ITP001 Axioms: ITP035+5.ax
%------------------------------------------------------------------------------
% File : ITP035+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 : listRange+2.ax [Gau20]
% : HL4035+5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 16 ( 2 unt; 0 def)
% Number of atoms : 53 ( 11 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 37 ( 0 ~; 0 |; 2 &)
% ( 2 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty)
% Number of functors : 22 ( 22 usr; 10 con; 0-2 aty)
% Number of variables : 29 ( 29 !; 0 ?)
% SPC : FOF_SAT_RFO_SEQ
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
fof(mem_c_2ElistRange_2ElistRangeINC,axiom,
mem(c_2ElistRange_2ElistRangeINC,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Elist_2Elist(ty_2Enum_2Enum)))) ).
fof(mem_c_2ElistRange_2ElistRangeLHI,axiom,
mem(c_2ElistRange_2ElistRangeLHI,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Elist_2Elist(ty_2Enum_2Enum)))) ).
fof(lameq_f535,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V2i] : ap(f535(V0m),V2i) = ap(ap(c_2Earithmetic_2E_2B,V0m),V2i) ) ).
fof(ax_thm_2ElistRange_2ElistRangeINC__def,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(ap(c_2ElistRange_2ElistRangeINC,V0m),V1n) = ap(ap(c_2Elist_2EGENLIST(ty_2Enum_2Enum),f535(V0m)),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2B,V1n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V0m)) ) ) ).
fof(conj_thm_2ElistRange_2ElistRangeINC__SING,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ap(ap(c_2ElistRange_2ElistRangeINC,V0m),V0m) = ap(ap(c_2Elist_2ECONS(ty_2Enum_2Enum),V0m),c_2Elist_2ENIL(ty_2Enum_2Enum)) ) ).
fof(conj_thm_2ElistRange_2EMEM__listRangeINC,axiom,
! [V0x] :
( mem(V0x,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),V0x),ap(c_2Elist_2ELIST__TO__SET(ty_2Enum_2Enum),ap(ap(c_2ElistRange_2ElistRangeINC,V1m),V2n))))
<=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),V0x))
& p(ap(ap(c_2Earithmetic_2E_3C_3D,V0x),V2n)) ) ) ) ) ) ).
fof(conj_thm_2ElistRange_2ElistRangeINC__CONS,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n))
=> ap(ap(c_2ElistRange_2ElistRangeINC,V0m),V1n) = ap(ap(c_2Elist_2ECONS(ty_2Enum_2Enum),V0m),ap(ap(c_2ElistRange_2ElistRangeINC,ap(ap(c_2Earithmetic_2E_2B,V0m),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V1n)) ) ) ) ).
fof(conj_thm_2ElistRange_2ElistRangeINC__EMPTY,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0n),V1m))
=> ap(ap(c_2ElistRange_2ElistRangeINC,V1m),V0n) = c_2Elist_2ENIL(ty_2Enum_2Enum) ) ) ) ).
fof(ax_thm_2ElistRange_2ElistRangeLHI__def,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(ap(c_2ElistRange_2ElistRangeLHI,V0m),V1n) = ap(ap(c_2Elist_2EGENLIST(ty_2Enum_2Enum),f535(V0m)),ap(ap(c_2Earithmetic_2E_2D,V1n),V0m)) ) ) ).
fof(conj_thm_2ElistRange_2ElistRangeLHI__EQ,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ap(ap(c_2ElistRange_2ElistRangeLHI,V0m),V0m) = c_2Elist_2ENIL(ty_2Enum_2Enum) ) ).
fof(conj_thm_2ElistRange_2EMEM__listRangeLHI,axiom,
! [V0x] :
( mem(V0x,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),V0x),ap(c_2Elist_2ELIST__TO__SET(ty_2Enum_2Enum),ap(ap(c_2ElistRange_2ElistRangeLHI,V1m),V2n))))
<=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),V0x))
& p(ap(ap(c_2Eprim__rec_2E_3C,V0x),V2n)) ) ) ) ) ) ).
fof(conj_thm_2ElistRange_2ElistRangeLHI__EMPTY,axiom,
! [V0hi] :
( mem(V0hi,ty_2Enum_2Enum)
=> ! [V1lo] :
( mem(V1lo,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0hi),V1lo))
=> ap(ap(c_2ElistRange_2ElistRangeLHI,V1lo),V0hi) = c_2Elist_2ENIL(ty_2Enum_2Enum) ) ) ) ).
fof(conj_thm_2ElistRange_2ElistRangeLHI__CONS,axiom,
! [V0lo] :
( mem(V0lo,ty_2Enum_2Enum)
=> ! [V1hi] :
( mem(V1hi,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0lo),V1hi))
=> ap(ap(c_2ElistRange_2ElistRangeLHI,V0lo),V1hi) = ap(ap(c_2Elist_2ECONS(ty_2Enum_2Enum),V0lo),ap(ap(c_2ElistRange_2ElistRangeLHI,ap(ap(c_2Earithmetic_2E_2B,V0lo),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V1hi)) ) ) ) ).
fof(conj_thm_2ElistRange_2ElistRangeLHI__ALL__DISTINCT,axiom,
! [V0lo] :
( mem(V0lo,ty_2Enum_2Enum)
=> ! [V1hi] :
( mem(V1hi,ty_2Enum_2Enum)
=> p(ap(c_2Elist_2EALL__DISTINCT(ty_2Enum_2Enum),ap(ap(c_2ElistRange_2ElistRangeLHI,V0lo),V1hi))) ) ) ).
fof(conj_thm_2ElistRange_2ELENGTH__listRangeLHI,axiom,
! [V0lo] :
( mem(V0lo,ty_2Enum_2Enum)
=> ! [V1hi] :
( mem(V1hi,ty_2Enum_2Enum)
=> ap(c_2Elist_2ELENGTH(ty_2Enum_2Enum),ap(ap(c_2ElistRange_2ElistRangeLHI,V0lo),V1hi)) = ap(ap(c_2Earithmetic_2E_2D,V1hi),V0lo) ) ) ).
fof(conj_thm_2ElistRange_2EEL__listRangeLHI,axiom,
! [V0lo] :
( mem(V0lo,ty_2Enum_2Enum)
=> ! [V1i] :
( mem(V1i,ty_2Enum_2Enum)
=> ! [V2hi] :
( mem(V2hi,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2B,V0lo),V1i)),V2hi))
=> ap(ap(c_2Elist_2EEL(ty_2Enum_2Enum),V1i),ap(ap(c_2ElistRange_2ElistRangeLHI,V0lo),V2hi)) = ap(ap(c_2Earithmetic_2E_2B,V0lo),V1i) ) ) ) ) ).
%------------------------------------------------------------------------------