ITP001 Axioms: ITP076+4.ax
%------------------------------------------------------------------------------
% File : ITP076+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 : ternaryComparisons.ax [Gau19]
% : HL4076+4.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 90 ( 44 unt; 0 def)
% Number of atoms : 212 ( 135 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 129 ( 7 ~; 7 |; 59 &)
% ( 32 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 15 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 84 ( 84 usr; 47 con; 0-4 aty)
% Number of variables : 300 ( 295 !; 5 ?)
% 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_2Ebool_2EDATATYPE_2E1_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E1(s(tyop_2Emin_2Ebool,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2EDATATYPE_2E0),s(tyop_2Emin_2Ebool,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(arityeq1_2Ec_2Earithmetic_2EBIT2_2E1,axiom,
! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_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_2EBIT2_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).
fof(arityeq1_2Ec_2EternaryComparisons_2Einvert__comparison_2E1,axiom,
! [X0_2E0] : s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Einvert__comparison_2E1(s(tyop_2EternaryComparisons_2Eordering,X0_2E0))) = s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2EternaryComparisons_2Eordering),c_2EternaryComparisons_2Einvert__comparison_2E0),s(tyop_2EternaryComparisons_2Eordering,X0_2E0))) ).
fof(arityeq1_2Ec_2EternaryComparisons_2Elist__compare_2E1_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2Estring_2Echar,axiom,
! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2EternaryComparisons_2Eordering)),c_2EternaryComparisons_2Elist__compare_2E1(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2EternaryComparisons_2Eordering)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2EternaryComparisons_2Eordering)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2EternaryComparisons_2Eordering))),c_2EternaryComparisons_2Elist__compare_2E0),s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2EternaryComparisons_2Eordering)),X0_2E0))) ).
fof(arityeq1_2Ec_2EternaryComparisons_2Enum2ordering_2E1,axiom,
! [X0_2E0] : s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Enum2ordering_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2EternaryComparisons_2Eordering),c_2EternaryComparisons_2Enum2ordering_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).
fof(arityeq1_2Ec_2EternaryComparisons_2Eordering2num_2E1,axiom,
! [X0_2E0] : s(tyop_2Enum_2Enum,c_2EternaryComparisons_2Eordering2num_2E1(s(tyop_2EternaryComparisons_2Eordering,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2Enum_2Enum),c_2EternaryComparisons_2Eordering2num_2E0),s(tyop_2EternaryComparisons_2Eordering,X0_2E0))) ).
fof(arityeq1_2Ec_2EternaryComparisons_2Eordering__size_2E1,axiom,
! [X0_2E0] : s(tyop_2Enum_2Enum,c_2EternaryComparisons_2Eordering__size_2E1(s(tyop_2EternaryComparisons_2Eordering,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2Enum_2Enum),c_2EternaryComparisons_2Eordering__size_2E0),s(tyop_2EternaryComparisons_2Eordering,X0_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_2Elist_2ECONS_2E2_2Emono_2EA_27b,axiom,
! [A_27b,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b))),c_2Elist_2ECONS_2E0),s(A_27b,X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) ).
fof(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27b,axiom,
! [A_27b,X0_2E0] : s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),c_2Eoption_2ESOME_2E0),s(A_27b,X0_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(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_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2EternaryComparisons_2Eordering,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Ebool_2ETYPE__DEFINITION_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2Enum_2Enum),X1_2E0))) ).
fof(arityeq2_2Ec_2EternaryComparisons_2Ebool__compare_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Ebool__compare_2E2(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2EternaryComparisons_2Eordering)),c_2EternaryComparisons_2Ebool__compare_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))) ).
fof(arityeq2_2Ec_2EternaryComparisons_2Echar__compare_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Echar__compare_2E2(s(tyop_2Estring_2Echar,X0_2E0),s(tyop_2Estring_2Echar,X1_2E0))) = s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2EternaryComparisons_2Eordering)),c_2EternaryComparisons_2Echar__compare_2E0),s(tyop_2Estring_2Echar,X0_2E0))),s(tyop_2Estring_2Echar,X1_2E0))) ).
fof(arityeq2_2Ec_2EternaryComparisons_2Enum__compare_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Enum__compare_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2EternaryComparisons_2Eordering)),c_2EternaryComparisons_2Enum__compare_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).
fof(arityeq1_2Ec_2Estring_2EORD_2E1,axiom,
! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Estring_2EORD_2E1(s(tyop_2Estring_2Echar,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),c_2Estring_2EORD_2E0),s(tyop_2Estring_2Echar,X0_2E0))) ).
fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0,X2_2E0] : s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))) ).
fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
! [A_27a,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Elist_2Elist(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_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(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) ).
fof(arityeq3_2Ec_2EternaryComparisons_2Elist__merge_2E3_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Elist_2Elist(A_27a),c_2EternaryComparisons_2Elist__merge_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_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(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))),c_2EternaryComparisons_2Elist__merge_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) ).
fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2EternaryComparisons_2Eordering,axiom,
! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2EternaryComparisons_2Eordering,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2EternaryComparisons_2Eordering,X1_2E0),s(tyop_2EternaryComparisons_2Eordering,X2_2E0))) = s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2EternaryComparisons_2Eordering)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2EternaryComparisons_2Eordering))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2EternaryComparisons_2Eordering,X1_2E0))),s(tyop_2EternaryComparisons_2Eordering,X2_2E0))) ).
fof(arityeq3_2Ec_2EternaryComparisons_2Elist__compare_2E3_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Elist__compare_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2EternaryComparisons_2Eordering)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2EternaryComparisons_2Eordering))),c_2EternaryComparisons_2Elist__compare_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) ).
fof(arityeq3_2Ec_2EternaryComparisons_2Elist__compare_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Elist__compare_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0),s(tyop_2Elist_2Elist(A_27b),X2_2E0))) = s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2EternaryComparisons_2Eordering)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2EternaryComparisons_2Eordering))),c_2EternaryComparisons_2Elist__compare_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))),s(tyop_2Elist_2Elist(A_27b),X2_2E0))) ).
fof(arityeq3_2Ec_2EternaryComparisons_2Eoption__compare_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Eoption__compare_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0),s(tyop_2Eoption_2Eoption(A_27b),X2_2E0))) = s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2EternaryComparisons_2Eordering)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2EternaryComparisons_2Eordering))),c_2EternaryComparisons_2Eoption__compare_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))),s(tyop_2Eoption_2Eoption(A_27b),X2_2E0))) ).
fof(arityeq4_2Ec_2EternaryComparisons_2Eordering__CASE_2E4_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(A_27a,c_2EternaryComparisons_2Eordering__CASE_2E4(s(tyop_2EternaryComparisons_2Eordering,X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0),s(A_27a,X3_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)))),c_2EternaryComparisons_2Eordering__CASE_2E0),s(tyop_2EternaryComparisons_2Eordering,X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))),s(A_27a,X3_2E0))) ).
fof(arityeq4_2Ec_2EternaryComparisons_2Eordering__CASE_2E4_2Emono_2Etyop_2EternaryComparisons_2Eordering,axiom,
! [X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Eordering__CASE_2E4(s(tyop_2EternaryComparisons_2Eordering,X0_2E0),s(tyop_2EternaryComparisons_2Eordering,X1_2E0),s(tyop_2EternaryComparisons_2Eordering,X2_2E0),s(tyop_2EternaryComparisons_2Eordering,X3_2E0))) = s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2EternaryComparisons_2Eordering)),app_2E2(s(tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2EternaryComparisons_2Eordering))),app_2E2(s(tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2EternaryComparisons_2Eordering)))),c_2EternaryComparisons_2Eordering__CASE_2E0),s(tyop_2EternaryComparisons_2Eordering,X0_2E0))),s(tyop_2EternaryComparisons_2Eordering,X1_2E0))),s(tyop_2EternaryComparisons_2Eordering,X2_2E0))),s(tyop_2EternaryComparisons_2Eordering,X3_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a,A_27c,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(A_27a,A_27c),c_2Epair_2E_2C_2E2(s(A_27a,X0_2E0),s(A_27c,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27a,A_27c))),c_2Epair_2E_2C_2E0),s(A_27a,X0_2E0))),s(A_27c,X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2EA_27d,axiom,
! [A_27b,A_27d,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(A_27b,A_27d),c_2Epair_2E_2C_2E2(s(A_27b,X0_2E0),s(A_27d,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27b,A_27d),app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Epair_2Eprod(A_27b,A_27d)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,tyop_2Epair_2Eprod(A_27b,A_27d))),c_2Epair_2E_2C_2E0),s(A_27b,X0_2E0))),s(A_27d,X1_2E0))) ).
fof(arityeq4_2Ec_2EternaryComparisons_2Epair__compare_2E4_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27a,A_27b,A_27c,A_27d,X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Epair__compare_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2EternaryComparisons_2Eordering)),X1_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27c),X2_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27d),X3_2E0))) = s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27d),tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27d),tyop_2EternaryComparisons_2Eordering)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27d),tyop_2EternaryComparisons_2Eordering))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27d),tyop_2EternaryComparisons_2Eordering)))),c_2EternaryComparisons_2Epair__compare_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2EternaryComparisons_2Eordering)),X1_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27c),X2_2E0))),s(tyop_2Epair_2Eprod(A_27b,A_27d),X3_2E0))) ).
fof(thm_2EternaryComparisons_2Eordering__TY__DEF,axiom,
! [F0_2E0] :
( ! [V1n_2E0] : s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_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_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))
=> ? [V0rep_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2Enum_2Enum),V0rep_2E0)))) ) ).
fof(thm_2EternaryComparisons_2Eordering__BIJ,axiom,
( ! [V0a_2E0] : s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Enum2ordering_2E1(s(tyop_2Enum_2Enum,c_2EternaryComparisons_2Eordering2num_2E1(s(tyop_2EternaryComparisons_2Eordering,V0a_2E0))))) = s(tyop_2EternaryComparisons_2Eordering,V0a_2E0)
& ! [V1r_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1r_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))
<=> s(tyop_2Enum_2Enum,c_2EternaryComparisons_2Eordering2num_2E1(s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Enum2ordering_2E1(s(tyop_2Enum_2Enum,V1r_2E0))))) = s(tyop_2Enum_2Enum,V1r_2E0) ) ) ).
fof(thm_2EternaryComparisons_2Eordering__size__def,axiom,
! [V0x_2E0] : s(tyop_2Enum_2Enum,c_2EternaryComparisons_2Eordering__size_2E1(s(tyop_2EternaryComparisons_2Eordering,V0x_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) ).
fof(thm_2EternaryComparisons_2Eordering__CASE,axiom,
! [A_27a,F0_2E0] :
( ! [V0x_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2EternaryComparisons_2Eordering,V0x_2E0))))
<=> s(tyop_2Enum_2Enum,c_2EternaryComparisons_2Eordering2num_2E1(s(tyop_2EternaryComparisons_2Eordering,V0x_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))))) )
=> ! [V0x_2E0,V1v0_2E0,V2v1_2E0,V3v2_2E0] : s(A_27a,c_2EternaryComparisons_2Eordering__CASE_2E4(s(tyop_2EternaryComparisons_2Eordering,V0x_2E0),s(A_27a,V1v0_2E0),s(A_27a,V2v1_2E0),s(A_27a,V3v2_2E0))) = s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2EternaryComparisons_2Eordering2num_2E1(s(tyop_2EternaryComparisons_2Eordering,V0x_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(A_27a,V1v0_2E0),s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2EternaryComparisons_2Eordering,V0x_2E0))),s(A_27a,V2v1_2E0),s(A_27a,V3v2_2E0))))) ) ).
fof(thm_2EternaryComparisons_2Epair__compare__def,axiom,
! [A_27a,A_27b,A_27c,A_27d,V0c1_2E0,V1c2_2E0,V2a_2E0,V3b_2E0,V4x_2E0,V5y_2E0] : s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Epair__compare_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V0c1_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2EternaryComparisons_2Eordering)),V1c2_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27c),c_2Epair_2E_2C_2E2(s(A_27a,V2a_2E0),s(A_27c,V3b_2E0))),s(tyop_2Epair_2Eprod(A_27b,A_27d),c_2Epair_2E_2C_2E2(s(A_27b,V4x_2E0),s(A_27d,V5y_2E0))))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Eordering__CASE_2E4(s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V0c1_2E0),s(A_27a,V2a_2E0))),s(A_27b,V4x_2E0))),s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0),s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2EternaryComparisons_2Eordering)),V1c2_2E0),s(A_27c,V3b_2E0))),s(A_27d,V5y_2E0))),s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EGREATER_2E0))) ).
fof(thm_2EternaryComparisons_2Enum__compare__def,axiom,
! [F0_2E0] :
( ! [V0n1_2E0,V1n2_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_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Enum_2Enum,V0n1_2E0))),s(tyop_2Enum_2Enum,V1n2_2E0))))
<=> s(tyop_2Enum_2Enum,V0n1_2E0) = s(tyop_2Enum_2Enum,V1n2_2E0) )
=> ! [V0n1_2E0,V1n2_2E0] : s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Enum__compare_2E2(s(tyop_2Enum_2Enum,V0n1_2E0),s(tyop_2Enum_2Enum,V1n2_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2Ebool_2ECOND_2E3(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)),F0_2E0),s(tyop_2Enum_2Enum,V0n1_2E0))),s(tyop_2Enum_2Enum,V1n2_2E0))),s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0),s(tyop_2EternaryComparisons_2Eordering,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n1_2E0),s(tyop_2Enum_2Enum,V1n2_2E0))),s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0),s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EGREATER_2E0))))) ) ).
fof(thm_2EternaryComparisons_2Echar__compare__def,axiom,
! [V0c1_2E0,V1c2_2E0] : s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Echar__compare_2E2(s(tyop_2Estring_2Echar,V0c1_2E0),s(tyop_2Estring_2Echar,V1c2_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Enum__compare_2E2(s(tyop_2Enum_2Enum,c_2Estring_2EORD_2E1(s(tyop_2Estring_2Echar,V0c1_2E0))),s(tyop_2Enum_2Enum,c_2Estring_2EORD_2E1(s(tyop_2Estring_2Echar,V1c2_2E0))))) ).
fof(thm_2EternaryComparisons_2Estring__compare__def,axiom,
s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2EternaryComparisons_2Eordering)),c_2EternaryComparisons_2Estring__compare_2E0) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2EternaryComparisons_2Eordering)),c_2EternaryComparisons_2Elist__compare_2E1(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2EternaryComparisons_2Eordering)),c_2EternaryComparisons_2Echar__compare_2E0))) ).
fof(thm_2EternaryComparisons_2Einvert__comparison__def,axiom,
( s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Einvert__comparison_2E1(s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EGREATER_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0)
& s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Einvert__comparison_2E1(s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EGREATER_2E0)
& s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Einvert__comparison_2E1(s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0) ) ).
fof(thm_2EternaryComparisons_2Enum2ordering__ordering2num,axiom,
! [V0a_2E0] : s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Enum2ordering_2E1(s(tyop_2Enum_2Enum,c_2EternaryComparisons_2Eordering2num_2E1(s(tyop_2EternaryComparisons_2Eordering,V0a_2E0))))) = s(tyop_2EternaryComparisons_2Eordering,V0a_2E0) ).
fof(thm_2EternaryComparisons_2Eordering2num__num2ordering,axiom,
! [V0r_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0r_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))
<=> s(tyop_2Enum_2Enum,c_2EternaryComparisons_2Eordering2num_2E1(s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Enum2ordering_2E1(s(tyop_2Enum_2Enum,V0r_2E0))))) = s(tyop_2Enum_2Enum,V0r_2E0) ) ).
fof(thm_2EternaryComparisons_2Enum2ordering__11,axiom,
! [V0r_2E0,V1r_27_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0r_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))
=> ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1r_27_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))
=> ( s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Enum2ordering_2E1(s(tyop_2Enum_2Enum,V0r_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Enum2ordering_2E1(s(tyop_2Enum_2Enum,V1r_27_2E0)))
<=> s(tyop_2Enum_2Enum,V0r_2E0) = s(tyop_2Enum_2Enum,V1r_27_2E0) ) ) ) ).
fof(thm_2EternaryComparisons_2Eordering2num__11,axiom,
! [V0a_2E0,V1a_27_2E0] :
( s(tyop_2Enum_2Enum,c_2EternaryComparisons_2Eordering2num_2E1(s(tyop_2EternaryComparisons_2Eordering,V0a_2E0))) = s(tyop_2Enum_2Enum,c_2EternaryComparisons_2Eordering2num_2E1(s(tyop_2EternaryComparisons_2Eordering,V1a_27_2E0)))
<=> s(tyop_2EternaryComparisons_2Eordering,V0a_2E0) = s(tyop_2EternaryComparisons_2Eordering,V1a_27_2E0) ) ).
fof(thm_2EternaryComparisons_2Enum2ordering__ONTO,axiom,
! [V0a_2E0] :
? [V1r_2E0] :
( s(tyop_2EternaryComparisons_2Eordering,V0a_2E0) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Enum2ordering_2E1(s(tyop_2Enum_2Enum,V1r_2E0)))
& p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1r_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))) ) ).
fof(thm_2EternaryComparisons_2Eordering2num__ONTO,axiom,
! [V0r_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0r_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))
<=> ? [V1a_2E0] : s(tyop_2Enum_2Enum,V0r_2E0) = s(tyop_2Enum_2Enum,c_2EternaryComparisons_2Eordering2num_2E1(s(tyop_2EternaryComparisons_2Eordering,V1a_2E0))) ) ).
fof(thm_2EternaryComparisons_2Enum2ordering__thm,axiom,
( s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Enum2ordering_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0)
& s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Enum2ordering_2E1(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_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)
& s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Enum2ordering_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EGREATER_2E0) ) ).
fof(thm_2EternaryComparisons_2Eordering2num__thm,axiom,
( s(tyop_2Enum_2Enum,c_2EternaryComparisons_2Eordering2num_2E1(s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)
& s(tyop_2Enum_2Enum,c_2EternaryComparisons_2Eordering2num_2E1(s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_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_2EternaryComparisons_2Eordering2num_2E1(s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EGREATER_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) ) ).
fof(thm_2EternaryComparisons_2Eordering__EQ__ordering,axiom,
! [V0a_2E0,V1a_27_2E0] :
( s(tyop_2EternaryComparisons_2Eordering,V0a_2E0) = s(tyop_2EternaryComparisons_2Eordering,V1a_27_2E0)
<=> s(tyop_2Enum_2Enum,c_2EternaryComparisons_2Eordering2num_2E1(s(tyop_2EternaryComparisons_2Eordering,V0a_2E0))) = s(tyop_2Enum_2Enum,c_2EternaryComparisons_2Eordering2num_2E1(s(tyop_2EternaryComparisons_2Eordering,V1a_27_2E0))) ) ).
fof(thm_2EternaryComparisons_2Eordering__case__def,axiom,
! [A_27a] :
( ! [V0v0_2E0,V1v1_2E0,V2v2_2E0] : s(A_27a,c_2EternaryComparisons_2Eordering__CASE_2E4(s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0),s(A_27a,V0v0_2E0),s(A_27a,V1v1_2E0),s(A_27a,V2v2_2E0))) = s(A_27a,V0v0_2E0)
& ! [V3v0_2E0,V4v1_2E0,V5v2_2E0] : s(A_27a,c_2EternaryComparisons_2Eordering__CASE_2E4(s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0),s(A_27a,V3v0_2E0),s(A_27a,V4v1_2E0),s(A_27a,V5v2_2E0))) = s(A_27a,V4v1_2E0)
& ! [V6v0_2E0,V7v1_2E0,V8v2_2E0] : s(A_27a,c_2EternaryComparisons_2Eordering__CASE_2E4(s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EGREATER_2E0),s(A_27a,V6v0_2E0),s(A_27a,V7v1_2E0),s(A_27a,V8v2_2E0))) = s(A_27a,V8v2_2E0) ) ).
fof(thm_2EternaryComparisons_2Edatatype__ordering,axiom,
! [V0ordering_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E1(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Ebool))),V0ordering_2E0),s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0))),s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0))),s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EGREATER_2E0)))))) ).
fof(thm_2EternaryComparisons_2Eordering__distinct,axiom,
( s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0) != s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)
& s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0) != s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EGREATER_2E0)
& s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0) != s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EGREATER_2E0) ) ).
fof(thm_2EternaryComparisons_2Eordering__nchotomy,axiom,
! [V0a_2E0] :
( s(tyop_2EternaryComparisons_2Eordering,V0a_2E0) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0)
| s(tyop_2EternaryComparisons_2Eordering,V0a_2E0) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)
| s(tyop_2EternaryComparisons_2Eordering,V0a_2E0) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EGREATER_2E0) ) ).
fof(thm_2EternaryComparisons_2Eordering__Axiom,axiom,
! [A_27a,V0x0_2E0,V1x1_2E0,V2x2_2E0] :
? [V3f_2E0] :
( s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,A_27a),V3f_2E0),s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0))) = s(A_27a,V0x0_2E0)
& s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,A_27a),V3f_2E0),s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0))) = s(A_27a,V1x1_2E0)
& s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,A_27a),V3f_2E0),s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EGREATER_2E0))) = s(A_27a,V2x2_2E0) ) ).
fof(thm_2EternaryComparisons_2Eordering__induction,axiom,
! [V0P_2E0] :
( ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0))))
& p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EGREATER_2E0))))
& p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0)))) )
=> ! [V1a_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2EternaryComparisons_2Eordering,V1a_2E0)))) ) ).
fof(thm_2EternaryComparisons_2Eordering__case__cong,axiom,
! [A_27a,V0v2_27_2E0,V1v1_27_2E0,V2v0_27_2E0,V3M_2E0,V4M_27_2E0,V5v0_2E0,V6v1_2E0,V7v2_2E0] :
( ( s(tyop_2EternaryComparisons_2Eordering,V3M_2E0) = s(tyop_2EternaryComparisons_2Eordering,V4M_27_2E0)
& ( s(tyop_2EternaryComparisons_2Eordering,V4M_27_2E0) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0)
=> s(A_27a,V5v0_2E0) = s(A_27a,V2v0_27_2E0) )
& ( s(tyop_2EternaryComparisons_2Eordering,V4M_27_2E0) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)
=> s(A_27a,V6v1_2E0) = s(A_27a,V1v1_27_2E0) )
& ( s(tyop_2EternaryComparisons_2Eordering,V4M_27_2E0) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EGREATER_2E0)
=> s(A_27a,V7v2_2E0) = s(A_27a,V0v2_27_2E0) ) )
=> s(A_27a,c_2EternaryComparisons_2Eordering__CASE_2E4(s(tyop_2EternaryComparisons_2Eordering,V3M_2E0),s(A_27a,V5v0_2E0),s(A_27a,V6v1_2E0),s(A_27a,V7v2_2E0))) = s(A_27a,c_2EternaryComparisons_2Eordering__CASE_2E4(s(tyop_2EternaryComparisons_2Eordering,V4M_27_2E0),s(A_27a,V2v0_27_2E0),s(A_27a,V1v1_27_2E0),s(A_27a,V0v2_27_2E0))) ) ).
fof(thm_2EternaryComparisons_2Eordering__case__eq,axiom,
! [A_27a,V0x_2E0,V1v2_2E0,V2v1_2E0,V3v0_2E0,V4v_2E0] :
( s(A_27a,c_2EternaryComparisons_2Eordering__CASE_2E4(s(tyop_2EternaryComparisons_2Eordering,V0x_2E0),s(A_27a,V3v0_2E0),s(A_27a,V2v1_2E0),s(A_27a,V1v2_2E0))) = s(A_27a,V4v_2E0)
<=> ( ( s(tyop_2EternaryComparisons_2Eordering,V0x_2E0) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0)
& s(A_27a,V3v0_2E0) = s(A_27a,V4v_2E0) )
| ( s(tyop_2EternaryComparisons_2Eordering,V0x_2E0) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)
& s(A_27a,V2v1_2E0) = s(A_27a,V4v_2E0) )
| ( s(tyop_2EternaryComparisons_2Eordering,V0x_2E0) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EGREATER_2E0)
& s(A_27a,V1v2_2E0) = s(A_27a,V4v_2E0) ) ) ) ).
fof(thm_2EternaryComparisons_2Eordering__eq__dec,axiom,
( ! [V0x_2E0] :
( s(tyop_2EternaryComparisons_2Eordering,V0x_2E0) = s(tyop_2EternaryComparisons_2Eordering,V0x_2E0)
<=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) )
& ( s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)
<=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) )
& ( s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EGREATER_2E0)
<=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) )
& ( s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EGREATER_2E0)
<=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) )
& ( s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0)
<=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) )
& ( s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EGREATER_2E0) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0)
<=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) )
& ( s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EGREATER_2E0) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)
<=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) )
& s(tyop_2Enum_2Enum,c_2EternaryComparisons_2Eordering2num_2E1(s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)
& s(tyop_2Enum_2Enum,c_2EternaryComparisons_2Eordering2num_2E1(s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_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_2EternaryComparisons_2Eordering2num_2E1(s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EGREATER_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))
& s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Enum2ordering_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0)
& s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Enum2ordering_2E1(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_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)
& s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Enum2ordering_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EGREATER_2E0) ) ).
fof(thm_2EternaryComparisons_2Ebool__compare__ind,axiom,
! [V0P_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)),V0P_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_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)),V0P_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_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)),V0P_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_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)),V0P_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)))) )
=> ! [V1v_2E0,V2v1_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)),V0P_2E0),s(tyop_2Emin_2Ebool,V1v_2E0))),s(tyop_2Emin_2Ebool,V2v1_2E0)))) ) ).
fof(thm_2EternaryComparisons_2Ebool__compare__def,axiom,
( s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Ebool__compare_2E2(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)
& s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Ebool__compare_2E2(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)
& s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Ebool__compare_2E2(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EGREATER_2E0)
& s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Ebool__compare_2E2(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0) ) ).
fof(thm_2EternaryComparisons_2Eoption__compare__ind,axiom,
! [A_27a,A_27b,V0P_2E0] :
( ( ! [V1c_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V1c_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))),s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0))))
& ! [V2c_2E0,V3v0_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V2c_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))),s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V3v0_2E0))))))
& ! [V4c_2E0,V5v3_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V4c_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V5v3_2E0))))),s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0))))
& ! [V6c_2E0,V7v1_2E0,V8v2_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V6c_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V7v1_2E0))))),s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V8v2_2E0)))))) )
=> ! [V9v_2E0,V10v1_2E0,V11v2_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V9v_2E0))),s(tyop_2Eoption_2Eoption(A_27a),V10v1_2E0))),s(tyop_2Eoption_2Eoption(A_27b),V11v2_2E0)))) ) ).
fof(thm_2EternaryComparisons_2Eoption__compare__def,axiom,
! [A_27a,A_27b,V0v3_2E0,V1v2_2E0,V2v1_2E0,V3v0_2E0,V4c_2E0] :
( s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Eoption__compare_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V4c_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)
& s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Eoption__compare_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V4c_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V3v0_2E0))))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0)
& s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Eoption__compare_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V4c_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0v3_2E0))),s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EGREATER_2E0)
& s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Eoption__compare_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V4c_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V2v1_2E0))),s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V1v2_2E0))))) = s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V4c_2E0),s(A_27a,V2v1_2E0))),s(A_27b,V1v2_2E0))) ) ).
fof(thm_2EternaryComparisons_2Elist__compare__ind,axiom,
! [A_27a,A_27b,V0P_2E0] :
( ( ! [V1cmp_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V1cmp_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))))
& ! [V2cmp_2E0,V3v8_2E0,V4v9_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V2cmp_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V3v8_2E0),s(tyop_2Elist_2Elist(A_27b),V4v9_2E0))))))
& ! [V5cmp_2E0,V6v4_2E0,V7v5_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V5cmp_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V6v4_2E0),s(tyop_2Elist_2Elist(A_27a),V7v5_2E0))))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))))
& ! [V8cmp_2E0,V9x_2E0,V10l1_2E0,V11y_2E0,V12l2_2E0] :
( ( s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V8cmp_2E0),s(A_27a,V9x_2E0))),s(A_27b,V11y_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V8cmp_2E0))),s(tyop_2Elist_2Elist(A_27a),V10l1_2E0))),s(tyop_2Elist_2Elist(A_27b),V12l2_2E0)))) )
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V8cmp_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V9x_2E0),s(tyop_2Elist_2Elist(A_27a),V10l1_2E0))))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V11y_2E0),s(tyop_2Elist_2Elist(A_27b),V12l2_2E0)))))) ) )
=> ! [V13v_2E0,V14v1_2E0,V15v2_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V13v_2E0))),s(tyop_2Elist_2Elist(A_27a),V14v1_2E0))),s(tyop_2Elist_2Elist(A_27b),V15v2_2E0)))) ) ).
fof(thm_2EternaryComparisons_2Elist__compare__def,axiom,
! [A_27a,A_27b] :
( ! [V0cmp_2E0] : s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Elist__compare_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)
& ! [V1v9_2E0,V2v8_2E0,V3cmp_2E0] : s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Elist__compare_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V3cmp_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V2v8_2E0),s(tyop_2Elist_2Elist(A_27b),V1v9_2E0))))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0)
& ! [V4v5_2E0,V5v4_2E0,V6cmp_2E0] : s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Elist__compare_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V6cmp_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V5v4_2E0),s(tyop_2Elist_2Elist(A_27a),V4v5_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EGREATER_2E0)
& ! [V7y_2E0,V8x_2E0,V9l2_2E0,V10l1_2E0,V11cmp_2E0] : s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Elist__compare_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V11cmp_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V8x_2E0),s(tyop_2Elist_2Elist(A_27a),V10l1_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V7y_2E0),s(tyop_2Elist_2Elist(A_27b),V9l2_2E0))))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Eordering__CASE_2E4(s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V11cmp_2E0),s(A_27a,V8x_2E0))),s(A_27b,V7y_2E0))),s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0),s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Elist__compare_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V11cmp_2E0),s(tyop_2Elist_2Elist(A_27a),V10l1_2E0),s(tyop_2Elist_2Elist(A_27b),V9l2_2E0))),s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EGREATER_2E0))) ) ).
fof(thm_2EternaryComparisons_2Ecompare__equal,axiom,
! [A_27a,V0cmp_2E0] :
( ! [V1x_2E0,V2y_2E0] :
( s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)
<=> s(A_27a,V1x_2E0) = s(A_27a,V2y_2E0) )
=> ! [V3l1_2E0,V4l2_2E0] :
( s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Elist__compare_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(tyop_2Elist_2Elist(A_27a),V3l1_2E0),s(tyop_2Elist_2Elist(A_27a),V4l2_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)
<=> s(tyop_2Elist_2Elist(A_27a),V3l1_2E0) = s(tyop_2Elist_2Elist(A_27a),V4l2_2E0) ) ) ).
fof(thm_2EternaryComparisons_2Elist__merge__ind,axiom,
! [A_27a,V0P_2E0] :
( ( ! [V1a__lt_2E0,V2l1_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),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_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1a__lt_2E0))),s(tyop_2Elist_2Elist(A_27a),V2l1_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))
& ! [V3a__lt_2E0,V4v4_2E0,V5v5_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),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_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3a__lt_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V4v4_2E0),s(tyop_2Elist_2Elist(A_27a),V5v5_2E0))))))
& ! [V6a__lt_2E0,V7x_2E0,V8l1_2E0,V9y_2E0,V10l2_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)),V6a__lt_2E0),s(A_27a,V7x_2E0))),s(A_27a,V9y_2E0))))
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),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_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V6a__lt_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V7x_2E0),s(tyop_2Elist_2Elist(A_27a),V8l1_2E0))))),s(tyop_2Elist_2Elist(A_27a),V10l2_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)),V6a__lt_2E0),s(A_27a,V7x_2E0))),s(A_27a,V9y_2E0))))
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),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_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V6a__lt_2E0))),s(tyop_2Elist_2Elist(A_27a),V8l1_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V9y_2E0),s(tyop_2Elist_2Elist(A_27a),V10l2_2E0)))))) ) )
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),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_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V6a__lt_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V7x_2E0),s(tyop_2Elist_2Elist(A_27a),V8l1_2E0))))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V9y_2E0),s(tyop_2Elist_2Elist(A_27a),V10l2_2E0)))))) ) )
=> ! [V11v_2E0,V12v1_2E0,V13v2_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),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_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V11v_2E0))),s(tyop_2Elist_2Elist(A_27a),V12v1_2E0))),s(tyop_2Elist_2Elist(A_27a),V13v2_2E0)))) ) ).
fof(thm_2EternaryComparisons_2Elist__merge__def,axiom,
! [A_27a] :
( ! [V0l1_2E0,V1a__lt_2E0] : s(tyop_2Elist_2Elist(A_27a),c_2EternaryComparisons_2Elist__merge_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1a__lt_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)
& ! [V2v5_2E0,V3v4_2E0,V4a__lt_2E0] : s(tyop_2Elist_2Elist(A_27a),c_2EternaryComparisons_2Elist__merge_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4a__lt_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3v4_2E0),s(tyop_2Elist_2Elist(A_27a),V2v5_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3v4_2E0),s(tyop_2Elist_2Elist(A_27a),V2v5_2E0)))
& ! [V5y_2E0,V6x_2E0,V7l2_2E0,V8l1_2E0,V9a__lt_2E0] : s(tyop_2Elist_2Elist(A_27a),c_2EternaryComparisons_2Elist__merge_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V9a__lt_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V6x_2E0),s(tyop_2Elist_2Elist(A_27a),V8l1_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V5y_2E0),s(tyop_2Elist_2Elist(A_27a),V7l2_2E0))))) = s(tyop_2Elist_2Elist(A_27a),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)),V9a__lt_2E0),s(A_27a,V6x_2E0))),s(A_27a,V5y_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V6x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2EternaryComparisons_2Elist__merge_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V9a__lt_2E0),s(tyop_2Elist_2Elist(A_27a),V8l1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V5y_2E0),s(tyop_2Elist_2Elist(A_27a),V7l2_2E0))))))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V5y_2E0),s(tyop_2Elist_2Elist(A_27a),c_2EternaryComparisons_2Elist__merge_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V9a__lt_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V6x_2E0),s(tyop_2Elist_2Elist(A_27a),V8l1_2E0))),s(tyop_2Elist_2Elist(A_27a),V7l2_2E0))))))) ) ).
fof(thm_2EternaryComparisons_2Einvert__eq__EQUAL,axiom,
! [V0x_2E0] :
( s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Einvert__comparison_2E1(s(tyop_2EternaryComparisons_2Eordering,V0x_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)
<=> s(tyop_2EternaryComparisons_2Eordering,V0x_2E0) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_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) ) ).
%------------------------------------------------------------------------------