TPTP Problem File: ITP005+4.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : ITP005+4 : TPTP v9.0.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Problem : HOL4 syntactic export of thm_2Eset__relation_2Erel__to__reln__inv.p, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau20] Gauthier (2020), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : thm_2Ebool_2ETRUTH.p [Gau20]
% : HL402001+4.p [TPAP]
% Status : Theorem
% Rating : 0.85 v9.0.0, 0.86 v8.2.0, 0.92 v8.1.0, 0.86 v7.5.0
% Syntax : Number of formulae : 5134 (2533 unt; 0 def)
% Number of atoms : 11177 (5222 equ)
% Maximal formula atoms : 40 ( 2 avg)
% Number of connectives : 6595 ( 552 ~; 401 |;1896 &)
% (1491 <=>;2255 =>; 0 <=; 0 <~>)
% Maximal formula depth : 37 ( 5 avg)
% Maximal term depth : 22 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 968 ( 968 usr; 446 con; 0-6 aty)
% Number of variables : 18441 (17964 !; 477 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments :
% Bugfixes : v7.5.0 - Bugfixes in axioms and export.
%------------------------------------------------------------------------------
include('Axioms/ITP001/ITP002+4.ax').
include('Axioms/ITP001/ITP003+4.ax').
include('Axioms/ITP001/ITP004+4.ax').
include('Axioms/ITP001/ITP005+4.ax').
include('Axioms/ITP001/ITP006+4.ax').
include('Axioms/ITP001/ITP007+4.ax').
include('Axioms/ITP001/ITP008+4.ax').
include('Axioms/ITP001/ITP009+4.ax').
include('Axioms/ITP001/ITP010+4.ax').
include('Axioms/ITP001/ITP011+4.ax').
include('Axioms/ITP001/ITP012+4.ax').
include('Axioms/ITP001/ITP013+4.ax').
include('Axioms/ITP001/ITP014+4.ax').
include('Axioms/ITP001/ITP015+4.ax').
include('Axioms/ITP001/ITP016+4.ax').
include('Axioms/ITP001/ITP017+4.ax').
include('Axioms/ITP001/ITP018+4.ax').
include('Axioms/ITP001/ITP019+4.ax').
include('Axioms/ITP001/ITP020+4.ax').
include('Axioms/ITP001/ITP021+4.ax').
include('Axioms/ITP001/ITP022+4.ax').
include('Axioms/ITP001/ITP023+4.ax').
include('Axioms/ITP001/ITP024+4.ax').
include('Axioms/ITP001/ITP025+4.ax').
include('Axioms/ITP001/ITP026+4.ax').
include('Axioms/ITP001/ITP027+4.ax').
include('Axioms/ITP001/ITP028+4.ax').
include('Axioms/ITP001/ITP029+4.ax').
include('Axioms/ITP001/ITP030+4.ax').
include('Axioms/ITP001/ITP031+4.ax').
include('Axioms/ITP001/ITP032+4.ax').
%------------------------------------------------------------------------------
fof(reserved_2Eho_2Eeq__ext,axiom,
! [A_27a,A_27b,V0f_2E0,V1g_2E0] :
( ! [V2x_2E0] : s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))
=> s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0) ) ).
fof(reserved_2Eho_2Eboolext,axiom,
! [V0_2E0,V1_2E0] :
( ( p(s(tyop_2Emin_2Ebool,V0_2E0))
<=> p(s(tyop_2Emin_2Ebool,V1_2E0)) )
=> s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0) ) ).
fof(reserved_2Eho_2Etruth,axiom,
p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ).
fof(reserved_2Eho_2Enotfalse,axiom,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) ).
fof(reserved_2Eho_2Ebool__cases__ax,axiom,
! [V0t_2E0] :
( s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
| s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ).
fof(reserved_2Eho_2Ei__thm,axiom,
! [A_27a,V0x_2E0] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0))) = s(A_27a,V0x_2E0) ).
fof(reserved_2Eho_2Ek__thm,axiom,
! [A_27a,A_27b,V0x_2E0,V1y_2E0] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0))) = s(A_27a,V0x_2E0) ).
fof(reserved_2Eho_2Es__thm,axiom,
! [A_27a,A_27b,A_27c,V0f_2E0,V1g_2E0,V2x_2E0] : s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))))) ).
fof(reserved_2Elogic_2E_2F_5C,axiom,
! [V0_2E0,V1_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,V0_2E0))
& p(s(tyop_2Emin_2Ebool,V1_2E0)) ) ) ).
fof(reserved_2Elogic_2E_5C_2F,axiom,
! [V0_2E0,V1_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,V0_2E0))
| p(s(tyop_2Emin_2Ebool,V1_2E0)) ) ) ).
fof(reserved_2Elogic_2E_7E,axiom,
! [V0_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0))))
<=> ~ p(s(tyop_2Emin_2Ebool,V0_2E0)) ) ).
fof(reserved_2Elogic_2E_3D_3D_3E,axiom,
! [V0_2E0,V1_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,V0_2E0))
=> p(s(tyop_2Emin_2Ebool,V1_2E0)) ) ) ).
fof(reserved_2Elogic_2E_3D,axiom,
! [A_27a,V0_2E0,V1_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0))))
<=> s(A_27a,V0_2E0) = s(A_27a,V1_2E0) ) ).
fof(reserved_2Equant_2E_21,axiom,
! [A_27a,V0f_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0))))
<=> ! [V1x_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0)))) ) ).
fof(reserved_2Equant_2E_3F,axiom,
! [A_27a,V0f_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0))))
<=> ? [V1x_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0)))) ) ).
fof(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
! [X0_2E0,X1_2E0] :
( ( p(s(tyop_2Emin_2Ebool,X0_2E0))
& p(s(tyop_2Emin_2Ebool,X1_2E0)) )
<=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) ) ).
fof(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,
! [X0_2E0,X1_2E0] :
( ( p(s(tyop_2Emin_2Ebool,X0_2E0))
| p(s(tyop_2Emin_2Ebool,X1_2E0)) )
<=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) ) ).
fof(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,
! [X0_2E0] :
( ~ p(s(tyop_2Emin_2Ebool,X0_2E0))
<=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))) ) ).
fof(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
! [X0_2E0,X1_2E0] :
( ( p(s(tyop_2Emin_2Ebool,X0_2E0))
=> p(s(tyop_2Emin_2Ebool,X1_2E0)) )
<=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) ) ).
fof(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] :
( s(A_27a,X0_2E0) = s(A_27a,X1_2E0)
<=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))) ) ).
fof(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_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_2Epred__set_2EFINITE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) ).
fof(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),X0_2E0))) ).
fof(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28tyop_2Epair_2Eprod_28A_27a_2CA_27a_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),X0_2E0))) ).
fof(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),X0_2E0))) ).
fof(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Epair_2Eprod_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),X0_2E0))) ).
fof(arityeq1_2Ec_2Eset__relation_2Eacyclic_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Eset__relation_2Eacyclic_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq1_2Ec_2Epred__set_2EBIGUNION_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIGUNION_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq1_2Ec_2Eset__relation_2Estrict_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Estrict_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Eset__relation_2Estrict_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(A_27a,A_27a)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(A_27a,A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),c_2Epred__set_2EUNION_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Eset__relation_2Errestrict_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),c_2Eset__relation_2Errestrict_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq1_2Ec_2Eset__relation_2Eantisym_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eantisym_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Eset__relation_2Eantisym_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq1_2Ec_2Eset__relation_2Edomain_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2Edomain_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq1_2Ec_2Eset__relation_2Erange_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2Erange_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq1_2Ec_2Eset__relation_2Erel__to__reln_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Eset__relation_2Erel__to__reln_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Eset__relation_2Erel__to__reln_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) ).
fof(arityeq1_2Ec_2Eset__relation_2Ereln__to__rel_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Eset__relation_2Ereln__to__rel_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq1_2Ec_2Eset__relation_2Etc_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Eset__relation_2Etc_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq1_2Ec_2Eset__relation_2Etransitive_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Eset__relation_2Etransitive_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Eset__relation_2Etransitive_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq1_2Ec_2Eset__relation_2Euniv__reln_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Euniv__reln_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Eset__relation_2Euniv__reln_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0] : s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))) ).
fof(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0] : s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),c_2Epair_2ESND_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,A_27a))),c_2Epair_2E_2C_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,X0_2E0),s(A_27b,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Epair_2E_2C_2E0),s(A_27a,X0_2E0))),s(A_27b,X1_2E0))) ).
fof(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27b,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27b,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0),s(A_27b,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27a),X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2EA_27b,axiom,
! [A_27b,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(A_27b,A_27b),c_2Epair_2E_2C_2E2(s(A_27b,X0_2E0),s(A_27b,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,A_27b))),c_2Epair_2E_2C_2E0),s(A_27b,X0_2E0))),s(A_27b,X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27b_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27b,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(A_27b,A_27b),X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27b),X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))) ).
fof(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Epred__set_2EDISJOINT_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EDISJOINT_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EUNION_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq1_2Ec_2Eset__relation_2Edomain_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2Edomain_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq1_2Ec_2Eset__relation_2Erange_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2Erange_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq2_2Ec_2Epred__set_2EDISJOINT_2E2_2Emono_2EA_27b,axiom,
! [A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EDISJOINT_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq1_2Ec_2Eset__relation_2Erange_2E1_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Eset__relation_2Erange_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),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(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27a),X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27a),c_2Epair_2EFST_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27a),X0_2E0))) ).
fof(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(A_27a,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27a),X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27a),c_2Epair_2ESND_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27a),X0_2E0))) ).
fof(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27b,axiom,
! [A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(A_27b,X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27c,axiom,
! [A_27c,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27c,X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(A_27c,X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28A_27a_2CA_27a_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a,A_27c,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(A_27a,A_27c),c_2Epair_2E_2C_2E2(s(A_27a,X0_2E0),s(A_27c,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27a,A_27c))),c_2Epair_2E_2C_2E0),s(A_27a,X0_2E0))),s(A_27c,X1_2E0))) ).
fof(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27c_29,axiom,
! [A_27a,A_27c,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27c),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(A_27b,A_27a),c_2Epair_2E_2C_2E2(s(A_27b,X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Epair_2E_2C_2E0),s(A_27b,X0_2E0))),s(A_27a,X1_2E0))) ).
fof(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27b,A_27a),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(A_27b,A_27c),c_2Epair_2E_2C_2E2(s(A_27b,X0_2E0),s(A_27c,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27b,A_27c))),c_2Epair_2E_2C_2E0),s(A_27b,X0_2E0))),s(A_27c,X1_2E0))) ).
fof(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27c_29,axiom,
! [A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27b,A_27c),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(A_27c,A_27b),c_2Epair_2E_2C_2E2(s(A_27c,X0_2E0),s(A_27b,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),c_2Epair_2E_2C_2E0),s(A_27c,X0_2E0))),s(A_27b,X1_2E0))) ).
fof(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27b_29,axiom,
! [A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27c,A_27b),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Epair_2Eprod(A_27c,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Epred__set_2EREL__RESTRICT_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EREL__RESTRICT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2Epred__set_2EREL__RESTRICT_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Eset__relation_2ERREFL__EXP_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2ERREFL__EXP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2Eset__relation_2ERREFL__EXP_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Erelation_2ERSUBSET_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Erelation_2ERSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,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_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)),c_2Erelation_2ERSUBSET_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0))) ).
fof(arityeq2_2Ec_2Erelation_2ERUNION_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2Erelation_2ERUNION_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0))) ).
fof(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2ESUBSET_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2EA_27b,axiom,
! [A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2ESUBSET_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2EA_27b_20mono_2EA_27b,axiom,
! [A_27b,X0_2E0] : s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) ).
fof(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2ESUBSET_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2ESUBSET_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Eset__relation_2Efinite__prefixes_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Eset__relation_2Efinite__prefixes_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Eset__relation_2Efinite__prefixes_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Eset__relation_2Efinite__prefixes_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2EA_27b,axiom,
! [A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Epred__set_2EUNION_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Epred__set_2EINTER_2E2_2Emono_2EA_27b,axiom,
! [A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Epred__set_2EINTER_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Epred__set_2EUNION_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Eset__relation_2Efinite__prefixes_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a,A_27c,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Eset__relation_2Efinite__prefixes_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Eset__relation_2Ercomp_2E2_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),c_2Eset__relation_2Ercomp_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool))),c_2Eset__relation_2Ercomp_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27b_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29,axiom,
! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool)),X0_2E0))) ).
fof(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28tyop_2Epair_2Eprod_28A_27b_2CA_27b_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool))),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool))),X0_2E0))) ).
fof(arityeq2_2Ec_2Eset__relation_2Efinite__prefixes_2E2_2Emono_2EA_27b_20mono_2EA_27b,axiom,
! [A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Eset__relation_2Efinite__prefixes_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Eset__relation_2Efinite__prefixes_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Eset__relation_2Efinite__prefixes_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Eset__relation_2Eirreflexive_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eirreflexive_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Eset__relation_2Eirreflexive_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Eset__relation_2Elinear__order_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Eset__relation_2Elinear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Eset__relation_2Elinear__order_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Eset__relation_2Epartial__order_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Eset__relation_2Epartial__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Eset__relation_2Epartial__order_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Eset__relation_2Ercomp_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Eset__relation_2Ercomp_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Eset__relation_2Ercomp_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Eset__relation_2Ereflexive_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Eset__relation_2Ereflexive_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereflexive_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Epred__set_2EINTER_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EINTER_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Eset__relation_2Estrict__linear__order_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Eset__relation_2Estrict__linear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Eset__relation_2Estrict__linear__order_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Eset__relation_2Etc_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Eset__relation_2Etc_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27a),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Eset__relation_2Etc_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27a),X1_2E0))) ).
fof(arityeq3_2Ec_2Eset__relation_2ERRUNIV_2E3_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2Eset__relation_2ERRUNIV_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0))) = 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Eset__relation_2ERRUNIV_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))) ).
fof(arityeq3_2Ec_2Eset__relation_2Ereln__to__rel_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2Eset__relation_2Ereln__to__rel_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0),s(A_27b,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Eset__relation_2Ereln__to__rel_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))),s(A_27b,X2_2E0))) ).
fof(thm_2Eset__relation_2Edomain__def,axiom,
! [A_27a,A_27b,F1_2E0,F0_2E0] :
( ! [V1x_2E0,V0r_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F1_2E0),s(A_27a,V1x_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0))))
<=> ? [V2y_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27b,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0)))) )
=> ( ! [V0r_2E0,V1x_2E0] : s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0))),s(A_27a,V1x_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F1_2E0),s(A_27a,V1x_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0)))))
=> ! [V0r_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0))))) ) ) ).
fof(thm_2Eset__relation_2Erange__def,axiom,
! [A_27a,A_27b,F1_2E0,F0_2E0] :
( ! [V1y_2E0,V0r_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F1_2E0),s(A_27a,V1y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))
<=> ? [V2x_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27b,A_27a),c_2Epair_2E_2C_2E2(s(A_27b,V2x_2E0),s(A_27a,V1y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) )
=> ( ! [V0r_2E0,V1y_2E0] : s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),V0r_2E0))),s(A_27a,V1y_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V1y_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F1_2E0),s(A_27a,V1y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))
=> ! [V0r_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),V0r_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))) ) ) ).
fof(thm_2Eset__relation_2Errestrict__def,axiom,
! [A_27a,F1_2E0,F0_2E0] :
( ! [V2x_2E0,V3y_2E0,V0r_2E0,V1s_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),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(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),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(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))),F1_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) ) )
=> ( ! [V0r_2E0,V1s_2E0,V2x_2E0,V3y_2E0] : s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V3y_2E0))),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),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(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),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(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))),F1_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))
=> ! [V0r_2E0,V1s_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))))) ) ) ).
fof(thm_2Eset__relation_2Ercomp__def,axiom,
! [A_27a,A_27b,A_27c,F1_2E0,F0_2E0] :
( ! [V2x_2E0,V0r1_2E0,V3y_2E0,V1r2_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))),F1_2E0),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),V0r1_2E0))),s(A_27b,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),V1r2_2E0))))
<=> ? [V4z_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27c),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27c,V4z_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),V0r1_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27c,A_27b),c_2Epair_2E_2C_2E2(s(A_27c,V4z_2E0),s(A_27b,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),V1r2_2E0)))) ) )
=> ( ! [V0r1_2E0,V1r2_2E0,V2x_2E0,V3y_2E0] : s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),V0r1_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),V1r2_2E0))),s(A_27a,V2x_2E0))),s(A_27b,V3y_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27b,V3y_2E0))),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))),F1_2E0),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),V0r1_2E0))),s(A_27b,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),V1r2_2E0)))))
=> ! [V0r1_2E0,V1r2_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Eset__relation_2Ercomp_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),V0r1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),V1r2_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),V0r1_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),V1r2_2E0))))))) ) ) ).
fof(thm_2Eset__relation_2Estrict__def,axiom,
! [A_27a,F1_2E0,F0_2E0] :
( ! [V1x_2E0,V2y_2E0,V0r_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F1_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))
& s(A_27a,V1x_2E0) != s(A_27a,V2y_2E0) ) )
=> ( ! [V0r_2E0,V1x_2E0,V2y_2E0] : s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F1_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))
=> ! [V0r_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Estrict_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))))) ) ) ).
fof(thm_2Eset__relation_2Euniv__reln__def,axiom,
! [A_27a,F1_2E0,F0_2E0] :
( ! [V1x1_2E0,V0xs_2E0,V2x2_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F1_2E0),s(A_27a,V1x1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0xs_2E0))),s(A_27a,V2x2_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0xs_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0xs_2E0)))) ) )
=> ( ! [V0xs_2E0,V1x1_2E0,V2x2_2E0] : s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0xs_2E0))),s(A_27a,V1x1_2E0))),s(A_27a,V2x2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x1_2E0),s(A_27a,V2x2_2E0))),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F1_2E0),s(A_27a,V1x1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0xs_2E0))),s(A_27a,V2x2_2E0)))))
=> ! [V0xs_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Euniv__reln_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0xs_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0xs_2E0))))))) ) ) ).
fof(thm_2Eset__relation_2Efinite__prefixes__def,axiom,
! [A_27a,A_27b,F0_2E0] :
( ! [V2e_2E0,V0r_2E0,V3e_27_2E0] : s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(A_27b,V2e_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0))),s(A_27a,V3e_27_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V3e_27_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V3e_27_2E0),s(A_27b,V2e_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0)))))
=> ! [V0r_2E0,V1s_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0))))
<=> ! [V2e_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V2e_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(A_27b,V2e_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0)))))))) ) ) ) ).
fof(thm_2Eset__relation_2Etc__def,axiom,
! [A_27a,V0x_2E0,V1x_27_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Etc_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27a),V1x_27_2E0))))
<=> ! [V2tc_27_2E0] :
( ! [V3a0_2E0] :
( ( ? [V4x_2E0,V5y_2E0] :
( s(tyop_2Epair_2Eprod(A_27a,A_27a),V3a0_2E0) = s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V4x_2E0),s(A_27a,V5y_2E0)))
& p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V4x_2E0),s(A_27a,V5y_2E0)))))) )
| ? [V6x_2E0,V7y_2E0] :
( s(tyop_2Epair_2Eprod(A_27a,A_27a),V3a0_2E0) = s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V6x_2E0),s(A_27a,V7y_2E0)))
& ? [V8z_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2tc_27_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V6x_2E0),s(A_27a,V8z_2E0))))))
& p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2tc_27_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V8z_2E0),s(A_27a,V7y_2E0)))))) ) ) )
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2tc_27_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27a),V3a0_2E0)))) )
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2tc_27_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27a),V1x_27_2E0)))) ) ) ).
fof(thm_2Eset__relation_2Eacyclic__def,axiom,
! [A_27a,V0r_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))
<=> ! [V1x_2E0] : ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V1x_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) ) ).
fof(thm_2Eset__relation_2Ereflexive__def,axiom,
! [A_27a,V0r_2E0,V1s_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Ereflexive_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))
<=> ! [V2x_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) ) ) ).
fof(thm_2Eset__relation_2Eirreflexive__def,axiom,
! [A_27a,V0r_2E0,V1s_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eirreflexive_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))
<=> ! [V2x_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))
=> ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) ) ) ).
fof(thm_2Eset__relation_2Etransitive__def,axiom,
! [A_27a,V0r_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Etransitive_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))
<=> ! [V1x_2E0,V2y_2E0,V3z_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2y_2E0),s(A_27a,V3z_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) )
=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V3z_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) ) ) ).
fof(thm_2Eset__relation_2Eantisym__def,axiom,
! [A_27a,V0r_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eantisym_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))
<=> ! [V1x_2E0,V2y_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2y_2E0),s(A_27a,V1x_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) )
=> s(A_27a,V1x_2E0) = s(A_27a,V2y_2E0) ) ) ).
fof(thm_2Eset__relation_2Epartial__order__def,axiom,
! [A_27a,V0r_2E0,V1s_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Epartial__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Etransitive_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Ereflexive_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eantisym_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) ) ) ).
fof(thm_2Eset__relation_2Elinear__order__def,axiom,
! [A_27a,V0r_2E0,V1s_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Elinear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Etransitive_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eantisym_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))
& ! [V2x_2E0,V3y_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) )
=> ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))
| p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V3y_2E0),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) ) ) ) ) ).
fof(thm_2Eset__relation_2Estrict__linear__order__def,axiom,
! [A_27a,V0r_2E0,V1s_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Estrict__linear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Etransitive_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))
& ! [V2x_2E0] : ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))
& ! [V3x_2E0,V4y_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))
& s(A_27a,V3x_2E0) != s(A_27a,V4y_2E0) )
=> ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V3x_2E0),s(A_27a,V4y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))
| p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V4y_2E0),s(A_27a,V3x_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) ) ) ) ) ).
fof(thm_2Eset__relation_2Ereln__to__rel__def,axiom,
! [A_27a,A_27b,V0r_2E0,V1x_2E0,V2x_27_2E0] : s(tyop_2Emin_2Ebool,c_2Eset__relation_2Ereln__to__rel_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0),s(A_27a,V1x_2E0),s(A_27b,V2x_27_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27b,V2x_27_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0))) ).
fof(thm_2Eset__relation_2Erel__to__reln__def,axiom,
! [A_27a,A_27b,F0_2E0] :
( ! [V0R_2E0,V1x_2E0,V2y_2E0] : s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0))),s(A_27a,V1x_2E0))),s(A_27b,V2y_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27b,V2y_2E0))),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27b,V2y_2E0)))))
=> ! [V0R_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Eset__relation_2Erel__to__reln_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0))))))) ) ).
fof(thm_2Eset__relation_2ERRUNIV__def,axiom,
! [A_27a,V0s_2E0,V1x_2E0,V2x_27_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2ERRUNIV_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V1x_2E0),s(A_27a,V2x_27_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) ) ) ).
fof(thm_2Eset__relation_2ERREFL__EXP__def,axiom,
! [A_27a,F0_2E0] :
( ! [V1s_2E0,V2x_2E0,V3y_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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0))))
<=> ( s(A_27a,V2x_2E0) = s(A_27a,V3y_2E0)
& ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) ) )
=> ! [V0R_2E0,V1s_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2ERREFL__EXP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))) ) ).
fof(thm_2Eset__relation_2Eacyclic__bigunion,axiom,
! [A_27a,V0rs_2E0] :
( ( ! [V1r_2E0,V2r_27_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0rs_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2r_27_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0rs_2E0))))
& s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0) != s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2r_27_2E0) )
=> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2r_27_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2r_27_2E0)))))))) )
& ! [V3r_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V3r_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0rs_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V3r_2E0)))) ) )
=> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0rs_2E0)))))) ) ).
fof(thm_2Eset__relation_2Eacyclic__SWAP,axiom,
! [A_27a,V0r_2E0] : s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(A_27a,A_27a)),c_2Epair_2ESWAP_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))) = s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))) ).
fof(thm_2Eset__relation_2Eacyclic__irreflexive,axiom,
! [A_27a,V0r_2E0,V1x_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))
=> ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V1x_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) ) ).
fof(thm_2Eset__relation_2Eacyclic__rrestrict,axiom,
! [A_27a,V0r_2E0,V1s_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) ) ).
fof(thm_2Eset__relation_2Etc__mono,axiom,
! [A_27a,V0s_2E0,V1r_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0s_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0s_2E0)))))) ) ).
fof(thm_2Eset__relation_2Etc__idemp,axiom,
! [A_27a,V0r_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))) ).
fof(thm_2Eset__relation_2Esubset__tc,axiom,
! [A_27a,V0r_2E0] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) ).
fof(thm_2Eset__relation_2Etc__closure,axiom,
! [A_27a,V0s_2E0,V1r_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0s_2E0))))))
=> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0s_2E0)))))) ) ).
fof(thm_2Eset__relation_2Etc__ind,axiom,
! [A_27a,V0r_2E0,V1tc_27_2E0] :
( ( ! [V2x_2E0,V3y_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_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)),V1tc_27_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))) )
& ! [V4x_2E0,V5y_2E0] :
( ? [V6z_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)),V1tc_27_2E0),s(A_27a,V4x_2E0))),s(A_27a,V6z_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)),V1tc_27_2E0),s(A_27a,V6z_2E0))),s(A_27a,V5y_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)),V1tc_27_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))) ) )
=> ! [V7x_2E0,V8y_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V7x_2E0),s(A_27a,V8y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_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)),V1tc_27_2E0),s(A_27a,V7x_2E0))),s(A_27a,V8y_2E0)))) ) ) ).
fof(thm_2Eset__relation_2Erextension,axiom,
! [A_27a,A_27b,V0s_2E0,V1t_2E0] :
( s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0s_2E0) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1t_2E0)
<=> ! [V2x_2E0,V3y_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27b,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0s_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27b,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1t_2E0))) ) ).
fof(thm_2Eset__relation_2Ein__domain,axiom,
! [A_27a,A_27b,V0x_2E0,V1r_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1r_2E0))))))
<=> ? [V2y_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V0x_2E0),s(A_27b,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1r_2E0)))) ) ).
fof(thm_2Eset__relation_2Ein__range,axiom,
! [A_27a,A_27b,V0y_2E0,V1r_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),V1r_2E0))))))
<=> ? [V2x_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27b,A_27a),c_2Epair_2E_2C_2E2(s(A_27b,V2x_2E0),s(A_27a,V0y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),V1r_2E0)))) ) ).
fof(thm_2Eset__relation_2Ein__dom__rg,axiom,
! [A_27a,A_27b,V0y_2E0,V1x_2E0,V2r_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27b,V0y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V2r_2E0))))
=> ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V2r_2E0))))))
& p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V0y_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V2r_2E0)))))) ) ) ).
fof(thm_2Eset__relation_2Edomain__mono,axiom,
! [A_27a,A_27b,V0r_27_2E0,V1r_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1r_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_27_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_27_2E0)))))) ) ).
fof(thm_2Eset__relation_2Erange__mono,axiom,
! [A_27a,A_27b,V0r_27_2E0,V1r_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1r_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_27_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1r_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_27_2E0)))))) ) ).
fof(thm_2Eset__relation_2Ein__rrestrict,axiom,
! [A_27a,V0x_2E0,V1y_2E0,V2r_2E0,V3s_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V0x_2E0),s(A_27a,V1y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0))))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V0x_2E0),s(A_27a,V1y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2r_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0)))) ) ) ).
fof(thm_2Eset__relation_2Ein__rrestrict__alt,axiom,
! [A_27a,V0x_2E0,V1s_2E0,V2r_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),V0x_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),V0x_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2r_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27a),V0x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27a),V0x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) ) ) ).
fof(thm_2Eset__relation_2Errestrict__SUBSET,axiom,
! [A_27a,V0s_2E0,V1r_2E0] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0)))) ).
fof(thm_2Eset__relation_2Errestrict__union,axiom,
! [A_27a,V0r1_2E0,V1r2_2E0,V2s_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))))) ).
fof(thm_2Eset__relation_2Errestrict__rrestrict,axiom,
! [A_27a,V0r_2E0,V1x_2E0,V2y_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2y_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2y_2E0))))) ).
fof(thm_2Eset__relation_2Edomain__rrestrict__SUBSET,axiom,
! [A_27a,V0s_2E0,V1r_2E0] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) ).
fof(thm_2Eset__relation_2Erange__rrestrict__SUBSET,axiom,
! [A_27a,V0s_2E0,V1r_2E0] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) ).
fof(thm_2Eset__relation_2Estrict__rrestrict,axiom,
! [A_27a,V0r_2E0,V1s_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Estrict_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Estrict_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) ).
fof(thm_2Eset__relation_2Efinite__prefixes__subset__s,axiom,
! [A_27a,A_27b,V0r_2E0,V1s_2E0,V2s_27_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s_27_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0)))) )
=> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s_27_2E0)))) ) ).
fof(thm_2Eset__relation_2Efinite__prefixes__subset__r,axiom,
! [A_27a,A_27b,V0r_2E0,V1r_27_2E0,V2s_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1r_27_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0)))) )
=> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1r_27_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s_2E0)))) ) ).
fof(thm_2Eset__relation_2Efinite__prefixes__subset__rs,axiom,
! [A_27a,A_27b,V0r_2E0,V1s_2E0,V2r_27_2E0,V3s_27_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0))))
=> ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V2r_27_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0))))
=> ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3s_27_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V2r_27_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3s_27_2E0)))) ) ) ) ).
fof(thm_2Eset__relation_2Efinite__prefixes__subset,axiom,
! [A_27a,V0r_2E0,V1s_2E0,V2s_27_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) )
=> ( p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_27_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_27_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_27_2E0)))) ) ) ).
fof(thm_2Eset__relation_2Efinite__prefixes__union,axiom,
! [A_27a,A_27b,V0r1_2E0,V1r2_2E0,V2s1_2E0,V3s2_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s1_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1r2_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3s2_2E0)))) )
=> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1r2_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3s2_2E0)))))) ) ).
fof(thm_2Eset__relation_2Efinite__prefixes__comp,axiom,
! [A_27a,A_27b,A_27c,F1_2E0,F0_2E0] :
( ! [V3s2_2E0,V4x_2E0,V1r2_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F1_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V3s2_2E0))),s(A_27b,V4x_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),V1r2_2E0))))
<=> ? [V5y_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27c,V5y_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V3s2_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27b,A_27c),c_2Epair_2E_2C_2E2(s(A_27b,V4x_2E0),s(A_27c,V5y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),V1r2_2E0)))) ) )
=> ( ! [V3s2_2E0,V1r2_2E0,V4x_2E0] : s(tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V3s2_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),V1r2_2E0))),s(A_27b,V4x_2E0))) = s(tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27b,V4x_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F1_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V3s2_2E0))),s(A_27b,V4x_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),V1r2_2E0)))))
=> ! [V0r1_2E0,V1r2_2E0,V2s1_2E0,V3s2_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s1_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),V1r2_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V3s2_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V3s2_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),V1r2_2E0))))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s1_2E0)))) )
=> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),c_2Eset__relation_2Ercomp_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),V1r2_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V3s2_2E0)))) ) ) ) ).
fof(thm_2Eset__relation_2Efinite__prefixes__inj__image,axiom,
! [A_27a,A_27b,F0_2E0] :
( ! [V0f_2E0,V1r_2E0,V5x_2E0,V6y_2E0] : s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool))))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0))),s(A_27a,V5x_2E0))),s(A_27a,V6y_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(A_27b,A_27b),c_2Epair_2E_2C_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V5x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V6y_2E0))))),s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V5x_2E0),s(A_27a,V6y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0)))))
=> ! [V0f_2E0,V1r_2E0,V2s_2E0] :
( ( ! [V3x_2E0,V4y_2E0] :
( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V4y_2E0)))
=> s(A_27a,V3x_2E0) = s(A_27a,V4y_2E0) )
& p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) )
=> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool))))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0))))))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))))) ) ) ).
fof(thm_2Eset__relation_2Efinite__prefixes__range,axiom,
! [A_27a,A_27b,V0r_2E0,V1s_2E0,V2t_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0)))))) )
=> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))))) ) ).
fof(thm_2Eset__relation_2Etc__rules,axiom,
! [A_27a,V0r_2E0] :
( ! [V1x_2E0,V2y_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) )
& ! [V3x_2E0,V4y_2E0] :
( ? [V5z_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V3x_2E0),s(A_27a,V5z_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))))
& p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V5z_2E0),s(A_27a,V4y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) )
=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V3x_2E0),s(A_27a,V4y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) ) ) ).
fof(thm_2Eset__relation_2Etc__cases,axiom,
! [A_27a,V0r_2E0,V1x_2E0,V2y_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))
| ? [V3z_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V3z_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))))
& p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V3z_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) ) ) ) ).
fof(thm_2Eset__relation_2Etc__strongind,axiom,
! [A_27a,V0r_2E0,V1tc_27_2E0] :
( ( ! [V2x_2E0,V3y_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_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)),V1tc_27_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))) )
& ! [V4x_2E0,V5y_2E0] :
( ? [V6z_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V4x_2E0),s(A_27a,V6z_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_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)),V1tc_27_2E0),s(A_27a,V4x_2E0))),s(A_27a,V6z_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V6z_2E0),s(A_27a,V5y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_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)),V1tc_27_2E0),s(A_27a,V6z_2E0))),s(A_27a,V5y_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)),V1tc_27_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))) ) )
=> ! [V7x_2E0,V8y_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V7x_2E0),s(A_27a,V8y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_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)),V1tc_27_2E0),s(A_27a,V7x_2E0))),s(A_27a,V8y_2E0)))) ) ) ).
fof(thm_2Eset__relation_2Etc__cases__right,axiom,
! [A_27a,V0r_2E0,V1x_2E0,V2y_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))
| ? [V3z_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V3z_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))))
& p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V3z_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) ) ) ) ).
fof(thm_2Eset__relation_2Etc__cases__left,axiom,
! [A_27a,V0r_2E0,V1x_2E0,V2y_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))
| ? [V3z_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V3z_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V3z_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) ) ) ) ).
fof(thm_2Eset__relation_2Etc__ind__left,axiom,
! [A_27a,V0r_2E0,V1tc_27_2E0] :
( ( ! [V2x_2E0,V3y_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_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)),V1tc_27_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))) )
& ! [V4x_2E0,V5y_2E0] :
( ? [V6z_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V4x_2E0),s(A_27a,V6z_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_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)),V1tc_27_2E0),s(A_27a,V6z_2E0))),s(A_27a,V5y_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)),V1tc_27_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))) ) )
=> ! [V7x_2E0,V8y_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V7x_2E0),s(A_27a,V8y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_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)),V1tc_27_2E0),s(A_27a,V7x_2E0))),s(A_27a,V8y_2E0)))) ) ) ).
fof(thm_2Eset__relation_2Etc__strongind__left,axiom,
! [A_27a,V0r_2E0,V1tc_27_2E0] :
( ( ! [V2x_2E0,V3y_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_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)),V1tc_27_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))) )
& ! [V4x_2E0,V5y_2E0] :
( ? [V6z_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V4x_2E0),s(A_27a,V6z_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V6z_2E0),s(A_27a,V5y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_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)),V1tc_27_2E0),s(A_27a,V6z_2E0))),s(A_27a,V5y_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)),V1tc_27_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))) ) )
=> ! [V7x_2E0,V8y_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V7x_2E0),s(A_27a,V8y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_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)),V1tc_27_2E0),s(A_27a,V7x_2E0))),s(A_27a,V8y_2E0)))) ) ) ).
fof(thm_2Eset__relation_2Etc__ind__right,axiom,
! [A_27a,V0r_2E0,V1tc_27_2E0] :
( ( ! [V2x_2E0,V3y_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_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)),V1tc_27_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))) )
& ! [V4x_2E0,V5y_2E0] :
( ? [V6z_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)),V1tc_27_2E0),s(A_27a,V4x_2E0))),s(A_27a,V6z_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V6z_2E0),s(A_27a,V5y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_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)),V1tc_27_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))) ) )
=> ! [V7x_2E0,V8y_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V7x_2E0),s(A_27a,V8y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_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)),V1tc_27_2E0),s(A_27a,V7x_2E0))),s(A_27a,V8y_2E0)))) ) ) ).
fof(thm_2Eset__relation_2Ertc__ind__right,axiom,
! [A_27a,V0r_2E0,V1tc_27_2E0] :
( ( ! [V2x_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))))
| p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_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)),V1tc_27_2E0),s(A_27a,V2x_2E0))),s(A_27a,V2x_2E0)))) )
& ! [V3x_2E0,V4y_2E0] :
( ? [V5z_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)),V1tc_27_2E0),s(A_27a,V3x_2E0))),s(A_27a,V5z_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V5z_2E0),s(A_27a,V4y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_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)),V1tc_27_2E0),s(A_27a,V3x_2E0))),s(A_27a,V4y_2E0)))) ) )
=> ! [V6x_2E0,V7y_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V6x_2E0),s(A_27a,V7y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_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)),V1tc_27_2E0),s(A_27a,V6x_2E0))),s(A_27a,V7y_2E0)))) ) ) ).
fof(thm_2Eset__relation_2Etc__strongind__right,axiom,
! [A_27a,V0r_2E0,V1tc_27_2E0] :
( ( ! [V2x_2E0,V3y_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_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)),V1tc_27_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))) )
& ! [V4x_2E0,V5y_2E0] :
( ? [V6z_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V4x_2E0),s(A_27a,V6z_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_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)),V1tc_27_2E0),s(A_27a,V4x_2E0))),s(A_27a,V6z_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V6z_2E0),s(A_27a,V5y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_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)),V1tc_27_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))) ) )
=> ! [V7x_2E0,V8y_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V7x_2E0),s(A_27a,V8y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_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)),V1tc_27_2E0),s(A_27a,V7x_2E0))),s(A_27a,V8y_2E0)))) ) ) ).
fof(thm_2Eset__relation_2Etc__union,axiom,
! [A_27a,V0r1_2E0,V1x_2E0,V2y_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r1_2E0))))))
=> ! [V3r2_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V3r2_2E0)))))))) ) ).
fof(thm_2Eset__relation_2Etc__implication,axiom,
! [A_27a,V0r1_2E0,V1r2_2E0] :
( ! [V2x_2E0,V3y_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r1_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r2_2E0)))) )
=> ! [V4x_2E0,V5y_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V4x_2E0),s(A_27a,V5y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r1_2E0))))))
=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V4x_2E0),s(A_27a,V5y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r2_2E0)))))) ) ) ).
fof(thm_2Eset__relation_2Etc__empty,axiom,
! [A_27a,V0x_2E0,V1y_2E0] : ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V0x_2E0),s(A_27a,V1y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))))) ).
fof(thm_2Eset__relation_2Etc__empty__eqn,axiom,
! [A_27a] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) ).
fof(thm_2Eset__relation_2Etc__domain__range,axiom,
! [A_27a,V0r_2E0,V1x_2E0,V2y_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))))
=> ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))))
& p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) ) ) ).
fof(thm_2Eset__relation_2Errestrict__tc,axiom,
! [A_27a,V0x_2E0,V1r_2E0,V2e_2E0,V3e_27_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2e_2E0),s(A_27a,V3e_27_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0))))))))
=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2e_2E0),s(A_27a,V3e_27_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0)))))) ) ).
fof(thm_2Eset__relation_2Etc__SWAP,axiom,
! [A_27a,V0r_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(A_27a,A_27a)),c_2Epair_2ESWAP_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(A_27a,A_27a)),c_2Epair_2ESWAP_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))) ).
fof(thm_2Eset__relation_2Eacyclic__subset,axiom,
! [A_27a,V0r1_2E0,V1r2_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r1_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r2_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r1_2E0)))) )
=> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r2_2E0)))) ) ).
fof(thm_2Eset__relation_2Eacyclic__union,axiom,
! [A_27a,V0r_2E0,V1r_27_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_27_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_27_2E0))))))))
& p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_27_2E0)))) )
=> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_27_2E0)))))) ) ).
fof(thm_2Eset__relation_2Etransitive__tc,axiom,
! [A_27a,V0r_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Etransitive_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))
=> s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0) ) ).
fof(thm_2Eset__relation_2Etc__transitive,axiom,
! [A_27a,V0r_2E0] : p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Etransitive_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) ).
fof(thm_2Eset__relation_2Eantisym__subset,axiom,
! [A_27a,V0t_2E0,V1s_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eantisym_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0t_2E0))))
=> ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0t_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eantisym_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1s_2E0)))) ) ) ).
fof(thm_2Eset__relation_2Epartial__order__dom__rng,axiom,
! [A_27a,V0r_2E0,V1s_2E0,V2x_2E0,V3y_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Epartial__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) )
=> ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) ) ) ).
fof(thm_2Eset__relation_2Epartial__order__subset,axiom,
! [A_27a,V0r_2E0,V1s_2E0,V2s_27_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Epartial__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) )
=> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Epartial__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_27_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_27_2E0)))) ) ).
fof(thm_2Eset__relation_2Estrict__partial__order,axiom,
! [A_27a,V0r_2E0,V1s_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Epartial__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))
=> ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Estrict_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Estrict_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Etransitive_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Estrict_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))))
& p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eantisym_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Estrict_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) ) ) ).
fof(thm_2Eset__relation_2Estrict__partial__order__acyclic,axiom,
! [A_27a,V0r_2E0,V1s_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Epartial__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Estrict_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) ) ).
fof(thm_2Eset__relation_2Elinear__order__subset,axiom,
! [A_27a,V0r_2E0,V1s_2E0,V2s_27_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Elinear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) )
=> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Elinear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_27_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_27_2E0)))) ) ).
fof(thm_2Eset__relation_2Epartial__order__linear__order,axiom,
! [A_27a,V0r_2E0,V1s_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Elinear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Epartial__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) ) ).
fof(thm_2Eset__relation_2Estrict__linear__order__dom__rng,axiom,
! [A_27a,V0r_2E0,V1s_2E0,V2x_2E0,V3y_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Estrict__linear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) )
=> ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) ) ) ).
fof(thm_2Eset__relation_2Elinear__order__dom__rng,axiom,
! [A_27a,V0r_2E0,V1s_2E0,V2x_2E0,V3y_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Elinear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) )
=> ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) ) ) ).
fof(thm_2Eset__relation_2ERREFL__EXP__RSUBSET,axiom,
! [A_27a,V0s_2E0,V1R_2E0] : p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2ERREFL__EXP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) ).
fof(thm_2Eset__relation_2ERREFL__EXP__UNIV,axiom,
! [A_27a,V0R_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2ERREFL__EXP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0) ).
fof(thm_2Eset__relation_2EREL__RESTRICT__UNIV,axiom,
! [A_27a,V0R_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EREL__RESTRICT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0) ).
fof(thm_2Eset__relation_2Ein__rel__to__reln,axiom,
! [A_27a,A_27b,V0xy_2E0,V1R_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),V0xy_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Eset__relation_2Erel__to__reln_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R_2E0))))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V0xy_2E0))))),s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V0xy_2E0))))) ).
fof(thm_2Eset__relation_2Ereln__to__rel__app,axiom,
! [A_27a,A_27b,V0y_2E0,V1x_2E0,V2r_2E0] : s(tyop_2Emin_2Ebool,c_2Eset__relation_2Ereln__to__rel_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V2r_2E0),s(A_27a,V1x_2E0),s(A_27b,V0y_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27b,V0y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V2r_2E0))) ).
fof(thm_2Eset__relation_2Erel__to__reln__IS__UNCURRY,axiom,
! [A_27a,A_27b] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Eset__relation_2Erel__to__reln_2E0) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E0) ).
fof(thm_2Eset__relation_2Ereln__to__rel__IS__CURRY,axiom,
! [A_27a,A_27b] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Eset__relation_2Ereln__to__rel_2E0) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Epair_2ECURRY_2E0) ).
fof(thm_2Eset__relation_2Erel__to__reln__inv,conjecture,
! [A_27a,A_27b,V0R_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Eset__relation_2Erel__to__reln_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0) ).
%------------------------------------------------------------------------------