ITP001 Axioms: ITP078+4.ax
%------------------------------------------------------------------------------
% File : ITP078+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 : update.ax [Gau19]
% : HL4078+4.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 87 ( 58 unt; 0 def)
% Number of atoms : 149 ( 101 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 72 ( 10 ~; 3 |; 15 &)
% ( 22 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Maximal term depth : 15 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 82 ( 82 usr; 40 con; 0-4 aty)
% Number of variables : 392 ( 391 !; 1 ?)
% 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_2Elist_2EALL__DISTINCT_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),c_2Elist_2EALL__DISTINCT_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))) ).
fof(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27a,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(A_27a))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) ).
fof(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0] : s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))) ).
fof(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Elist_2ECONS_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) ).
fof(arityeq2_2Ec_2Elist_2EFILTER_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Elist_2EFILTER_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) ).
fof(arityeq1_2Ec_2Ecombin_2EI_2E1_2Emono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29,axiom,
! [A_27a,A_27b,X0_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Ecombin_2EI_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Ecombin_2EI_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))) ).
fof(arityeq1_2Ec_2Eupdate_2ELIST__UPDATE_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Eupdate_2ELIST__UPDATE_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))),c_2Eupdate_2ELIST__UPDATE_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))) ).
fof(arityeq1_2Ec_2Eupdate_2EOVERRIDE_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eupdate_2EOVERRIDE_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Eupdate_2EOVERRIDE_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))) ).
fof(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Elist_2EAPPEND_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,X0_2E0),s(A_27b,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Epair_2E_2C_2E0),s(A_27a,X0_2E0))),s(A_27b,X1_2E0))) ).
fof(arityeq2_2Ec_2Esorting_2EQSORT_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Esorting_2EQSORT_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Esorting_2EQSORT_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27c,A_27d,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(A_27c,A_27d),c_2Epair_2E_2C_2E2(s(A_27c,X0_2E0),s(A_27d,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27c,A_27d),app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Epair_2Eprod(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Epair_2Eprod(A_27c,A_27d))),c_2Epair_2E_2C_2E0),s(A_27c,X0_2E0))),s(A_27d,X1_2E0))) ).
fof(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27d_29,axiom,
! [A_27c,A_27d,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27c,A_27d),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)))),c_2Elist_2ECONS_2E0),s(tyop_2Epair_2Eprod(A_27c,A_27d),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),X1_2E0))) ).
fof(arityeq1_2Ec_2Eupdate_2ELIST__UPDATE_2E1_2Emono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27c,A_27d,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),c_2Eupdate_2ELIST__UPDATE_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d))),c_2Eupdate_2ELIST__UPDATE_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),X0_2E0))) ).
fof(arityeq2_2Ec_2Elist_2ESNOC_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27d_29,axiom,
! [A_27c,A_27d,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),c_2Elist_2ESNOC_2E2(s(tyop_2Epair_2Eprod(A_27c,A_27d),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)))),c_2Elist_2ESNOC_2E0),s(tyop_2Epair_2Eprod(A_27c,A_27d),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),X1_2E0))) ).
fof(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29,axiom,
! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWF_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),X0_2E0))) ).
fof(arityeq2_2Ec_2Eupdate_2EFIND_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Eoption_2Eoption(A_27a),c_2Eupdate_2EFIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a))),c_2Eupdate_2EFIND_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) ).
fof(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Elist_2ECONS_2E0),s(A_27a,X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) ).
fof(arityeq2_2Ec_2Eupdate_2ELIST__UPDATE_2E2_2Emono_2EA_27e_20mono_2EA_27f,axiom,
! [A_27e,A_27f,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27e,A_27f),c_2Eupdate_2ELIST__UPDATE_2E2(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27e,A_27f)),X0_2E0),s(tyop_2Emin_2Efun(A_27e,A_27f),X1_2E0))) = s(tyop_2Emin_2Efun(A_27e,A_27f),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,A_27f),tyop_2Emin_2Efun(A_27e,A_27f)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27e,A_27f)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,A_27f),tyop_2Emin_2Efun(A_27e,A_27f))),c_2Eupdate_2ELIST__UPDATE_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27e,A_27f)),X0_2E0))),s(tyop_2Emin_2Efun(A_27e,A_27f),X1_2E0))) ).
fof(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27e_2CA_27f_29,axiom,
! [A_27e,A_27f,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27e,A_27f)),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27e,A_27f)),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27e,A_27f)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27e,A_27f)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27e,A_27f)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27e,A_27f))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27e,A_27f)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27e,A_27f)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27e,A_27f)))),c_2Elist_2EAPPEND_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27e,A_27f)),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27e,A_27f)),X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27e_20mono_2EA_27f,axiom,
! [A_27e,A_27f,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(A_27e,A_27f),c_2Epair_2E_2C_2E2(s(A_27e,X0_2E0),s(A_27f,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27e,A_27f),app_2E2(s(tyop_2Emin_2Efun(A_27f,tyop_2Epair_2Eprod(A_27e,A_27f)),app_2E2(s(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27f,tyop_2Epair_2Eprod(A_27e,A_27f))),c_2Epair_2E_2C_2E0),s(A_27e,X0_2E0))),s(A_27f,X1_2E0))) ).
fof(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27e_2CA_27f_29,axiom,
! [A_27e,A_27f,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27e,A_27f)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27e,A_27f),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27e,A_27f)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27e,A_27f)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27e,A_27f)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27e,A_27f))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27e,A_27f),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27e,A_27f)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27e,A_27f)))),c_2Elist_2ECONS_2E0),s(tyop_2Epair_2Eprod(A_27e,A_27f),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27e,A_27f)),X1_2E0))) ).
fof(arityeq2_2Ec_2Eupdate_2ELIST__UPDATE_2E2_2Emono_2EA_27g_20mono_2EA_27h,axiom,
! [A_27g,A_27h,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27g,A_27h),c_2Eupdate_2ELIST__UPDATE_2E2(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27g,A_27h)),X0_2E0),s(tyop_2Emin_2Efun(A_27g,A_27h),X1_2E0))) = s(tyop_2Emin_2Efun(A_27g,A_27h),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27g,A_27h),tyop_2Emin_2Efun(A_27g,A_27h)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27g,A_27h)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27g,A_27h),tyop_2Emin_2Efun(A_27g,A_27h))),c_2Eupdate_2ELIST__UPDATE_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27g,A_27h)),X0_2E0))),s(tyop_2Emin_2Efun(A_27g,A_27h),X1_2E0))) ).
fof(arityeq3_2Ec_2Ecombin_2EUPDATE_2E3_2Emono_2EA_27g_20mono_2EA_27h,axiom,
! [A_27g,A_27h,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Efun(A_27g,A_27h),c_2Ecombin_2EUPDATE_2E3(s(A_27g,X0_2E0),s(A_27h,X1_2E0),s(tyop_2Emin_2Efun(A_27g,A_27h),X2_2E0))) = s(tyop_2Emin_2Efun(A_27g,A_27h),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27g,A_27h),tyop_2Emin_2Efun(A_27g,A_27h)),app_2E2(s(tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27g,A_27h),tyop_2Emin_2Efun(A_27g,A_27h))),app_2E2(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27g,A_27h),tyop_2Emin_2Efun(A_27g,A_27h)))),c_2Ecombin_2EUPDATE_2E0),s(A_27g,X0_2E0))),s(A_27h,X1_2E0))),s(tyop_2Emin_2Efun(A_27g,A_27h),X2_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27g_20mono_2EA_27h,axiom,
! [A_27g,A_27h,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(A_27g,A_27h),c_2Epair_2E_2C_2E2(s(A_27g,X0_2E0),s(A_27h,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27g,A_27h),app_2E2(s(tyop_2Emin_2Efun(A_27h,tyop_2Epair_2Eprod(A_27g,A_27h)),app_2E2(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Epair_2Eprod(A_27g,A_27h))),c_2Epair_2E_2C_2E0),s(A_27g,X0_2E0))),s(A_27h,X1_2E0))) ).
fof(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27g_2CA_27h_29,axiom,
! [A_27g,A_27h,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27g,A_27h)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27g,A_27h),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27g,A_27h)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27g,A_27h)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27g,A_27h)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27g,A_27h))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27g,A_27h),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27g,A_27h)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27g,A_27h)))),c_2Elist_2ECONS_2E0),s(tyop_2Epair_2Eprod(A_27g,A_27h),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27g,A_27h)),X1_2E0))) ).
fof(arityeq2_2Ec_2Elist_2ESNOC_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27g_2CA_27h_29,axiom,
! [A_27g,A_27h,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27g,A_27h)),c_2Elist_2ESNOC_2E2(s(tyop_2Epair_2Eprod(A_27g,A_27h),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27g,A_27h)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27g,A_27h)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27g,A_27h)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27g,A_27h))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27g,A_27h),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27g,A_27h)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27g,A_27h)))),c_2Elist_2ESNOC_2E0),s(tyop_2Epair_2Eprod(A_27g,A_27h),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27g,A_27h)),X1_2E0))) ).
fof(arityeq2_2Ec_2Esorting_2EPERM_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Esorting_2EPERM_2E2(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),c_2Esorting_2EPERM_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) ).
fof(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),c_2Emin_2E_40_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq2_2Ec_2Erelation_2EWFREC_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Erelation_2EWFREC_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),c_2Erelation_2EWFREC_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),X1_2E0))) ).
fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0))) ).
fof(arityeq2_2Ec_2Ecombin_2EUPDATE_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ecombin_2EUPDATE_2E2(s(A_27a,X0_2E0),s(A_27b,X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)))),c_2Ecombin_2EUPDATE_2E0),s(A_27a,X0_2E0))),s(A_27b,X1_2E0))) ).
fof(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0] : s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),c_2Epair_2ESND_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))) ).
fof(arityeq2_2Ec_2Ecombin_2EUPDATE_2E2_2Emono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27c,A_27d,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),c_2Ecombin_2EUPDATE_2E2(s(A_27c,X0_2E0),s(A_27d,X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d))),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)))),c_2Ecombin_2EUPDATE_2E0),s(A_27c,X0_2E0))),s(A_27d,X1_2E0))) ).
fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27c_2CA_27d_29_20mono_2Etyop_2Emin_2Efun_28A_27c_2CA_27d_29_20mono_2Etyop_2Emin_2Efun_28A_27c_2CA_27d_29,axiom,
! [A_27c,A_27d,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2EA_27b_20mono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(A_27b,c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),X1_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),A_27b)),c_2Epair_2Epair__CASE_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),X1_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_2Eoption_2Eoption_28A_27a_29,axiom,
! [A_27a,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0),s(tyop_2Eoption_2Eoption(A_27a),X2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X2_2E0))) ).
fof(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ESOME_2E0),s(A_27a,X0_2E0))) ).
fof(arityeq3_2Ec_2Eupdate_2ELIST__UPDATE_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(A_27b,c_2Eupdate_2ELIST__UPDATE_2E3(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0),s(A_27a,X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))),c_2Eupdate_2ELIST__UPDATE_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))),s(A_27a,X2_2E0))) ).
fof(arityeq3_2Ec_2Ecombin_2EUPDATE_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,X0_2E0),s(A_27b,X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)))),c_2Ecombin_2EUPDATE_2E0),s(A_27a,X0_2E0))),s(A_27b,X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0))) ).
fof(arityeq3_2Ec_2Ecombin_2EUPDATE_2E3_2Emono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27c,A_27d,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Efun(A_27c,A_27d),c_2Ecombin_2EUPDATE_2E3(s(A_27c,X0_2E0),s(A_27d,X1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27d),X2_2E0))) = s(tyop_2Emin_2Efun(A_27c,A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d))),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)))),c_2Ecombin_2EUPDATE_2E0),s(A_27c,X0_2E0))),s(A_27d,X1_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27d),X2_2E0))) ).
fof(arityeq3_2Ec_2Ecombin_2EUPDATE_2E3_2Emono_2EA_27e_20mono_2EA_27f,axiom,
! [A_27e,A_27f,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Efun(A_27e,A_27f),c_2Ecombin_2EUPDATE_2E3(s(A_27e,X0_2E0),s(A_27f,X1_2E0),s(tyop_2Emin_2Efun(A_27e,A_27f),X2_2E0))) = s(tyop_2Emin_2Efun(A_27e,A_27f),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,A_27f),tyop_2Emin_2Efun(A_27e,A_27f)),app_2E2(s(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,A_27f),tyop_2Emin_2Efun(A_27e,A_27f))),app_2E2(s(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,A_27f),tyop_2Emin_2Efun(A_27e,A_27f)))),c_2Ecombin_2EUPDATE_2E0),s(A_27e,X0_2E0))),s(A_27f,X1_2E0))),s(tyop_2Emin_2Efun(A_27e,A_27f),X2_2E0))) ).
fof(arityeq3_2Ec_2Elist_2Elist__CASE_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),X2_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),c_2Elist_2Elist__CASE_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),X2_2E0))) ).
fof(arityeq2_2Ec_2Eupdate_2EFIND_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eupdate_2EFIND_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Eupdate_2EFIND_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) ).
fof(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(A_27b,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),s(A_27b,X1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),A_27b))),c_2Eoption_2Eoption__CASE_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))),s(A_27b,X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),X2_2E0))) ).
fof(arityeq4_2Ec_2Ecombin_2EUPDATE_2E4_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(A_27b,c_2Ecombin_2EUPDATE_2E4(s(A_27a,X0_2E0),s(A_27b,X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0),s(A_27a,X3_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)))),c_2Ecombin_2EUPDATE_2E0),s(A_27a,X0_2E0))),s(A_27b,X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0))),s(A_27a,X3_2E0))) ).
fof(thm_2Eupdate_2EFIND__def,axiom,
! [A_27a] :
( ! [V0P_2E0] : s(tyop_2Eoption_2Eoption(A_27a),c_2Eupdate_2EFIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0)
& ! [V1P_2E0,V2h_2E0,V3t_2E0] : s(tyop_2Eoption_2Eoption(A_27a),c_2Eupdate_2EFIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V3t_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2h_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V2h_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eupdate_2EFIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),V3t_2E0))))) ) ).
fof(thm_2Eupdate_2EOVERRIDE__primitive__def,axiom,
! [A_27a,A_27b,F4_2E0,F3_2E0,F1_2E0,F2_2E0,F0_2E0] :
( ! [V6x_2E0,V8y_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),F4_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V6x_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),V8y_2E0))))
<=> s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V6x_2E0))) != s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V8y_2E0))) )
=> ( ! [V4OVERRIDE_2E0,V6x_2E0,V7t_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),F3_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V4OVERRIDE_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),V6x_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V7t_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Ecombin_2EI_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),V6x_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V4OVERRIDE_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),F4_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V6x_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V7t_2E0)))))))))
=> ( ! [V4OVERRIDE_2E0,V5a_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V4OVERRIDE_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V5a_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V5a_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Ecombin_2EI_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),F3_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V4OVERRIDE_2E0)))))
=> ( ! [V2x_2E0,V3y_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),F2_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V2x_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),V3y_2E0))))
<=> s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V2x_2E0))) != s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V3y_2E0))) )
=> ( ! [V0R_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),V0R_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),V0R_2E0))))
& ! [V1t_2E0,V2x_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),F2_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V2x_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1t_2E0))))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),V2x_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1t_2E0)))))) ) )
=> s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Eupdate_2EOVERRIDE_2E0) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Erelation_2EWFREC_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),F0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),F1_2E0))) ) ) ) ) ) ).
fof(thm_2Eupdate_2ELIST__UPDATE__def,axiom,
! [A_27a,A_27b] :
( s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Eupdate_2ELIST__UPDATE_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ecombin_2EI_2E0)
& ! [V0h_2E0,V1t_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Eupdate_2ELIST__UPDATE_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),V0h_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1t_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ecombin_2EUPDATE_2E2(s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V0h_2E0))),s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V0h_2E0))))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Eupdate_2ELIST__UPDATE_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1t_2E0))))) ) ).
fof(thm_2Eupdate_2EOVERRIDE__ind,axiom,
! [A_27a,A_27b,F0_2E0] :
( ! [V1x_2E0,V3y_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V1x_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),V3y_2E0))))
<=> s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V1x_2E0))) != s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V3y_2E0))) )
=> ! [V0P_2E0] :
( ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0))))
& ! [V1x_2E0,V2t_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V1x_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2t_2E0))))))
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),V1x_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2t_2E0)))))) ) )
=> ! [V4v_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V4v_2E0)))) ) ) ).
fof(thm_2Eupdate_2EOVERRIDE__def,axiom,
! [A_27a,A_27b,F0_2E0] :
( ! [V0x_2E0,V2y_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V0x_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),V2y_2E0))))
<=> s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V0x_2E0))) != s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V2y_2E0))) )
=> ( s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eupdate_2EOVERRIDE_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0)
& ! [V0x_2E0,V1t_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eupdate_2EOVERRIDE_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),V0x_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1t_2E0))))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),V0x_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eupdate_2EOVERRIDE_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V0x_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1t_2E0))))))) ) ) ).
fof(thm_2Eupdate_2ELIST__UPDATE__LOOKUP,axiom,
! [A_27a,A_27b,F2_2E0,F1_2E0,F0_2E0] :
( ! [V5v1_2E0,V6e_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)),F2_2E0),s(A_27a,V5v1_2E0))),s(A_27b,V6e_2E0))) = s(A_27b,V6e_2E0)
=> ( ! [V4v_2E0] : s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),F1_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V4v_2E0))) = s(A_27b,c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),V4v_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),F2_2E0)))
=> ( ! [V2i_2E0,V3x_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),F0_2E0),s(A_27a,V2i_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),V3x_2E0))))
<=> s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V3x_2E0))) = s(A_27a,V2i_2E0) )
=> ! [V0l_2E0,V1f_2E0,V2i_2E0] : s(A_27b,c_2Eupdate_2ELIST__UPDATE_2E3(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0l_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(A_27a,V2i_2E0))) = s(A_27b,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eupdate_2EFIND_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),F0_2E0),s(A_27a,V2i_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0l_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(A_27a,V2i_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),F1_2E0))) ) ) ) ).
fof(thm_2Eupdate_2ELIST__UPDATE__OVERRIDE,axiom,
! [A_27a,A_27b,V0l_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Eupdate_2ELIST__UPDATE_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0l_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Eupdate_2ELIST__UPDATE_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eupdate_2EOVERRIDE_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0l_2E0))))) ).
fof(thm_2Eupdate_2ELIST__UPDATE__ALL__DISTINCT,axiom,
! [A_27a,A_27b,V0l1_2E0,V1l2_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l2_2E0))))))
& p(s(tyop_2Emin_2Ebool,c_2Esorting_2EPERM_2E2(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0l1_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l2_2E0)))) )
=> s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Eupdate_2ELIST__UPDATE_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0l1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Eupdate_2ELIST__UPDATE_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l2_2E0))) ) ).
fof(thm_2Eupdate_2ELIST__UPDATE__SORT__OVERRIDE,axiom,
! [A_27a,A_27b,V0R_2E0,V1l_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Eupdate_2ELIST__UPDATE_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Eupdate_2ELIST__UPDATE_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Esorting_2EQSORT_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eupdate_2EOVERRIDE_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l_2E0))))))) ).
fof(thm_2Eupdate_2ELIST__UPDATE__THMS,axiom,
! [A_27a,A_27b,A_27c,A_27d,A_27e,A_27f,A_27g,A_27h] :
( ! [V0l1_2E0,V1l2_2E0,V2r1_2E0,V3r2_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ecombin_2EUPDATE_2E2(s(A_27a,V0l1_2E0),s(A_27b,V2r1_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ecombin_2EUPDATE_2E2(s(A_27a,V1l2_2E0),s(A_27b,V3r2_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Eupdate_2ELIST__UPDATE_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V0l1_2E0),s(A_27b,V2r1_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1l2_2E0),s(A_27b,V3r2_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0)))))))
& ! [V4l_2E0,V5r_2E0,V6t_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),c_2Ecombin_2EUPDATE_2E2(s(A_27c,V4l_2E0),s(A_27d,V5r_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),c_2Eupdate_2ELIST__UPDATE_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),V6t_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),c_2Eupdate_2ELIST__UPDATE_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27c,A_27d),c_2Epair_2E_2C_2E2(s(A_27c,V4l_2E0),s(A_27d,V5r_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),V6t_2E0)))))
& ! [V7l1_2E0,V8l2_2E0,V9r1_2E0,V10r2_2E0,V11f_2E0] : s(tyop_2Emin_2Efun(A_27e,A_27f),c_2Ecombin_2EUPDATE_2E3(s(A_27e,V7l1_2E0),s(A_27f,V9r1_2E0),s(tyop_2Emin_2Efun(A_27e,A_27f),c_2Ecombin_2EUPDATE_2E3(s(A_27e,V8l2_2E0),s(A_27f,V10r2_2E0),s(tyop_2Emin_2Efun(A_27e,A_27f),V11f_2E0))))) = s(tyop_2Emin_2Efun(A_27e,A_27f),c_2Eupdate_2ELIST__UPDATE_2E2(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27e,A_27f)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27e,A_27f),c_2Epair_2E_2C_2E2(s(A_27e,V7l1_2E0),s(A_27f,V9r1_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27e,A_27f)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27e,A_27f),c_2Epair_2E_2C_2E2(s(A_27e,V8l2_2E0),s(A_27f,V10r2_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27e,A_27f)),c_2Elist_2ENIL_2E0))))),s(tyop_2Emin_2Efun(A_27e,A_27f),V11f_2E0)))
& ! [V12l_2E0,V13r_2E0,V14t_2E0,V15f_2E0] : s(tyop_2Emin_2Efun(A_27g,A_27h),c_2Ecombin_2EUPDATE_2E3(s(A_27g,V12l_2E0),s(A_27h,V13r_2E0),s(tyop_2Emin_2Efun(A_27g,A_27h),c_2Eupdate_2ELIST__UPDATE_2E2(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27g,A_27h)),V14t_2E0),s(tyop_2Emin_2Efun(A_27g,A_27h),V15f_2E0))))) = s(tyop_2Emin_2Efun(A_27g,A_27h),c_2Eupdate_2ELIST__UPDATE_2E2(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27g,A_27h)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27g,A_27h),c_2Epair_2E_2C_2E2(s(A_27g,V12l_2E0),s(A_27h,V13r_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27g,A_27h)),V14t_2E0))),s(tyop_2Emin_2Efun(A_27g,A_27h),V15f_2E0)))
& ! [V16l1_2E0,V17l2_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Eupdate_2ELIST__UPDATE_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V16l1_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Eupdate_2ELIST__UPDATE_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V17l2_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Eupdate_2ELIST__UPDATE_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V16l1_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V17l2_2E0)))))
& ! [V18l1_2E0,V19l2_2E0,V20r_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),c_2Eupdate_2ELIST__UPDATE_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),V18l1_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),c_2Ecombin_2EUPDATE_2E2(s(A_27c,V19l2_2E0),s(A_27d,V20r_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),c_2Eupdate_2ELIST__UPDATE_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),c_2Elist_2ESNOC_2E2(s(tyop_2Epair_2Eprod(A_27c,A_27d),c_2Epair_2E_2C_2E2(s(A_27c,V19l2_2E0),s(A_27d,V20r_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),V18l1_2E0)))))
& ! [V21l1_2E0,V22l2_2E0,V23f_2E0] : s(tyop_2Emin_2Efun(A_27e,A_27f),c_2Eupdate_2ELIST__UPDATE_2E2(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27e,A_27f)),V21l1_2E0),s(tyop_2Emin_2Efun(A_27e,A_27f),c_2Eupdate_2ELIST__UPDATE_2E2(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27e,A_27f)),V22l2_2E0),s(tyop_2Emin_2Efun(A_27e,A_27f),V23f_2E0))))) = s(tyop_2Emin_2Efun(A_27e,A_27f),c_2Eupdate_2ELIST__UPDATE_2E2(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27e,A_27f)),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27e,A_27f)),V21l1_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27e,A_27f)),V22l2_2E0))),s(tyop_2Emin_2Efun(A_27e,A_27f),V23f_2E0)))
& ! [V24l1_2E0,V25l2_2E0,V26r_2E0,V27f_2E0] : s(tyop_2Emin_2Efun(A_27g,A_27h),c_2Eupdate_2ELIST__UPDATE_2E2(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27g,A_27h)),V24l1_2E0),s(tyop_2Emin_2Efun(A_27g,A_27h),c_2Ecombin_2EUPDATE_2E3(s(A_27g,V25l2_2E0),s(A_27h,V26r_2E0),s(tyop_2Emin_2Efun(A_27g,A_27h),V27f_2E0))))) = s(tyop_2Emin_2Efun(A_27g,A_27h),c_2Eupdate_2ELIST__UPDATE_2E2(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27g,A_27h)),c_2Elist_2ESNOC_2E2(s(tyop_2Epair_2Eprod(A_27g,A_27h),c_2Epair_2E_2C_2E2(s(A_27g,V25l2_2E0),s(A_27h,V26r_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27g,A_27h)),V24l1_2E0))),s(tyop_2Emin_2Efun(A_27g,A_27h),V27f_2E0))) ) ).
fof(thm_2Eupdate_2EAPPLY__UPDATE__ID,axiom,
! [A_27a,A_27b,V0f_2E0,V1a_2E0] : s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V1a_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V1a_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) ).
fof(thm_2Eupdate_2EAPPLY__UPDATE__THM,axiom,
! [A_27a,A_27b,F0_2E0] :
( ! [V1a_2E0,V3c_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,V1a_2E0))),s(A_27a,V3c_2E0))))
<=> s(A_27a,V1a_2E0) = s(A_27a,V3c_2E0) )
=> ! [V0f_2E0,V1a_2E0,V2b_2E0,V3c_2E0] : s(A_27b,c_2Ecombin_2EUPDATE_2E4(s(A_27a,V1a_2E0),s(A_27b,V2b_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3c_2E0))) = s(A_27b,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,V1a_2E0))),s(A_27a,V3c_2E0))),s(A_27b,V2b_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3c_2E0))))) ) ).
fof(thm_2Eupdate_2ESAME__KEY__UPDATE__DIFFER,axiom,
! [A_27a,A_27b,A_27c,A_27d,V0f_2E0,V1f1_2E0,V2f2_2E0,V3a_2E0,V4b_2E0,V5c_2E0] :
( s(A_27d,V4b_2E0) != s(A_27d,V5c_2E0)
=> s(tyop_2Emin_2Efun(A_27c,A_27d),c_2Ecombin_2EUPDATE_2E3(s(A_27c,V3a_2E0),s(A_27d,V4b_2E0),s(tyop_2Emin_2Efun(A_27c,A_27d),V0f_2E0))) != s(tyop_2Emin_2Efun(A_27c,A_27d),c_2Ecombin_2EUPDATE_2E3(s(A_27c,V3a_2E0),s(A_27d,V5c_2E0),s(tyop_2Emin_2Efun(A_27c,A_27d),V0f_2E0))) ) ).
fof(thm_2Eupdate_2EUPDATE__APPLY__ID,axiom,
! [A_27a,A_27b,V0f_2E0,V1a_2E0,V2b_2E0] :
( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V1a_2E0))) = s(A_27b,V2b_2E0)
<=> s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V1a_2E0),s(A_27b,V2b_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) ) ).
fof(thm_2Eupdate_2EUPDATE__APPLY__IMP__ID,axiom,
! [A_27a,A_27b,V0f_2E0,V1b_2E0,V2a_2E0] :
( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2a_2E0))) = s(A_27b,V1b_2E0)
=> s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V2a_2E0),s(A_27b,V1b_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) ) ).
fof(thm_2Eupdate_2EUPDATE__COMMUTES,axiom,
! [A_27a,A_27b,V0f_2E0,V1a_2E0,V2b_2E0,V3c_2E0,V4d_2E0] :
( s(A_27a,V1a_2E0) != s(A_27a,V2b_2E0)
=> s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V1a_2E0),s(A_27b,V3c_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V2b_2E0),s(A_27b,V4d_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))))) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V2b_2E0),s(A_27b,V4d_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V1a_2E0),s(A_27b,V3c_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))))) ) ).
fof(thm_2Eupdate_2EUPDATE__EQ,axiom,
! [A_27a,A_27b,V0f_2E0,V1a_2E0,V2b_2E0,V3c_2E0] : s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V1a_2E0),s(A_27b,V3c_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V1a_2E0),s(A_27b,V2b_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))))) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V1a_2E0),s(A_27b,V3c_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) ).
fof(thm_2Eupdate_2EUPDATE__def,axiom,
! [A_27a,A_27b,F0_2E0] :
( ! [V0a_2E0,V3x_27_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,V0a_2E0))),s(A_27a,V3x_27_2E0))))
<=> s(A_27a,V0a_2E0) = s(A_27a,V3x_27_2E0) )
=> ! [V0a_2E0,V1b_2E0,V2x_2E0,V3x_27_2E0] : s(A_27b,c_2Ecombin_2EUPDATE_2E4(s(A_27a,V0a_2E0),s(A_27b,V1b_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V2x_2E0),s(A_27a,V3x_27_2E0))) = s(A_27b,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,V0a_2E0))),s(A_27a,V3x_27_2E0))),s(A_27b,V1b_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2x_2E0),s(A_27a,V3x_27_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) ) ).
%------------------------------------------------------------------------------