ITP001 Axioms: ITP004+4.ax


%------------------------------------------------------------------------------
% File     : ITP004+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    : ConseqConv.ax [Gau19]
%          : HL4004+4.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   66 (  15 unt;   0 def)
%            Number of atoms       :  217 (  22 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  168 (  17   ~;  12   |;  23   &)
%                                         (  37 <=>;  79  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :   11 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :   27 (  27 usr;  15 con; 0-3 aty)
%            Number of variables   :  152 ( 149   !;   3   ?)
% 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(arityeq2_2Ec_2EConseqConv_2EASM__MARKER_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2EConseqConv_2EASM__MARKER_2E2(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Emin_2Ebool,X1_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)),c_2EConseqConv_2EASM__MARKER_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))) ).

fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0,X2_2E0] : s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_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_2EConseqConv_2EASM__MARKER__DEF,axiom,
    ! [V0x_2E0,V1x_27_2E0] : s(tyop_2Emin_2Ebool,c_2EConseqConv_2EASM__MARKER_2E2(s(tyop_2Emin_2Ebool,V0x_2E0),s(tyop_2Emin_2Ebool,V1x_27_2E0))) = s(tyop_2Emin_2Ebool,V1x_27_2E0) ).

fof(thm_2EConseqConv_2Eforall__eq__thm,axiom,
    ! [A_27a,V0Q_2E0,V1P_2E0] :
      ( ! [V2s_2E0] : s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2s_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0Q_2E0),s(A_27a,V2s_2E0)))
     => ( ! [V3s_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V3s_2E0))))
      <=> ! [V4s_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0Q_2E0),s(A_27a,V4s_2E0)))) ) ) ).

fof(thm_2EConseqConv_2Eexists__eq__thm,axiom,
    ! [A_27a,V0Q_2E0,V1P_2E0] :
      ( ! [V2s_2E0] : s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2s_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0Q_2E0),s(A_27a,V2s_2E0)))
     => ( ? [V3s_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V3s_2E0))))
      <=> ? [V4s_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0Q_2E0),s(A_27a,V4s_2E0)))) ) ) ).

fof(thm_2EConseqConv_2Etrue__imp,axiom,
    ! [V0t_2E0] :
      ( p(s(tyop_2Emin_2Ebool,V0t_2E0))
     => p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ) ).

fof(thm_2EConseqConv_2Efalse__imp,axiom,
    ! [V0t_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))
     => p(s(tyop_2Emin_2Ebool,V0t_2E0)) ) ).

fof(thm_2EConseqConv_2ENOT__CLAUSES__X,axiom,
    ! [V0t_2E0] :
      ( ~ ~ p(s(tyop_2Emin_2Ebool,V0t_2E0))
    <=> p(s(tyop_2Emin_2Ebool,V0t_2E0)) ) ).

fof(thm_2EConseqConv_2ENOT__CLAUSES__T,axiom,
    ( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))
  <=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) ) ).

fof(thm_2EConseqConv_2ENOT__CLAUSES__F,axiom,
    ( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))
  <=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ) ).

fof(thm_2EConseqConv_2EIMP__CONG__conj__strengthen,axiom,
    ! [V0x_2E0,V1x_27_2E0,V2y_2E0,V3y_27_2E0] :
      ( ( ( p(s(tyop_2Emin_2Ebool,V2y_2E0))
         => ( p(s(tyop_2Emin_2Ebool,V1x_27_2E0))
           => p(s(tyop_2Emin_2Ebool,V0x_2E0)) ) )
        & ( p(s(tyop_2Emin_2Ebool,V1x_27_2E0))
         => ( p(s(tyop_2Emin_2Ebool,V3y_27_2E0))
           => p(s(tyop_2Emin_2Ebool,V2y_2E0)) ) ) )
     => ( ( p(s(tyop_2Emin_2Ebool,V1x_27_2E0))
          & p(s(tyop_2Emin_2Ebool,V3y_27_2E0)) )
       => ( p(s(tyop_2Emin_2Ebool,V0x_2E0))
          & p(s(tyop_2Emin_2Ebool,V2y_2E0)) ) ) ) ).

fof(thm_2EConseqConv_2EIMP__CONG__conj__weaken,axiom,
    ! [V0x_2E0,V1x_27_2E0,V2y_2E0,V3y_27_2E0] :
      ( ( ( p(s(tyop_2Emin_2Ebool,V2y_2E0))
         => ( p(s(tyop_2Emin_2Ebool,V0x_2E0))
           => p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) ) )
        & ( p(s(tyop_2Emin_2Ebool,V1x_27_2E0))
         => ( p(s(tyop_2Emin_2Ebool,V2y_2E0))
           => p(s(tyop_2Emin_2Ebool,V3y_27_2E0)) ) ) )
     => ( ( p(s(tyop_2Emin_2Ebool,V0x_2E0))
          & p(s(tyop_2Emin_2Ebool,V2y_2E0)) )
       => ( p(s(tyop_2Emin_2Ebool,V1x_27_2E0))
          & p(s(tyop_2Emin_2Ebool,V3y_27_2E0)) ) ) ) ).

fof(thm_2EConseqConv_2EAND__CLAUSES__TX,axiom,
    ! [V0t_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))
        & p(s(tyop_2Emin_2Ebool,V0t_2E0)) )
    <=> p(s(tyop_2Emin_2Ebool,V0t_2E0)) ) ).

fof(thm_2EConseqConv_2EAND__CLAUSES__XT,axiom,
    ! [V0t_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,V0t_2E0))
        & p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) )
    <=> p(s(tyop_2Emin_2Ebool,V0t_2E0)) ) ).

fof(thm_2EConseqConv_2EAND__CLAUSES__FX,axiom,
    ! [V0t_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))
        & p(s(tyop_2Emin_2Ebool,V0t_2E0)) )
    <=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) ) ).

fof(thm_2EConseqConv_2EAND__CLAUSES__XF,axiom,
    ! [V0t_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,V0t_2E0))
        & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) )
    <=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) ) ).

fof(thm_2EConseqConv_2EAND__CLAUSES__XX,axiom,
    ! [V0t_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,V0t_2E0))
        & p(s(tyop_2Emin_2Ebool,V0t_2E0)) )
    <=> p(s(tyop_2Emin_2Ebool,V0t_2E0)) ) ).

fof(thm_2EConseqConv_2EIMP__CONG__disj__strengthen,axiom,
    ! [V0x_2E0,V1x_27_2E0,V2y_2E0,V3y_27_2E0] :
      ( ( ( ~ p(s(tyop_2Emin_2Ebool,V2y_2E0))
         => ( p(s(tyop_2Emin_2Ebool,V1x_27_2E0))
           => p(s(tyop_2Emin_2Ebool,V0x_2E0)) ) )
        & ( ~ p(s(tyop_2Emin_2Ebool,V1x_27_2E0))
         => ( p(s(tyop_2Emin_2Ebool,V3y_27_2E0))
           => p(s(tyop_2Emin_2Ebool,V2y_2E0)) ) ) )
     => ( ( p(s(tyop_2Emin_2Ebool,V1x_27_2E0))
          | p(s(tyop_2Emin_2Ebool,V3y_27_2E0)) )
       => ( p(s(tyop_2Emin_2Ebool,V0x_2E0))
          | p(s(tyop_2Emin_2Ebool,V2y_2E0)) ) ) ) ).

fof(thm_2EConseqConv_2EIMP__CONG__disj__weaken,axiom,
    ! [V0x_2E0,V1x_27_2E0,V2y_2E0,V3y_27_2E0] :
      ( ( ( ~ p(s(tyop_2Emin_2Ebool,V2y_2E0))
         => ( p(s(tyop_2Emin_2Ebool,V0x_2E0))
           => p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) ) )
        & ( ~ p(s(tyop_2Emin_2Ebool,V1x_27_2E0))
         => ( p(s(tyop_2Emin_2Ebool,V2y_2E0))
           => p(s(tyop_2Emin_2Ebool,V3y_27_2E0)) ) ) )
     => ( ( p(s(tyop_2Emin_2Ebool,V0x_2E0))
          | p(s(tyop_2Emin_2Ebool,V2y_2E0)) )
       => ( p(s(tyop_2Emin_2Ebool,V1x_27_2E0))
          | p(s(tyop_2Emin_2Ebool,V3y_27_2E0)) ) ) ) ).

fof(thm_2EConseqConv_2EOR__CLAUSES__TX,axiom,
    ! [V0t_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))
        | p(s(tyop_2Emin_2Ebool,V0t_2E0)) )
    <=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ) ).

fof(thm_2EConseqConv_2EOR__CLAUSES__XT,axiom,
    ! [V0t_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,V0t_2E0))
        | p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) )
    <=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ) ).

fof(thm_2EConseqConv_2EOR__CLAUSES__FX,axiom,
    ! [V0t_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))
        | p(s(tyop_2Emin_2Ebool,V0t_2E0)) )
    <=> p(s(tyop_2Emin_2Ebool,V0t_2E0)) ) ).

fof(thm_2EConseqConv_2EOR__CLAUSES__XF,axiom,
    ! [V0t_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,V0t_2E0))
        | p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) )
    <=> p(s(tyop_2Emin_2Ebool,V0t_2E0)) ) ).

fof(thm_2EConseqConv_2EOR__CLAUSES__XX,axiom,
    ! [V0t_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,V0t_2E0))
        | p(s(tyop_2Emin_2Ebool,V0t_2E0)) )
    <=> p(s(tyop_2Emin_2Ebool,V0t_2E0)) ) ).

fof(thm_2EConseqConv_2EIMP__CONG__imp__strengthen,axiom,
    ! [V0x_2E0,V1x_27_2E0,V2y_2E0,V3y_27_2E0] :
      ( ( ( p(s(tyop_2Emin_2Ebool,V0x_2E0))
         => ( p(s(tyop_2Emin_2Ebool,V3y_27_2E0))
           => p(s(tyop_2Emin_2Ebool,V2y_2E0)) ) )
        & ( ~ p(s(tyop_2Emin_2Ebool,V3y_27_2E0))
         => ( p(s(tyop_2Emin_2Ebool,V0x_2E0))
           => p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) ) ) )
     => ( ( p(s(tyop_2Emin_2Ebool,V1x_27_2E0))
         => p(s(tyop_2Emin_2Ebool,V3y_27_2E0)) )
       => ( p(s(tyop_2Emin_2Ebool,V0x_2E0))
         => p(s(tyop_2Emin_2Ebool,V2y_2E0)) ) ) ) ).

fof(thm_2EConseqConv_2EIMP__CONG__imp__weaken,axiom,
    ! [V0x_2E0,V1x_27_2E0,V2y_2E0,V3y_27_2E0] :
      ( ( ( p(s(tyop_2Emin_2Ebool,V0x_2E0))
         => ( p(s(tyop_2Emin_2Ebool,V2y_2E0))
           => p(s(tyop_2Emin_2Ebool,V3y_27_2E0)) ) )
        & ( ~ p(s(tyop_2Emin_2Ebool,V3y_27_2E0))
         => ( p(s(tyop_2Emin_2Ebool,V1x_27_2E0))
           => p(s(tyop_2Emin_2Ebool,V0x_2E0)) ) ) )
     => ( ( p(s(tyop_2Emin_2Ebool,V0x_2E0))
         => p(s(tyop_2Emin_2Ebool,V2y_2E0)) )
       => ( p(s(tyop_2Emin_2Ebool,V1x_27_2E0))
         => p(s(tyop_2Emin_2Ebool,V3y_27_2E0)) ) ) ) ).

fof(thm_2EConseqConv_2EIMP__CONG__simple__imp__strengthen,axiom,
    ! [V0x_2E0,V1x_27_2E0,V2y_2E0,V3y_27_2E0] :
      ( ( ( p(s(tyop_2Emin_2Ebool,V0x_2E0))
         => p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) )
        & ( p(s(tyop_2Emin_2Ebool,V1x_27_2E0))
         => ( p(s(tyop_2Emin_2Ebool,V3y_27_2E0))
           => p(s(tyop_2Emin_2Ebool,V2y_2E0)) ) ) )
     => ( ( p(s(tyop_2Emin_2Ebool,V1x_27_2E0))
         => p(s(tyop_2Emin_2Ebool,V3y_27_2E0)) )
       => ( p(s(tyop_2Emin_2Ebool,V0x_2E0))
         => p(s(tyop_2Emin_2Ebool,V2y_2E0)) ) ) ) ).

fof(thm_2EConseqConv_2EIMP__CONG__simple__imp__weaken,axiom,
    ! [V0x_2E0,V1x_27_2E0,V2y_2E0,V3y_27_2E0] :
      ( ( ( p(s(tyop_2Emin_2Ebool,V1x_27_2E0))
         => p(s(tyop_2Emin_2Ebool,V0x_2E0)) )
        & ( p(s(tyop_2Emin_2Ebool,V1x_27_2E0))
         => ( p(s(tyop_2Emin_2Ebool,V2y_2E0))
           => p(s(tyop_2Emin_2Ebool,V3y_27_2E0)) ) ) )
     => ( ( p(s(tyop_2Emin_2Ebool,V0x_2E0))
         => p(s(tyop_2Emin_2Ebool,V2y_2E0)) )
       => ( p(s(tyop_2Emin_2Ebool,V1x_27_2E0))
         => p(s(tyop_2Emin_2Ebool,V3y_27_2E0)) ) ) ) ).

fof(thm_2EConseqConv_2EIMP__CLAUSES__TX,axiom,
    ! [V0t_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))
       => p(s(tyop_2Emin_2Ebool,V0t_2E0)) )
    <=> p(s(tyop_2Emin_2Ebool,V0t_2E0)) ) ).

fof(thm_2EConseqConv_2EIMP__CLAUSES__XT,axiom,
    ! [V0t_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,V0t_2E0))
       => p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) )
    <=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ) ).

fof(thm_2EConseqConv_2EIMP__CLAUSES__FX,axiom,
    ! [V0t_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))
       => p(s(tyop_2Emin_2Ebool,V0t_2E0)) )
    <=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ) ).

fof(thm_2EConseqConv_2EIMP__CLAUSES__XX,axiom,
    ! [V0t_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,V0t_2E0))
       => p(s(tyop_2Emin_2Ebool,V0t_2E0)) )
    <=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ) ).

fof(thm_2EConseqConv_2EIMP__CLAUSES__XF,axiom,
    ! [V0t_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,V0t_2E0))
       => p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) )
    <=> ~ p(s(tyop_2Emin_2Ebool,V0t_2E0)) ) ).

fof(thm_2EConseqConv_2EIMP__CONG__cond__simple,axiom,
    ! [V0c_2E0,V1x_2E0,V2x_27_2E0,V3y_2E0,V4y_27_2E0] :
      ( ( ( p(s(tyop_2Emin_2Ebool,V2x_27_2E0))
         => p(s(tyop_2Emin_2Ebool,V1x_2E0)) )
        & ( p(s(tyop_2Emin_2Ebool,V4y_27_2E0))
         => p(s(tyop_2Emin_2Ebool,V3y_2E0)) ) )
     => ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0c_2E0),s(tyop_2Emin_2Ebool,V2x_27_2E0),s(tyop_2Emin_2Ebool,V4y_27_2E0))))
       => p(s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0c_2E0),s(tyop_2Emin_2Ebool,V1x_2E0),s(tyop_2Emin_2Ebool,V3y_2E0)))) ) ) ).

fof(thm_2EConseqConv_2EIMP__CONG__cond,axiom,
    ! [V0c_2E0,V1x_2E0,V2x_27_2E0,V3y_2E0,V4y_27_2E0] :
      ( ( ( p(s(tyop_2Emin_2Ebool,V0c_2E0))
         => ( p(s(tyop_2Emin_2Ebool,V2x_27_2E0))
           => p(s(tyop_2Emin_2Ebool,V1x_2E0)) ) )
        & ( ~ p(s(tyop_2Emin_2Ebool,V0c_2E0))
         => ( p(s(tyop_2Emin_2Ebool,V4y_27_2E0))
           => p(s(tyop_2Emin_2Ebool,V3y_2E0)) ) ) )
     => ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0c_2E0),s(tyop_2Emin_2Ebool,V2x_27_2E0),s(tyop_2Emin_2Ebool,V4y_27_2E0))))
       => p(s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0c_2E0),s(tyop_2Emin_2Ebool,V1x_2E0),s(tyop_2Emin_2Ebool,V3y_2E0)))) ) ) ).

fof(thm_2EConseqConv_2ECOND__CLAUSES__CT,axiom,
    ! [A_27a,V0t1_2E0,V1t2_2E0] : s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(A_27a,V0t1_2E0),s(A_27a,V1t2_2E0))) = s(A_27a,V0t1_2E0) ).

fof(thm_2EConseqConv_2ECOND__CLAUSES__CF,axiom,
    ! [A_27a,V0t1_2E0,V1t2_2E0] : s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(A_27a,V0t1_2E0),s(A_27a,V1t2_2E0))) = s(A_27a,V1t2_2E0) ).

fof(thm_2EConseqConv_2ECOND__CLAUSES__ID,axiom,
    ! [A_27a,V0b_2E0,V1t_2E0] : s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0b_2E0),s(A_27a,V1t_2E0),s(A_27a,V1t_2E0))) = s(A_27a,V1t_2E0) ).

fof(thm_2EConseqConv_2ECOND__CLAUSES__TT,axiom,
    ! [V0c_2E0,V1x_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0c_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Emin_2Ebool,V1x_2E0))))
    <=> ( ~ p(s(tyop_2Emin_2Ebool,V0c_2E0))
       => p(s(tyop_2Emin_2Ebool,V1x_2E0)) ) ) ).

fof(thm_2EConseqConv_2ECOND__CLAUSES__FT,axiom,
    ! [V0c_2E0,V1x_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0c_2E0),s(tyop_2Emin_2Ebool,V1x_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))))
    <=> ( p(s(tyop_2Emin_2Ebool,V0c_2E0))
       => p(s(tyop_2Emin_2Ebool,V1x_2E0)) ) ) ).

fof(thm_2EConseqConv_2ECOND__CLAUSES__TF,axiom,
    ! [V0c_2E0,V1x_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0c_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Emin_2Ebool,V1x_2E0))))
    <=> ( ~ p(s(tyop_2Emin_2Ebool,V0c_2E0))
        & p(s(tyop_2Emin_2Ebool,V1x_2E0)) ) ) ).

fof(thm_2EConseqConv_2ECOND__CLAUSES__FF,axiom,
    ! [V0c_2E0,V1x_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0c_2E0),s(tyop_2Emin_2Ebool,V1x_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))))
    <=> ( p(s(tyop_2Emin_2Ebool,V0c_2E0))
        & p(s(tyop_2Emin_2Ebool,V1x_2E0)) ) ) ).

fof(thm_2EConseqConv_2EASM__MARKER__THM,axiom,
    ! [V0y_2E0,V1x_2E0] : s(tyop_2Emin_2Ebool,c_2EConseqConv_2EASM__MARKER_2E2(s(tyop_2Emin_2Ebool,V0y_2E0),s(tyop_2Emin_2Ebool,V1x_2E0))) = s(tyop_2Emin_2Ebool,V1x_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) ) ).

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