TPTP Problem File: ITP023+1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : ITP023+1 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Problem : HOL4 syntactic export of thm_2Ereal__topology_2EBOUNDED__BALL.p, bushy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : thm_2Ereal__topology_2EBOUNDED__BALL.p [Gau19]
% : HL411001+1.p [TPAP]
% Status : Theorem
% Rating : 0.33 v8.2.0, 0.36 v7.5.0
% Syntax : Number of formulae : 53 ( 16 unt; 0 def)
% Number of atoms : 191 ( 25 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 186 ( 48 ~; 36 |; 26 &)
% ( 44 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 35 ( 35 usr; 19 con; 0-2 aty)
% Number of variables : 107 ( 105 !; 2 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments :
% Bugfixes : v7.5.0 - Bugfixes in axioms and export.
%------------------------------------------------------------------------------
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_2Ereal__topology_2Ebounded__def_2E1,axiom,
! [X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ereal__topology_2Ebounded__def_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,X0_2E0),s(tyop_2Erealax_2Ereal,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal))),c_2Epair_2E_2C_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))),s(tyop_2Erealax_2Ereal,X1_2E0))) ).
fof(arityeq1_2Ec_2Ereal__topology_2Eball_2E1,axiom,
! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),c_2Ereal__topology_2Eball_2E0),s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X0_2E0))) ).
fof(arityeq1_2Ec_2Ereal__topology_2Ecball_2E1,axiom,
! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),c_2Ereal__topology_2Ecball_2E0),s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X0_2E0))) ).
fof(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2ESUBSET_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X1_2E0))) ).
fof(thm_2Ebool_2ETRUTH,axiom,
p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ).
fof(thm_2Ebool_2EIMP__ANTISYM__AX,axiom,
! [V0t1_2E0,V1t2_2E0] :
( ( p(s(tyop_2Emin_2Ebool,V0t1_2E0))
=> p(s(tyop_2Emin_2Ebool,V1t2_2E0)) )
=> ( ( p(s(tyop_2Emin_2Ebool,V1t2_2E0))
=> p(s(tyop_2Emin_2Ebool,V0t1_2E0)) )
=> s(tyop_2Emin_2Ebool,V0t1_2E0) = s(tyop_2Emin_2Ebool,V1t2_2E0) ) ) ).
fof(thm_2Ebool_2EIMP__F,axiom,
! [V0t_2E0] :
( ( p(s(tyop_2Emin_2Ebool,V0t_2E0))
=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) )
=> ~ p(s(tyop_2Emin_2Ebool,V0t_2E0)) ) ).
fof(thm_2Ebool_2EF__IMP,axiom,
! [V0t_2E0] :
( ~ p(s(tyop_2Emin_2Ebool,V0t_2E0))
=> ( p(s(tyop_2Emin_2Ebool,V0t_2E0))
=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) ) ) ).
fof(thm_2Ebool_2EIMP__CLAUSES,axiom,
! [V0t_2E0] :
( ( ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))
=> p(s(tyop_2Emin_2Ebool,V0t_2E0)) )
<=> p(s(tyop_2Emin_2Ebool,V0t_2E0)) )
& ( ( p(s(tyop_2Emin_2Ebool,V0t_2E0))
=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) )
<=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) )
& ( ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))
=> p(s(tyop_2Emin_2Ebool,V0t_2E0)) )
<=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) )
& ( ( p(s(tyop_2Emin_2Ebool,V0t_2E0))
=> p(s(tyop_2Emin_2Ebool,V0t_2E0)) )
<=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) )
& ( ( p(s(tyop_2Emin_2Ebool,V0t_2E0))
=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) )
<=> ~ p(s(tyop_2Emin_2Ebool,V0t_2E0)) ) ) ).
fof(thm_2Ebool_2ENOT__CLAUSES,axiom,
( ! [V0t_2E0] :
( ~ ~ p(s(tyop_2Emin_2Ebool,V0t_2E0))
<=> p(s(tyop_2Emin_2Ebool,V0t_2E0)) )
& ( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))
<=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) )
& ( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))
<=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ) ) ).
fof(thm_2Ebool_2EEQ__SYM__EQ,axiom,
! [A_27a,V0x_2E0,V1y_2E0] :
( s(A_27a,V0x_2E0) = s(A_27a,V1y_2E0)
<=> s(A_27a,V1y_2E0) = s(A_27a,V0x_2E0) ) ).
fof(thm_2Ebool_2EEQ__CLAUSES,axiom,
! [V0t_2E0] :
( ( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0)
<=> p(s(tyop_2Emin_2Ebool,V0t_2E0)) )
& ( s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
<=> p(s(tyop_2Emin_2Ebool,V0t_2E0)) )
& ( s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0)
<=> ~ p(s(tyop_2Emin_2Ebool,V0t_2E0)) )
& ( s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
<=> ~ p(s(tyop_2Emin_2Ebool,V0t_2E0)) ) ) ).
fof(thm_2Ebool_2ENOT__FORALL__THM,axiom,
! [A_27a,V0P_2E0] :
( ~ ! [V1x_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V1x_2E0))))
<=> ? [V2x_2E0] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))) ) ).
fof(thm_2Ebool_2EDISJ__ASSOC,axiom,
! [V0A_2E0,V1B_2E0,V2C_2E0] :
( ( p(s(tyop_2Emin_2Ebool,V0A_2E0))
| p(s(tyop_2Emin_2Ebool,V1B_2E0))
| p(s(tyop_2Emin_2Ebool,V2C_2E0)) )
<=> ( p(s(tyop_2Emin_2Ebool,V0A_2E0))
| p(s(tyop_2Emin_2Ebool,V1B_2E0))
| p(s(tyop_2Emin_2Ebool,V2C_2E0)) ) ) ).
fof(thm_2Ebool_2EDISJ__SYM,axiom,
! [V0A_2E0,V1B_2E0] :
( ( p(s(tyop_2Emin_2Ebool,V0A_2E0))
| p(s(tyop_2Emin_2Ebool,V1B_2E0)) )
<=> ( p(s(tyop_2Emin_2Ebool,V1B_2E0))
| p(s(tyop_2Emin_2Ebool,V0A_2E0)) ) ) ).
fof(thm_2Ebool_2EDE__MORGAN__THM,axiom,
! [V0A_2E0,V1B_2E0] :
( ( ~ ( p(s(tyop_2Emin_2Ebool,V0A_2E0))
& p(s(tyop_2Emin_2Ebool,V1B_2E0)) )
<=> ( ~ p(s(tyop_2Emin_2Ebool,V0A_2E0))
| ~ p(s(tyop_2Emin_2Ebool,V1B_2E0)) ) )
& ( ~ ( p(s(tyop_2Emin_2Ebool,V0A_2E0))
| p(s(tyop_2Emin_2Ebool,V1B_2E0)) )
<=> ( ~ p(s(tyop_2Emin_2Ebool,V0A_2E0))
& ~ p(s(tyop_2Emin_2Ebool,V1B_2E0)) ) ) ) ).
fof(thm_2Ereal__topology_2EBALL__SUBSET__CBALL,axiom,
! [V0x_2E0,V1e_2E0] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V0x_2E0),s(tyop_2Erealax_2Ereal,V1e_2E0))))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V0x_2E0),s(tyop_2Erealax_2Ereal,V1e_2E0)))))))) ).
fof(thm_2Ereal__topology_2EBOUNDED__SUBSET,axiom,
! [V0s_2E0,V1t_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),V1t_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),V1t_2E0)))) )
=> p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),V0s_2E0)))) ) ).
fof(thm_2Ereal__topology_2EBOUNDED__CBALL,axiom,
! [V0x_2E0,V1e_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V0x_2E0),s(tyop_2Erealax_2Ereal,V1e_2E0)))))))) ).
fof(thm_2Esat_2ENOT__NOT,axiom,
! [V0t_2E0] :
( ~ ~ p(s(tyop_2Emin_2Ebool,V0t_2E0))
<=> p(s(tyop_2Emin_2Ebool,V0t_2E0)) ) ).
fof(thm_2Esat_2EAND__INV__IMP,axiom,
! [V0A_2E0] :
( p(s(tyop_2Emin_2Ebool,V0A_2E0))
=> ( ~ p(s(tyop_2Emin_2Ebool,V0A_2E0))
=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) ) ) ).
fof(thm_2Esat_2EOR__DUAL2,axiom,
! [V0B_2E0,V1A_2E0] :
( ( ~ ( p(s(tyop_2Emin_2Ebool,V1A_2E0))
| p(s(tyop_2Emin_2Ebool,V0B_2E0)) )
=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) )
<=> ( ( p(s(tyop_2Emin_2Ebool,V1A_2E0))
=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) )
=> ( ~ p(s(tyop_2Emin_2Ebool,V0B_2E0))
=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) ) ) ) ).
fof(thm_2Esat_2EOR__DUAL3,axiom,
! [V0B_2E0,V1A_2E0] :
( ( ~ ( ~ p(s(tyop_2Emin_2Ebool,V1A_2E0))
| p(s(tyop_2Emin_2Ebool,V0B_2E0)) )
=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) )
<=> ( p(s(tyop_2Emin_2Ebool,V1A_2E0))
=> ( ~ p(s(tyop_2Emin_2Ebool,V0B_2E0))
=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) ) ) ) ).
fof(thm_2Esat_2EAND__INV2,axiom,
! [V0A_2E0] :
( ( ~ p(s(tyop_2Emin_2Ebool,V0A_2E0))
=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) )
=> ( ( p(s(tyop_2Emin_2Ebool,V0A_2E0))
=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) )
=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) ) ) ).
fof(thm_2Esat_2Edc__eq,axiom,
! [V0r_2E0,V1q_2E0,V2p_2E0] :
( ( p(s(tyop_2Emin_2Ebool,V2p_2E0))
<=> s(tyop_2Emin_2Ebool,V1q_2E0) = s(tyop_2Emin_2Ebool,V0r_2E0) )
<=> ( ( p(s(tyop_2Emin_2Ebool,V2p_2E0))
| p(s(tyop_2Emin_2Ebool,V1q_2E0))
| p(s(tyop_2Emin_2Ebool,V0r_2E0)) )
& ( p(s(tyop_2Emin_2Ebool,V2p_2E0))
| ~ p(s(tyop_2Emin_2Ebool,V0r_2E0))
| ~ p(s(tyop_2Emin_2Ebool,V1q_2E0)) )
& ( p(s(tyop_2Emin_2Ebool,V1q_2E0))
| ~ p(s(tyop_2Emin_2Ebool,V0r_2E0))
| ~ p(s(tyop_2Emin_2Ebool,V2p_2E0)) )
& ( p(s(tyop_2Emin_2Ebool,V0r_2E0))
| ~ p(s(tyop_2Emin_2Ebool,V1q_2E0))
| ~ p(s(tyop_2Emin_2Ebool,V2p_2E0)) ) ) ) ).
fof(thm_2Esat_2Edc__conj,axiom,
! [V0r_2E0,V1q_2E0,V2p_2E0] :
( ( p(s(tyop_2Emin_2Ebool,V2p_2E0))
<=> ( p(s(tyop_2Emin_2Ebool,V1q_2E0))
& p(s(tyop_2Emin_2Ebool,V0r_2E0)) ) )
<=> ( ( p(s(tyop_2Emin_2Ebool,V2p_2E0))
| ~ p(s(tyop_2Emin_2Ebool,V1q_2E0))
| ~ p(s(tyop_2Emin_2Ebool,V0r_2E0)) )
& ( p(s(tyop_2Emin_2Ebool,V1q_2E0))
| ~ p(s(tyop_2Emin_2Ebool,V2p_2E0)) )
& ( p(s(tyop_2Emin_2Ebool,V0r_2E0))
| ~ p(s(tyop_2Emin_2Ebool,V2p_2E0)) ) ) ) ).
fof(thm_2Esat_2Edc__disj,axiom,
! [V0r_2E0,V1q_2E0,V2p_2E0] :
( ( p(s(tyop_2Emin_2Ebool,V2p_2E0))
<=> ( p(s(tyop_2Emin_2Ebool,V1q_2E0))
| p(s(tyop_2Emin_2Ebool,V0r_2E0)) ) )
<=> ( ( p(s(tyop_2Emin_2Ebool,V2p_2E0))
| ~ p(s(tyop_2Emin_2Ebool,V1q_2E0)) )
& ( p(s(tyop_2Emin_2Ebool,V2p_2E0))
| ~ p(s(tyop_2Emin_2Ebool,V0r_2E0)) )
& ( p(s(tyop_2Emin_2Ebool,V1q_2E0))
| p(s(tyop_2Emin_2Ebool,V0r_2E0))
| ~ p(s(tyop_2Emin_2Ebool,V2p_2E0)) ) ) ) ).
fof(thm_2Esat_2Edc__imp,axiom,
! [V0r_2E0,V1q_2E0,V2p_2E0] :
( ( p(s(tyop_2Emin_2Ebool,V2p_2E0))
<=> ( p(s(tyop_2Emin_2Ebool,V1q_2E0))
=> p(s(tyop_2Emin_2Ebool,V0r_2E0)) ) )
<=> ( ( p(s(tyop_2Emin_2Ebool,V2p_2E0))
| p(s(tyop_2Emin_2Ebool,V1q_2E0)) )
& ( p(s(tyop_2Emin_2Ebool,V2p_2E0))
| ~ p(s(tyop_2Emin_2Ebool,V0r_2E0)) )
& ( ~ p(s(tyop_2Emin_2Ebool,V1q_2E0))
| p(s(tyop_2Emin_2Ebool,V0r_2E0))
| ~ p(s(tyop_2Emin_2Ebool,V2p_2E0)) ) ) ) ).
fof(thm_2Esat_2Edc__neg,axiom,
! [V0q_2E0,V1p_2E0] :
( ( p(s(tyop_2Emin_2Ebool,V1p_2E0))
<=> ~ p(s(tyop_2Emin_2Ebool,V0q_2E0)) )
<=> ( ( p(s(tyop_2Emin_2Ebool,V1p_2E0))
| p(s(tyop_2Emin_2Ebool,V0q_2E0)) )
& ( ~ p(s(tyop_2Emin_2Ebool,V0q_2E0))
| ~ p(s(tyop_2Emin_2Ebool,V1p_2E0)) ) ) ) ).
fof(thm_2Ereal__topology_2EBOUNDED__BALL,conjecture,
! [V0x_2E0,V1e_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V0x_2E0),s(tyop_2Erealax_2Ereal,V1e_2E0)))))))) ).
%------------------------------------------------------------------------------