ITP001 Axioms: ITP084+4.ax
%------------------------------------------------------------------------------
% File : ITP084+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 : hrat.ax [Gau19]
% : HL4084+4.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 96 ( 64 unt; 0 def)
% Number of atoms : 146 ( 74 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 55 ( 5 ~; 7 |; 13 &)
% ( 18 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 72 ( 72 usr; 39 con; 0-3 aty)
% Number of variables : 197 ( 184 !; 13 ?)
% 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_2Emin_2E_40_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
! [X0_2E0] : s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Emin_2E_40_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq1_2Ec_2Ehrat_2Ehrat__REP__CLASS_2E1,axiom,
! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Ehrat_2Ehrat__REP__CLASS_2E1(s(tyop_2Ehrat_2Ehrat,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ehrat_2Ehrat,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Ehrat_2Ehrat__REP__CLASS_2E0),s(tyop_2Ehrat_2Ehrat,X0_2E0))) ).
fof(arityeq1_2Ec_2Ehrat_2Ehrat__ABS_2E1,axiom,
! [X0_2E0] : s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__ABS_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Ehrat_2Ehrat,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Ehrat_2Ehrat),c_2Ehrat_2Ehrat__ABS_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) ).
fof(arityeq1_2Ec_2Ehrat_2Ehrat__REP_2E1,axiom,
! [X0_2E0] : s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Ehrat__REP_2E1(s(tyop_2Ehrat_2Ehrat,X0_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ehrat_2Ehrat,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ehrat_2Ehrat__REP_2E0),s(tyop_2Ehrat_2Ehrat,X0_2E0))) ).
fof(arityeq1_2Ec_2Ehrat_2Etrat__inv_2E1,axiom,
! [X0_2E0] : s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ehrat_2Etrat__inv_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) ).
fof(arityeq1_2Ec_2Ehrat_2Etrat__sucint_2E1,axiom,
! [X0_2E0] : s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__sucint_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ehrat_2Etrat__sucint_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).
fof(arityeq2_2Ec_2Ehrat_2Etrat__add_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__add_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Ehrat_2Etrat__add_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0))) ).
fof(arityeq2_2Ec_2Ehrat_2Etrat__mul_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__mul_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Ehrat_2Etrat__mul_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0))) ).
fof(arityeq1_2Ec_2Ehrat_2Ehrat__ABS__CLASS_2E1,axiom,
! [X0_2E0] : s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__ABS__CLASS_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Ehrat_2Ehrat,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Ehrat_2Ehrat),c_2Ehrat_2Ehrat__ABS__CLASS_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq1_2Ec_2Ehrat_2Etrat__eq_2E1,axiom,
! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Ehrat_2Etrat__eq_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Ehrat_2Etrat__eq_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) ).
fof(arityeq1_2Ec_2Ehrat_2Ehrat__inv_2E1,axiom,
! [X0_2E0] : s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__inv_2E1(s(tyop_2Ehrat_2Ehrat,X0_2E0))) = s(tyop_2Ehrat_2Ehrat,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ehrat_2Ehrat,tyop_2Ehrat_2Ehrat),c_2Ehrat_2Ehrat__inv_2E0),s(tyop_2Ehrat_2Ehrat,X0_2E0))) ).
fof(arityeq1_2Ec_2Ehrat_2Ehrat__sucint_2E1,axiom,
! [X0_2E0] : s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__sucint_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Ehrat_2Ehrat,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Ehrat_2Ehrat),c_2Ehrat_2Ehrat__sucint_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).
fof(arityeq1_2Ec_2Enum_2ESUC_2E1,axiom,
! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enum_2ESUC_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Epair_2E_2C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).
fof(arityeq2_2Ec_2Earithmetic_2E_2A_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2A_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).
fof(arityeq1_2Ec_2Eprim__rec_2EPRE_2E1,axiom,
! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eprim__rec_2EPRE_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).
fof(arityeq2_2Ec_2Earithmetic_2E_2B_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2B_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).
fof(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Ehrat_2Ehrat,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Ehrat_2Ehrat,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ehrat_2Ehrat,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ehrat_2Ehrat,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)),c_2Ebool_2ETYPE__DEFINITION_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ehrat_2Ehrat,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),X1_2E0))) ).
fof(arityeq2_2Ec_2Ehrat_2Ehrat__add_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__add_2E2(s(tyop_2Ehrat_2Ehrat,X0_2E0),s(tyop_2Ehrat_2Ehrat,X1_2E0))) = s(tyop_2Ehrat_2Ehrat,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ehrat_2Ehrat,tyop_2Ehrat_2Ehrat),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ehrat_2Ehrat,tyop_2Emin_2Efun(tyop_2Ehrat_2Ehrat,tyop_2Ehrat_2Ehrat)),c_2Ehrat_2Ehrat__add_2E0),s(tyop_2Ehrat_2Ehrat,X0_2E0))),s(tyop_2Ehrat_2Ehrat,X1_2E0))) ).
fof(arityeq2_2Ec_2Ehrat_2Ehrat__mul_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__mul_2E2(s(tyop_2Ehrat_2Ehrat,X0_2E0),s(tyop_2Ehrat_2Ehrat,X1_2E0))) = s(tyop_2Ehrat_2Ehrat,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ehrat_2Ehrat,tyop_2Ehrat_2Ehrat),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ehrat_2Ehrat,tyop_2Emin_2Efun(tyop_2Ehrat_2Ehrat,tyop_2Ehrat_2Ehrat)),c_2Ehrat_2Ehrat__mul_2E0),s(tyop_2Ehrat_2Ehrat,X0_2E0))),s(tyop_2Ehrat_2Ehrat,X1_2E0))) ).
fof(arityeq2_2Ec_2Ehrat_2Etrat__eq_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ehrat_2Etrat__eq_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Ehrat_2Etrat__eq_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0))) ).
fof(arityeq3_2Ec_2Equotient_2EQUOTIENT_2E3_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Ehrat_2Ehrat,axiom,
! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Ehrat_2Ehrat),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Ehrat_2Ehrat,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ehrat_2Ehrat,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Ehrat_2Ehrat),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ehrat_2Ehrat,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Ehrat_2Ehrat),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ehrat_2Ehrat,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool))),c_2Equotient_2EQUOTIENT_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Ehrat_2Ehrat),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Ehrat_2Ehrat,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X2_2E0))) ).
fof(thm_2Ehrat_2Etrat__1,axiom,
s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__1_2E0) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) ).
fof(thm_2Ehrat_2Etrat__inv,axiom,
! [V0x_2E0,V1y_2E0] : s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1y_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V1y_2E0),s(tyop_2Enum_2Enum,V0x_2E0))) ).
fof(thm_2Ehrat_2Etrat__add,axiom,
! [V0x_2E0,V1y_2E0,V2x_27_2E0,V3y_27_2E0] : s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__add_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1y_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V2x_27_2E0),s(tyop_2Enum_2Enum,V3y_27_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0x_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V3y_27_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2x_27_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1y_2E0))))))))),s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1y_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V3y_27_2E0))))))))) ).
fof(thm_2Ehrat_2Etrat__mul,axiom,
! [V0x_2E0,V1y_2E0,V2x_27_2E0,V3y_27_2E0] : s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__mul_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1y_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V2x_27_2E0),s(tyop_2Enum_2Enum,V3y_27_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0x_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2x_27_2E0))))))),s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1y_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V3y_27_2E0))))))))) ).
fof(thm_2Ehrat_2Etrat__sucint,axiom,
( s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__sucint_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__1_2E0)
& ! [V0n_2E0] : s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__sucint_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__add_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__sucint_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__1_2E0))) ) ).
fof(thm_2Ehrat_2Etrat__eq,axiom,
! [V0x_2E0,V1y_2E0,V2x_27_2E0,V3y_27_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ehrat_2Etrat__eq_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1y_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V2x_27_2E0),s(tyop_2Enum_2Enum,V3y_27_2E0))))))
<=> s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0x_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V3y_27_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2x_27_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1y_2E0))))) ) ).
fof(thm_2Ehrat_2Ehrat__TY__DEF,axiom,
! [F0_2E0] :
( ! [V1c_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V1c_2E0))))
<=> ? [V2r_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ehrat_2Etrat__eq_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2r_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2r_2E0))))
& s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V1c_2E0) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Ehrat_2Etrat__eq_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2r_2E0))) ) )
=> ? [V0rep_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Ehrat_2Ehrat,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),V0rep_2E0)))) ) ).
fof(thm_2Ehrat_2Ehrat__bijections,axiom,
( ! [V0a_2E0] : s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__ABS__CLASS_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Ehrat_2Ehrat__REP__CLASS_2E1(s(tyop_2Ehrat_2Ehrat,V0a_2E0))))) = s(tyop_2Ehrat_2Ehrat,V0a_2E0)
& ! [V1r_2E0] :
( ? [V2r_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ehrat_2Etrat__eq_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2r_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2r_2E0))))
& s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V1r_2E0) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Ehrat_2Etrat__eq_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2r_2E0))) )
<=> s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Ehrat_2Ehrat__REP__CLASS_2E1(s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__ABS__CLASS_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V1r_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V1r_2E0) ) ) ).
fof(thm_2Ehrat_2Ehrat__REP__def,axiom,
! [V0a_2E0] : s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Ehrat__REP_2E1(s(tyop_2Ehrat_2Ehrat,V0a_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Ehrat_2Ehrat__REP__CLASS_2E1(s(tyop_2Ehrat_2Ehrat,V0a_2E0))))) ).
fof(thm_2Ehrat_2Ehrat__ABS__def,axiom,
! [V0r_2E0] : s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__ABS_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0r_2E0))) = s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__ABS__CLASS_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Ehrat_2Etrat__eq_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0r_2E0))))) ).
fof(thm_2Ehrat_2Ehrat__1,axiom,
s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__1_2E0) = s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__ABS_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__1_2E0))) ).
fof(thm_2Ehrat_2Ehrat__inv,axiom,
! [V0T1_2E0] : s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__inv_2E1(s(tyop_2Ehrat_2Ehrat,V0T1_2E0))) = s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__ABS_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Ehrat__REP_2E1(s(tyop_2Ehrat_2Ehrat,V0T1_2E0))))))) ).
fof(thm_2Ehrat_2Ehrat__add,axiom,
! [V0T1_2E0,V1T2_2E0] : s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__add_2E2(s(tyop_2Ehrat_2Ehrat,V0T1_2E0),s(tyop_2Ehrat_2Ehrat,V1T2_2E0))) = s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__ABS_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__add_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Ehrat__REP_2E1(s(tyop_2Ehrat_2Ehrat,V0T1_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Ehrat__REP_2E1(s(tyop_2Ehrat_2Ehrat,V1T2_2E0))))))) ).
fof(thm_2Ehrat_2Ehrat__mul,axiom,
! [V0T1_2E0,V1T2_2E0] : s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__mul_2E2(s(tyop_2Ehrat_2Ehrat,V0T1_2E0),s(tyop_2Ehrat_2Ehrat,V1T2_2E0))) = s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__ABS_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__mul_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Ehrat__REP_2E1(s(tyop_2Ehrat_2Ehrat,V0T1_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Ehrat__REP_2E1(s(tyop_2Ehrat_2Ehrat,V1T2_2E0))))))) ).
fof(thm_2Ehrat_2Ehrat__sucint,axiom,
! [V0T1_2E0] : s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__sucint_2E1(s(tyop_2Enum_2Enum,V0T1_2E0))) = s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__ABS_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__sucint_2E1(s(tyop_2Enum_2Enum,V0T1_2E0))))) ).
fof(thm_2Ehrat_2ETRAT__EQ__REFL,axiom,
! [V0p_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ehrat_2Etrat__eq_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0p_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0p_2E0)))) ).
fof(thm_2Ehrat_2ETRAT__EQ__SYM,axiom,
! [V0p_2E0,V1q_2E0] : s(tyop_2Emin_2Ebool,c_2Ehrat_2Etrat__eq_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0p_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1q_2E0))) = s(tyop_2Emin_2Ebool,c_2Ehrat_2Etrat__eq_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1q_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0p_2E0))) ).
fof(thm_2Ehrat_2ETRAT__EQ__TRANS,axiom,
! [V0p_2E0,V1q_2E0,V2r_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ehrat_2Etrat__eq_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0p_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1q_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ehrat_2Etrat__eq_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1q_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2r_2E0)))) )
=> p(s(tyop_2Emin_2Ebool,c_2Ehrat_2Etrat__eq_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0p_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2r_2E0)))) ) ).
fof(thm_2Ehrat_2ETRAT__EQ__AP,axiom,
! [V0p_2E0,V1q_2E0] :
( s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0p_2E0) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1q_2E0)
=> p(s(tyop_2Emin_2Ebool,c_2Ehrat_2Etrat__eq_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0p_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1q_2E0)))) ) ).
fof(thm_2Ehrat_2ETRAT__ADD__SYM__EQ,axiom,
! [V0h_2E0,V1i_2E0] : s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__add_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0h_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1i_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__add_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1i_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0h_2E0))) ).
fof(thm_2Ehrat_2ETRAT__MUL__SYM__EQ,axiom,
! [V0h_2E0,V1i_2E0] : s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__mul_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0h_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1i_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__mul_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1i_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0h_2E0))) ).
fof(thm_2Ehrat_2ETRAT__INV__WELLDEFINED,axiom,
! [V0p_2E0,V1q_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ehrat_2Etrat__eq_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0p_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1q_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Ehrat_2Etrat__eq_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0p_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1q_2E0)))))) ) ).
fof(thm_2Ehrat_2ETRAT__ADD__WELLDEFINED,axiom,
! [V0p_2E0,V1q_2E0,V2r_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ehrat_2Etrat__eq_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0p_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1q_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Ehrat_2Etrat__eq_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__add_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0p_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2r_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__add_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1q_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2r_2E0)))))) ) ).
fof(thm_2Ehrat_2ETRAT__ADD__WELLDEFINED2,axiom,
! [V0p1_2E0,V1p2_2E0,V2q1_2E0,V3q2_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ehrat_2Etrat__eq_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0p1_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p2_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ehrat_2Etrat__eq_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2q1_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V3q2_2E0)))) )
=> p(s(tyop_2Emin_2Ebool,c_2Ehrat_2Etrat__eq_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__add_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0p1_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2q1_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__add_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p2_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V3q2_2E0)))))) ) ).
fof(thm_2Ehrat_2ETRAT__MUL__WELLDEFINED,axiom,
! [V0p_2E0,V1q_2E0,V2r_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ehrat_2Etrat__eq_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0p_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1q_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Ehrat_2Etrat__eq_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__mul_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0p_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2r_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__mul_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1q_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2r_2E0)))))) ) ).
fof(thm_2Ehrat_2ETRAT__MUL__WELLDEFINED2,axiom,
! [V0p1_2E0,V1p2_2E0,V2q1_2E0,V3q2_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ehrat_2Etrat__eq_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0p1_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p2_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ehrat_2Etrat__eq_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2q1_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V3q2_2E0)))) )
=> p(s(tyop_2Emin_2Ebool,c_2Ehrat_2Etrat__eq_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__mul_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0p1_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2q1_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__mul_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p2_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V3q2_2E0)))))) ) ).
fof(thm_2Ehrat_2ETRAT__ADD__SYM,axiom,
! [V0h_2E0,V1i_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ehrat_2Etrat__eq_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__add_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0h_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1i_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__add_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1i_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0h_2E0)))))) ).
fof(thm_2Ehrat_2ETRAT__ADD__ASSOC,axiom,
! [V0h_2E0,V1i_2E0,V2j_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ehrat_2Etrat__eq_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__add_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0h_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__add_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1i_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2j_2E0))))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__add_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__add_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0h_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1i_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2j_2E0)))))) ).
fof(thm_2Ehrat_2ETRAT__MUL__SYM,axiom,
! [V0h_2E0,V1i_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ehrat_2Etrat__eq_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__mul_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0h_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1i_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__mul_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1i_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0h_2E0)))))) ).
fof(thm_2Ehrat_2ETRAT__MUL__ASSOC,axiom,
! [V0h_2E0,V1i_2E0,V2j_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ehrat_2Etrat__eq_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__mul_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0h_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__mul_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1i_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2j_2E0))))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__mul_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__mul_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0h_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1i_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2j_2E0)))))) ).
fof(thm_2Ehrat_2ETRAT__LDISTRIB,axiom,
! [V0h_2E0,V1i_2E0,V2j_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ehrat_2Etrat__eq_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__mul_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0h_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__add_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1i_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2j_2E0))))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__add_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__mul_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0h_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1i_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__mul_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0h_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2j_2E0)))))))) ).
fof(thm_2Ehrat_2ETRAT__MUL__LID,axiom,
! [V0h_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ehrat_2Etrat__eq_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__mul_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__1_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0h_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0h_2E0)))) ).
fof(thm_2Ehrat_2ETRAT__MUL__LINV,axiom,
! [V0h_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ehrat_2Etrat__eq_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__mul_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0h_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0h_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__1_2E0)))) ).
fof(thm_2Ehrat_2ETRAT__NOZERO,axiom,
! [V0h_2E0,V1i_2E0] : ~ p(s(tyop_2Emin_2Ebool,c_2Ehrat_2Etrat__eq_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__add_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0h_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1i_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0h_2E0)))) ).
fof(thm_2Ehrat_2ETRAT__ADD__TOTAL,axiom,
! [V0h_2E0,V1i_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ehrat_2Etrat__eq_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0h_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1i_2E0))))
| ? [V2d_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ehrat_2Etrat__eq_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0h_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__add_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1i_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2d_2E0))))))
| ? [V3d_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ehrat_2Etrat__eq_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1i_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__add_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0h_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V3d_2E0)))))) ) ).
fof(thm_2Ehrat_2ETRAT__SUCINT__0,axiom,
! [V0n_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ehrat_2Etrat__eq_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__sucint_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))))) ).
fof(thm_2Ehrat_2ETRAT__ARCH,axiom,
! [V0h_2E0] :
? [V1n_2E0,V2d_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ehrat_2Etrat__eq_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__sucint_2E1(s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__add_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0h_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2d_2E0)))))) ).
fof(thm_2Ehrat_2ETRAT__SUCINT,axiom,
( p(s(tyop_2Emin_2Ebool,c_2Ehrat_2Etrat__eq_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__sucint_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__1_2E0))))
& ! [V0n_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ehrat_2Etrat__eq_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__sucint_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__add_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__sucint_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ehrat_2Etrat__1_2E0)))))) ) ).
fof(thm_2Ehrat_2ETRAT__EQ__EQUIV,axiom,
! [V0p_2E0,V1q_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ehrat_2Etrat__eq_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0p_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1q_2E0))))
<=> s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Ehrat_2Etrat__eq_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0p_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Ehrat_2Etrat__eq_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1q_2E0))) ) ).
fof(thm_2Ehrat_2Ehrat__ABS__REP__CLASS,axiom,
( ! [V0a_2E0] : s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__ABS__CLASS_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Ehrat_2Ehrat__REP__CLASS_2E1(s(tyop_2Ehrat_2Ehrat,V0a_2E0))))) = s(tyop_2Ehrat_2Ehrat,V0a_2E0)
& ! [V1c_2E0] :
( ? [V2r_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ehrat_2Etrat__eq_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2r_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2r_2E0))))
& s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V1c_2E0) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Ehrat_2Etrat__eq_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2r_2E0))) )
<=> s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Ehrat_2Ehrat__REP__CLASS_2E1(s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__ABS__CLASS_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V1c_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V1c_2E0) ) ) ).
fof(thm_2Ehrat_2Ehrat__QUOTIENT,axiom,
p(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Ehrat_2Etrat__eq_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Ehrat_2Ehrat),c_2Ehrat_2Ehrat__ABS_2E0),s(tyop_2Emin_2Efun(tyop_2Ehrat_2Ehrat,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ehrat_2Ehrat__REP_2E0)))) ).
fof(thm_2Ehrat_2EHRAT__ADD__SYM,axiom,
! [V0h_2E0,V1i_2E0] : s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__add_2E2(s(tyop_2Ehrat_2Ehrat,V0h_2E0),s(tyop_2Ehrat_2Ehrat,V1i_2E0))) = s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__add_2E2(s(tyop_2Ehrat_2Ehrat,V1i_2E0),s(tyop_2Ehrat_2Ehrat,V0h_2E0))) ).
fof(thm_2Ehrat_2EHRAT__ADD__ASSOC,axiom,
! [V0h_2E0,V1i_2E0,V2j_2E0] : s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__add_2E2(s(tyop_2Ehrat_2Ehrat,V0h_2E0),s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__add_2E2(s(tyop_2Ehrat_2Ehrat,V1i_2E0),s(tyop_2Ehrat_2Ehrat,V2j_2E0))))) = s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__add_2E2(s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__add_2E2(s(tyop_2Ehrat_2Ehrat,V0h_2E0),s(tyop_2Ehrat_2Ehrat,V1i_2E0))),s(tyop_2Ehrat_2Ehrat,V2j_2E0))) ).
fof(thm_2Ehrat_2EHRAT__MUL__SYM,axiom,
! [V0h_2E0,V1i_2E0] : s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__mul_2E2(s(tyop_2Ehrat_2Ehrat,V0h_2E0),s(tyop_2Ehrat_2Ehrat,V1i_2E0))) = s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__mul_2E2(s(tyop_2Ehrat_2Ehrat,V1i_2E0),s(tyop_2Ehrat_2Ehrat,V0h_2E0))) ).
fof(thm_2Ehrat_2EHRAT__MUL__ASSOC,axiom,
! [V0h_2E0,V1i_2E0,V2j_2E0] : s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__mul_2E2(s(tyop_2Ehrat_2Ehrat,V0h_2E0),s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__mul_2E2(s(tyop_2Ehrat_2Ehrat,V1i_2E0),s(tyop_2Ehrat_2Ehrat,V2j_2E0))))) = s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__mul_2E2(s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__mul_2E2(s(tyop_2Ehrat_2Ehrat,V0h_2E0),s(tyop_2Ehrat_2Ehrat,V1i_2E0))),s(tyop_2Ehrat_2Ehrat,V2j_2E0))) ).
fof(thm_2Ehrat_2EHRAT__LDISTRIB,axiom,
! [V0h_2E0,V1i_2E0,V2j_2E0] : s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__mul_2E2(s(tyop_2Ehrat_2Ehrat,V0h_2E0),s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__add_2E2(s(tyop_2Ehrat_2Ehrat,V1i_2E0),s(tyop_2Ehrat_2Ehrat,V2j_2E0))))) = s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__add_2E2(s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__mul_2E2(s(tyop_2Ehrat_2Ehrat,V0h_2E0),s(tyop_2Ehrat_2Ehrat,V1i_2E0))),s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__mul_2E2(s(tyop_2Ehrat_2Ehrat,V0h_2E0),s(tyop_2Ehrat_2Ehrat,V2j_2E0))))) ).
fof(thm_2Ehrat_2EHRAT__MUL__LID,axiom,
! [V0h_2E0] : s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__mul_2E2(s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__1_2E0),s(tyop_2Ehrat_2Ehrat,V0h_2E0))) = s(tyop_2Ehrat_2Ehrat,V0h_2E0) ).
fof(thm_2Ehrat_2EHRAT__MUL__LINV,axiom,
! [V0h_2E0] : s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__mul_2E2(s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__inv_2E1(s(tyop_2Ehrat_2Ehrat,V0h_2E0))),s(tyop_2Ehrat_2Ehrat,V0h_2E0))) = s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__1_2E0) ).
fof(thm_2Ehrat_2EHRAT__NOZERO,axiom,
! [V0h_2E0,V1i_2E0] : s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__add_2E2(s(tyop_2Ehrat_2Ehrat,V0h_2E0),s(tyop_2Ehrat_2Ehrat,V1i_2E0))) != s(tyop_2Ehrat_2Ehrat,V0h_2E0) ).
fof(thm_2Ehrat_2EHRAT__ADD__TOTAL,axiom,
! [V0h_2E0,V1i_2E0] :
( s(tyop_2Ehrat_2Ehrat,V0h_2E0) = s(tyop_2Ehrat_2Ehrat,V1i_2E0)
| ? [V2d_2E0] : s(tyop_2Ehrat_2Ehrat,V0h_2E0) = s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__add_2E2(s(tyop_2Ehrat_2Ehrat,V1i_2E0),s(tyop_2Ehrat_2Ehrat,V2d_2E0)))
| ? [V3d_2E0] : s(tyop_2Ehrat_2Ehrat,V1i_2E0) = s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__add_2E2(s(tyop_2Ehrat_2Ehrat,V0h_2E0),s(tyop_2Ehrat_2Ehrat,V3d_2E0))) ) ).
fof(thm_2Ehrat_2EHRAT__ARCH,axiom,
! [V0h_2E0] :
? [V1n_2E0,V2d_2E0] : s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__sucint_2E1(s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__add_2E2(s(tyop_2Ehrat_2Ehrat,V0h_2E0),s(tyop_2Ehrat_2Ehrat,V2d_2E0))) ).
fof(thm_2Ehrat_2EHRAT__SUCINT,axiom,
( s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__sucint_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__1_2E0)
& ! [V0n_2E0] : s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__sucint_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__add_2E2(s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__sucint_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Ehrat_2Ehrat,c_2Ehrat_2Ehrat__1_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) ) ).
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