ITP001 Axioms: ITP005+5.ax


%------------------------------------------------------------------------------
% File     : ITP005+5 : TPTP v9.0.0. 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    : marker+2.ax [Gau20]
%          : HL4005+5.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   18 (   5 unt;   0 def)
%            Number of atoms       :  108 (   2 equ)
%            Maximal formula atoms :   19 (   6 avg)
%            Number of connectives :   90 (   0   ~;  20   |;  29   &)
%                                         (  17 <=>;  24  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   7 con; 0-2 aty)
%            Number of variables   :   24 (  24   !;   0   ?)
% SPC      : FOF_SAT_RFO_SEQ

% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
fof(mem_c_2Emarker_2E_3A_2D,axiom,
    mem(c_2Emarker_2E_3A_2D,arr(ind,arr(bool,bool))) ).

fof(mem_c_2Emarker_2EAC,axiom,
    mem(c_2Emarker_2EAC,arr(bool,arr(bool,bool))) ).

fof(mem_c_2Emarker_2EAbbrev,axiom,
    mem(c_2Emarker_2EAbbrev,arr(bool,bool)) ).

fof(mem_c_2Emarker_2ECong,axiom,
    mem(c_2Emarker_2ECong,arr(bool,bool)) ).

fof(mem_c_2Emarker_2EIfCases,axiom,
    mem(c_2Emarker_2EIfCases,bool) ).

fof(mem_c_2Emarker_2Estmarker,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => mem(c_2Emarker_2Estmarker(A_27a),arr(A_27a,A_27a)) ) ).

fof(mem_c_2Emarker_2Eunint,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => mem(c_2Emarker_2Eunint(A_27a),arr(A_27a,A_27a)) ) ).

fof(ax_thm_2Emarker_2Estmarker__def,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => ! [V0x] :
          ( mem(V0x,A_27a)
         => ap(c_2Emarker_2Estmarker(A_27a),V0x) = V0x ) ) ).

fof(conj_thm_2Emarker_2Emove__left__conj,axiom,
    ! [V0p] :
      ( mem(V0p,bool)
     => ! [V1q] :
          ( mem(V1q,bool)
         => ! [V2m] :
              ( mem(V2m,bool)
             => ( ( ( p(V0p)
                    & p(ap(c_2Emarker_2Estmarker(bool),V2m)) )
                <=> ( p(ap(c_2Emarker_2Estmarker(bool),V2m))
                    & p(V0p) ) )
                & ( ( p(ap(c_2Emarker_2Estmarker(bool),V2m))
                    & p(V0p)
                    & p(V1q) )
                <=> ( p(ap(c_2Emarker_2Estmarker(bool),V2m))
                    & p(V0p)
                    & p(V1q) ) )
                & ( ( p(V0p)
                    & p(ap(c_2Emarker_2Estmarker(bool),V2m))
                    & p(V1q) )
                <=> ( p(ap(c_2Emarker_2Estmarker(bool),V2m))
                    & p(V0p)
                    & p(V1q) ) ) ) ) ) ) ).

fof(conj_thm_2Emarker_2Emove__right__conj,axiom,
    ! [V0p] :
      ( mem(V0p,bool)
     => ! [V1q] :
          ( mem(V1q,bool)
         => ! [V2m] :
              ( mem(V2m,bool)
             => ( ( ( p(ap(c_2Emarker_2Estmarker(bool),V2m))
                    & p(V0p) )
                <=> ( p(V0p)
                    & p(ap(c_2Emarker_2Estmarker(bool),V2m)) ) )
                & ( ( p(V0p)
                    & p(V1q)
                    & p(ap(c_2Emarker_2Estmarker(bool),V2m)) )
                <=> ( p(V0p)
                    & p(V1q)
                    & p(ap(c_2Emarker_2Estmarker(bool),V2m)) ) )
                & ( ( p(V0p)
                    & p(ap(c_2Emarker_2Estmarker(bool),V2m))
                    & p(V1q) )
                <=> ( p(V0p)
                    & p(V1q)
                    & p(ap(c_2Emarker_2Estmarker(bool),V2m)) ) ) ) ) ) ) ).

fof(conj_thm_2Emarker_2Emove__left__disj,axiom,
    ! [V0p] :
      ( mem(V0p,bool)
     => ! [V1q] :
          ( mem(V1q,bool)
         => ! [V2m] :
              ( mem(V2m,bool)
             => ( ( ( p(V0p)
                    | p(ap(c_2Emarker_2Estmarker(bool),V2m)) )
                <=> ( p(ap(c_2Emarker_2Estmarker(bool),V2m))
                    | p(V0p) ) )
                & ( ( p(ap(c_2Emarker_2Estmarker(bool),V2m))
                    | p(V0p)
                    | p(V1q) )
                <=> ( p(ap(c_2Emarker_2Estmarker(bool),V2m))
                    | p(V0p)
                    | p(V1q) ) )
                & ( ( p(V0p)
                    | p(ap(c_2Emarker_2Estmarker(bool),V2m))
                    | p(V1q) )
                <=> ( p(ap(c_2Emarker_2Estmarker(bool),V2m))
                    | p(V0p)
                    | p(V1q) ) ) ) ) ) ) ).

fof(conj_thm_2Emarker_2Emove__right__disj,axiom,
    ! [V0p] :
      ( mem(V0p,bool)
     => ! [V1q] :
          ( mem(V1q,bool)
         => ! [V2m] :
              ( mem(V2m,bool)
             => ( ( ( p(ap(c_2Emarker_2Estmarker(bool),V2m))
                    | p(V0p) )
                <=> ( p(V0p)
                    | p(ap(c_2Emarker_2Estmarker(bool),V2m)) ) )
                & ( ( p(V0p)
                    | p(V1q)
                    | p(ap(c_2Emarker_2Estmarker(bool),V2m)) )
                <=> ( p(V0p)
                    | p(V1q)
                    | p(ap(c_2Emarker_2Estmarker(bool),V2m)) ) )
                & ( ( p(V0p)
                    | p(ap(c_2Emarker_2Estmarker(bool),V2m))
                    | p(V1q) )
                <=> ( p(V0p)
                    | p(V1q)
                    | p(ap(c_2Emarker_2Estmarker(bool),V2m)) ) ) ) ) ) ) ).

fof(ax_thm_2Emarker_2Eunint__def,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => ! [V0x] :
          ( mem(V0x,A_27a)
         => ap(c_2Emarker_2Eunint(A_27a),V0x) = V0x ) ) ).

fof(ax_thm_2Emarker_2EAbbrev__def,axiom,
    ! [V0x] :
      ( mem(V0x,bool)
     => ( p(ap(c_2Emarker_2EAbbrev,V0x))
      <=> p(V0x) ) ) ).

fof(ax_thm_2Emarker_2EIfCases__def,axiom,
    ( p(c_2Emarker_2EIfCases)
  <=> $true ) ).

fof(ax_thm_2Emarker_2EAC__DEF,axiom,
    ! [V0b1] :
      ( mem(V0b1,bool)
     => ! [V1b2] :
          ( mem(V1b2,bool)
         => ( p(ap(ap(c_2Emarker_2EAC,V0b1),V1b2))
          <=> ( p(V0b1)
              & p(V1b2) ) ) ) ) ).

fof(ax_thm_2Emarker_2ECong__def,axiom,
    ! [V0x] :
      ( mem(V0x,bool)
     => ( p(ap(c_2Emarker_2ECong,V0x))
      <=> p(V0x) ) ) ).

fof(ax_thm_2Emarker_2Elabel__def,axiom,
    ! [V0lab] :
      ( mem(V0lab,ind)
     => ! [V1argument] :
          ( mem(V1argument,bool)
         => ( p(ap(ap(c_2Emarker_2E_3A_2D,V0lab),V1argument))
          <=> p(V1argument) ) ) ) ).

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