TPTP Problem File: ITP006+1.p

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%------------------------------------------------------------------------------
% File     : ITP006+1 : TPTP v7.4.0. Released v7.4.0.
% Domain   : Interactive Theorem Proving
% Problem  : HOL4 syntactic export of thm_2EquantHeuristics_2EGUESS__RULES__WEAKEN__FORALL__POINT.p, bushy 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    : thm_2EquantHeuristics_2EGUESS__RULES__WEAKEN__FORALL__POINT.p [Gau19]
%          : HL402501+1.p [TPAP]

% Status   : Theorem
% Rating   : 0.53 v7.4.0
% Syntax   : Number of formulae    :   49 (  15 unit)
%            Number of atoms       :  185 (  30 equality)
%            Maximal formula depth :   16 (   6 average)
%            Number of connectives :  177 (  41   ~;  24   |;  26   &)
%                                         (  45 <=>;  41  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of predicates  :    2 (   0 propositional; 1-2 arity)
%            Number of functors    :   35 (  19 constant; 0-2 arity)
%            Number of variables   :  141 (   0 sgn; 136   !;   5   ?)
%            Maximal term depth    :   11 (   3 average)
% SPC      : FOF_THM_RFO_SEQ

% Comments : 
%------------------------------------------------------------------------------
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) ) )).

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_2EquantHeuristics_2EGUESS__EXISTS_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,(
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2EquantHeuristics_2EGUESS__EXISTS_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) )).

fof(arityeq2_2Ec_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,(
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) )).

fof(arityeq2_2Ec_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,(
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) )).

fof(arityeq2_2Ec_2EquantHeuristics_2EGUESS__FORALL_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,(
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2EquantHeuristics_2EGUESS__FORALL_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) )).

fof(arityeq2_2Ec_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,(
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) )).

fof(arityeq2_2Ec_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,(
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) )).

fof(arityeq2_2Ec_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,(
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) )).

fof(thm_2Ebool_2ETRUTH,axiom,(
    p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) )).

fof(thm_2Ebool_2EIMP__CLAUSES,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)) )
      & ( ( 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)) )
      & ( ( 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)) )
      & ( ( p(s(tyop_2Emin_2Ebool,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))
         => p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) )
      <=> ~ p(s(tyop_2Emin_2Ebool,V0t_2E0)) ) ) )).

fof(thm_2Ebool_2ENOT__CLAUSES,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))
    <=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) )
    & ( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))
    <=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ) )).

fof(thm_2Ebool_2EEQ__SYM__EQ,axiom,(
    ! [A_27a,V0x_2E0,V1y_2E0] :
      ( s(A_27a,V0x_2E0) = s(A_27a,V1y_2E0)
    <=> s(A_27a,V1y_2E0) = s(A_27a,V0x_2E0) ) )).

fof(thm_2Ebool_2EEQ__CLAUSES,axiom,(
    ! [V0t_2E0] :
      ( ( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0)
      <=> p(s(tyop_2Emin_2Ebool,V0t_2E0)) )
      & ( s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
      <=> p(s(tyop_2Emin_2Ebool,V0t_2E0)) )
      & ( s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0)
      <=> ~ p(s(tyop_2Emin_2Ebool,V0t_2E0)) )
      & ( s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
      <=> ~ p(s(tyop_2Emin_2Ebool,V0t_2E0)) ) ) )).

fof(thm_2Ebool_2EAND__IMP__INTRO,axiom,(
    ! [V0t1_2E0,V1t2_2E0,V2t3_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,V0t1_2E0))
       => ( p(s(tyop_2Emin_2Ebool,V1t2_2E0))
         => p(s(tyop_2Emin_2Ebool,V2t3_2E0)) ) )
    <=> ( ( p(s(tyop_2Emin_2Ebool,V0t1_2E0))
          & p(s(tyop_2Emin_2Ebool,V1t2_2E0)) )
       => p(s(tyop_2Emin_2Ebool,V2t3_2E0)) ) ) )).

fof(thm_2Ebool_2EIMP__CONG,axiom,(
    ! [V0x_2E0,V1x_27_2E0,V2y_2E0,V3y_27_2E0] :
      ( ( s(tyop_2Emin_2Ebool,V0x_2E0) = s(tyop_2Emin_2Ebool,V1x_27_2E0)
        & ( p(s(tyop_2Emin_2Ebool,V1x_27_2E0))
         => s(tyop_2Emin_2Ebool,V2y_2E0) = 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_2EquantHeuristics_2EGUESS__REWRITES,axiom,(
    ! [A_27a,A_27b,V0i_2E0,V1P_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0))))
      <=> ! [V2v_2E0] :
            ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(A_27b,V2v_2E0))))
           => ? [V3fv_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0i_2E0),s(A_27a,V3fv_2E0)))))) ) )
      & ( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0))))
      <=> ! [V4v_2E0] :
            ( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(A_27b,V4v_2E0))))
           => ? [V5fv_2E0] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0i_2E0),s(A_27a,V5fv_2E0)))))) ) )
      & ! [V6i_2E0,V7P_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V6i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V7P_2E0))))
        <=> ! [V8fv_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V7P_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V6i_2E0),s(A_27a,V8fv_2E0)))))) )
      & ! [V9i_2E0,V10P_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V9i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V10P_2E0))))
        <=> ! [V11fv_2E0] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V10P_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V9i_2E0),s(A_27a,V11fv_2E0)))))) )
      & ! [V12i_2E0,V13P_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V12i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V13P_2E0))))
        <=> ! [V14v_2E0] :
              ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V13P_2E0),s(A_27b,V14v_2E0))))
             => ? [V15fv_2E0] : s(A_27b,V14v_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V12i_2E0),s(A_27a,V15fv_2E0))) ) )
      & ! [V16i_2E0,V17P_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V16i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V17P_2E0))))
        <=> ! [V18v_2E0] :
              ( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V17P_2E0),s(A_27b,V18v_2E0))))
             => ? [V19fv_2E0] : s(A_27b,V18v_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V16i_2E0),s(A_27a,V19fv_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__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__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_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__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_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_2EquantHeuristics_2EGUESS__RULES__WEAKEN__FORALL__POINT,conjecture,(
    ! [A_27a,A_27b,V0i_2E0,V1P_2E0,V2Q_2E0] :
      ( ! [V3x_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0),s(A_27a,V3x_2E0))))
         => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V3x_2E0)))) )
     => ( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V0i_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0))))
       => p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V0i_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0)))) ) ) )).

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