ITP001 Axioms: ITP058+4.ax
%------------------------------------------------------------------------------
% File : ITP058+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 : wot.ax [Gau19]
% : HL4058+4.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 62 ( 38 unt; 0 def)
% Number of atoms : 105 ( 46 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 47 ( 4 ~; 4 |; 9 &)
% ( 20 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 74 ( 74 usr; 39 con; 0-2 aty)
% Number of variables : 150 ( 147 !; 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(arityeq1_2Ec_2Epred__set_2ECHOICE_2E1_2Emono_2EA_27x,axiom,
! [A_27x,X0_2E0] : s(A_27x,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),X0_2E0))) = s(A_27x,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),A_27x),c_2Epred__set_2ECHOICE_2E0),s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq1_2Ec_2Epred__set_2ECOMPL_2E1_2Emono_2EA_27x,axiom,
! [A_27x,X0_2E0] : s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool)),c_2Epred__set_2ECOMPL_2E0),s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27x_2Ctyop_2Emin_2Ebool_29_20mono_2EA_27x,axiom,
! [A_27x,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27x,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(A_27x,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X0_2E0))) ).
fof(arityeq1_2Ec_2Erelation_2ESTRORD_2E1_2Emono_2EA_27x,axiom,
! [A_27x,X0_2E0] : s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool)),c_2Erelation_2ESTRORD_2E1(s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool))),c_2Erelation_2ESTRORD_2E0),s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool)),X0_2E0))) ).
fof(arityeq1_2Ec_2Erelation_2EStrongLinearOrder_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Erelation_2EStrongLinearOrder_2E1(s(tyop_2Emin_2Efun(A_27a,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_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EStrongLinearOrder_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) ).
fof(arityeq1_2Ec_2Ewot_2EStrongWellOrder_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ewot_2EStrongWellOrder_2E1(s(tyop_2Emin_2Efun(A_27a,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_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Ewot_2EStrongWellOrder_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) ).
fof(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,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_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWF_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) ).
fof(arityeq1_2Ec_2Erelation_2EWeakOrder_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Erelation_2EWeakOrder_2E1(s(tyop_2Emin_2Efun(A_27a,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_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWeakOrder_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) ).
fof(arityeq1_2Ec_2Ewot_2EWeakWellOrder_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ewot_2EWeakWellOrder_2E1(s(tyop_2Emin_2Efun(A_27a,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_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Ewot_2EWeakWellOrder_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) ).
fof(arityeq1_2Ec_2Ewot_2Echain_2E1_2Emono_2EA_27x,axiom,
! [A_27x,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ewot_2Echain_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ewot_2Echain_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq1_2Ec_2Ewot_2Emex_2E1_2Emono_2EA_27x,axiom,
! [A_27x,X0_2E0] : s(A_27x,c_2Ewot_2Emex_2E1(s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),X0_2E0))) = s(A_27x,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),A_27x),c_2Ewot_2Emex_2E0),s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq1_2Ec_2Ewot_2Epreds__image_2E1_2Emono_2EA_27x,axiom,
! [A_27x,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ewot_2Epreds__image_2E1(s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ewot_2Epreds__image_2E0),s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq1_2Ec_2Ewot_2Esetsuc_2E1_2Emono_2EA_27x,axiom,
! [A_27x,X0_2E0] : s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),c_2Ewot_2Esetsuc_2E1(s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool)),c_2Ewot_2Esetsuc_2E0),s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq1_2Ec_2Ewot_2Esuccl_2E1_2Emono_2EA_27x,axiom,
! [A_27x,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ewot_2Esuccl_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ewot_2Esuccl_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq1_2Ec_2Ewot_2Etower_2E1_2Emono_2EA_27x,axiom,
! [A_27x,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ewot_2Etower_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ewot_2Etower_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq1_2Ec_2Ewot_2Euncl_2E1_2Emono_2EA_27x,axiom,
! [A_27x,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ewot_2Euncl_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ewot_2Euncl_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27x_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27x,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0),s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))) ).
fof(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27x,axiom,
! [A_27x,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27x,X0_2E0),s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(A_27x,X0_2E0))),s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq1_2Ec_2Ewot_2Epreds_2E1_2Emono_2EA_27x,axiom,
! [A_27x,X0_2E0] : s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),c_2Ewot_2Epreds_2E1(s(A_27x,X0_2E0))) = s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool)),c_2Ewot_2Epreds_2E0),s(A_27x,X0_2E0))) ).
fof(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(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(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27x_2Ctyop_2Emin_2Ebool_29,axiom,
! [A_27x,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq1_2Ec_2Epred__set_2EBIGUNION_2E1_2Emono_2EA_27x,axiom,
! [A_27x,X0_2E0] : s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool)),c_2Epred__set_2EBIGUNION_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2EA_27x,axiom,
! [A_27x,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27x,X0_2E0),s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool))),c_2Epred__set_2EINSERT_2E0),s(A_27x,X0_2E0))),s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2EA_27x,axiom,
! [A_27x,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2ESUBSET_2E0),s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27x_2Ctyop_2Emin_2Ebool_29,axiom,
! [A_27x,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2ESUBSET_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Ewot_2Ecpl_2E2_2Emono_2EA_27x,axiom,
! [A_27x,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ewot_2Ecpl_2E2(s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ewot_2Ecpl_2E0),s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Ewot_2Emex__less__eq_2E2_2Emono_2EA_27x,axiom,
! [A_27x,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ewot_2Emex__less__eq_2E2(s(A_27x,X0_2E0),s(A_27x,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool)),c_2Ewot_2Emex__less__eq_2E0),s(A_27x,X0_2E0))),s(A_27x,X1_2E0))) ).
fof(thm_2Ewot_2Ecpl__def,axiom,
! [A_27x,V0A_2E0,V1B_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ewot_2Ecpl_2E2(s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),V0A_2E0),s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),V1B_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),V0A_2E0),s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),V1B_2E0))))
| p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),V1B_2E0),s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),V0A_2E0)))) ) ) ).
fof(thm_2Ewot_2Echain__def,axiom,
! [A_27x,V0C_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ewot_2Echain_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0C_2E0))))
<=> ! [V1a_2E0,V2b_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),V1a_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0C_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),V2b_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0C_2E0)))) )
=> p(s(tyop_2Emin_2Ebool,c_2Ewot_2Ecpl_2E2(s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),V1a_2E0),s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),V2b_2E0)))) ) ) ).
fof(thm_2Ewot_2Emex__def,axiom,
! [A_27x,V0s_2E0] : s(A_27x,c_2Ewot_2Emex_2E1(s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),V0s_2E0))) = s(A_27x,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),V0s_2E0))))) ).
fof(thm_2Ewot_2Esetsuc__def,axiom,
! [A_27x,V0s_2E0] : s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),c_2Ewot_2Esetsuc_2E1(s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),V0s_2E0))) = s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27x,c_2Ewot_2Emex_2E1(s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),V0s_2E0))) ).
fof(thm_2Ewot_2Esuccl__def,axiom,
! [A_27x,V0c_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ewot_2Esuccl_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0c_2E0))))
<=> ! [V1s_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0c_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),c_2Ewot_2Esetsuc_2E1(s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0c_2E0)))) ) ) ).
fof(thm_2Ewot_2Euncl__def,axiom,
! [A_27x,V0c_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ewot_2Euncl_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0c_2E0))))
<=> ! [V1w_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1w_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0c_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ewot_2Echain_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1w_2E0)))) )
=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1w_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0c_2E0)))) ) ) ).
fof(thm_2Ewot_2Etower__def,axiom,
! [A_27x,V0A_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ewot_2Etower_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0A_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Ewot_2Esuccl_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0A_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ewot_2Euncl_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0A_2E0)))) ) ) ).
fof(thm_2Ewot_2Emex__less__eq__def,axiom,
! [A_27x,V0a_2E0,V1b_2E0] : s(tyop_2Emin_2Ebool,c_2Ewot_2Emex__less__eq_2E2(s(A_27x,V0a_2E0),s(A_27x,V1b_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),c_2Ewot_2Epreds_2E1(s(A_27x,V0a_2E0))),s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),c_2Ewot_2Epreds_2E1(s(A_27x,V1b_2E0))))) ).
fof(thm_2Ewot_2Emex__less__def,axiom,
! [A_27x] : s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool)),c_2Ewot_2Emex__less_2E0) = s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool)),c_2Erelation_2ESTRORD_2E1(s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool)),c_2Ewot_2Emex__less__eq_2E0))) ).
fof(thm_2Ewot_2EWeakWellOrder__def,axiom,
! [A_27a,V0R_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ewot_2EWeakWellOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWeakOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))
& ! [V1B_2E0] :
( s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1B_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)
=> ? [V2m_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2m_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1B_2E0))))
& ! [V3b_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3b_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1B_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)),V0R_2E0),s(A_27a,V2m_2E0))),s(A_27a,V3b_2E0)))) ) ) ) ) ) ).
fof(thm_2Ewot_2Epreds__image__def,axiom,
! [A_27x,F0_2E0] :
( ! [V0X_2E0,V1x_2E0] : s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27x,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27x,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),V0X_2E0))),s(A_27x,V1x_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),c_2Ewot_2Epreds_2E1(s(A_27x,V1x_2E0))),s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27x,V1x_2E0),s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),V0X_2E0)))))
=> ! [V0X_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ewot_2Epreds__image_2E1(s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),V0X_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27x,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27x,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27x,tyop_2Emin_2Ebool),V0X_2E0))))) ) ).
fof(thm_2Ewot_2EStrongWellOrder__def,axiom,
! [A_27a,V0R_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ewot_2EStrongWellOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Erelation_2EStrongLinearOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) ) ) ).
fof(thm_2Ewot_2EStrongWellOrderExists,axiom,
! [A_27a] :
? [V0R_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Erelation_2EStrongLinearOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_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) ) ).
%------------------------------------------------------------------------------