ITP001 Axioms: ITP020_5.ax
%------------------------------------------------------------------------------
% File : ITP020_5 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 set theory export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau20] Gauthier (2020), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : basicSize_2.ax [Gau20]
% : HL4020_5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 23 ( 9 unt; 9 typ; 0 def)
% Number of atoms : 142 ( 11 equ)
% Maximal formula atoms : 8 ( 6 avg)
% Number of connectives : 18 ( 0 ~; 0 |; 2 &)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 110 ( 110 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 16 ( 7 >; 9 *; 0 +; 0 <<)
% Number of predicates : 26 ( 25 usr; 10 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-5 aty)
% Number of variables : 36 ( 36 !; 0 ?; 36 :)
% SPC : TF0_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(tp_c_2EbasicSize_2Ebool__size,type,
c_2EbasicSize_2Ebool__size: $i ).
tff(mem_c_2EbasicSize_2Ebool__size,axiom,
mem(c_2EbasicSize_2Ebool__size,arr(bool,ty_2Enum_2Enum)) ).
tff(stp_fo_c_2EbasicSize_2Ebool__size,type,
fo__c_2EbasicSize_2Ebool__size: tp__o > tp__ty_2Enum_2Enum ).
tff(stp_eq_fo_c_2EbasicSize_2Ebool__size,axiom,
! [X0: tp__o] : ( inj__ty_2Enum_2Enum(fo__c_2EbasicSize_2Ebool__size(X0)) = ap(c_2EbasicSize_2Ebool__size,inj__o(X0)) ) ).
tff(tp_c_2EbasicSize_2Eone__size,type,
c_2EbasicSize_2Eone__size: $i ).
tff(mem_c_2EbasicSize_2Eone__size,axiom,
mem(c_2EbasicSize_2Eone__size,arr(ty_2Eone_2Eone,ty_2Enum_2Enum)) ).
tff(stp_fo_c_2EbasicSize_2Eone__size,type,
fo__c_2EbasicSize_2Eone__size: tp__ty_2Eone_2Eone > tp__ty_2Enum_2Enum ).
tff(stp_eq_fo_c_2EbasicSize_2Eone__size,axiom,
! [X0: tp__ty_2Eone_2Eone] : ( inj__ty_2Enum_2Enum(fo__c_2EbasicSize_2Eone__size(X0)) = ap(c_2EbasicSize_2Eone__size,inj__ty_2Eone_2Eone(X0)) ) ).
tff(tp_c_2EbasicSize_2Eoption__size,type,
c_2EbasicSize_2Eoption__size: del > $i ).
tff(mem_c_2EbasicSize_2Eoption__size,axiom,
! [A_27a: del] : mem(c_2EbasicSize_2Eoption__size(A_27a),arr(arr(A_27a,ty_2Enum_2Enum),arr(ty_2Eoption_2Eoption(A_27a),ty_2Enum_2Enum))) ).
tff(tp_c_2EbasicSize_2Epair__size,type,
c_2EbasicSize_2Epair__size: ( del * del ) > $i ).
tff(mem_c_2EbasicSize_2Epair__size,axiom,
! [A_27a: del,A_27b: del] : mem(c_2EbasicSize_2Epair__size(A_27a,A_27b),arr(arr(A_27a,ty_2Enum_2Enum),arr(arr(A_27b,ty_2Enum_2Enum),arr(ty_2Epair_2Eprod(A_27a,A_27b),ty_2Enum_2Enum)))) ).
tff(tp_c_2EbasicSize_2Esum__size,type,
c_2EbasicSize_2Esum__size: ( del * del ) > $i ).
tff(mem_c_2EbasicSize_2Esum__size,axiom,
! [A_27a: del,A_27b: del] : mem(c_2EbasicSize_2Esum__size(A_27a,A_27b),arr(arr(A_27a,ty_2Enum_2Enum),arr(arr(A_27b,ty_2Enum_2Enum),arr(ty_2Esum_2Esum(A_27a,A_27b),ty_2Enum_2Enum)))) ).
tff(ax_thm_2EbasicSize_2Ebool__size__def,axiom,
! [V0b: tp__o] : ( surj__ty_2Enum_2Enum(ap(c_2EbasicSize_2Ebool__size,inj__o(V0b))) = fo__c_2Enum_2E0 ) ).
tff(lamtp_f226,type,
f226: ( del * del * $i * $i * $i ) > $i ).
tff(lameq_f226,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,arr(A_27a,ty_2Enum_2Enum))
=> ! [V2x: $i] :
( mem(V2x,A_27a)
=> ! [V1g: $i] :
( mem(V1g,arr(A_27b,ty_2Enum_2Enum))
=> ! [V3y: $i] : ( ap(f226(A_27a,A_27b,V0f,V2x,V1g),V3y) = ap(ap(c_2Earithmetic_2E_2B,ap(V0f,V2x)),ap(V1g,V3y)) ) ) ) ) ).
tff(lamtp_f227,type,
f227: ( del * del * $i * $i ) > $i ).
tff(lameq_f227,axiom,
! [A_27b: del,A_27a: del,V0f: $i] :
( mem(V0f,arr(A_27a,ty_2Enum_2Enum))
=> ! [V1g: $i] :
( mem(V1g,arr(A_27b,ty_2Enum_2Enum))
=> ! [V2x: $i] : ( ap(f227(A_27b,A_27a,V0f,V1g),V2x) = f226(A_27a,A_27b,V0f,V2x,V1g) ) ) ) ).
tff(ax_thm_2EbasicSize_2Epair__size__def,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,arr(A_27a,ty_2Enum_2Enum))
=> ! [V1g: $i] :
( mem(V1g,arr(A_27b,ty_2Enum_2Enum))
=> ( ap(ap(c_2EbasicSize_2Epair__size(A_27a,A_27b),V0f),V1g) = ap(c_2Epair_2EUNCURRY(A_27a,A_27b,ty_2Enum_2Enum),f227(A_27b,A_27a,V0f,V1g)) ) ) ) ).
tff(ax_thm_2EbasicSize_2Eone__size__def,axiom,
! [V0x: tp__ty_2Eone_2Eone] : ( surj__ty_2Enum_2Enum(ap(c_2EbasicSize_2Eone__size,inj__ty_2Eone_2Eone(V0x))) = fo__c_2Enum_2E0 ) ).
tff(ax_thm_2EbasicSize_2Esum__size__def,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0f: $i] :
( mem(V0f,arr(A_27a,ty_2Enum_2Enum))
=> ! [V1g: $i] :
( mem(V1g,arr(A_27b,ty_2Enum_2Enum))
=> ! [V2x: $i] :
( mem(V2x,A_27a)
=> ( surj__ty_2Enum_2Enum(ap(ap(ap(c_2EbasicSize_2Esum__size(A_27a,A_27b),V0f),V1g),ap(c_2Esum_2EINL(A_27a,A_27b),V2x))) = surj__ty_2Enum_2Enum(ap(V0f,V2x)) ) ) ) )
& ! [V3f: $i] :
( mem(V3f,arr(A_27a,ty_2Enum_2Enum))
=> ! [V4g: $i] :
( mem(V4g,arr(A_27b,ty_2Enum_2Enum))
=> ! [V5y: $i] :
( mem(V5y,A_27b)
=> ( surj__ty_2Enum_2Enum(ap(ap(ap(c_2EbasicSize_2Esum__size(A_27a,A_27b),V3f),V4g),ap(c_2Esum_2EINR(A_27a,A_27b),V5y))) = surj__ty_2Enum_2Enum(ap(V4g,V5y)) ) ) ) ) ) ).
tff(ax_thm_2EbasicSize_2Eoption__size__def,axiom,
! [A_27a: del] :
( ! [V0f: $i] :
( mem(V0f,arr(A_27a,ty_2Enum_2Enum))
=> ( surj__ty_2Enum_2Enum(ap(ap(c_2EbasicSize_2Eoption__size(A_27a),V0f),c_2Eoption_2ENONE(A_27a))) = fo__c_2Enum_2E0 ) )
& ! [V1f: $i] :
( mem(V1f,arr(A_27a,ty_2Enum_2Enum))
=> ! [V2x: $i] :
( mem(V2x,A_27a)
=> ( surj__ty_2Enum_2Enum(ap(ap(c_2EbasicSize_2Eoption__size(A_27a),V1f),ap(c_2Eoption_2ESOME(A_27a),V2x))) = surj__ty_2Enum_2Enum(ap(c_2Enum_2ESUC,ap(V1f,V2x))) ) ) ) ) ).
%------------------------------------------------------------------------------