ITP001 Axioms: ITP062+4.ax
%------------------------------------------------------------------------------
% File : ITP062+4 : TPTP v9.0.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 syntactic export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : bft.ax [Gau19]
% : HL4062+4.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 54 ( 31 unt; 0 def)
% Number of atoms : 100 ( 45 equ)
% Maximal formula atoms : 9 ( 1 avg)
% Number of connectives : 51 ( 5 ~; 4 |; 13 &)
% ( 13 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 18 ( 3 avg)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 61 ( 61 usr; 32 con; 0-5 aty)
% Number of variables : 204 ( 203 !; 1 ?)
% SPC : FOF_SAT_RFO_SEQ
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
fof(reserved_2Eho_2Eboolext,axiom,
! [V0_2E0,V1_2E0] :
( ( p(s(tyop_2Emin_2Ebool,V0_2E0))
<=> p(s(tyop_2Emin_2Ebool,V1_2E0)) )
=> s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0) ) ).
fof(reserved_2Eho_2Etruth,axiom,
p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ).
fof(reserved_2Eho_2Enotfalse,axiom,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) ).
fof(reserved_2Eho_2Ebool__cases__ax,axiom,
! [V0t_2E0] :
( s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
| s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ).
fof(reserved_2Eho_2Ei__thm,axiom,
! [A_27a,V0x_2E0] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0))) = s(A_27a,V0x_2E0) ).
fof(reserved_2Eho_2Ek__thm,axiom,
! [A_27a,A_27b,V0x_2E0,V1y_2E0] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0))) = s(A_27a,V0x_2E0) ).
fof(reserved_2Eho_2Es__thm,axiom,
! [A_27a,A_27b,A_27c,V0f_2E0,V1g_2E0,V2x_2E0] : s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))))) ).
fof(reserved_2Elogic_2E_2F_5C,axiom,
! [V0_2E0,V1_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,V0_2E0))
& p(s(tyop_2Emin_2Ebool,V1_2E0)) ) ) ).
fof(reserved_2Elogic_2E_5C_2F,axiom,
! [V0_2E0,V1_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,V0_2E0))
| p(s(tyop_2Emin_2Ebool,V1_2E0)) ) ) ).
fof(reserved_2Elogic_2E_7E,axiom,
! [V0_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0))))
<=> ~ p(s(tyop_2Emin_2Ebool,V0_2E0)) ) ).
fof(reserved_2Elogic_2E_3D_3D_3E,axiom,
! [V0_2E0,V1_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,V0_2E0))
=> p(s(tyop_2Emin_2Ebool,V1_2E0)) ) ) ).
fof(reserved_2Elogic_2E_3D,axiom,
! [A_27a,V0_2E0,V1_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0))))
<=> s(A_27a,V0_2E0) = s(A_27a,V1_2E0) ) ).
fof(reserved_2Equant_2E_21,axiom,
! [A_27a,V0f_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0))))
<=> ! [V1x_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0)))) ) ).
fof(reserved_2Equant_2E_3F,axiom,
! [A_27a,V0f_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0))))
<=> ? [V1x_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0)))) ) ).
fof(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
! [X0_2E0,X1_2E0] :
( ( p(s(tyop_2Emin_2Ebool,X0_2E0))
& p(s(tyop_2Emin_2Ebool,X1_2E0)) )
<=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) ) ).
fof(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,
! [X0_2E0,X1_2E0] :
( ( p(s(tyop_2Emin_2Ebool,X0_2E0))
| p(s(tyop_2Emin_2Ebool,X1_2E0)) )
<=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) ) ).
fof(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,
! [X0_2E0] :
( ~ p(s(tyop_2Emin_2Ebool,X0_2E0))
<=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))) ) ).
fof(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
! [X0_2E0,X1_2E0] :
( ( p(s(tyop_2Emin_2Ebool,X0_2E0))
=> p(s(tyop_2Emin_2Ebool,X1_2E0)) )
<=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) ) ).
fof(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] :
( s(A_27a,X0_2E0) = s(A_27a,X1_2E0)
<=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))) ) ).
fof(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq1_2Ec_2Elist_2EALL__DISTINCT_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),c_2Elist_2EALL__DISTINCT_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))) ).
fof(arityeq5_2Ec_2Ebft_2EBFT_2E5_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0,X2_2E0,X3_2E0,X4_2E0] : s(tyop_2Elist_2Elist(A_27a),c_2Ebft_2EBFT_2E5(s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0),s(tyop_2Elist_2Elist(A_27a),X3_2E0),s(tyop_2Elist_2Elist(A_27a),X4_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))))),c_2Ebft_2EBFT_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0))),s(tyop_2Elist_2Elist(A_27a),X3_2E0))),s(tyop_2Elist_2Elist(A_27a),X4_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_2EdirGraph_2EParents_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EdirGraph_2EParents_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2EdirGraph_2EParents_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),X0_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27c_20mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27d_29_2CA_27e_29_29,axiom,
! [A_27a,A_27c,A_27d,A_27e,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e))),c_2Epair_2E_2C_2E2(s(A_27c,X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e)),X1_2E0))) = s(tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e)),tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e)))),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e)),tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e))))),c_2Epair_2E_2C_2E0),s(A_27c,X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e)),X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Elist_2Elist_28A_27b_29_29_20mono_2Etyop_2Epair_2Eprod_28A_27c_2Ctyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27d_29_2CA_27e_29_29_29,axiom,
! [A_27a,A_27b,A_27c,A_27d,A_27e,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e)))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),X0_2E0),s(tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e))),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e)))))),c_2Epair_2E_2C_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),X0_2E0))),s(tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e))),X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27d_29_2CA_27e_29,axiom,
! [A_27a,A_27d,A_27e,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e)))),c_2Epair_2E_2C_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e),X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27d_29_20mono_2EA_27e,axiom,
! [A_27d,A_27e,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27d),X0_2E0),s(A_27e,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e),app_2E2(s(tyop_2Emin_2Efun(A_27e,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27d),tyop_2Emin_2Efun(A_27e,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e))),c_2Epair_2E_2C_2E0),s(tyop_2Elist_2Elist(A_27d),X0_2E0))),s(A_27e,X1_2E0))) ).
fof(arityeq1_2Ec_2Ebft_2ERel_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d_20mono_2EA_27e,axiom,
! [A_27a,A_27b,A_27c,A_27d,A_27e,X0_2E0] : s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebft_2ERel_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e)))),X0_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e)))),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebft_2ERel_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e)))),X0_2E0))) ).
fof(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Elist_2ECONS_2E0),s(A_27a,X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) ).
fof(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Elist_2EAPPEND_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Epair_2E_2C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).
fof(arityeq1_2Ec_2Epred__set_2ECARD_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),c_2Epred__set_2ECARD_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq2_2Ec_2Epred__set_2EDIFF_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_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_2EDIFF_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_2Elist_2ELENGTH_2E1_2Emono_2EA_27d,axiom,
! [A_27d,X0_2E0] : s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27d),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27d),tyop_2Enum_2Enum),c_2Elist_2ELENGTH_2E0),s(tyop_2Elist_2Elist(A_27d),X0_2E0))) ).
fof(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Elist_2ELIST__TO__SET_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))) ).
fof(arityeq1_2Ec_2EdirGraph_2EParents_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EdirGraph_2EParents_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2EdirGraph_2EParents_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),X0_2E0))) ).
fof(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2EdirGraph_2EREACH__LIST_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EdirGraph_2EREACH__LIST_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2EdirGraph_2EREACH__LIST_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) ).
fof(arityeq2_2Ec_2EdirGraph_2EEXCLUDE_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),c_2EdirGraph_2EEXCLUDE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)))),c_2EdirGraph_2EEXCLUDE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq5_2Ec_2Ebft_2EBFT_2E5_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0,X3_2E0,X4_2E0] : s(A_27b,c_2Ebft_2EBFT_2E5(s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0),s(tyop_2Elist_2Elist(A_27a),X3_2E0),s(A_27b,X4_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,A_27b))))),c_2Ebft_2EBFT_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0))),s(tyop_2Elist_2Elist(A_27a),X3_2E0))),s(A_27b,X4_2E0))) ).
fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27b,axiom,
! [A_27b,X0_2E0,X1_2E0,X2_2E0] : s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(A_27b,X1_2E0),s(A_27b,X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(A_27b,X1_2E0))),s(A_27b,X2_2E0))) ).
fof(arityeq3_2Ec_2Elist_2EFOLDR_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(A_27b,c_2Elist_2EFOLDR_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),X0_2E0),s(A_27b,X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))),c_2Elist_2EFOLDR_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),X0_2E0))),s(A_27b,X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) ).
fof(thm_2Ebft_2ERel__def,axiom,
! [A_27a,A_27b,A_27c,A_27d,A_27e,V0G_2E0,V1f_2E0,V2seen_2E0,V3fringe_2E0,V4acc_2E0] : s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebft_2ERel_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e)))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),V0G_2E0),s(tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e))),c_2Epair_2E_2C_2E2(s(A_27c,V1f_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V2seen_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27d),V3fringe_2E0),s(A_27e,V4acc_2E0))))))))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EdirGraph_2EParents_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),V0G_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V2seen_2E0))))))),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27d),V3fringe_2E0))))) ).
fof(thm_2Ebft_2EBFT__def,axiom,
! [A_27a,A_27b,V0t_2E0,V1seen_2E0,V2h_2E0,V3f_2E0,V4acc_2E0,V5G_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EdirGraph_2EParents_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),V5G_2E0))))))
=> ( s(A_27b,c_2Ebft_2EBFT_2E5(s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),V5G_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V3f_2E0),s(tyop_2Elist_2Elist(A_27a),V1seen_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(A_27b,V4acc_2E0))) = s(A_27b,V4acc_2E0)
& s(A_27b,c_2Ebft_2EBFT_2E5(s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),V5G_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V3f_2E0),s(tyop_2Elist_2Elist(A_27a),V1seen_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V0t_2E0))),s(A_27b,V4acc_2E0))) = s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2h_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1seen_2E0))))),s(A_27b,c_2Ebft_2EBFT_2E5(s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),V5G_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V3f_2E0),s(tyop_2Elist_2Elist(A_27a),V1seen_2E0),s(tyop_2Elist_2Elist(A_27a),V0t_2E0),s(A_27b,V4acc_2E0))),s(A_27b,c_2Ebft_2EBFT_2E5(s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),V5G_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V3f_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V1seen_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0t_2E0),s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),V5G_2E0),s(A_27a,V2h_2E0))))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V3f_2E0),s(A_27a,V2h_2E0))),s(A_27b,V4acc_2E0))))))) ) ) ).
fof(thm_2Ebft_2EBFT__ind,axiom,
! [A_27a,A_27b,V0P_2E0] :
( ! [V1G_2E0,V2f_2E0,V3seen_2E0,V4h_2E0,V5t_2E0,V6acc_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))))),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),V1G_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V2f_2E0))),s(tyop_2Elist_2Elist(A_27a),V3seen_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))),s(A_27b,V6acc_2E0))))
& ( ( ( ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EdirGraph_2EParents_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),V1G_2E0))))))
& ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4h_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V3seen_2E0)))))) )
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))))),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),V1G_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V2f_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V4h_2E0),s(tyop_2Elist_2Elist(A_27a),V3seen_2E0))))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V5t_2E0),s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),V1G_2E0),s(A_27a,V4h_2E0))))))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V2f_2E0),s(A_27a,V4h_2E0))),s(A_27b,V6acc_2E0)))))) )
& ( ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EdirGraph_2EParents_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),V1G_2E0))))))
& p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4h_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V3seen_2E0)))))) )
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))))),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),V1G_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V2f_2E0))),s(tyop_2Elist_2Elist(A_27a),V3seen_2E0))),s(tyop_2Elist_2Elist(A_27a),V5t_2E0))),s(A_27b,V6acc_2E0)))) ) )
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))))),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),V1G_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V2f_2E0))),s(tyop_2Elist_2Elist(A_27a),V3seen_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V4h_2E0),s(tyop_2Elist_2Elist(A_27a),V5t_2E0))))),s(A_27b,V6acc_2E0)))) ) )
=> ! [V7v_2E0,V8v1_2E0,V9v2_2E0,V10v3_2E0,V11v4_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))))),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),V7v_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V8v1_2E0))),s(tyop_2Elist_2Elist(A_27a),V9v2_2E0))),s(tyop_2Elist_2Elist(A_27a),V10v3_2E0))),s(A_27b,V11v4_2E0)))) ) ).
fof(thm_2Ebft_2EBFT__CONS,axiom,
! [A_27a,V0G_2E0,V1f_2E0,V2seen_2E0,V3fringe_2E0,V4acc_2E0,V5a_2E0,V6b_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EdirGraph_2EParents_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),V0G_2E0))))))
& s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),V1f_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Elist_2ECONS_2E0)
& s(tyop_2Elist_2Elist(A_27a),V4acc_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V5a_2E0),s(tyop_2Elist_2Elist(A_27a),V6b_2E0))) )
=> s(tyop_2Elist_2Elist(A_27a),c_2Ebft_2EBFT_2E5(s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),V0G_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),V1f_2E0),s(tyop_2Elist_2Elist(A_27a),V2seen_2E0),s(tyop_2Elist_2Elist(A_27a),V3fringe_2E0),s(tyop_2Elist_2Elist(A_27a),V4acc_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Ebft_2EBFT_2E5(s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),V0G_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),V1f_2E0),s(tyop_2Elist_2Elist(A_27a),V2seen_2E0),s(tyop_2Elist_2Elist(A_27a),V3fringe_2E0),s(tyop_2Elist_2Elist(A_27a),V5a_2E0))),s(tyop_2Elist_2Elist(A_27a),V6b_2E0))) ) ).
fof(thm_2Ebft_2EBFT__FOLD,axiom,
! [A_27a,A_27b,V0G_2E0,V1f_2E0,V2seen_2E0,V3fringe_2E0,V4acc_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EdirGraph_2EParents_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),V0G_2E0))))))
=> s(A_27b,c_2Ebft_2EBFT_2E5(s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),V0G_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V1f_2E0),s(tyop_2Elist_2Elist(A_27a),V2seen_2E0),s(tyop_2Elist_2Elist(A_27a),V3fringe_2E0),s(A_27b,V4acc_2E0))) = s(A_27b,c_2Elist_2EFOLDR_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V1f_2E0),s(A_27b,V4acc_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Ebft_2EBFT_2E5(s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),V0G_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Elist_2ECONS_2E0),s(tyop_2Elist_2Elist(A_27a),V2seen_2E0),s(tyop_2Elist_2Elist(A_27a),V3fringe_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))) ) ).
fof(thm_2Ebft_2EBFT__ALL__DISTINCT,axiom,
! [A_27a,V0G_2E0,V1seen_2E0,V2fringe_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EdirGraph_2EParents_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),V0G_2E0))))))
=> p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Ebft_2EBFT_2E5(s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),V0G_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Elist_2ECONS_2E0),s(tyop_2Elist_2Elist(A_27a),V1seen_2E0),s(tyop_2Elist_2Elist(A_27a),V2fringe_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))))) ) ).
fof(thm_2Ebft_2EBFT__REACH__1,axiom,
! [A_27a,V0G_2E0,V1f_2E0,V2seen_2E0,V3fringe_2E0,V4acc_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EdirGraph_2EParents_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),V0G_2E0))))))
& s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),V1f_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Elist_2ECONS_2E0) )
=> ! [V5x_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V5x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Ebft_2EBFT_2E5(s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),V0G_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),V1f_2E0),s(tyop_2Elist_2Elist(A_27a),V2seen_2E0),s(tyop_2Elist_2Elist(A_27a),V3fringe_2E0),s(tyop_2Elist_2Elist(A_27a),V4acc_2E0))))))))
=> ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V5x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EdirGraph_2EREACH__LIST_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),V0G_2E0),s(tyop_2Elist_2Elist(A_27a),V3fringe_2E0))))))
| p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V5x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V4acc_2E0)))))) ) ) ) ).
fof(thm_2Ebft_2EBFT__REACH__2,axiom,
! [A_27a,V0G_2E0,V1f_2E0,V2seen_2E0,V3fringe_2E0,V4acc_2E0,V5x_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EdirGraph_2EParents_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),V0G_2E0))))))
& s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),V1f_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Elist_2ECONS_2E0)
& p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V5x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EdirGraph_2EREACH__LIST_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),c_2EdirGraph_2EEXCLUDE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),V0G_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V2seen_2E0))))),s(tyop_2Elist_2Elist(A_27a),V3fringe_2E0))))))
& ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V5x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V2seen_2E0)))))) )
=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V5x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Ebft_2EBFT_2E5(s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),V0G_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),V1f_2E0),s(tyop_2Elist_2Elist(A_27a),V2seen_2E0),s(tyop_2Elist_2Elist(A_27a),V3fringe_2E0),s(tyop_2Elist_2Elist(A_27a),V4acc_2E0)))))))) ) ).
fof(thm_2Ebft_2EBFT__REACH__THM,axiom,
! [A_27a,V0G_2E0,V1fringe_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EdirGraph_2EParents_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),V0G_2E0))))))
=> ! [V2x_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EdirGraph_2EREACH__LIST_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),V0G_2E0),s(tyop_2Elist_2Elist(A_27a),V1fringe_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Ebft_2EBFT_2E5(s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),V0G_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Elist_2ECONS_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27a),V1fringe_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))))) ) ).
fof(reserved_2Eho_2Eeq__ext,axiom,
! [A_27a,A_27b,V0f_2E0,V1g_2E0] :
( ! [V2x_2E0] : s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))
=> s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0) ) ).
%------------------------------------------------------------------------------