,V3y_2E0,V4z_2E0] : s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V0f_2E0),s(A_27a,V3y_2E0))),s(A_27b,V4z_2E0))))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V0f_2E0),s(A_27a,V3y_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,V4z_2E0)))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0)))) )
=> ! [V5x_2E0,V6a_2E0] : s(A_27b,c_2Ebag_2EITBAG_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V5x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))),s(A_27b,V6a_2E0))) = s(A_27b,c_2Ebag_2EITBAG_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V0f_2E0),s(A_27a,V5x_2E0))),s(A_27b,V6a_2E0))))) ) ).
fof(thm_2Ebag_2ECOMMUTING__ITBAG__RECURSES,axiom,
! [A_27a,A_27b,V0f_2E0,V1e_2E0,V2b_2E0,V3a_2E0] :
( ( ! [V4x_2E0,V5y_2E0,V6z_2E0] : s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V0f_2E0),s(A_27a,V4x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V0f_2E0),s(A_27a,V5y_2E0))),s(A_27b,V6z_2E0))))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V0f_2E0),s(A_27a,V5y_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V0f_2E0),s(A_27a,V4x_2E0))),s(A_27b,V6z_2E0)))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b_2E0)))) )
=> s(A_27b,c_2Ebag_2EITBAG_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b_2E0))),s(A_27b,V3a_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V0f_2E0),s(A_27a,V1e_2E0))),s(A_27b,c_2Ebag_2EITBAG_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b_2E0),s(A_27b,V3a_2E0))))) ) ).
fof(thm_2Ebag_2EBAG__GEN__SUM__EMPTY,axiom,
! [V0n_2E0] : s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__GEN__SUM_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,V0n_2E0) ).
fof(thm_2Ebag_2EBAG__GEN__PROD__EMPTY,axiom,
! [V0n_2E0] : s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__GEN__PROD_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,V0n_2E0) ).
fof(thm_2Ebag_2EBAG__GEN__SUM__TAILREC,axiom,
! [V0b_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0b_2E0))))
=> ! [V1x_2E0,V2a_2E0] : s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__GEN__SUM_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0b_2E0))),s(tyop_2Enum_2Enum,V2a_2E0))) = s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__GEN__SUM_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0b_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V2a_2E0))))) ) ).
fof(thm_2Ebag_2EBAG__GEN__SUM__REC,axiom,
! [V0b_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0b_2E0))))
=> ! [V1x_2E0,V2a_2E0] : s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__GEN__SUM_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0b_2E0))),s(tyop_2Enum_2Enum,V2a_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__GEN__SUM_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0b_2E0),s(tyop_2Enum_2Enum,V2a_2E0))))) ) ).
fof(thm_2Ebag_2EBAG__GEN__PROD__TAILREC,axiom,
! [V0b_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0b_2E0))))
=> ! [V1x_2E0,V2a_2E0] : s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__GEN__PROD_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0b_2E0))),s(tyop_2Enum_2Enum,V2a_2E0))) = s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__GEN__PROD_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0b_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V2a_2E0))))) ) ).
fof(thm_2Ebag_2EBAG__GEN__PROD__REC,axiom,
! [V0b_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0b_2E0))))
=> ! [V1x_2E0,V2a_2E0] : s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__GEN__PROD_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0b_2E0))),s(tyop_2Enum_2Enum,V2a_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__GEN__PROD_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0b_2E0),s(tyop_2Enum_2Enum,V2a_2E0))))) ) ).
fof(thm_2Ebag_2EBAG__GEN__PROD__EQ__1,axiom,
! [V0b_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0b_2E0))))
=> ! [V1e_2E0] :
( s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__GEN__PROD_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0b_2E0),s(tyop_2Enum_2Enum,V1e_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))
=> s(tyop_2Enum_2Enum,V1e_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) ) ) ).
fof(thm_2Ebag_2EBAG__GEN__PROD__ALL__ONES,axiom,
! [V0b_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0b_2E0))))
=> ( s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__GEN__PROD_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0b_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))
=> ! [V1x_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0b_2E0))))
=> s(tyop_2Enum_2Enum,V1x_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) ) ) ) ).
fof(thm_2Ebag_2EBAG__GEN__PROD__POSITIVE,axiom,
! [V0b_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0b_2E0))))
=> ( ! [V1x_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0b_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1x_2E0)))) )
=> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__GEN__PROD_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0b_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))) ) ) ).
fof(thm_2Ebag_2EBAG__EVERY__THM,axiom,
! [A_27a,A_27b] :
( ! [V0P_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__EVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0))))
& ! [V1P_2E0,V2e_2E0,V3b_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__EVERY_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27b,V2e_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V3b_2E0))))))
<=> ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(A_27b,V2e_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__EVERY_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V3b_2E0)))) ) ) ) ).
fof(thm_2Ebag_2EBAG__EVERY__UNION,axiom,
! [A_27a,V0b2_2E0,V1b1_2E0,V2P_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__EVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b2_2E0))))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__EVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__EVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b2_2E0)))) ) ) ).
fof(thm_2Ebag_2EBAG__EVERY__MERGE,axiom,
! [A_27a,V0b2_2E0,V1b1_2E0,V2P_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__EVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__MERGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b2_2E0))))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__EVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__EVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b2_2E0)))) ) ) ).
fof(thm_2Ebag_2EBAG__EVERY__SET,axiom,
! [A_27a,F0_2E0] :
( ! [V1P_2E0,V2x_2E0] : s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0))),s(A_27a,V2x_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2x_2E0)))))
=> ! [V0b_2E0,V1P_2E0] : s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__EVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebag_2ESET__OF__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0))))))) ) ).
fof(thm_2Ebag_2EBAG__FILTER__EQ__EMPTY,axiom,
! [A_27a,V0b_2E0,V1P_2E0] :
( s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__FILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0)
<=> p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__EVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0)))) ) ).
fof(thm_2Ebag_2ESET__OF__BAG__IMAGE,axiom,
! [A_27a,A_27b,V0f_2E0,V1b_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebag_2ESET__OF__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V1b_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Ebag_2ESET__OF__BAG_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V1b_2E0))))) ).
fof(thm_2Ebag_2EBAG__IMAGE__FINITE__RESTRICTED__I,axiom,
! [A_27a,F0_2E0] :
( ! [V0f_2E0,V2e_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0))),s(A_27a,V2e_2E0))))
<=> s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,V2e_2E0))) = s(A_27a,V2e_2E0) )
=> ! [V0f_2E0,V1b_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__EVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0)))) )
=> s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0) ) ) ).
fof(thm_2Ebag_2EBAG__ALL__DISTINCT__THM,axiom,
! [A_27a,A_27b] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__ALL__DISTINCT_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0))))
& ! [V0e_2E0,V1b_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__ALL__DISTINCT_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27b,V0e_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V1b_2E0))))))
<=> ( ~ p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27b,V0e_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V1b_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__ALL__DISTINCT_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V1b_2E0)))) ) ) ) ).
fof(thm_2Ebag_2EBAG__ALL__DISTINCT__BAG__MERGE,axiom,
! [A_27a,V0b1_2E0,V1b2_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__ALL__DISTINCT_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__MERGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__ALL__DISTINCT_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__ALL__DISTINCT_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0)))) ) ) ).
fof(thm_2Ebag_2EBAG__ALL__DISTINCT__BAG__UNION,axiom,
! [A_27a,V0b1_2E0,V1b2_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__ALL__DISTINCT_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__ALL__DISTINCT_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__ALL__DISTINCT_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__DISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0)))) ) ) ).
fof(thm_2Ebag_2EBAG__ALL__DISTINCT__DIFF,axiom,
! [A_27a,V0b1_2E0,V1b2_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__ALL__DISTINCT_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__ALL__DISTINCT_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0)))))) ) ).
fof(thm_2Ebag_2EBAG__ALL__DISTINCT__DELETE,axiom,
! [A_27a,V0b_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__ALL__DISTINCT_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))))
<=> ! [V1e_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))))
=> ~ p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0)))))))) ) ) ).
fof(thm_2Ebag_2EBAG__ALL__DISTINCT__SET,axiom,
! [A_27a,V0b_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__ALL__DISTINCT_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))))
<=> s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__OF__SET_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebag_2ESET__OF__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0) ) ).
fof(thm_2Ebag_2EBAG__ALL__DISTINCT__BAG__OF__SET,axiom,
! [A_27a,V0s_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__ALL__DISTINCT_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__OF__SET_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) ).
fof(thm_2Ebag_2EBAG__IN__BAG__DIFF__ALL__DISTINCT,axiom,
! [A_27a,V0b1_2E0,V1b2_2E0,V2e_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__ALL__DISTINCT_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0))))
=> ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0))))
& ~ p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0)))) ) ) ) ).
fof(thm_2Ebag_2ESUB__BAG__ALL__DISTINCT,axiom,
! [A_27a,V0b1_2E0,V1b2_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__ALL__DISTINCT_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0))))
=> ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))))
<=> ! [V2x_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0)))) ) ) ) ).
fof(thm_2Ebag_2EBAG__ALL__DISTINCT__BAG__INN,axiom,
! [A_27a,V0b_2E0,V1n_2E0,V2e_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__ALL__DISTINCT_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))))
=> ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__INN_2E3(s(A_27a,V2e_2E0),s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0))))
<=> ( s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)
| ( s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0)))) ) ) ) ) ).
fof(thm_2Ebag_2EBAG__ALL__DISTINCT__EXTENSION,axiom,
! [A_27a,V0b1_2E0,V1b2_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__ALL__DISTINCT_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__ALL__DISTINCT_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0)))) )
=> ( s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0)
<=> ! [V2x_2E0] : s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))) ) ) ).
fof(thm_2Ebag_2ENOT__BAG__IN,axiom,
! [A_27a,V0b_2E0,V1x_2E0] :
( s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0),s(A_27a,V1x_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)
<=> ~ p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0)))) ) ).
fof(thm_2Ebag_2EBAG__UNION__EQ__LEFT,axiom,
! [A_27a,V0b_2E0,V1c_2E0,V2d_2E0] :
( s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1c_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2d_2E0)))
=> s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1c_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2d_2E0) ) ).
fof(thm_2Ebag_2EBAG__IN__DIVIDES,axiom,
! [V0b_2E0,V1x_2E0,V2a_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0b_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0b_2E0)))) )
=> p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__GEN__PROD_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0b_2E0),s(tyop_2Enum_2Enum,V2a_2E0)))))) ) ).
fof(thm_2Ebag_2EBAG__GEN__PROD__UNION__LEM,axiom,
! [V0b1_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0b1_2E0))))
=> ! [V1b2_2E0,V2a_2E0,V3b_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1b2_2E0))))
=> s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__GEN__PROD_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1b2_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,V3b_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__GEN__PROD_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Enum_2Enum,V2a_2E0))),s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__GEN__PROD_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1b2_2E0),s(tyop_2Enum_2Enum,V3b_2E0))))) ) ) ).
fof(thm_2Ebag_2EBAG__GEN__PROD__UNION,axiom,
! [V0b1_2E0,V1b2_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0b1_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1b2_2E0)))) )
=> s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__GEN__PROD_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1b2_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__GEN__PROD_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0b1_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Ebag_2EBAG__GEN__PROD_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1b2_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))) ) ).
fof(thm_2Ebag_2EBIG__BAG__UNION__EMPTY,axiom,
! [A_27a] : s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBIG__BAG__UNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0) ).
fof(thm_2Ebag_2EBIG__BAG__UNION__INSERT,axiom,
! [A_27a,V0sob_2E0,V1b_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V0sob_2E0))))
=> s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBIG__BAG__UNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V0sob_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBIG__BAG__UNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V0sob_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))))))) ) ).
fof(thm_2Ebag_2EBIG__BAG__UNION__DELETE,axiom,
! [A_27a,V0sob_2E0,V1b_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V0sob_2E0))))
=> s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBIG__BAG__UNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V0sob_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V0sob_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBIG__BAG__UNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V0sob_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBIG__BAG__UNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V0sob_2E0))))) ) ).
fof(thm_2Ebag_2EBIG__BAG__UNION__ITSET__BAG__UNION,axiom,
! [A_27a,V0sob_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V0sob_2E0))))
=> s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBIG__BAG__UNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V0sob_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Epred__set_2EITSET_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))),c_2Ebag_2EBAG__UNION_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V0sob_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0))) ) ).
fof(thm_2Ebag_2EFINITE__BIG__BAG__UNION,axiom,
! [A_27a,V0sob_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V0sob_2E0))))
& ! [V1b_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V0sob_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0)))) ) )
=> p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBIG__BAG__UNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V0sob_2E0)))))) ) ).
fof(thm_2Ebag_2EBAG__IN__BIG__BAG__UNION,axiom,
! [A_27a,V0e_2E0,V1P_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V1P_2E0))))
=> ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBIG__BAG__UNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V1P_2E0))))))
<=> ? [V2b_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V1P_2E0)))) ) ) ) ).
fof(thm_2Ebag_2EBIG__BAG__UNION__EQ__EMPTY__BAG,axiom,
! [A_27a,V0sob_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V0sob_2E0))))
=> ( s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBIG__BAG__UNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V0sob_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0)
<=> ! [V1b_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V0sob_2E0))))
=> s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0) ) ) ) ).
fof(thm_2Ebag_2EBIG__BAG__UNION__UNION,axiom,
! [A_27a,V0s2_2E0,V1s1_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V1s1_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V0s2_2E0)))) )
=> s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBIG__BAG__UNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V1s1_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V0s2_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBIG__BAG__UNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V1s1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBIG__BAG__UNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V0s2_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBIG__BAG__UNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V1s1_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V0s2_2E0))))))) ) ).
fof(thm_2Ebag_2EBIG__BAG__UNION__EQ__ELEMENT,axiom,
! [A_27a,V0sob_2E0,V1b_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V0sob_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V0sob_2E0)))) )
=> ( s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBIG__BAG__UNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V0sob_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0)
<=> ! [V2b_27_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b_27_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V0sob_2E0))))
=> ( s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b_27_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0)
| s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b_27_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0) ) ) ) ) ).
fof(thm_2Ebag_2EBAG__NOT__LESS__EMPTY,axiom,
! [A_27a,V0r_2E0,V1b_2E0] : ~ p(s(tyop_2Emin_2Ebool,c_2Ebag_2Emlt1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0)))) ).
fof(thm_2Ebag_2ENOT__mlt__EMPTY,axiom,
! [A_27a,V0b_2E0,V1R_2E0] : ~ p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Ebag_2Emlt1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0)))) ).
fof(thm_2Ebag_2EBAG__LESS__ADD,axiom,
! [A_27a,V0r_2E0,V1a_2E0,V2N_2E0,V3M0_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2Emlt1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2N_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3M0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V1a_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0))))))))
=> ( ? [V4M_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2Emlt1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V4M_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3M0_2E0))))
& s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2N_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V4M_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V1a_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0))))) )
| ? [V5KK_2E0] :
( ! [V6b_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V6b_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V5KK_2E0))))
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0r_2E0),s(A_27a,V6b_2E0))),s(A_27a,V1a_2E0)))) )
& s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2N_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3M0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V5KK_2E0))) ) ) ) ).
fof(thm_2Ebag_2Emlt1__all__accessible,axiom,
! [A_27a,V0R_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))
=> ! [V1M_2E0] : p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWFP_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Ebag_2Emlt1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1M_2E0)))) ) ).
fof(thm_2Ebag_2EWF__mlt1,axiom,
! [A_27a,V0R_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Ebag_2Emlt1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) ) ).
fof(thm_2Ebag_2ETC__mlt1__FINITE__BAG,axiom,
! [A_27a,V0R_2E0,V1b1_2E0,V2b2_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Ebag_2Emlt1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b2_2E0))))
=> ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b2_2E0)))) ) ) ).
fof(thm_2Ebag_2ETC__mlt1__UNION2__I,axiom,
! [A_27a,V0R_2E0,V1b2_2E0,V2b1_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b1_2E0))))
& s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0) )
=> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Ebag_2Emlt1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0)))))) ) ).
fof(thm_2Ebag_2ETC__mlt1__UNION1__I,axiom,
! [A_27a,V0R_2E0,V1b2_2E0,V2b1_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b1_2E0))))
& s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b1_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0) )
=> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Ebag_2Emlt1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b2_2E0)))))) ) ).
fof(thm_2Ebag_2Emlt__NOT__REFL,axiom,
! [A_27a,V0a_2E0,V1R_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0))))
=> ~ p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Ebag_2Emlt1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0a_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0a_2E0)))) ) ).
fof(thm_2Ebag_2Emlt__INSERT__CANCEL__I,axiom,
! [A_27a,V0e_2E0,V1R_2E0,V2a_2E0,V3b_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Ebag_2Emlt1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2a_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3b_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Ebag_2Emlt1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2a_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3b_2E0)))))) ) ).
fof(thm_2Ebag_2Emlt1__INSERT__CANCEL,axiom,
! [A_27a,V0e_2E0,V1b_2E0,V2a_2E0,V3R_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_2E0))))
=> s(tyop_2Emin_2Ebool,c_2Ebag_2Emlt1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2a_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebag_2Emlt1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2a_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))) ) ).
fof(thm_2Ebag_2Edominates__EMPTY,axiom,
! [A_27a,A_27b,V0b_2E0,V1R_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebag_2Edominates_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0b_2E0)))) ).
fof(thm_2Ebag_2Edominates__SUBSET,axiom,
! [A_27a,V0Y_2E0,V1X_2E0,V2R_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0Y_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2Edominates_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0Y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0Y_2E0))))
& s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) )
=> ? [V3x_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0))))
& p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(A_27a,V3x_2E0))),s(A_27a,V3x_2E0)))) ) ) ).
fof(thm_2Ebag_2Emlt__dominates__thm1,axiom,
! [A_27a,V0R_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))
=> ! [V1b1_2E0,V2b2_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Ebag_2Emlt1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b2_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b2_2E0))))
& ? [V3x_2E0,V4y_2E0] :
( s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3x_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0)
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b2_2E0))))
& s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V4y_2E0)))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2Edominates_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebag_2ESET__OF__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V4y_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebag_2ESET__OF__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3x_2E0)))))) ) ) ) ) ).
fof(thm_2Ebag_2Edominates__DIFF,axiom,
! [A_27a,V0y_2E0,V1x_2E0,V2i_2E0,V3R_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2Edominates_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0y_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2i_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2i_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2i_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0y_2E0)))) )
=> p(s(tyop_2Emin_2Ebool,c_2Ebag_2Edominates_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2i_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2i_2E0)))))) ) ).
fof(thm_2Ebag_2EBAG__INSERT__SUB__BAG__E,axiom,
! [A_27a,V0e_2E0,V1c_2E0,V2b_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1c_2E0))))
=> ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__IN_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1c_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1c_2E0)))) ) ) ).
fof(thm_2Ebag_2Ebdominates__BAG__DIFF,axiom,
! [A_27a,V0y_2E0,V1x_2E0,V2i_2E0,V3R_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2Edominates_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebag_2ESET__OF__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebag_2ESET__OF__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0y_2E0))))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2i_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2i_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1x_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2i_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0y_2E0)))) )
=> p(s(tyop_2Emin_2Ebool,c_2Ebag_2Edominates_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebag_2ESET__OF__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2i_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebag_2ESET__OF__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2i_2E0)))))))) ) ).
fof(thm_2Ebag_2EBAG__INTER__SUB__BAG,axiom,
! [A_27a,V0b2_2E0,V1b1_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b2_2E0)))) ) ).
fof(thm_2Ebag_2EBAG__INTER__FINITE,axiom,
! [A_27a,V0b2_2E0,V1b1_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0))))
| p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b2_2E0)))) )
=> p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b2_2E0)))))) ) ).
fof(thm_2Ebag_2Emlt__dominates__thm2,axiom,
! [A_27a,V0R_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) )
=> ! [V1b1_2E0,V2b2_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Ebag_2Emlt1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b2_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b2_2E0))))
& ? [V3x_2E0,V4y_2E0] :
( s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3x_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0)
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b2_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2EBAG__DISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V4y_2E0))))
& s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V4y_2E0)))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2Edominates_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebag_2ESET__OF__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V4y_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebag_2ESET__OF__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3x_2E0)))))) ) ) ) ) ).
fof(thm_2Ebag_2EBAG__DIFF__INSERT__SUB__BAG,axiom,
! [A_27a,V0e_2E0,V1c_2E0,V2b_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1c_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b_2E0))))
=> s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1c_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1c_2E0))))) ) ).
fof(thm_2Ebag_2Emlt__INSERT__CANCEL,axiom,
! [A_27a,V0e_2E0,V1b_2E0,V2a_2E0,V3R_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_2E0)))) )
=> s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Ebag_2Emlt1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2a_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))))) = s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Ebag_2Emlt1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2a_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))) ) ).
fof(thm_2Ebag_2Emlt__UNION__RCANCEL__I,axiom,
! [A_27a,V0c_2E0,V1b_2E0,V2a_2E0,V3R_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Ebag_2Emlt1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2a_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0c_2E0)))) )
=> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Ebag_2Emlt1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2a_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0c_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0c_2E0)))))) ) ).
fof(thm_2Ebag_2Emlt__UNION__RCANCEL,axiom,
! [A_27a,V0c_2E0,V1b_2E0,V2a_2E0,V3R_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_2E0)))) )
=> ( p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Ebag_2Emlt1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2a_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0c_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0c_2E0))))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Ebag_2Emlt1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2a_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0c_2E0)))) ) ) ) ).
fof(thm_2Ebag_2Emlt__UNION__LCANCEL__I,axiom,
! [A_27a,V0c_2E0,V1b_2E0,V2a_2E0,V3R_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Ebag_2Emlt1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2a_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0c_2E0)))) )
=> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Ebag_2Emlt1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0c_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2a_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0c_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0)))))) ) ).
fof(thm_2Ebag_2Emlt__UNION__LCANCEL,axiom,
! [A_27a,V0c_2E0,V1b_2E0,V2a_2E0,V3R_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_2E0)))) )
=> ( p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Ebag_2Emlt1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0c_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2a_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0c_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Ebag_2Emlt1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2a_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0c_2E0)))) ) ) ) ).
fof(thm_2Ebag_2Emlt__UNION__CANCEL__EQN,axiom,
! [A_27a,V0b2_2E0,V1b1_2E0,V2R_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0))))
=> ( ( p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Ebag_2Emlt1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b2_2E0))))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b2_2E0))))
& s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b2_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0) ) )
& ( p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Ebag_2Emlt1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__UNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0))))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b1_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b2_2E0))))
& s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0b2_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0) ) ) ) ) ).
fof(thm_2Ebag_2Emlt__UNION__EMPTY__EQN,axiom,
p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ).
fof(thm_2Ebag_2ESUB__BAG__SING,axiom,
! [A_27a,V0e_2E0,V1b_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0))))))
<=> ( s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0)
| s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0))) ) ) ).
fof(thm_2Ebag_2ESUB__BAG__DIFF__simple,axiom,
! [A_27a,V0c_2E0,V1b_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebag_2ESUB__BAG_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__DIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0c_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1b_2E0)))) ).
fof(thm_2Ebag_2EmltLT__SING0,axiom,
! [V0b_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Ebag_2Emlt1_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Eprim__rec_2E_3C_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0b_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0b_2E0))))
& s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0b_2E0) != s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0)))
& s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0b_2E0) != s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0) ) ) ).
fof(thm_2Ebag_2EBAG__SIZE__EMPTY,axiom,
! [A_27a,V0eltsize_2E0] : s(tyop_2Enum_2Enum,c_2Ebag_2Ebag__size_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0eltsize_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) ).
fof(thm_2Ebag_2EBAG__SIZE__INSERT,axiom,
! [A_27a,V0eltsize_2E0,V1e_2E0,V2b_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebag_2EFINITE__BAG_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b_2E0))))
=> s(tyop_2Enum_2Enum,c_2Ebag_2Ebag__size_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0eltsize_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27a,V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0eltsize_2E0),s(A_27a,V1e_2E0))))),s(tyop_2Enum_2Enum,c_2Ebag_2Ebag__size_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0eltsize_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2b_2E0))))) ) ).
fof(reserved_2Eho_2Eeq__ext,axiom,
! [A_27a,A_27b,V0f_2E0,V1g_2E0] :
( ! [V2x_2E0] : s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))
=> s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0) ) ).
%------------------------------------------------------------------------------