ITP001 Axioms: ITP007+4.ax


%------------------------------------------------------------------------------
% File     : ITP007+4 : TPTP v9.0.0. Bugfixed v7.5.0.
% Domain   : Interactive Theorem Proving
% Axioms   : HOL4 syntactic export, chainy mode
% Version  : [BG+19] axioms.
% English  :

% Refs     : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
%          : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source   : [BG+19]
% Names    : sat.ax [Gau19]
%          : HL4007+4.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   47 (   8 unt;   0 def)
%            Number of atoms       :  176 (  17 equ)
%            Maximal formula atoms :   16 (   3 avg)
%            Number of connectives :  183 (  54   ~;  41   |;  21   &)
%                                         (  31 <=>;  36  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Maximal term depth    :   11 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :   25 (  25 usr;  14 con; 0-3 aty)
%            Number of variables   :  100 (  99   !;   1   ?)
% SPC      : FOF_SAT_RFO_SEQ

% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
fof(reserved_2Eho_2Eboolext,axiom,
    ! [V0_2E0,V1_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,V0_2E0))
      <=> p(s(tyop_2Emin_2Ebool,V1_2E0)) )
     => s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0) ) ).

fof(reserved_2Eho_2Etruth,axiom,
    p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ).

fof(reserved_2Eho_2Enotfalse,axiom,
    ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) ).

fof(reserved_2Eho_2Ebool__cases__ax,axiom,
    ! [V0t_2E0] :
      ( s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
      | s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ).

fof(reserved_2Eho_2Ei__thm,axiom,
    ! [A_27a,V0x_2E0] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0))) = s(A_27a,V0x_2E0) ).

fof(reserved_2Eho_2Ek__thm,axiom,
    ! [A_27a,A_27b,V0x_2E0,V1y_2E0] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0))) = s(A_27a,V0x_2E0) ).

fof(reserved_2Eho_2Es__thm,axiom,
    ! [A_27a,A_27b,A_27c,V0f_2E0,V1g_2E0,V2x_2E0] : s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))))) ).

fof(reserved_2Elogic_2E_2F_5C,axiom,
    ! [V0_2E0,V1_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0))))
    <=> ( p(s(tyop_2Emin_2Ebool,V0_2E0))
        & p(s(tyop_2Emin_2Ebool,V1_2E0)) ) ) ).

fof(reserved_2Elogic_2E_5C_2F,axiom,
    ! [V0_2E0,V1_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0))))
    <=> ( p(s(tyop_2Emin_2Ebool,V0_2E0))
        | p(s(tyop_2Emin_2Ebool,V1_2E0)) ) ) ).

fof(reserved_2Elogic_2E_7E,axiom,
    ! [V0_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0))))
    <=> ~ p(s(tyop_2Emin_2Ebool,V0_2E0)) ) ).

fof(reserved_2Elogic_2E_3D_3D_3E,axiom,
    ! [V0_2E0,V1_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0))))
    <=> ( p(s(tyop_2Emin_2Ebool,V0_2E0))
       => p(s(tyop_2Emin_2Ebool,V1_2E0)) ) ) ).

fof(reserved_2Elogic_2E_3D,axiom,
    ! [A_27a,V0_2E0,V1_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0))))
    <=> s(A_27a,V0_2E0) = s(A_27a,V1_2E0) ) ).

fof(reserved_2Equant_2E_21,axiom,
    ! [A_27a,V0f_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0))))
    <=> ! [V1x_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0)))) ) ).

fof(reserved_2Equant_2E_3F,axiom,
    ! [A_27a,V0f_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0))))
    <=> ? [V1x_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0)))) ) ).

fof(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
    ! [X0_2E0,X1_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,X0_2E0))
        & p(s(tyop_2Emin_2Ebool,X1_2E0)) )
    <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) ) ).

fof(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,
    ! [X0_2E0,X1_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,X0_2E0))
        | p(s(tyop_2Emin_2Ebool,X1_2E0)) )
    <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) ) ).

fof(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,
    ! [X0_2E0] :
      ( ~ p(s(tyop_2Emin_2Ebool,X0_2E0))
    <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))) ) ).

fof(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
    ! [X0_2E0,X1_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,X0_2E0))
       => p(s(tyop_2Emin_2Ebool,X1_2E0)) )
    <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) ) ).

fof(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] :
      ( s(A_27a,X0_2E0) = s(A_27a,X1_2E0)
    <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))) ) ).

fof(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) ).

fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0),s(tyop_2Emin_2Ebool,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))),s(tyop_2Emin_2Ebool,X2_2E0))) ).

fof(thm_2Esat_2EAND__IMP,axiom,
    ! [V0A_2E0,V1B_2E0,V2C_2E0] :
      ( ( ( p(s(tyop_2Emin_2Ebool,V0A_2E0))
          & p(s(tyop_2Emin_2Ebool,V1B_2E0)) )
       => p(s(tyop_2Emin_2Ebool,V2C_2E0)) )
    <=> ( p(s(tyop_2Emin_2Ebool,V0A_2E0))
       => ( p(s(tyop_2Emin_2Ebool,V1B_2E0))
         => p(s(tyop_2Emin_2Ebool,V2C_2E0)) ) ) ) ).

fof(thm_2Esat_2ENOT__NOT,axiom,
    ! [V0t_2E0] :
      ( ~ ~ p(s(tyop_2Emin_2Ebool,V0t_2E0))
    <=> p(s(tyop_2Emin_2Ebool,V0t_2E0)) ) ).

fof(thm_2Esat_2EAND__INV,axiom,
    ! [V0A_2E0] :
      ( ( ~ p(s(tyop_2Emin_2Ebool,V0A_2E0))
        & p(s(tyop_2Emin_2Ebool,V0A_2E0)) )
    <=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) ) ).

fof(thm_2Esat_2EAND__INV__IMP,axiom,
    ! [V0A_2E0] :
      ( p(s(tyop_2Emin_2Ebool,V0A_2E0))
     => ( ~ p(s(tyop_2Emin_2Ebool,V0A_2E0))
       => p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) ) ) ).

fof(thm_2Esat_2EOR__DUAL,axiom,
    ! [V0B_2E0,V1A_2E0] :
      ( ( ~ ( p(s(tyop_2Emin_2Ebool,V1A_2E0))
            | p(s(tyop_2Emin_2Ebool,V0B_2E0)) )
       => p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) )
    <=> ( ~ p(s(tyop_2Emin_2Ebool,V1A_2E0))
       => ( ~ p(s(tyop_2Emin_2Ebool,V0B_2E0))
         => p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) ) ) ) ).

fof(thm_2Esat_2EOR__DUAL2,axiom,
    ! [V0B_2E0,V1A_2E0] :
      ( ( ~ ( p(s(tyop_2Emin_2Ebool,V1A_2E0))
            | p(s(tyop_2Emin_2Ebool,V0B_2E0)) )
       => p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) )
    <=> ( ( p(s(tyop_2Emin_2Ebool,V1A_2E0))
         => p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) )
       => ( ~ p(s(tyop_2Emin_2Ebool,V0B_2E0))
         => p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) ) ) ) ).

fof(thm_2Esat_2EOR__DUAL3,axiom,
    ! [V0B_2E0,V1A_2E0] :
      ( ( ~ ( ~ p(s(tyop_2Emin_2Ebool,V1A_2E0))
            | p(s(tyop_2Emin_2Ebool,V0B_2E0)) )
       => p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) )
    <=> ( p(s(tyop_2Emin_2Ebool,V1A_2E0))
       => ( ~ p(s(tyop_2Emin_2Ebool,V0B_2E0))
         => p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) ) ) ) ).

fof(thm_2Esat_2EAND__INV2,axiom,
    ! [V0A_2E0] :
      ( ( ~ p(s(tyop_2Emin_2Ebool,V0A_2E0))
       => p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) )
     => ( ( p(s(tyop_2Emin_2Ebool,V0A_2E0))
         => p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) )
       => p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) ) ) ).

fof(thm_2Esat_2ENOT__ELIM2,axiom,
    ! [V0A_2E0] :
      ( ( ~ p(s(tyop_2Emin_2Ebool,V0A_2E0))
       => p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) )
    <=> p(s(tyop_2Emin_2Ebool,V0A_2E0)) ) ).

fof(thm_2Esat_2EEQT__Imp1,axiom,
    ! [V0b_2E0] :
      ( p(s(tyop_2Emin_2Ebool,V0b_2E0))
     => s(tyop_2Emin_2Ebool,V0b_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ) ).

fof(thm_2Esat_2EEQF__Imp1,axiom,
    ! [V0t_2E0] :
      ( ~ p(s(tyop_2Emin_2Ebool,V0t_2E0))
     => s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ).

fof(thm_2Esat_2Edc__eq,axiom,
    ! [V0r_2E0,V1q_2E0,V2p_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,V2p_2E0))
      <=> s(tyop_2Emin_2Ebool,V1q_2E0) = s(tyop_2Emin_2Ebool,V0r_2E0) )
    <=> ( ( p(s(tyop_2Emin_2Ebool,V2p_2E0))
          | p(s(tyop_2Emin_2Ebool,V1q_2E0))
          | p(s(tyop_2Emin_2Ebool,V0r_2E0)) )
        & ( p(s(tyop_2Emin_2Ebool,V2p_2E0))
          | ~ p(s(tyop_2Emin_2Ebool,V0r_2E0))
          | ~ p(s(tyop_2Emin_2Ebool,V1q_2E0)) )
        & ( p(s(tyop_2Emin_2Ebool,V1q_2E0))
          | ~ p(s(tyop_2Emin_2Ebool,V0r_2E0))
          | ~ p(s(tyop_2Emin_2Ebool,V2p_2E0)) )
        & ( p(s(tyop_2Emin_2Ebool,V0r_2E0))
          | ~ p(s(tyop_2Emin_2Ebool,V1q_2E0))
          | ~ p(s(tyop_2Emin_2Ebool,V2p_2E0)) ) ) ) ).

fof(thm_2Esat_2Edc__conj,axiom,
    ! [V0r_2E0,V1q_2E0,V2p_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,V2p_2E0))
      <=> ( p(s(tyop_2Emin_2Ebool,V1q_2E0))
          & p(s(tyop_2Emin_2Ebool,V0r_2E0)) ) )
    <=> ( ( p(s(tyop_2Emin_2Ebool,V2p_2E0))
          | ~ p(s(tyop_2Emin_2Ebool,V1q_2E0))
          | ~ p(s(tyop_2Emin_2Ebool,V0r_2E0)) )
        & ( p(s(tyop_2Emin_2Ebool,V1q_2E0))
          | ~ p(s(tyop_2Emin_2Ebool,V2p_2E0)) )
        & ( p(s(tyop_2Emin_2Ebool,V0r_2E0))
          | ~ p(s(tyop_2Emin_2Ebool,V2p_2E0)) ) ) ) ).

fof(thm_2Esat_2Edc__disj,axiom,
    ! [V0r_2E0,V1q_2E0,V2p_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,V2p_2E0))
      <=> ( p(s(tyop_2Emin_2Ebool,V1q_2E0))
          | p(s(tyop_2Emin_2Ebool,V0r_2E0)) ) )
    <=> ( ( p(s(tyop_2Emin_2Ebool,V2p_2E0))
          | ~ p(s(tyop_2Emin_2Ebool,V1q_2E0)) )
        & ( p(s(tyop_2Emin_2Ebool,V2p_2E0))
          | ~ p(s(tyop_2Emin_2Ebool,V0r_2E0)) )
        & ( p(s(tyop_2Emin_2Ebool,V1q_2E0))
          | p(s(tyop_2Emin_2Ebool,V0r_2E0))
          | ~ p(s(tyop_2Emin_2Ebool,V2p_2E0)) ) ) ) ).

fof(thm_2Esat_2Edc__imp,axiom,
    ! [V0r_2E0,V1q_2E0,V2p_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,V2p_2E0))
      <=> ( p(s(tyop_2Emin_2Ebool,V1q_2E0))
         => p(s(tyop_2Emin_2Ebool,V0r_2E0)) ) )
    <=> ( ( p(s(tyop_2Emin_2Ebool,V2p_2E0))
          | p(s(tyop_2Emin_2Ebool,V1q_2E0)) )
        & ( p(s(tyop_2Emin_2Ebool,V2p_2E0))
          | ~ p(s(tyop_2Emin_2Ebool,V0r_2E0)) )
        & ( ~ p(s(tyop_2Emin_2Ebool,V1q_2E0))
          | p(s(tyop_2Emin_2Ebool,V0r_2E0))
          | ~ p(s(tyop_2Emin_2Ebool,V2p_2E0)) ) ) ) ).

fof(thm_2Esat_2Edc__neg,axiom,
    ! [V0q_2E0,V1p_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,V1p_2E0))
      <=> ~ p(s(tyop_2Emin_2Ebool,V0q_2E0)) )
    <=> ( ( p(s(tyop_2Emin_2Ebool,V1p_2E0))
          | p(s(tyop_2Emin_2Ebool,V0q_2E0)) )
        & ( ~ p(s(tyop_2Emin_2Ebool,V0q_2E0))
          | ~ p(s(tyop_2Emin_2Ebool,V1p_2E0)) ) ) ) ).

fof(thm_2Esat_2Edc__cond,axiom,
    ! [V0s_2E0,V1r_2E0,V2q_2E0,V3p_2E0] :
      ( s(tyop_2Emin_2Ebool,V3p_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V2q_2E0),s(tyop_2Emin_2Ebool,V1r_2E0),s(tyop_2Emin_2Ebool,V0s_2E0)))
    <=> ( ( p(s(tyop_2Emin_2Ebool,V3p_2E0))
          | p(s(tyop_2Emin_2Ebool,V2q_2E0))
          | ~ p(s(tyop_2Emin_2Ebool,V0s_2E0)) )
        & ( p(s(tyop_2Emin_2Ebool,V3p_2E0))
          | ~ p(s(tyop_2Emin_2Ebool,V1r_2E0))
          | ~ p(s(tyop_2Emin_2Ebool,V2q_2E0)) )
        & ( p(s(tyop_2Emin_2Ebool,V3p_2E0))
          | ~ p(s(tyop_2Emin_2Ebool,V1r_2E0))
          | ~ p(s(tyop_2Emin_2Ebool,V0s_2E0)) )
        & ( ~ p(s(tyop_2Emin_2Ebool,V2q_2E0))
          | p(s(tyop_2Emin_2Ebool,V1r_2E0))
          | ~ p(s(tyop_2Emin_2Ebool,V3p_2E0)) )
        & ( p(s(tyop_2Emin_2Ebool,V2q_2E0))
          | p(s(tyop_2Emin_2Ebool,V0s_2E0))
          | ~ p(s(tyop_2Emin_2Ebool,V3p_2E0)) ) ) ) ).

fof(thm_2Esat_2Epth__ni1,axiom,
    ! [V0q_2E0,V1p_2E0] :
      ( ~ ( p(s(tyop_2Emin_2Ebool,V1p_2E0))
         => p(s(tyop_2Emin_2Ebool,V0q_2E0)) )
     => p(s(tyop_2Emin_2Ebool,V1p_2E0)) ) ).

fof(thm_2Esat_2Epth__ni2,axiom,
    ! [V0q_2E0,V1p_2E0] :
      ( ~ ( p(s(tyop_2Emin_2Ebool,V1p_2E0))
         => p(s(tyop_2Emin_2Ebool,V0q_2E0)) )
     => ~ p(s(tyop_2Emin_2Ebool,V0q_2E0)) ) ).

fof(thm_2Esat_2Epth__no1,axiom,
    ! [V0q_2E0,V1p_2E0] :
      ( ~ ( p(s(tyop_2Emin_2Ebool,V1p_2E0))
          | p(s(tyop_2Emin_2Ebool,V0q_2E0)) )
     => ~ p(s(tyop_2Emin_2Ebool,V1p_2E0)) ) ).

fof(thm_2Esat_2Epth__no2,axiom,
    ! [V0q_2E0,V1p_2E0] :
      ( ~ ( p(s(tyop_2Emin_2Ebool,V1p_2E0))
          | p(s(tyop_2Emin_2Ebool,V0q_2E0)) )
     => ~ p(s(tyop_2Emin_2Ebool,V0q_2E0)) ) ).

fof(thm_2Esat_2Epth__an1,axiom,
    ! [V0q_2E0,V1p_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,V1p_2E0))
        & p(s(tyop_2Emin_2Ebool,V0q_2E0)) )
     => p(s(tyop_2Emin_2Ebool,V1p_2E0)) ) ).

fof(thm_2Esat_2Epth__an2,axiom,
    ! [V0q_2E0,V1p_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,V1p_2E0))
        & p(s(tyop_2Emin_2Ebool,V0q_2E0)) )
     => p(s(tyop_2Emin_2Ebool,V0q_2E0)) ) ).

fof(thm_2Esat_2Epth__nn,axiom,
    ! [V0p_2E0] :
      ( ~ ~ p(s(tyop_2Emin_2Ebool,V0p_2E0))
     => p(s(tyop_2Emin_2Ebool,V0p_2E0)) ) ).

fof(reserved_2Eho_2Eeq__ext,axiom,
    ! [A_27a,A_27b,V0f_2E0,V1g_2E0] :
      ( ! [V2x_2E0] : s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))
     => s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0) ) ).

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