TPTP Problem File: ITP022_2.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : ITP022_2 : TPTP v8.2.0. Bugfixed v8.0.0.
% Domain : Interactive Theorem Proving
% Problem : HOL4 set theory export of thm_2Ereal__topology_2EINDEPENDENT__STDBASIS.p, bushy 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 : thm_2Ereal__topology_2EINDEPENDENT__STDBASIS.p [Gau19]
% : HL410501_2.p [TPAP]
% Status : Theorem
% Rating : 1.00 v8.1.0
% Syntax : Number of formulae : 227 ( 89 unt; 94 typ; 0 def)
% Number of atoms : 930 ( 122 equ)
% Maximal formula atoms : 53 ( 4 avg)
% Number of connectives : 270 ( 34 ~; 18 |; 94 &)
% ( 76 <=>; 48 =>; 0 <=; 0 <~>)
% Maximal formula depth : 37 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 561 ( 561 fml; 0 var)
% Number of types : 6 ( 4 usr)
% Number of type conns : 71 ( 48 >; 23 *; 0 +; 0 <<)
% Number of predicates : 8 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 88 ( 88 usr; 42 con; 0-2 aty)
% Number of variables : 195 ( 195 !; 0 ?; 195 :)
% SPC : TF0_THM_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Bugfixes in axioms and export.
% : v8.0.0 - Added missing type declarations.
%------------------------------------------------------------------------------
include('Axioms/ITP001/ITP001_2.ax').
%------------------------------------------------------------------------------
tff(stp_o,type,
tp__o: $tType ).
tff(stp_inj_o,type,
inj__o: tp__o > $i ).
tff(stp_surj_o,type,
surj__o: $i > tp__o ).
tff(stp_inj_surj_o,axiom,
! [X: tp__o] : surj__o(inj__o(X)) = X ).
tff(stp_inj_mem_o,axiom,
! [X: tp__o] : mem(inj__o(X),bool) ).
tff(stp_iso_mem_o,axiom,
! [X: $i] :
( mem(X,bool)
=> ( X = inj__o(surj__o(X)) ) ) ).
tff(tp_ty_2Enum_2Enum,type,
ty_2Enum_2Enum: del ).
tff(stp_ty_2Enum_2Enum,type,
tp__ty_2Enum_2Enum: $tType ).
tff(stp_inj_ty_2Enum_2Enum,type,
inj__ty_2Enum_2Enum: tp__ty_2Enum_2Enum > $i ).
tff(stp_surj_ty_2Enum_2Enum,type,
surj__ty_2Enum_2Enum: $i > tp__ty_2Enum_2Enum ).
tff(stp_inj_surj_ty_2Enum_2Enum,axiom,
! [X: tp__ty_2Enum_2Enum] : surj__ty_2Enum_2Enum(inj__ty_2Enum_2Enum(X)) = X ).
tff(stp_inj_mem_ty_2Enum_2Enum,axiom,
! [X: tp__ty_2Enum_2Enum] : mem(inj__ty_2Enum_2Enum(X),ty_2Enum_2Enum) ).
tff(stp_iso_mem_ty_2Enum_2Enum,axiom,
! [X: $i] :
( mem(X,ty_2Enum_2Enum)
=> ( X = inj__ty_2Enum_2Enum(surj__ty_2Enum_2Enum(X)) ) ) ).
tff(tp_c_2Earithmetic_2EEVEN,type,
c_2Earithmetic_2EEVEN: $i ).
tff(mem_c_2Earithmetic_2EEVEN,axiom,
mem(c_2Earithmetic_2EEVEN,arr(ty_2Enum_2Enum,bool)) ).
tff(stp_fo_c_2Earithmetic_2EEVEN,type,
fo__c_2Earithmetic_2EEVEN: tp__ty_2Enum_2Enum > tp__o ).
tff(stp_eq_fo_c_2Earithmetic_2EEVEN,axiom,
! [X0: tp__ty_2Enum_2Enum] : inj__o(fo__c_2Earithmetic_2EEVEN(X0)) = ap(c_2Earithmetic_2EEVEN,inj__ty_2Enum_2Enum(X0)) ).
tff(tp_c_2Earithmetic_2EODD,type,
c_2Earithmetic_2EODD: $i ).
tff(mem_c_2Earithmetic_2EODD,axiom,
mem(c_2Earithmetic_2EODD,arr(ty_2Enum_2Enum,bool)) ).
tff(stp_fo_c_2Earithmetic_2EODD,type,
fo__c_2Earithmetic_2EODD: tp__ty_2Enum_2Enum > tp__o ).
tff(stp_eq_fo_c_2Earithmetic_2EODD,axiom,
! [X0: tp__ty_2Enum_2Enum] : inj__o(fo__c_2Earithmetic_2EODD(X0)) = ap(c_2Earithmetic_2EODD,inj__ty_2Enum_2Enum(X0)) ).
tff(tp_c_2Earithmetic_2E_3E_3D,type,
c_2Earithmetic_2E_3E_3D: $i ).
tff(mem_c_2Earithmetic_2E_3E_3D,axiom,
mem(c_2Earithmetic_2E_3E_3D,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool))) ).
tff(stp_fo_c_2Earithmetic_2E_3E_3D,type,
fo__c_2Earithmetic_2E_3E_3D: ( tp__ty_2Enum_2Enum * tp__ty_2Enum_2Enum ) > tp__o ).
tff(stp_eq_fo_c_2Earithmetic_2E_3E_3D,axiom,
! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] : inj__o(fo__c_2Earithmetic_2E_3E_3D(X0,X1)) = ap(ap(c_2Earithmetic_2E_3E_3D,inj__ty_2Enum_2Enum(X0)),inj__ty_2Enum_2Enum(X1)) ).
tff(tp_c_2Ebool_2ET,type,
c_2Ebool_2ET: $i ).
tff(mem_c_2Ebool_2ET,axiom,
mem(c_2Ebool_2ET,bool) ).
tff(stp_fo_c_2Ebool_2ET,type,
fo__c_2Ebool_2ET: tp__o ).
tff(stp_eq_fo_c_2Ebool_2ET,axiom,
inj__o(fo__c_2Ebool_2ET) = c_2Ebool_2ET ).
tff(ax_true_p,axiom,
p(c_2Ebool_2ET) ).
tff(tp_c_2Earithmetic_2E_3E,type,
c_2Earithmetic_2E_3E: $i ).
tff(mem_c_2Earithmetic_2E_3E,axiom,
mem(c_2Earithmetic_2E_3E,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool))) ).
tff(stp_fo_c_2Earithmetic_2E_3E,type,
fo__c_2Earithmetic_2E_3E: ( tp__ty_2Enum_2Enum * tp__ty_2Enum_2Enum ) > tp__o ).
tff(stp_eq_fo_c_2Earithmetic_2E_3E,axiom,
! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] : inj__o(fo__c_2Earithmetic_2E_3E(X0,X1)) = ap(ap(c_2Earithmetic_2E_3E,inj__ty_2Enum_2Enum(X0)),inj__ty_2Enum_2Enum(X1)) ).
tff(tp_c_2Eprim__rec_2E_3C,type,
c_2Eprim__rec_2E_3C: $i ).
tff(mem_c_2Eprim__rec_2E_3C,axiom,
mem(c_2Eprim__rec_2E_3C,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool))) ).
tff(stp_fo_c_2Eprim__rec_2E_3C,type,
fo__c_2Eprim__rec_2E_3C: ( tp__ty_2Enum_2Enum * tp__ty_2Enum_2Enum ) > tp__o ).
tff(stp_eq_fo_c_2Eprim__rec_2E_3C,axiom,
! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] : inj__o(fo__c_2Eprim__rec_2E_3C(X0,X1)) = ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(X0)),inj__ty_2Enum_2Enum(X1)) ).
tff(tp_c_2Eprim__rec_2EPRE,type,
c_2Eprim__rec_2EPRE: $i ).
tff(mem_c_2Eprim__rec_2EPRE,axiom,
mem(c_2Eprim__rec_2EPRE,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) ).
tff(stp_fo_c_2Eprim__rec_2EPRE,type,
fo__c_2Eprim__rec_2EPRE: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
tff(stp_eq_fo_c_2Eprim__rec_2EPRE,axiom,
! [X0: tp__ty_2Enum_2Enum] : inj__ty_2Enum_2Enum(fo__c_2Eprim__rec_2EPRE(X0)) = ap(c_2Eprim__rec_2EPRE,inj__ty_2Enum_2Enum(X0)) ).
tff(tp_c_2Earithmetic_2EEXP,type,
c_2Earithmetic_2EEXP: $i ).
tff(mem_c_2Earithmetic_2EEXP,axiom,
mem(c_2Earithmetic_2EEXP,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) ).
tff(stp_fo_c_2Earithmetic_2EEXP,type,
fo__c_2Earithmetic_2EEXP: ( tp__ty_2Enum_2Enum * tp__ty_2Enum_2Enum ) > tp__ty_2Enum_2Enum ).
tff(stp_eq_fo_c_2Earithmetic_2EEXP,axiom,
! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] : inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EEXP(X0,X1)) = ap(ap(c_2Earithmetic_2EEXP,inj__ty_2Enum_2Enum(X0)),inj__ty_2Enum_2Enum(X1)) ).
tff(tp_c_2Earithmetic_2E_2D,type,
c_2Earithmetic_2E_2D: $i ).
tff(mem_c_2Earithmetic_2E_2D,axiom,
mem(c_2Earithmetic_2E_2D,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) ).
tff(stp_fo_c_2Earithmetic_2E_2D,type,
fo__c_2Earithmetic_2E_2D: ( tp__ty_2Enum_2Enum * tp__ty_2Enum_2Enum ) > tp__ty_2Enum_2Enum ).
tff(stp_eq_fo_c_2Earithmetic_2E_2D,axiom,
! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] : inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2E_2D(X0,X1)) = ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(X0)),inj__ty_2Enum_2Enum(X1)) ).
tff(tp_c_2Enumeral_2EiiSUC,type,
c_2Enumeral_2EiiSUC: $i ).
tff(mem_c_2Enumeral_2EiiSUC,axiom,
mem(c_2Enumeral_2EiiSUC,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) ).
tff(stp_fo_c_2Enumeral_2EiiSUC,type,
fo__c_2Enumeral_2EiiSUC: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
tff(stp_eq_fo_c_2Enumeral_2EiiSUC,axiom,
! [X0: tp__ty_2Enum_2Enum] : inj__ty_2Enum_2Enum(fo__c_2Enumeral_2EiiSUC(X0)) = ap(c_2Enumeral_2EiiSUC,inj__ty_2Enum_2Enum(X0)) ).
tff(tp_c_2Enum_2ESUC,type,
c_2Enum_2ESUC: $i ).
tff(mem_c_2Enum_2ESUC,axiom,
mem(c_2Enum_2ESUC,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) ).
tff(stp_fo_c_2Enum_2ESUC,type,
fo__c_2Enum_2ESUC: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
tff(stp_eq_fo_c_2Enum_2ESUC,axiom,
! [X0: tp__ty_2Enum_2Enum] : inj__ty_2Enum_2Enum(fo__c_2Enum_2ESUC(X0)) = ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(X0)) ).
tff(tp_c_2Earithmetic_2EBIT2,type,
c_2Earithmetic_2EBIT2: $i ).
tff(mem_c_2Earithmetic_2EBIT2,axiom,
mem(c_2Earithmetic_2EBIT2,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) ).
tff(stp_fo_c_2Earithmetic_2EBIT2,type,
fo__c_2Earithmetic_2EBIT2: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
tff(stp_eq_fo_c_2Earithmetic_2EBIT2,axiom,
! [X0: tp__ty_2Enum_2Enum] : inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EBIT2(X0)) = ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(X0)) ).
tff(tp_c_2Enumeral_2EiDUB,type,
c_2Enumeral_2EiDUB: $i ).
tff(mem_c_2Enumeral_2EiDUB,axiom,
mem(c_2Enumeral_2EiDUB,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) ).
tff(stp_fo_c_2Enumeral_2EiDUB,type,
fo__c_2Enumeral_2EiDUB: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
tff(stp_eq_fo_c_2Enumeral_2EiDUB,axiom,
! [X0: tp__ty_2Enum_2Enum] : inj__ty_2Enum_2Enum(fo__c_2Enumeral_2EiDUB(X0)) = ap(c_2Enumeral_2EiDUB,inj__ty_2Enum_2Enum(X0)) ).
tff(tp_c_2Enumeral_2EiZ,type,
c_2Enumeral_2EiZ: $i ).
tff(mem_c_2Enumeral_2EiZ,axiom,
mem(c_2Enumeral_2EiZ,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) ).
tff(stp_fo_c_2Enumeral_2EiZ,type,
fo__c_2Enumeral_2EiZ: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
tff(stp_eq_fo_c_2Enumeral_2EiZ,axiom,
! [X0: tp__ty_2Enum_2Enum] : inj__ty_2Enum_2Enum(fo__c_2Enumeral_2EiZ(X0)) = ap(c_2Enumeral_2EiZ,inj__ty_2Enum_2Enum(X0)) ).
tff(tp_ty_2Epair_2Eprod,type,
ty_2Epair_2Eprod: ( del * del ) > del ).
tff(tp_c_2Epair_2E_2C,type,
c_2Epair_2E_2C: ( del * del ) > $i ).
tff(mem_c_2Epair_2E_2C,axiom,
! [A_27a: del,A_27b: del] : mem(c_2Epair_2E_2C(A_27a,A_27b),arr(A_27a,arr(A_27b,ty_2Epair_2Eprod(A_27a,A_27b)))) ).
tff(tp_c_2Epred__set_2EGSPEC,type,
c_2Epred__set_2EGSPEC: ( del * del ) > $i ).
tff(mem_c_2Epred__set_2EGSPEC,axiom,
! [A_27a: del,A_27b: del] : mem(c_2Epred__set_2EGSPEC(A_27a,A_27b),arr(arr(A_27b,ty_2Epair_2Eprod(A_27a,bool)),arr(A_27a,bool))) ).
tff(tp_c_2Earithmetic_2EZERO,type,
c_2Earithmetic_2EZERO: $i ).
tff(mem_c_2Earithmetic_2EZERO,axiom,
mem(c_2Earithmetic_2EZERO,ty_2Enum_2Enum) ).
tff(stp_fo_c_2Earithmetic_2EZERO,type,
fo__c_2Earithmetic_2EZERO: tp__ty_2Enum_2Enum ).
tff(stp_eq_fo_c_2Earithmetic_2EZERO,axiom,
inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO) = c_2Earithmetic_2EZERO ).
tff(tp_c_2Earithmetic_2EBIT1,type,
c_2Earithmetic_2EBIT1: $i ).
tff(mem_c_2Earithmetic_2EBIT1,axiom,
mem(c_2Earithmetic_2EBIT1,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) ).
tff(stp_fo_c_2Earithmetic_2EBIT1,type,
fo__c_2Earithmetic_2EBIT1: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
tff(stp_eq_fo_c_2Earithmetic_2EBIT1,axiom,
! [X0: tp__ty_2Enum_2Enum] : inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EBIT1(X0)) = ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(X0)) ).
tff(tp_c_2Earithmetic_2ENUMERAL,type,
c_2Earithmetic_2ENUMERAL: $i ).
tff(mem_c_2Earithmetic_2ENUMERAL,axiom,
mem(c_2Earithmetic_2ENUMERAL,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) ).
tff(stp_fo_c_2Earithmetic_2ENUMERAL,type,
fo__c_2Earithmetic_2ENUMERAL: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
tff(stp_eq_fo_c_2Earithmetic_2ENUMERAL,axiom,
! [X0: tp__ty_2Enum_2Enum] : inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2ENUMERAL(X0)) = ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(X0)) ).
tff(tp_c_2Earithmetic_2E_2B,type,
c_2Earithmetic_2E_2B: $i ).
tff(mem_c_2Earithmetic_2E_2B,axiom,
mem(c_2Earithmetic_2E_2B,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) ).
tff(stp_fo_c_2Earithmetic_2E_2B,type,
fo__c_2Earithmetic_2E_2B: ( tp__ty_2Enum_2Enum * tp__ty_2Enum_2Enum ) > tp__ty_2Enum_2Enum ).
tff(stp_eq_fo_c_2Earithmetic_2E_2B,axiom,
! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] : inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2E_2B(X0,X1)) = ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(X0)),inj__ty_2Enum_2Enum(X1)) ).
tff(tp_ty_2Erealax_2Ereal,type,
ty_2Erealax_2Ereal: del ).
tff(stp_ty_2Erealax_2Ereal,type,
tp__ty_2Erealax_2Ereal: $tType ).
tff(stp_inj_ty_2Erealax_2Ereal,type,
inj__ty_2Erealax_2Ereal: tp__ty_2Erealax_2Ereal > $i ).
tff(stp_surj_ty_2Erealax_2Ereal,type,
surj__ty_2Erealax_2Ereal: $i > tp__ty_2Erealax_2Ereal ).
tff(stp_inj_surj_ty_2Erealax_2Ereal,axiom,
! [X: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(inj__ty_2Erealax_2Ereal(X)) = X ).
tff(stp_inj_mem_ty_2Erealax_2Ereal,axiom,
! [X: tp__ty_2Erealax_2Ereal] : mem(inj__ty_2Erealax_2Ereal(X),ty_2Erealax_2Ereal) ).
tff(stp_iso_mem_ty_2Erealax_2Ereal,axiom,
! [X: $i] :
( mem(X,ty_2Erealax_2Ereal)
=> ( X = inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(X)) ) ) ).
tff(tp_c_2Erealax_2Ereal__lt,type,
c_2Erealax_2Ereal__lt: $i ).
tff(mem_c_2Erealax_2Ereal__lt,axiom,
mem(c_2Erealax_2Ereal__lt,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,bool))) ).
tff(stp_fo_c_2Erealax_2Ereal__lt,type,
fo__c_2Erealax_2Ereal__lt: ( tp__ty_2Erealax_2Ereal * tp__ty_2Erealax_2Ereal ) > tp__o ).
tff(stp_eq_fo_c_2Erealax_2Ereal__lt,axiom,
! [X0: tp__ty_2Erealax_2Ereal,X1: tp__ty_2Erealax_2Ereal] : inj__o(fo__c_2Erealax_2Ereal__lt(X0,X1)) = ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(X0)),inj__ty_2Erealax_2Ereal(X1)) ).
tff(tp_c_2Erealax_2Ereal__add,type,
c_2Erealax_2Ereal__add: $i ).
tff(mem_c_2Erealax_2Ereal__add,axiom,
mem(c_2Erealax_2Ereal__add,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))) ).
tff(stp_fo_c_2Erealax_2Ereal__add,type,
fo__c_2Erealax_2Ereal__add: ( tp__ty_2Erealax_2Ereal * tp__ty_2Erealax_2Ereal ) > tp__ty_2Erealax_2Ereal ).
tff(stp_eq_fo_c_2Erealax_2Ereal__add,axiom,
! [X0: tp__ty_2Erealax_2Ereal,X1: tp__ty_2Erealax_2Ereal] : inj__ty_2Erealax_2Ereal(fo__c_2Erealax_2Ereal__add(X0,X1)) = ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(X0)),inj__ty_2Erealax_2Ereal(X1)) ).
tff(tp_c_2Erealax_2Ereal__neg,type,
c_2Erealax_2Ereal__neg: $i ).
tff(mem_c_2Erealax_2Ereal__neg,axiom,
mem(c_2Erealax_2Ereal__neg,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ).
tff(stp_fo_c_2Erealax_2Ereal__neg,type,
fo__c_2Erealax_2Ereal__neg: tp__ty_2Erealax_2Ereal > tp__ty_2Erealax_2Ereal ).
tff(stp_eq_fo_c_2Erealax_2Ereal__neg,axiom,
! [X0: tp__ty_2Erealax_2Ereal] : inj__ty_2Erealax_2Ereal(fo__c_2Erealax_2Ereal__neg(X0)) = ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(X0)) ).
tff(tp_c_2Earithmetic_2E_3C_3D,type,
c_2Earithmetic_2E_3C_3D: $i ).
tff(mem_c_2Earithmetic_2E_3C_3D,axiom,
mem(c_2Earithmetic_2E_3C_3D,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool))) ).
tff(stp_fo_c_2Earithmetic_2E_3C_3D,type,
fo__c_2Earithmetic_2E_3C_3D: ( tp__ty_2Enum_2Enum * tp__ty_2Enum_2Enum ) > tp__o ).
tff(stp_eq_fo_c_2Earithmetic_2E_3C_3D,axiom,
! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] : inj__o(fo__c_2Earithmetic_2E_3C_3D(X0,X1)) = ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(X0)),inj__ty_2Enum_2Enum(X1)) ).
tff(tp_c_2Ereal_2Ereal__lte,type,
c_2Ereal_2Ereal__lte: $i ).
tff(mem_c_2Ereal_2Ereal__lte,axiom,
mem(c_2Ereal_2Ereal__lte,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,bool))) ).
tff(stp_fo_c_2Ereal_2Ereal__lte,type,
fo__c_2Ereal_2Ereal__lte: ( tp__ty_2Erealax_2Ereal * tp__ty_2Erealax_2Ereal ) > tp__o ).
tff(stp_eq_fo_c_2Ereal_2Ereal__lte,axiom,
! [X0: tp__ty_2Erealax_2Ereal,X1: tp__ty_2Erealax_2Ereal] : inj__o(fo__c_2Ereal_2Ereal__lte(X0,X1)) = ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(X0)),inj__ty_2Erealax_2Ereal(X1)) ).
tff(tp_c_2Earithmetic_2E_2A,type,
c_2Earithmetic_2E_2A: $i ).
tff(mem_c_2Earithmetic_2E_2A,axiom,
mem(c_2Earithmetic_2E_2A,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) ).
tff(stp_fo_c_2Earithmetic_2E_2A,type,
fo__c_2Earithmetic_2E_2A: ( tp__ty_2Enum_2Enum * tp__ty_2Enum_2Enum ) > tp__ty_2Enum_2Enum ).
tff(stp_eq_fo_c_2Earithmetic_2E_2A,axiom,
! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] : inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2E_2A(X0,X1)) = ap(ap(c_2Earithmetic_2E_2A,inj__ty_2Enum_2Enum(X0)),inj__ty_2Enum_2Enum(X1)) ).
tff(tp_c_2Erealax_2Ereal__mul,type,
c_2Erealax_2Ereal__mul: $i ).
tff(mem_c_2Erealax_2Ereal__mul,axiom,
mem(c_2Erealax_2Ereal__mul,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))) ).
tff(stp_fo_c_2Erealax_2Ereal__mul,type,
fo__c_2Erealax_2Ereal__mul: ( tp__ty_2Erealax_2Ereal * tp__ty_2Erealax_2Ereal ) > tp__ty_2Erealax_2Ereal ).
tff(stp_eq_fo_c_2Erealax_2Ereal__mul,axiom,
! [X0: tp__ty_2Erealax_2Ereal,X1: tp__ty_2Erealax_2Ereal] : inj__ty_2Erealax_2Ereal(fo__c_2Erealax_2Ereal__mul(X0,X1)) = ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(X0)),inj__ty_2Erealax_2Ereal(X1)) ).
tff(tp_c_2Enum_2E0,type,
c_2Enum_2E0: $i ).
tff(mem_c_2Enum_2E0,axiom,
mem(c_2Enum_2E0,ty_2Enum_2Enum) ).
tff(stp_fo_c_2Enum_2E0,type,
fo__c_2Enum_2E0: tp__ty_2Enum_2Enum ).
tff(stp_eq_fo_c_2Enum_2E0,axiom,
inj__ty_2Enum_2Enum(fo__c_2Enum_2E0) = c_2Enum_2E0 ).
tff(tp_c_2Ereal_2Ereal__of__num,type,
c_2Ereal_2Ereal__of__num: $i ).
tff(mem_c_2Ereal_2Ereal__of__num,axiom,
mem(c_2Ereal_2Ereal__of__num,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)) ).
tff(stp_fo_c_2Ereal_2Ereal__of__num,type,
fo__c_2Ereal_2Ereal__of__num: tp__ty_2Enum_2Enum > tp__ty_2Erealax_2Ereal ).
tff(stp_eq_fo_c_2Ereal_2Ereal__of__num,axiom,
! [X0: tp__ty_2Enum_2Enum] : inj__ty_2Erealax_2Ereal(fo__c_2Ereal_2Ereal__of__num(X0)) = ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(X0)) ).
tff(tp_c_2Epred__set_2EEMPTY,type,
c_2Epred__set_2EEMPTY: del > $i ).
tff(mem_c_2Epred__set_2EEMPTY,axiom,
! [A_27a: del] : mem(c_2Epred__set_2EEMPTY(A_27a),arr(A_27a,bool)) ).
tff(tp_c_2Epred__set_2EINSERT,type,
c_2Epred__set_2EINSERT: del > $i ).
tff(mem_c_2Epred__set_2EINSERT,axiom,
! [A_27a: del] : mem(c_2Epred__set_2EINSERT(A_27a),arr(A_27a,arr(arr(A_27a,bool),arr(A_27a,bool)))) ).
tff(tp_c_2Ereal__topology_2Eindependent,type,
c_2Ereal__topology_2Eindependent: $i ).
tff(mem_c_2Ereal__topology_2Eindependent,axiom,
mem(c_2Ereal__topology_2Eindependent,arr(arr(ty_2Erealax_2Ereal,bool),bool)) ).
tff(tp_c_2Ebool_2EF,type,
c_2Ebool_2EF: $i ).
tff(mem_c_2Ebool_2EF,axiom,
mem(c_2Ebool_2EF,bool) ).
tff(stp_fo_c_2Ebool_2EF,type,
fo__c_2Ebool_2EF: tp__o ).
tff(stp_eq_fo_c_2Ebool_2EF,axiom,
inj__o(fo__c_2Ebool_2EF) = c_2Ebool_2EF ).
tff(ax_false_p,axiom,
~ p(c_2Ebool_2EF) ).
tff(tp_c_2Emin_2E_3D_3D_3E,type,
c_2Emin_2E_3D_3D_3E: $i ).
tff(mem_c_2Emin_2E_3D_3D_3E,axiom,
mem(c_2Emin_2E_3D_3D_3E,arr(bool,arr(bool,bool))) ).
tff(stp_fo_c_2Emin_2E_3D_3D_3E,type,
fo__c_2Emin_2E_3D_3D_3E: ( tp__o * tp__o ) > tp__o ).
tff(stp_eq_fo_c_2Emin_2E_3D_3D_3E,axiom,
! [X0: tp__o,X1: tp__o] : inj__o(fo__c_2Emin_2E_3D_3D_3E(X0,X1)) = ap(ap(c_2Emin_2E_3D_3D_3E,inj__o(X0)),inj__o(X1)) ).
tff(ax_imp_p,axiom,
! [Q: $i] :
( mem(Q,bool)
=> ! [R: $i] :
( mem(R,bool)
=> ( p(ap(ap(c_2Emin_2E_3D_3D_3E,Q),R))
<=> ( p(Q)
=> p(R) ) ) ) ) ).
tff(tp_c_2Ebool_2E_5C_2F,type,
c_2Ebool_2E_5C_2F: $i ).
tff(mem_c_2Ebool_2E_5C_2F,axiom,
mem(c_2Ebool_2E_5C_2F,arr(bool,arr(bool,bool))) ).
tff(stp_fo_c_2Ebool_2E_5C_2F,type,
fo__c_2Ebool_2E_5C_2F: ( tp__o * tp__o ) > tp__o ).
tff(stp_eq_fo_c_2Ebool_2E_5C_2F,axiom,
! [X0: tp__o,X1: tp__o] : inj__o(fo__c_2Ebool_2E_5C_2F(X0,X1)) = ap(ap(c_2Ebool_2E_5C_2F,inj__o(X0)),inj__o(X1)) ).
tff(ax_or_p,axiom,
! [Q: $i] :
( mem(Q,bool)
=> ! [R: $i] :
( mem(R,bool)
=> ( p(ap(ap(c_2Ebool_2E_5C_2F,Q),R))
<=> ( p(Q)
| p(R) ) ) ) ) ).
tff(tp_c_2Ebool_2E_2F_5C,type,
c_2Ebool_2E_2F_5C: $i ).
tff(mem_c_2Ebool_2E_2F_5C,axiom,
mem(c_2Ebool_2E_2F_5C,arr(bool,arr(bool,bool))) ).
tff(stp_fo_c_2Ebool_2E_2F_5C,type,
fo__c_2Ebool_2E_2F_5C: ( tp__o * tp__o ) > tp__o ).
tff(stp_eq_fo_c_2Ebool_2E_2F_5C,axiom,
! [X0: tp__o,X1: tp__o] : inj__o(fo__c_2Ebool_2E_2F_5C(X0,X1)) = ap(ap(c_2Ebool_2E_2F_5C,inj__o(X0)),inj__o(X1)) ).
tff(ax_and_p,axiom,
! [Q: $i] :
( mem(Q,bool)
=> ! [R: $i] :
( mem(R,bool)
=> ( p(ap(ap(c_2Ebool_2E_2F_5C,Q),R))
<=> ( p(Q)
& p(R) ) ) ) ) ).
tff(tp_c_2Ebool_2E_7E,type,
c_2Ebool_2E_7E: $i ).
tff(mem_c_2Ebool_2E_7E,axiom,
mem(c_2Ebool_2E_7E,arr(bool,bool)) ).
tff(stp_fo_c_2Ebool_2E_7E,type,
fo__c_2Ebool_2E_7E: tp__o > tp__o ).
tff(stp_eq_fo_c_2Ebool_2E_7E,axiom,
! [X0: tp__o] : inj__o(fo__c_2Ebool_2E_7E(X0)) = ap(c_2Ebool_2E_7E,inj__o(X0)) ).
tff(ax_neg_p,axiom,
! [Q: $i] :
( mem(Q,bool)
=> ( p(ap(c_2Ebool_2E_7E,Q))
<=> ~ p(Q) ) ) ).
tff(tp_c_2Emin_2E_3D,type,
c_2Emin_2E_3D: del > $i ).
tff(mem_c_2Emin_2E_3D,axiom,
! [A_27a: del] : mem(c_2Emin_2E_3D(A_27a),arr(A_27a,arr(A_27a,bool))) ).
tff(ax_eq_p,axiom,
! [A: del,X: $i] :
( mem(X,A)
=> ! [Y: $i] :
( mem(Y,A)
=> ( p(ap(ap(c_2Emin_2E_3D(A),X),Y))
<=> ( X = Y ) ) ) ) ).
tff(tp_c_2Ebool_2E_21,type,
c_2Ebool_2E_21: del > $i ).
tff(mem_c_2Ebool_2E_21,axiom,
! [A_27a: del] : mem(c_2Ebool_2E_21(A_27a),arr(arr(A_27a,bool),bool)) ).
tff(ax_all_p,axiom,
! [A: del,Q: $i] :
( mem(Q,arr(A,bool))
=> ( p(ap(c_2Ebool_2E_21(A),Q))
<=> ! [X: $i] :
( mem(X,A)
=> p(ap(Q,X)) ) ) ) ).
tff(conj_thm_2Earithmetic_2EZERO__LESS__EQ,axiom,
! [V0n: tp__ty_2Enum_2Enum] : p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),inj__ty_2Enum_2Enum(V0n))) ).
tff(conj_thm_2Earithmetic_2EADD__EQ__0,axiom,
! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V0m)),inj__ty_2Enum_2Enum(V1n))) = fo__c_2Enum_2E0 )
<=> ( ( V0m = fo__c_2Enum_2E0 )
& ( V1n = fo__c_2Enum_2E0 ) ) ) ).
tff(conj_thm_2Earithmetic_2EEQ__LESS__EQ,axiom,
! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
( ( V0m = V1n )
<=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V0m)),inj__ty_2Enum_2Enum(V1n)))
& p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V1n)),inj__ty_2Enum_2Enum(V0m))) ) ) ).
tff(conj_thm_2Earithmetic_2ELE,axiom,
( ! [V0n: tp__ty_2Enum_2Enum] :
( p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))
<=> ( V0n = fo__c_2Enum_2E0 ) )
& ! [V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
( p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V1m)),ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V2n))))
<=> ( ( V1m = surj__ty_2Enum_2Enum(ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V2n))) )
| p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V1m)),inj__ty_2Enum_2Enum(V2n))) ) ) ) ).
tff(conj_thm_2Ebool_2ETRUTH,axiom,
$true ).
tff(conj_thm_2Ebool_2EAND__CLAUSES,axiom,
! [V0t: tp__o] :
( ( ( $true
& p(inj__o(V0t)) )
<=> p(inj__o(V0t)) )
& ( ( p(inj__o(V0t))
& $true )
<=> p(inj__o(V0t)) )
& ( ( $false
& p(inj__o(V0t)) )
<=> $false )
& ( ( p(inj__o(V0t))
& $false )
<=> $false )
& ( ( p(inj__o(V0t))
& p(inj__o(V0t)) )
<=> p(inj__o(V0t)) ) ) ).
tff(conj_thm_2Ebool_2EIMP__CLAUSES,axiom,
! [V0t: tp__o] :
( ( ( $true
=> p(inj__o(V0t)) )
<=> p(inj__o(V0t)) )
& ( ( p(inj__o(V0t))
=> $true )
<=> $true )
& ( ( $false
=> p(inj__o(V0t)) )
<=> $true )
& ( ( p(inj__o(V0t))
=> p(inj__o(V0t)) )
<=> $true )
& ( ( p(inj__o(V0t))
=> $false )
<=> ~ p(inj__o(V0t)) ) ) ).
tff(conj_thm_2Ebool_2ENOT__CLAUSES,axiom,
( ! [V0t: tp__o] :
( ~ ~ p(inj__o(V0t))
<=> p(inj__o(V0t)) )
& ( ~ $true
<=> $false )
& ( ~ $false
<=> $true ) ) ).
tff(conj_thm_2Ebool_2EREFL__CLAUSE,axiom,
! [A_27a: del,V0x: $i] :
( mem(V0x,A_27a)
=> ( ( V0x = V0x )
<=> $true ) ) ).
tff(conj_thm_2Ebool_2EEQ__SYM__EQ,axiom,
! [A_27a: del,V0x: $i] :
( mem(V0x,A_27a)
=> ! [V1y: $i] :
( mem(V1y,A_27a)
=> ( ( V0x = V1y )
<=> ( V1y = V0x ) ) ) ) ).
tff(conj_thm_2Ebool_2EEQ__CLAUSES,axiom,
! [V0t: tp__o] :
( ( ( $true
<=> p(inj__o(V0t)) )
<=> p(inj__o(V0t)) )
& ( ( p(inj__o(V0t))
<=> $true )
<=> p(inj__o(V0t)) )
& ( ( $false
<=> p(inj__o(V0t)) )
<=> ~ p(inj__o(V0t)) )
& ( ( p(inj__o(V0t))
<=> $false )
<=> ~ p(inj__o(V0t)) ) ) ).
tff(conj_thm_2Enumeral_2Enumeral__distrib,axiom,
( ! [V0n: tp__ty_2Enum_2Enum] : surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),inj__ty_2Enum_2Enum(V0n))) = V0n
& ! [V1n: tp__ty_2Enum_2Enum] : surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V1n)),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = V1n
& ! [V2n: tp__ty_2Enum_2Enum,V3m: tp__ty_2Enum_2Enum] : surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V2n))),ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V3m)))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2ENUMERAL,ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V2n)),inj__ty_2Enum_2Enum(V3m)))))
& ! [V4n: tp__ty_2Enum_2Enum] : surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2A,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),inj__ty_2Enum_2Enum(V4n))) = fo__c_2Enum_2E0
& ! [V5n: tp__ty_2Enum_2Enum] : surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2A,inj__ty_2Enum_2Enum(V5n)),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = fo__c_2Enum_2E0
& ! [V6n: tp__ty_2Enum_2Enum,V7m: tp__ty_2Enum_2Enum] : surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V6n))),ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V7m)))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2ENUMERAL,ap(ap(c_2Earithmetic_2E_2A,inj__ty_2Enum_2Enum(V6n)),inj__ty_2Enum_2Enum(V7m))))
& ! [V8n: tp__ty_2Enum_2Enum] : surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),inj__ty_2Enum_2Enum(V8n))) = fo__c_2Enum_2E0
& ! [V9n: tp__ty_2Enum_2Enum] : surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V9n)),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = V9n
& ! [V10n: tp__ty_2Enum_2Enum,V11m: tp__ty_2Enum_2Enum] : surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V10n))),ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V11m)))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2ENUMERAL,ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V10n)),inj__ty_2Enum_2Enum(V11m))))
& ! [V12n: tp__ty_2Enum_2Enum] : surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2EEXP,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V12n))))) = fo__c_2Enum_2E0
& ! [V13n: tp__ty_2Enum_2Enum] : surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2EEXP,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V13n))))) = fo__c_2Enum_2E0
& ! [V14n: tp__ty_2Enum_2Enum] : surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2EEXP,inj__ty_2Enum_2Enum(V14n)),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))
& ! [V15n: tp__ty_2Enum_2Enum,V16m: tp__ty_2Enum_2Enum] : surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V15n))),ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V16m)))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2ENUMERAL,ap(ap(c_2Earithmetic_2EEXP,inj__ty_2Enum_2Enum(V15n)),inj__ty_2Enum_2Enum(V16m))))
& ( surj__ty_2Enum_2Enum(ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))) )
& ! [V17n: tp__ty_2Enum_2Enum] : surj__ty_2Enum_2Enum(ap(c_2Enum_2ESUC,ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V17n)))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2ENUMERAL,ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V17n))))
& ( surj__ty_2Enum_2Enum(ap(c_2Eprim__rec_2EPRE,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = fo__c_2Enum_2E0 )
& ! [V18n: tp__ty_2Enum_2Enum] : surj__ty_2Enum_2Enum(ap(c_2Eprim__rec_2EPRE,ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V18n)))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2ENUMERAL,ap(c_2Eprim__rec_2EPRE,inj__ty_2Enum_2Enum(V18n))))
& ! [V19n: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V19n))) = fo__c_2Enum_2E0 )
<=> ( V19n = fo__c_2Earithmetic_2EZERO ) )
& ! [V20n: tp__ty_2Enum_2Enum] :
( ( fo__c_2Enum_2E0 = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V20n))) )
<=> ( V20n = fo__c_2Earithmetic_2EZERO ) )
& ! [V21n: tp__ty_2Enum_2Enum,V22m: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V21n))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V22m))) )
<=> ( V21n = V22m ) )
& ! [V23n: tp__ty_2Enum_2Enum] :
( p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V23n)),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))
<=> $false )
& ! [V24n: tp__ty_2Enum_2Enum] :
( p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V24n))))
<=> p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)),inj__ty_2Enum_2Enum(V24n))) )
& ! [V25n: tp__ty_2Enum_2Enum,V26m: tp__ty_2Enum_2Enum] :
( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V25n))),ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V26m))))
<=> p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V25n)),inj__ty_2Enum_2Enum(V26m))) )
& ! [V27n: tp__ty_2Enum_2Enum] :
( p(ap(ap(c_2Earithmetic_2E_3E,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),inj__ty_2Enum_2Enum(V27n)))
<=> $false )
& ! [V28n: tp__ty_2Enum_2Enum] :
( p(ap(ap(c_2Earithmetic_2E_3E,ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V28n))),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))
<=> p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)),inj__ty_2Enum_2Enum(V28n))) )
& ! [V29n: tp__ty_2Enum_2Enum,V30m: tp__ty_2Enum_2Enum] :
( p(ap(ap(c_2Earithmetic_2E_3E,ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V29n))),ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V30m))))
<=> p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V30m)),inj__ty_2Enum_2Enum(V29n))) )
& ! [V31n: tp__ty_2Enum_2Enum] :
( p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),inj__ty_2Enum_2Enum(V31n)))
<=> $true )
& ! [V32n: tp__ty_2Enum_2Enum] :
( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V32n))),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))
<=> p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V32n)),inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))) )
& ! [V33n: tp__ty_2Enum_2Enum,V34m: tp__ty_2Enum_2Enum] :
( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V33n))),ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V34m))))
<=> p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V33n)),inj__ty_2Enum_2Enum(V34m))) )
& ! [V35n: tp__ty_2Enum_2Enum] :
( p(ap(ap(c_2Earithmetic_2E_3E_3D,inj__ty_2Enum_2Enum(V35n)),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))
<=> $true )
& ! [V36n: tp__ty_2Enum_2Enum] :
( p(ap(ap(c_2Earithmetic_2E_3E_3D,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),inj__ty_2Enum_2Enum(V36n)))
<=> ( V36n = fo__c_2Enum_2E0 ) )
& ! [V37n: tp__ty_2Enum_2Enum,V38m: tp__ty_2Enum_2Enum] :
( p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V37n))),ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V38m))))
<=> p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V38m)),inj__ty_2Enum_2Enum(V37n))) )
& ! [V39n: tp__ty_2Enum_2Enum] :
( p(ap(c_2Earithmetic_2EODD,ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V39n))))
<=> p(ap(c_2Earithmetic_2EODD,inj__ty_2Enum_2Enum(V39n))) )
& ! [V40n: tp__ty_2Enum_2Enum] :
( p(ap(c_2Earithmetic_2EEVEN,ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V40n))))
<=> p(ap(c_2Earithmetic_2EEVEN,inj__ty_2Enum_2Enum(V40n))) )
& ~ p(ap(c_2Earithmetic_2EODD,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))
& p(ap(c_2Earithmetic_2EEVEN,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ) ).
tff(conj_thm_2Enumeral_2Enumeral__add,axiom,
! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum(ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)),inj__ty_2Enum_2Enum(V0n)))) = V0n )
& ( surj__ty_2Enum_2Enum(ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))) = V0n )
& ( surj__ty_2Enum_2Enum(ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0n))),ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V1m))))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT2,ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(V1m))))) )
& ( surj__ty_2Enum_2Enum(ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0n))),ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V1m))))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT1,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(V1m))))) )
& ( surj__ty_2Enum_2Enum(ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V0n))),ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V1m))))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT1,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(V1m))))) )
& ( surj__ty_2Enum_2Enum(ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V0n))),ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V1m))))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT2,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(V1m))))) )
& ( surj__ty_2Enum_2Enum(ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)),inj__ty_2Enum_2Enum(V0n)))) = surj__ty_2Enum_2Enum(ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V0n))) )
& ( surj__ty_2Enum_2Enum(ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))) = surj__ty_2Enum_2Enum(ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V0n))) )
& ( surj__ty_2Enum_2Enum(ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0n))),ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V1m))))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT1,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(V1m))))) )
& ( surj__ty_2Enum_2Enum(ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0n))),ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V1m))))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT2,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(V1m))))) )
& ( surj__ty_2Enum_2Enum(ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V0n))),ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V1m))))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT2,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(V1m))))) )
& ( surj__ty_2Enum_2Enum(ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V0n))),ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V1m))))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT1,ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(V1m))))) )
& ( surj__ty_2Enum_2Enum(ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)),inj__ty_2Enum_2Enum(V0n)))) = surj__ty_2Enum_2Enum(ap(c_2Enumeral_2EiiSUC,inj__ty_2Enum_2Enum(V0n))) )
& ( surj__ty_2Enum_2Enum(ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))) = surj__ty_2Enum_2Enum(ap(c_2Enumeral_2EiiSUC,inj__ty_2Enum_2Enum(V0n))) )
& ( surj__ty_2Enum_2Enum(ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0n))),ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V1m))))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT2,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(V1m))))) )
& ( surj__ty_2Enum_2Enum(ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0n))),ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V1m))))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT1,ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(V1m))))) )
& ( surj__ty_2Enum_2Enum(ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V0n))),ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V1m))))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT1,ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(V1m))))) )
& ( surj__ty_2Enum_2Enum(ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V0n))),ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V1m))))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT2,ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(V1m))))) ) ) ).
tff(conj_thm_2Enumeral_2Enumeral__eq,axiom,
! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
( ( ( fo__c_2Earithmetic_2EZERO = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0n))) )
<=> $false )
& ( ( surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0n))) = fo__c_2Earithmetic_2EZERO )
<=> $false )
& ( ( fo__c_2Earithmetic_2EZERO = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V0n))) )
<=> $false )
& ( ( surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V0n))) = fo__c_2Earithmetic_2EZERO )
<=> $false )
& ( ( surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0n))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V1m))) )
<=> $false )
& ( ( surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V0n))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V1m))) )
<=> $false )
& ( ( surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0n))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V1m))) )
<=> ( V0n = V1m ) )
& ( ( surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V0n))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V1m))) )
<=> ( V0n = V1m ) ) ) ).
tff(conj_thm_2Enumeral_2EiDUB__removal,axiom,
! [V0n: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum(ap(c_2Enumeral_2EiDUB,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0n)))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT2,ap(c_2Enumeral_2EiDUB,inj__ty_2Enum_2Enum(V0n)))) )
& ( surj__ty_2Enum_2Enum(ap(c_2Enumeral_2EiDUB,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V0n)))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0n)))) )
& ( surj__ty_2Enum_2Enum(ap(c_2Enumeral_2EiDUB,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))) = fo__c_2Earithmetic_2EZERO ) ) ).
tff(conj_thm_2Enumeral_2Enumeral__mult,axiom,
! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2A,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)),inj__ty_2Enum_2Enum(V0n))) = fo__c_2Earithmetic_2EZERO )
& ( surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2A,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))) = fo__c_2Earithmetic_2EZERO )
& ( surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0n))),inj__ty_2Enum_2Enum(V1m))) = surj__ty_2Enum_2Enum(ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Enumeral_2EiDUB,ap(ap(c_2Earithmetic_2E_2A,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(V1m)))),inj__ty_2Enum_2Enum(V1m)))) )
& ( surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V0n))),inj__ty_2Enum_2Enum(V1m))) = surj__ty_2Enum_2Enum(ap(c_2Enumeral_2EiDUB,ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(V1m))),inj__ty_2Enum_2Enum(V1m))))) ) ) ).
%----Manually added. This problem is broken.
tff(f295_type,type,
f295: ( del * $i ) > $i ).
tff(conj_thm_2Epred__set_2EGSPEC__EQ2,axiom,
! [A_27a: del,V0y: $i] :
( mem(V0y,A_27a)
=> ( ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f295(A_27a,V0y)) = ap(ap(c_2Epred__set_2EINSERT(A_27a),V0y),c_2Epred__set_2EEMPTY(A_27a)) ) ) ).
tff(conj_thm_2Ereal_2EREAL__ADD__LID,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V0x))) = V0x ).
tff(conj_thm_2Ereal_2EREAL__MUL__RID,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) = V0x ).
tff(conj_thm_2Ereal_2EREAL__LE__ANTISYM,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( ( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))
& p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x))) )
<=> ( V0x = V1y ) ) ).
tff(conj_thm_2Ereal_2EREAL__ADD,axiom,
! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0m))),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V1n)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V0m)),inj__ty_2Enum_2Enum(V1n)))) ).
tff(conj_thm_2Ereal_2EREAL__MUL__RNEG,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V1y)))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))) ).
tff(conj_thm_2Ereal_2EREAL__MUL__LNEG,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0x))),inj__ty_2Erealax_2Ereal(V1y))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))) ).
tff(conj_thm_2Ereal_2Ereal__lt,axiom,
! [V0y: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1x)),inj__ty_2Erealax_2Ereal(V0y)))
<=> ~ p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0y)),inj__ty_2Erealax_2Ereal(V1x))) ) ).
tff(conj_thm_2Ereal_2EREAL__LE__LNEG,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0x))),inj__ty_2Erealax_2Ereal(V1y)))
<=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))) ) ).
tff(conj_thm_2Ereal_2EREAL__LE__NEG2,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0x))),ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V1y))))
<=> p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x))) ) ).
tff(conj_thm_2Ereal_2EREAL__NEG__NEG,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] : surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0x)))) = V0x ).
tff(conj_thm_2Ereal_2EREAL__LE__RNEG,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V1y))))
<=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) ) ).
tff(conj_thm_2Ereal_2EREAL__OF__NUM__LE,axiom,
! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0m))),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V1n))))
<=> p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V0m)),inj__ty_2Enum_2Enum(V1n))) ) ).
tff(conj_thm_2Ereal_2EREAL__OF__NUM__MUL,axiom,
! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] : surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0m))),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V1n)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,ap(ap(c_2Earithmetic_2E_2A,inj__ty_2Enum_2Enum(V0m)),inj__ty_2Enum_2Enum(V1n)))) ).
tff(conj_thm_2Ereal__topology_2EINDEPENDENT__SING,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] :
( p(ap(c_2Ereal__topology_2Eindependent,ap(ap(c_2Epred__set_2EINSERT(ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(V0x)),c_2Epred__set_2EEMPTY(ty_2Erealax_2Ereal))))
<=> ( V0x != surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ) ) ).
tff(conj_thm_2Esat_2ENOT__NOT,axiom,
! [V0t: tp__o] :
( ~ ~ p(inj__o(V0t))
<=> p(inj__o(V0t)) ) ).
tff(conj_thm_2Esat_2EAND__INV__IMP,axiom,
! [V0A: tp__o] :
( p(inj__o(V0A))
=> ( ~ p(inj__o(V0A))
=> $false ) ) ).
tff(conj_thm_2Esat_2EOR__DUAL2,axiom,
! [V0A: tp__o,V1B: tp__o] :
( ( ~ ( p(inj__o(V0A))
| p(inj__o(V1B)) )
=> $false )
<=> ( ( p(inj__o(V0A))
=> $false )
=> ( ~ p(inj__o(V1B))
=> $false ) ) ) ).
tff(conj_thm_2Esat_2EOR__DUAL3,axiom,
! [V0A: tp__o,V1B: tp__o] :
( ( ~ ( ~ p(inj__o(V0A))
| p(inj__o(V1B)) )
=> $false )
<=> ( p(inj__o(V0A))
=> ( ~ p(inj__o(V1B))
=> $false ) ) ) ).
tff(conj_thm_2Esat_2EAND__INV2,axiom,
! [V0A: tp__o] :
( ( ~ p(inj__o(V0A))
=> $false )
=> ( ( p(inj__o(V0A))
=> $false )
=> $false ) ) ).
tff(conj_thm_2Esat_2Edc__eq,axiom,
! [V0p: tp__o,V1q: tp__o,V2r: tp__o] :
( ( p(inj__o(V0p))
<=> ( p(inj__o(V1q))
<=> p(inj__o(V2r)) ) )
<=> ( ( p(inj__o(V0p))
| p(inj__o(V1q))
| p(inj__o(V2r)) )
& ( p(inj__o(V0p))
| ~ p(inj__o(V2r))
| ~ p(inj__o(V1q)) )
& ( p(inj__o(V1q))
| ~ p(inj__o(V2r))
| ~ p(inj__o(V0p)) )
& ( p(inj__o(V2r))
| ~ p(inj__o(V1q))
| ~ p(inj__o(V0p)) ) ) ) ).
tff(conj_thm_2Esat_2Edc__conj,axiom,
! [V0p: tp__o,V1q: tp__o,V2r: tp__o] :
( ( p(inj__o(V0p))
<=> ( p(inj__o(V1q))
& p(inj__o(V2r)) ) )
<=> ( ( p(inj__o(V0p))
| ~ p(inj__o(V1q))
| ~ p(inj__o(V2r)) )
& ( p(inj__o(V1q))
| ~ p(inj__o(V0p)) )
& ( p(inj__o(V2r))
| ~ p(inj__o(V0p)) ) ) ) ).
tff(conj_thm_2Esat_2Edc__neg,axiom,
! [V0p: tp__o,V1q: tp__o] :
( ( p(inj__o(V0p))
<=> ~ p(inj__o(V1q)) )
<=> ( ( p(inj__o(V0p))
| p(inj__o(V1q)) )
& ( ~ p(inj__o(V1q))
| ~ p(inj__o(V0p)) ) ) ) ).
%----Manually added. This problem is broken.
tff(f3557_type,type,
f3557: $i ).
tff(conj_thm_2Ereal__topology_2EINDEPENDENT__STDBASIS,conjecture,
p(ap(c_2Ereal__topology_2Eindependent,ap(c_2Epred__set_2EGSPEC(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),f3557))) ).
%------------------------------------------------------------------------------