ITP001 Axioms: ITP007+5.ax


%------------------------------------------------------------------------------
% File     : ITP007+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    : sat+2.ax [Gau20]
%          : HL4007+5.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   24 (   0 unt;   0 def)
%            Number of atoms       :  182 (   0 equ)
%            Maximal formula atoms :   21 (   7 avg)
%            Number of connectives :  209 (  51   ~;  38   |;  19   &)
%                                         (  22 <=>;  79  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   9 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   2 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   1 con; 0-2 aty)
%            Number of variables   :   47 (  47   !;   0   ?)
% SPC      : FOF_SAT_RFO_NEQ

% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
fof(conj_thm_2Esat_2EAND__IMP,axiom,
    ! [V0A] :
      ( mem(V0A,bool)
     => ! [V1B] :
          ( mem(V1B,bool)
         => ! [V2C] :
              ( mem(V2C,bool)
             => ( ( ( p(V0A)
                    & p(V1B) )
                 => p(V2C) )
              <=> ( p(V0A)
                 => ( p(V1B)
                   => p(V2C) ) ) ) ) ) ) ).

fof(conj_thm_2Esat_2ENOT__NOT,axiom,
    ! [V0t] :
      ( mem(V0t,bool)
     => ( ~ ~ p(V0t)
      <=> p(V0t) ) ) ).

fof(conj_thm_2Esat_2EAND__INV,axiom,
    ! [V0A] :
      ( mem(V0A,bool)
     => ( ( ~ p(V0A)
          & p(V0A) )
      <=> $false ) ) ).

fof(conj_thm_2Esat_2EAND__INV__IMP,axiom,
    ! [V0A] :
      ( mem(V0A,bool)
     => ( p(V0A)
       => ( ~ p(V0A)
         => $false ) ) ) ).

fof(conj_thm_2Esat_2EOR__DUAL,axiom,
    ! [V0A] :
      ( mem(V0A,bool)
     => ! [V1B] :
          ( mem(V1B,bool)
         => ( ( ~ ( p(V0A)
                  | p(V1B) )
             => $false )
          <=> ( ~ p(V0A)
             => ( ~ p(V1B)
               => $false ) ) ) ) ) ).

fof(conj_thm_2Esat_2EOR__DUAL2,axiom,
    ! [V0A] :
      ( mem(V0A,bool)
     => ! [V1B] :
          ( mem(V1B,bool)
         => ( ( ~ ( p(V0A)
                  | p(V1B) )
             => $false )
          <=> ( ( p(V0A)
               => $false )
             => ( ~ p(V1B)
               => $false ) ) ) ) ) ).

fof(conj_thm_2Esat_2EOR__DUAL3,axiom,
    ! [V0A] :
      ( mem(V0A,bool)
     => ! [V1B] :
          ( mem(V1B,bool)
         => ( ( ~ ( ~ p(V0A)
                  | p(V1B) )
             => $false )
          <=> ( p(V0A)
             => ( ~ p(V1B)
               => $false ) ) ) ) ) ).

fof(conj_thm_2Esat_2EAND__INV2,axiom,
    ! [V0A] :
      ( mem(V0A,bool)
     => ( ( ~ p(V0A)
         => $false )
       => ( ( p(V0A)
           => $false )
         => $false ) ) ) ).

fof(conj_thm_2Esat_2ENOT__ELIM2,axiom,
    ! [V0A] :
      ( mem(V0A,bool)
     => ( ( ~ p(V0A)
         => $false )
      <=> p(V0A) ) ) ).

fof(conj_thm_2Esat_2EEQT__Imp1,axiom,
    ! [V0b] :
      ( mem(V0b,bool)
     => ( p(V0b)
       => ( p(V0b)
        <=> $true ) ) ) ).

fof(conj_thm_2Esat_2EEQF__Imp1,axiom,
    ! [V0b] :
      ( mem(V0b,bool)
     => ( ~ p(V0b)
       => ( p(V0b)
        <=> $false ) ) ) ).

fof(conj_thm_2Esat_2Edc__eq,axiom,
    ! [V0p] :
      ( mem(V0p,bool)
     => ! [V1q] :
          ( mem(V1q,bool)
         => ! [V2r] :
              ( mem(V2r,bool)
             => ( ( p(V0p)
                <=> ( p(V1q)
                  <=> p(V2r) ) )
              <=> ( ( p(V0p)
                    | p(V1q)
                    | p(V2r) )
                  & ( p(V0p)
                    | ~ p(V2r)
                    | ~ p(V1q) )
                  & ( p(V1q)
                    | ~ p(V2r)
                    | ~ p(V0p) )
                  & ( p(V2r)
                    | ~ p(V1q)
                    | ~ p(V0p) ) ) ) ) ) ) ).

fof(conj_thm_2Esat_2Edc__conj,axiom,
    ! [V0p] :
      ( mem(V0p,bool)
     => ! [V1q] :
          ( mem(V1q,bool)
         => ! [V2r] :
              ( mem(V2r,bool)
             => ( ( p(V0p)
                <=> ( p(V1q)
                    & p(V2r) ) )
              <=> ( ( p(V0p)
                    | ~ p(V1q)
                    | ~ p(V2r) )
                  & ( p(V1q)
                    | ~ p(V0p) )
                  & ( p(V2r)
                    | ~ p(V0p) ) ) ) ) ) ) ).

fof(conj_thm_2Esat_2Edc__disj,axiom,
    ! [V0p] :
      ( mem(V0p,bool)
     => ! [V1q] :
          ( mem(V1q,bool)
         => ! [V2r] :
              ( mem(V2r,bool)
             => ( ( p(V0p)
                <=> ( p(V1q)
                    | p(V2r) ) )
              <=> ( ( p(V0p)
                    | ~ p(V1q) )
                  & ( p(V0p)
                    | ~ p(V2r) )
                  & ( p(V1q)
                    | p(V2r)
                    | ~ p(V0p) ) ) ) ) ) ) ).

fof(conj_thm_2Esat_2Edc__imp,axiom,
    ! [V0p] :
      ( mem(V0p,bool)
     => ! [V1q] :
          ( mem(V1q,bool)
         => ! [V2r] :
              ( mem(V2r,bool)
             => ( ( p(V0p)
                <=> ( p(V1q)
                   => p(V2r) ) )
              <=> ( ( p(V0p)
                    | p(V1q) )
                  & ( p(V0p)
                    | ~ p(V2r) )
                  & ( ~ p(V1q)
                    | p(V2r)
                    | ~ p(V0p) ) ) ) ) ) ) ).

fof(conj_thm_2Esat_2Edc__neg,axiom,
    ! [V0p] :
      ( mem(V0p,bool)
     => ! [V1q] :
          ( mem(V1q,bool)
         => ( ( p(V0p)
            <=> ~ p(V1q) )
          <=> ( ( p(V0p)
                | p(V1q) )
              & ( ~ p(V1q)
                | ~ p(V0p) ) ) ) ) ) ).

fof(conj_thm_2Esat_2Edc__cond,axiom,
    ! [V0p] :
      ( mem(V0p,bool)
     => ! [V1q] :
          ( mem(V1q,bool)
         => ! [V2r] :
              ( mem(V2r,bool)
             => ! [V3s] :
                  ( mem(V3s,bool)
                 => ( ( p(V0p)
                    <=> p(ap(ap(ap(c_2Ebool_2ECOND(bool),V1q),V2r),V3s)) )
                  <=> ( ( p(V0p)
                        | p(V1q)
                        | ~ p(V3s) )
                      & ( p(V0p)
                        | ~ p(V2r)
                        | ~ p(V1q) )
                      & ( p(V0p)
                        | ~ p(V2r)
                        | ~ p(V3s) )
                      & ( ~ p(V1q)
                        | p(V2r)
                        | ~ p(V0p) )
                      & ( p(V1q)
                        | p(V3s)
                        | ~ p(V0p) ) ) ) ) ) ) ) ).

fof(conj_thm_2Esat_2Epth__ni1,axiom,
    ! [V0p] :
      ( mem(V0p,bool)
     => ! [V1q] :
          ( mem(V1q,bool)
         => ( ~ ( p(V0p)
               => p(V1q) )
           => p(V0p) ) ) ) ).

fof(conj_thm_2Esat_2Epth__ni2,axiom,
    ! [V0p] :
      ( mem(V0p,bool)
     => ! [V1q] :
          ( mem(V1q,bool)
         => ( ~ ( p(V0p)
               => p(V1q) )
           => ~ p(V1q) ) ) ) ).

fof(conj_thm_2Esat_2Epth__no1,axiom,
    ! [V0p] :
      ( mem(V0p,bool)
     => ! [V1q] :
          ( mem(V1q,bool)
         => ( ~ ( p(V0p)
                | p(V1q) )
           => ~ p(V0p) ) ) ) ).

fof(conj_thm_2Esat_2Epth__no2,axiom,
    ! [V0p] :
      ( mem(V0p,bool)
     => ! [V1q] :
          ( mem(V1q,bool)
         => ( ~ ( p(V0p)
                | p(V1q) )
           => ~ p(V1q) ) ) ) ).

fof(conj_thm_2Esat_2Epth__an1,axiom,
    ! [V0p] :
      ( mem(V0p,bool)
     => ! [V1q] :
          ( mem(V1q,bool)
         => ( ( p(V0p)
              & p(V1q) )
           => p(V0p) ) ) ) ).

fof(conj_thm_2Esat_2Epth__an2,axiom,
    ! [V0p] :
      ( mem(V0p,bool)
     => ! [V1q] :
          ( mem(V1q,bool)
         => ( ( p(V0p)
              & p(V1q) )
           => p(V1q) ) ) ) ).

fof(conj_thm_2Esat_2Epth__nn,axiom,
    ! [V0p] :
      ( mem(V0p,bool)
     => ( ~ ~ p(V0p)
       => p(V0p) ) ) ).

%------------------------------------------------------------------------------