ITP001 Axioms: ITP039+4.ax
%------------------------------------------------------------------------------
% File : ITP039+4 : TPTP v8.2.0. 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 : defCNF.ax [Gau19]
% : HL4039+4.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 47 ( 21 unt; 0 def)
% Number of atoms : 107 ( 38 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 63 ( 3 ~; 3 |; 24 &)
% ( 24 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 15 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 54 ( 54 usr; 28 con; 0-3 aty)
% Number of variables : 165 ( 161 !; 4 ?)
% 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_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))))),c_2Epair_2E_2C_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(s(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),c_2Epair_2E_2C_2E0),s(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq1_2Ec_2Esum_2EINR_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0] : s(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esum_2EINR_2E1(s(tyop_2Emin_2Ebool,X0_2E0))) = s(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Esum_2EINR_2E0),s(tyop_2Emin_2Ebool,X0_2E0))) ).
fof(arityeq1_2Ec_2Esum_2EINL_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0] : s(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esum_2EINL_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Esum_2EINL_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).
fof(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Eprim__rec_2E_3C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).
fof(arityeq2_2Ec_2EdefCNF_2EOK_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2EdefCNF_2EOK_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool)),c_2EdefCNF_2EOK_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),X1_2E0))) ).
fof(arityeq2_2Ec_2Earithmetic_2E_2B_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2B_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).
fof(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Epair_2Eprod_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),tyop_2Enum_2Enum),c_2Elist_2ELENGTH_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),X0_2E0))) ).
fof(arityeq2_2Ec_2EdefCNF_2EOKDEF_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2EdefCNF_2EOKDEF_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),tyop_2Emin_2Ebool)),c_2EdefCNF_2EOKDEF_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),X1_2E0))) ).
fof(arityeq2_2Ec_2Elist_2ESNOC_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Epair_2Eprod_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),c_2Elist_2ESNOC_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))))),c_2Elist_2ESNOC_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),X1_2E0))) ).
fof(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Epair_2Eprod_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))))),c_2Elist_2ECONS_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),X1_2E0))) ).
fof(arityeq1_2Ec_2Enum_2ESUC_2E1,axiom,
! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enum_2ESUC_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).
fof(arityeq3_2Ec_2EdefCNF_2EDEF_2E3,axiom,
! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2EdefCNF_2EDEF_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),tyop_2Emin_2Ebool))),c_2EdefCNF_2EDEF_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),X2_2E0))) ).
fof(arityeq3_2Ec_2EdefCNF_2EUNIQUE_2E3,axiom,
! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2EdefCNF_2EUNIQUE_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool))),c_2EdefCNF_2EUNIQUE_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),X2_2E0))) ).
fof(thm_2EdefCNF_2EDEF__def,axiom,
( ! [V0v_2E0,V1n_2E0] : s(tyop_2Emin_2Ebool,c_2EdefCNF_2EDEF_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0v_2E0),s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),c_2Elist_2ENIL_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
& ! [V2v_2E0,V3n_2E0,V4x_2E0,V5xs_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2EdefCNF_2EDEF_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2v_2E0),s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V4x_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),V5xs_2E0))))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2EdefCNF_2EUNIQUE_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2v_2E0),s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V4x_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2EdefCNF_2EDEF_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2v_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V3n_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),V5xs_2E0)))) ) ) ) ).
fof(thm_2EdefCNF_2EOKDEF__def,axiom,
( ! [V0n_2E0] : s(tyop_2Emin_2Ebool,c_2EdefCNF_2EOKDEF_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),c_2Elist_2ENIL_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
& ! [V1n_2E0,V2x_2E0,V3xs_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2EdefCNF_2EOKDEF_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V2x_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),V3xs_2E0))))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2EdefCNF_2EOK_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V2x_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2EdefCNF_2EOKDEF_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),V3xs_2E0)))) ) ) ) ).
fof(thm_2EdefCNF_2EUNIQUE__ind,axiom,
! [V0P_2E0] :
( ( ! [V1v_2E0,V2n_2E0,V3conn_2E0,V4i_2E0,V5j_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1v_2E0))),s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V3conn_2E0),s(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(s(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esum_2EINL_2E1(s(tyop_2Enum_2Enum,V4i_2E0))),s(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esum_2EINL_2E1(s(tyop_2Enum_2Enum,V5j_2E0))))))))))
& ! [V6v_2E0,V7n_2E0,V8conn_2E0,V9i_2E0,V10b_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V6v_2E0))),s(tyop_2Enum_2Enum,V7n_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V8conn_2E0),s(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(s(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esum_2EINL_2E1(s(tyop_2Enum_2Enum,V9i_2E0))),s(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esum_2EINR_2E1(s(tyop_2Emin_2Ebool,V10b_2E0))))))))))
& ! [V11v_2E0,V12n_2E0,V13conn_2E0,V14a_2E0,V15j_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V11v_2E0))),s(tyop_2Enum_2Enum,V12n_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V13conn_2E0),s(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(s(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esum_2EINR_2E1(s(tyop_2Emin_2Ebool,V14a_2E0))),s(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esum_2EINL_2E1(s(tyop_2Enum_2Enum,V15j_2E0))))))))))
& ! [V16v_2E0,V17n_2E0,V18conn_2E0,V19a_2E0,V20b_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V16v_2E0))),s(tyop_2Enum_2Enum,V17n_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V18conn_2E0),s(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(s(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esum_2EINR_2E1(s(tyop_2Emin_2Ebool,V19a_2E0))),s(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esum_2EINR_2E1(s(tyop_2Emin_2Ebool,V20b_2E0)))))))))) )
=> ! [V21v_2E0,V22v1_2E0,V23v2_2E0,V24v3_2E0,V25v4_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V21v_2E0))),s(tyop_2Enum_2Enum,V22v1_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V23v2_2E0),s(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(s(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V24v3_2E0),s(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V25v4_2E0)))))))) ) ).
fof(thm_2EdefCNF_2EUNIQUE__def,axiom,
! [V0v_2E0,V1n_2E0,V2j_2E0,V3i_2E0,V4conn_2E0,V5b_2E0,V6a_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2EdefCNF_2EUNIQUE_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0v_2E0),s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V4conn_2E0),s(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(s(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esum_2EINL_2E1(s(tyop_2Enum_2Enum,V3i_2E0))),s(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esum_2EINL_2E1(s(tyop_2Enum_2Enum,V2j_2E0))))))))))
<=> s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0v_2E0),s(tyop_2Enum_2Enum,V1n_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)),V4conn_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0v_2E0),s(tyop_2Enum_2Enum,V3i_2E0))))),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0v_2E0),s(tyop_2Enum_2Enum,V2j_2E0))))) )
& ( p(s(tyop_2Emin_2Ebool,c_2EdefCNF_2EUNIQUE_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0v_2E0),s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V4conn_2E0),s(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(s(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esum_2EINL_2E1(s(tyop_2Enum_2Enum,V3i_2E0))),s(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esum_2EINR_2E1(s(tyop_2Emin_2Ebool,V5b_2E0))))))))))
<=> s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0v_2E0),s(tyop_2Enum_2Enum,V1n_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)),V4conn_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0v_2E0),s(tyop_2Enum_2Enum,V3i_2E0))))),s(tyop_2Emin_2Ebool,V5b_2E0))) )
& ( p(s(tyop_2Emin_2Ebool,c_2EdefCNF_2EUNIQUE_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0v_2E0),s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V4conn_2E0),s(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(s(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esum_2EINR_2E1(s(tyop_2Emin_2Ebool,V6a_2E0))),s(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esum_2EINL_2E1(s(tyop_2Enum_2Enum,V2j_2E0))))))))))
<=> s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0v_2E0),s(tyop_2Enum_2Enum,V1n_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)),V4conn_2E0),s(tyop_2Emin_2Ebool,V6a_2E0))),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0v_2E0),s(tyop_2Enum_2Enum,V2j_2E0))))) )
& ( p(s(tyop_2Emin_2Ebool,c_2EdefCNF_2EUNIQUE_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0v_2E0),s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V4conn_2E0),s(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(s(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esum_2EINR_2E1(s(tyop_2Emin_2Ebool,V6a_2E0))),s(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esum_2EINR_2E1(s(tyop_2Emin_2Ebool,V5b_2E0))))))))))
<=> s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0v_2E0),s(tyop_2Enum_2Enum,V1n_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)),V4conn_2E0),s(tyop_2Emin_2Ebool,V6a_2E0))),s(tyop_2Emin_2Ebool,V5b_2E0))) ) ) ).
fof(thm_2EdefCNF_2EOK__ind,axiom,
! [V0P_2E0] :
( ( ! [V1n_2E0,V2conn_2E0,V3i_2E0,V4j_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V2conn_2E0),s(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(s(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esum_2EINL_2E1(s(tyop_2Enum_2Enum,V3i_2E0))),s(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esum_2EINL_2E1(s(tyop_2Enum_2Enum,V4j_2E0))))))))))
& ! [V5n_2E0,V6conn_2E0,V7i_2E0,V8b_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Enum_2Enum,V5n_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V6conn_2E0),s(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(s(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esum_2EINL_2E1(s(tyop_2Enum_2Enum,V7i_2E0))),s(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esum_2EINR_2E1(s(tyop_2Emin_2Ebool,V8b_2E0))))))))))
& ! [V9n_2E0,V10conn_2E0,V11a_2E0,V12j_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Enum_2Enum,V9n_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V10conn_2E0),s(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(s(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esum_2EINR_2E1(s(tyop_2Emin_2Ebool,V11a_2E0))),s(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esum_2EINL_2E1(s(tyop_2Enum_2Enum,V12j_2E0))))))))))
& ! [V13n_2E0,V14conn_2E0,V15a_2E0,V16b_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Enum_2Enum,V13n_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V14conn_2E0),s(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(s(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esum_2EINR_2E1(s(tyop_2Emin_2Ebool,V15a_2E0))),s(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esum_2EINR_2E1(s(tyop_2Emin_2Ebool,V16b_2E0)))))))))) )
=> ! [V17v_2E0,V18v1_2E0,V19v2_2E0,V20v3_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Enum_2Enum,V17v_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V18v1_2E0),s(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(s(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V19v2_2E0),s(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V20v3_2E0)))))))) ) ).
fof(thm_2EdefCNF_2EOK__def,axiom,
! [V0n_2E0,V1j_2E0,V2i_2E0,V3conn_2E0,V4b_2E0,V5a_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2EdefCNF_2EOK_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V3conn_2E0),s(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(s(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esum_2EINL_2E1(s(tyop_2Enum_2Enum,V2i_2E0))),s(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esum_2EINL_2E1(s(tyop_2Enum_2Enum,V1j_2E0))))))))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2i_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1j_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) ) )
& s(tyop_2Emin_2Ebool,c_2EdefCNF_2EOK_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V3conn_2E0),s(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(s(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esum_2EINL_2E1(s(tyop_2Enum_2Enum,V2i_2E0))),s(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esum_2EINR_2E1(s(tyop_2Emin_2Ebool,V4b_2E0))))))))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2i_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))
& s(tyop_2Emin_2Ebool,c_2EdefCNF_2EOK_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V3conn_2E0),s(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(s(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esum_2EINR_2E1(s(tyop_2Emin_2Ebool,V5a_2E0))),s(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esum_2EINL_2E1(s(tyop_2Enum_2Enum,V1j_2E0))))))))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1j_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))
& s(tyop_2Emin_2Ebool,c_2EdefCNF_2EOK_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V3conn_2E0),s(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(s(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esum_2EINR_2E1(s(tyop_2Emin_2Ebool,V5a_2E0))),s(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esum_2EINR_2E1(s(tyop_2Emin_2Ebool,V4b_2E0))))))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ) ).
fof(thm_2EdefCNF_2EDEF__SNOC,axiom,
! [V0n_2E0,V1x_2E0,V2l_2E0,V3v_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2EdefCNF_2EDEF_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3v_2E0),s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),c_2Elist_2ESNOC_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V1x_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),V2l_2E0))))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2EdefCNF_2EDEF_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3v_2E0),s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),V2l_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2EdefCNF_2EUNIQUE_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3v_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),V2l_2E0))))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V1x_2E0)))) ) ) ).
fof(thm_2EdefCNF_2EOKDEF__SNOC,axiom,
! [V0n_2E0,V1x_2E0,V2l_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2EdefCNF_2EOKDEF_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),c_2Elist_2ESNOC_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V1x_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),V2l_2E0))))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2EdefCNF_2EOKDEF_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),V2l_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2EdefCNF_2EOK_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),V2l_2E0))))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V1x_2E0)))) ) ) ).
fof(thm_2EdefCNF_2ECONSISTENCY,axiom,
! [V0n_2E0,V1l_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2EdefCNF_2EOKDEF_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),V1l_2E0))))
=> ? [V2v_2E0] : p(s(tyop_2Emin_2Ebool,c_2EdefCNF_2EDEF_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2v_2E0),s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),V1l_2E0)))) ) ).
fof(thm_2EdefCNF_2EBIGSTEP,axiom,
! [V0P_2E0,V1Q_2E0,V2R_2E0] :
( ! [V3v_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3v_2E0))))
=> s(tyop_2Emin_2Ebool,V1Q_2E0) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V2R_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3v_2E0))) )
=> ( ( ? [V4v_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V4v_2E0))))
& p(s(tyop_2Emin_2Ebool,V1Q_2E0)) )
<=> ? [V5v_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V5v_2E0))))
& p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V2R_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V5v_2E0)))) ) ) ) ).
fof(thm_2EdefCNF_2EFINAL__DEF,axiom,
! [V0v_2E0,V1n_2E0,V2x_2E0] :
( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0v_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Emin_2Ebool,V2x_2E0)
<=> ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0v_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Emin_2Ebool,V2x_2E0)
& p(s(tyop_2Emin_2Ebool,c_2EdefCNF_2EDEF_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0v_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),c_2Elist_2ENIL_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) ) ).
%------------------------------------------------------------------------------