ITP001 Axioms: ITP075+5.ax
%------------------------------------------------------------------------------
% File : ITP075+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 : string_num+2.ax [Gau20]
% : HL4075+5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 36 ( 9 unt; 0 def)
% Number of atoms : 87 ( 36 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 52 ( 1 ~; 0 |; 6 &)
% ( 2 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 17 ( 3 avg)
% Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty)
% Number of functors : 54 ( 54 usr; 27 con; 0-4 aty)
% Number of variables : 54 ( 52 !; 2 ?)
% SPC : FOF_SAT_RFO_SEQ
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
fof(mem_c_2Estring__num_2En2nsum,axiom,
mem(c_2Estring__num_2En2nsum,arr(ty_2Enum_2Enum,ty_2Esum_2Esum(ty_2Enum_2Enum,ty_2Enum_2Enum))) ).
fof(mem_c_2Estring__num_2En2s,axiom,
mem(c_2Estring__num_2En2s,arr(ty_2Enum_2Enum,ty_2Elist_2Elist(ty_2Estring_2Echar))) ).
fof(mem_c_2Estring__num_2Ensum2n,axiom,
mem(c_2Estring__num_2Ensum2n,arr(ty_2Esum_2Esum(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum)) ).
fof(mem_c_2Estring__num_2Es2n,axiom,
mem(c_2Estring__num_2Es2n,arr(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Enum_2Enum)) ).
fof(mem_c_2Estring__num_2Es2ssum,axiom,
mem(c_2Estring__num_2Es2ssum,arr(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Esum_2Esum(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Elist_2Elist(ty_2Estring_2Echar)))) ).
fof(mem_c_2Estring__num_2Essum2s,axiom,
mem(c_2Estring__num_2Essum2s,arr(ty_2Esum_2Esum(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Elist_2Elist(ty_2Estring_2Echar)),ty_2Elist_2Elist(ty_2Estring_2Echar))) ).
fof(lameq_f1823,axiom,
! [V2r0] :
( mem(V2r0,ty_2Enum_2Enum)
=> ! [V0R] :
( mem(V0R,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool)))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V3r] : ap(f1823(V2r0,V0R,V1n),V3r) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Ebool_2E_7E,ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V1n),c_2Enum_2E0))),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V2r0),ap(ap(c_2Earithmetic_2EMOD,V1n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))))))),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V3r),ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V2r0),c_2Enum_2E0)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))))),V2r0))))),ap(ap(V0R,ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2D,V1n),V3r)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))))))),V1n)) ) ) ) ).
fof(lameq_f1824,axiom,
! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V0R] :
( mem(V0R,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool)))
=> ! [V2r0] : ap(f1824(V1n,V0R),V2r0) = ap(c_2Ebool_2E_21(ty_2Enum_2Enum),f1823(V2r0,V0R,V1n)) ) ) ).
fof(lameq_f1825,axiom,
! [V0R] :
( mem(V0R,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool)))
=> ! [V1n] : ap(f1825(V0R),V1n) = ap(c_2Ebool_2E_21(ty_2Enum_2Enum),f1824(V1n,V0R)) ) ).
fof(lameq_f1826,axiom,
! [V0R] : ap(f1826,V0R) = ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Erelation_2EWF(ty_2Enum_2Enum),V0R)),ap(c_2Ebool_2E_21(ty_2Enum_2Enum),f1825(V0R))) ).
fof(lameq_f1827,axiom,
! [V7r] :
( mem(V7r,ty_2Enum_2Enum)
=> ! [V8s0] : ap(f1827(V7r),V8s0) = ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),ap(c_2Estring_2ECHR,ap(ap(c_2Earithmetic_2E_2D,V7r),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),V8s0) ) ).
fof(lameq_f1828,axiom,
! [V4n2s] :
( mem(V4n2s,arr(ty_2Enum_2Enum,ty_2Elist_2Elist(ty_2Estring_2Echar)))
=> ! [V5a] :
( mem(V5a,ty_2Enum_2Enum)
=> ! [V7r] : ap(f1828(V4n2s,V5a),V7r) = ap(ap(c_2Ebool_2ELET(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Elist_2Elist(ty_2Estring_2Echar)),f1827(V7r)),ap(V4n2s,ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2D,V5a),V7r)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))))))) ) ) ).
fof(lameq_f1829,axiom,
! [V4n2s] :
( mem(V4n2s,arr(ty_2Enum_2Enum,ty_2Elist_2Elist(ty_2Estring_2Echar)))
=> ! [V5a] :
( mem(V5a,ty_2Enum_2Enum)
=> ! [V6r0] : ap(f1829(V4n2s,V5a),V6r0) = ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Elist_2Elist(ty_2Estring_2Echar)),f1828(V4n2s,V5a)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V6r0),c_2Enum_2E0)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))))),V6r0)) ) ) ).
fof(lameq_f1830,axiom,
! [V4n2s] :
( mem(V4n2s,arr(ty_2Enum_2Enum,ty_2Elist_2Elist(ty_2Estring_2Echar)))
=> ! [V5a] : ap(f1830(V4n2s),V5a) = ap(c_2Ecombin_2EI(ty_2Elist_2Elist(ty_2Estring_2Echar)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(ty_2Estring_2Echar)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V5a),c_2Enum_2E0)),c_2Elist_2ENIL(ty_2Estring_2Echar)),ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Elist_2Elist(ty_2Estring_2Echar)),f1829(V4n2s,V5a)),ap(ap(c_2Earithmetic_2EMOD,V5a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))))))))) ) ).
fof(lameq_f1831,axiom,
! [V4n2s] : ap(f1831,V4n2s) = f1830(V4n2s) ).
fof(ax_thm_2Estring__num_2En2s__primitive__def,axiom,
c_2Estring__num_2En2s = ap(ap(c_2Erelation_2EWFREC(ty_2Enum_2Enum,ty_2Elist_2Elist(ty_2Estring_2Echar)),ap(c_2Emin_2E_40(arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool))),f1826)),f1831) ).
fof(conj_thm_2Estring__num_2En2s__ind,axiom,
! [V0P] :
( mem(V0P,arr(ty_2Enum_2Enum,bool))
=> ( ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( ! [V2r0] :
( mem(V2r0,ty_2Enum_2Enum)
=> ! [V3r] :
( mem(V3r,ty_2Enum_2Enum)
=> ( ( V1n != c_2Enum_2E0
& V2r0 = ap(ap(c_2Earithmetic_2EMOD,V1n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))))))
& V3r = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V2r0),c_2Enum_2E0)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))))),V2r0) )
=> p(ap(V0P,ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2D,V1n),V3r)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))))))) ) ) )
=> p(ap(V0P,V1n)) ) )
=> ! [V4v] :
( mem(V4v,ty_2Enum_2Enum)
=> p(ap(V0P,V4v)) ) ) ) ).
fof(lameq_f1832,axiom,
! [V2r] :
( mem(V2r,ty_2Enum_2Enum)
=> ! [V3s0] : ap(f1832(V2r),V3s0) = ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),ap(c_2Estring_2ECHR,ap(ap(c_2Earithmetic_2E_2D,V2r),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),V3s0) ) ).
fof(lameq_f1833,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V2r] : ap(f1833(V0n),V2r) = ap(ap(c_2Ebool_2ELET(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Elist_2Elist(ty_2Estring_2Echar)),f1832(V2r)),ap(c_2Estring__num_2En2s,ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2D,V0n),V2r)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))))))) ) ).
fof(lameq_f1834,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1r0] : ap(f1834(V0n),V1r0) = ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Elist_2Elist(ty_2Estring_2Echar)),f1833(V0n)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V1r0),c_2Enum_2E0)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))))),V1r0)) ) ).
fof(conj_thm_2Estring__num_2En2s__def,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(c_2Estring__num_2En2s,V0n) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(ty_2Estring_2Echar)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V0n),c_2Enum_2E0)),c_2Elist_2ENIL(ty_2Estring_2Echar)),ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Elist_2Elist(ty_2Estring_2Echar)),f1834(V0n)),ap(ap(c_2Earithmetic_2EMOD,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))))))) ) ).
fof(ax_thm_2Estring__num_2Es2n__def,axiom,
( ap(c_2Estring__num_2Es2n,c_2Elist_2ENIL(ty_2Estring_2Echar)) = c_2Enum_2E0
& ! [V0c] :
( mem(V0c,ty_2Estring_2Echar)
=> ! [V1s] :
( mem(V1s,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ap(c_2Estring__num_2Es2n,ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),V0c),V1s)) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Estring__num_2Es2n,V1s)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))))))),ap(c_2Estring_2EORD,V0c))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) ) ) ).
fof(conj_thm_2Estring__num_2Es2n__n2s,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(c_2Estring__num_2Es2n,ap(c_2Estring__num_2En2s,V0n)) = V0n ) ).
fof(conj_thm_2Estring__num_2En2s__s2n,axiom,
! [V0s] :
( mem(V0s,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ap(c_2Estring__num_2En2s,ap(c_2Estring__num_2Es2n,V0s)) = V0s ) ).
fof(conj_thm_2Estring__num_2En2s__11,axiom,
! [V0x] :
( mem(V0x,ty_2Enum_2Enum)
=> ! [V1y] :
( mem(V1y,ty_2Enum_2Enum)
=> ( ap(c_2Estring__num_2En2s,V0x) = ap(c_2Estring__num_2En2s,V1y)
<=> V0x = V1y ) ) ) ).
fof(conj_thm_2Estring__num_2Es2n__11,axiom,
! [V0x] :
( mem(V0x,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ! [V1y] :
( mem(V1y,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ( ap(c_2Estring__num_2Es2n,V0x) = ap(c_2Estring__num_2Es2n,V1y)
<=> V0x = V1y ) ) ) ).
fof(conj_thm_2Estring__num_2En2s__onto,axiom,
! [V0s] :
( mem(V0s,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ? [V1n] :
( mem(V1n,ty_2Enum_2Enum)
& V0s = ap(c_2Estring__num_2En2s,V1n) ) ) ).
fof(conj_thm_2Estring__num_2Es2n__onto,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ? [V1s] :
( mem(V1s,ty_2Elist_2Elist(ty_2Estring_2Echar))
& V0n = ap(c_2Estring__num_2Es2n,V1s) ) ) ).
fof(ax_thm_2Estring__num_2En2nsum__def,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(c_2Estring__num_2En2nsum,V0n) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Esum_2Esum(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(c_2Earithmetic_2EODD,V0n)),ap(c_2Esum_2EINL(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2EDIV,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))),ap(c_2Esum_2EINR(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2EDIV,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))) ) ).
fof(ax_thm_2Estring__num_2Ensum2n__def,axiom,
( ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(c_2Estring__num_2Ensum2n,ap(c_2Esum_2EINL(ty_2Enum_2Enum,ty_2Enum_2Enum),V0n)) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) )
& ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(c_2Estring__num_2Ensum2n,ap(c_2Esum_2EINR(ty_2Enum_2Enum,ty_2Enum_2Enum),V1n)) = ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1n) ) ) ).
fof(conj_thm_2Estring__num_2En2nsum__nsum2n,axiom,
! [V0ns] :
( mem(V0ns,ty_2Esum_2Esum(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ap(c_2Estring__num_2En2nsum,ap(c_2Estring__num_2Ensum2n,V0ns)) = V0ns ) ).
fof(conj_thm_2Estring__num_2Ensum2n__n2nsum,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(c_2Estring__num_2Ensum2n,ap(c_2Estring__num_2En2nsum,V0n)) = V0n ) ).
fof(ax_thm_2Estring__num_2Es2ssum__def,axiom,
! [V0s] :
( mem(V0s,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ap(c_2Estring__num_2Es2ssum,V0s) = ap(ap(ap(c_2Esum_2E_2B_2B(ty_2Enum_2Enum,ty_2Enum_2Enum,ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Elist_2Elist(ty_2Estring_2Echar)),c_2Estring__num_2En2s),c_2Estring__num_2En2s),ap(c_2Estring__num_2En2nsum,ap(c_2Estring__num_2Es2n,V0s))) ) ).
fof(ax_thm_2Estring__num_2Essum2s__def,axiom,
! [V0sm] :
( mem(V0sm,ty_2Esum_2Esum(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Elist_2Elist(ty_2Estring_2Echar)))
=> ap(c_2Estring__num_2Essum2s,V0sm) = ap(c_2Estring__num_2En2s,ap(c_2Estring__num_2Ensum2n,ap(ap(ap(c_2Esum_2E_2B_2B(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Estring__num_2Es2n),c_2Estring__num_2Es2n),V0sm))) ) ).
fof(conj_thm_2Estring__num_2Es2ssum__ssum2s,axiom,
! [V0sm] :
( mem(V0sm,ty_2Esum_2Esum(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Elist_2Elist(ty_2Estring_2Echar)))
=> ap(c_2Estring__num_2Es2ssum,ap(c_2Estring__num_2Essum2s,V0sm)) = V0sm ) ).
fof(conj_thm_2Estring__num_2Essum2s__s2ssum,axiom,
! [V0s] :
( mem(V0s,ty_2Elist_2Elist(ty_2Estring_2Echar))
=> ap(c_2Estring__num_2Essum2s,ap(c_2Estring__num_2Es2ssum,V0s)) = V0s ) ).
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