ITP001 Axioms: ITP004+4.ax
%------------------------------------------------------------------------------
% File : ITP004+4 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 syntactic export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : ConseqConv.ax [Gau19]
% : HL4004+4.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 66 ( 15 unt; 0 def)
% Number of atoms : 217 ( 22 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 168 ( 17 ~; 12 |; 23 &)
% ( 37 <=>; 79 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 27 ( 27 usr; 15 con; 0-3 aty)
% Number of variables : 152 ( 149 !; 3 ?)
% SPC : FOF_SAT_RFO_SEQ
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
fof(reserved_2Eho_2Eboolext,axiom,
! [V0_2E0,V1_2E0] :
( ( p(s(tyop_2Emin_2Ebool,V0_2E0))
<=> p(s(tyop_2Emin_2Ebool,V1_2E0)) )
=> s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0) ) ).
fof(reserved_2Eho_2Etruth,axiom,
p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ).
fof(reserved_2Eho_2Enotfalse,axiom,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) ).
fof(reserved_2Eho_2Ebool__cases__ax,axiom,
! [V0t_2E0] :
( s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
| s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ).
fof(reserved_2Eho_2Ei__thm,axiom,
! [A_27a,V0x_2E0] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0))) = s(A_27a,V0x_2E0) ).
fof(reserved_2Eho_2Ek__thm,axiom,
! [A_27a,A_27b,V0x_2E0,V1y_2E0] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0))) = s(A_27a,V0x_2E0) ).
fof(reserved_2Eho_2Es__thm,axiom,
! [A_27a,A_27b,A_27c,V0f_2E0,V1g_2E0,V2x_2E0] : s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))))) ).
fof(reserved_2Elogic_2E_2F_5C,axiom,
! [V0_2E0,V1_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,V0_2E0))
& p(s(tyop_2Emin_2Ebool,V1_2E0)) ) ) ).
fof(reserved_2Elogic_2E_5C_2F,axiom,
! [V0_2E0,V1_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,V0_2E0))
| p(s(tyop_2Emin_2Ebool,V1_2E0)) ) ) ).
fof(reserved_2Elogic_2E_7E,axiom,
! [V0_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0))))
<=> ~ p(s(tyop_2Emin_2Ebool,V0_2E0)) ) ).
fof(reserved_2Elogic_2E_3D_3D_3E,axiom,
! [V0_2E0,V1_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,V0_2E0))
=> p(s(tyop_2Emin_2Ebool,V1_2E0)) ) ) ).
fof(reserved_2Elogic_2E_3D,axiom,
! [A_27a,V0_2E0,V1_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0))))
<=> s(A_27a,V0_2E0) = s(A_27a,V1_2E0) ) ).
fof(reserved_2Equant_2E_21,axiom,
! [A_27a,V0f_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0))))
<=> ! [V1x_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0)))) ) ).
fof(reserved_2Equant_2E_3F,axiom,
! [A_27a,V0f_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0))))
<=> ? [V1x_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0)))) ) ).
fof(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
! [X0_2E0,X1_2E0] :
( ( p(s(tyop_2Emin_2Ebool,X0_2E0))
& p(s(tyop_2Emin_2Ebool,X1_2E0)) )
<=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) ) ).
fof(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,
! [X0_2E0,X1_2E0] :
( ( p(s(tyop_2Emin_2Ebool,X0_2E0))
| p(s(tyop_2Emin_2Ebool,X1_2E0)) )
<=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) ) ).
fof(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,
! [X0_2E0] :
( ~ p(s(tyop_2Emin_2Ebool,X0_2E0))
<=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))) ) ).
fof(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
! [X0_2E0,X1_2E0] :
( ( p(s(tyop_2Emin_2Ebool,X0_2E0))
=> p(s(tyop_2Emin_2Ebool,X1_2E0)) )
<=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) ) ).
fof(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] :
( s(A_27a,X0_2E0) = s(A_27a,X1_2E0)
<=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))) ) ).
fof(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq2_2Ec_2EConseqConv_2EASM__MARKER_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2EConseqConv_2EASM__MARKER_2E2(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2EConseqConv_2EASM__MARKER_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))) ).
fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0,X2_2E0] : s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))) ).
fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0),s(tyop_2Emin_2Ebool,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))),s(tyop_2Emin_2Ebool,X2_2E0))) ).
fof(thm_2EConseqConv_2EASM__MARKER__DEF,axiom,
! [V0x_2E0,V1x_27_2E0] : s(tyop_2Emin_2Ebool,c_2EConseqConv_2EASM__MARKER_2E2(s(tyop_2Emin_2Ebool,V0x_2E0),s(tyop_2Emin_2Ebool,V1x_27_2E0))) = s(tyop_2Emin_2Ebool,V1x_27_2E0) ).
fof(thm_2EConseqConv_2Eforall__eq__thm,axiom,
! [A_27a,V0Q_2E0,V1P_2E0] :
( ! [V2s_2E0] : s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2s_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0Q_2E0),s(A_27a,V2s_2E0)))
=> ( ! [V3s_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V3s_2E0))))
<=> ! [V4s_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0Q_2E0),s(A_27a,V4s_2E0)))) ) ) ).
fof(thm_2EConseqConv_2Eexists__eq__thm,axiom,
! [A_27a,V0Q_2E0,V1P_2E0] :
( ! [V2s_2E0] : s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2s_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0Q_2E0),s(A_27a,V2s_2E0)))
=> ( ? [V3s_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V3s_2E0))))
<=> ? [V4s_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0Q_2E0),s(A_27a,V4s_2E0)))) ) ) ).
fof(thm_2EConseqConv_2Etrue__imp,axiom,
! [V0t_2E0] :
( p(s(tyop_2Emin_2Ebool,V0t_2E0))
=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ) ).
fof(thm_2EConseqConv_2Efalse__imp,axiom,
! [V0t_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))
=> p(s(tyop_2Emin_2Ebool,V0t_2E0)) ) ).
fof(thm_2EConseqConv_2ENOT__CLAUSES__X,axiom,
! [V0t_2E0] :
( ~ ~ p(s(tyop_2Emin_2Ebool,V0t_2E0))
<=> p(s(tyop_2Emin_2Ebool,V0t_2E0)) ) ).
fof(thm_2EConseqConv_2ENOT__CLAUSES__T,axiom,
( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))
<=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) ) ).
fof(thm_2EConseqConv_2ENOT__CLAUSES__F,axiom,
( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))
<=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ) ).
fof(thm_2EConseqConv_2EIMP__CONG__conj__strengthen,axiom,
! [V0x_2E0,V1x_27_2E0,V2y_2E0,V3y_27_2E0] :
( ( ( p(s(tyop_2Emin_2Ebool,V2y_2E0))
=> ( p(s(tyop_2Emin_2Ebool,V1x_27_2E0))
=> p(s(tyop_2Emin_2Ebool,V0x_2E0)) ) )
& ( p(s(tyop_2Emin_2Ebool,V1x_27_2E0))
=> ( p(s(tyop_2Emin_2Ebool,V3y_27_2E0))
=> p(s(tyop_2Emin_2Ebool,V2y_2E0)) ) ) )
=> ( ( p(s(tyop_2Emin_2Ebool,V1x_27_2E0))
& p(s(tyop_2Emin_2Ebool,V3y_27_2E0)) )
=> ( p(s(tyop_2Emin_2Ebool,V0x_2E0))
& p(s(tyop_2Emin_2Ebool,V2y_2E0)) ) ) ) ).
fof(thm_2EConseqConv_2EIMP__CONG__conj__weaken,axiom,
! [V0x_2E0,V1x_27_2E0,V2y_2E0,V3y_27_2E0] :
( ( ( p(s(tyop_2Emin_2Ebool,V2y_2E0))
=> ( p(s(tyop_2Emin_2Ebool,V0x_2E0))
=> p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) ) )
& ( p(s(tyop_2Emin_2Ebool,V1x_27_2E0))
=> ( p(s(tyop_2Emin_2Ebool,V2y_2E0))
=> p(s(tyop_2Emin_2Ebool,V3y_27_2E0)) ) ) )
=> ( ( p(s(tyop_2Emin_2Ebool,V0x_2E0))
& p(s(tyop_2Emin_2Ebool,V2y_2E0)) )
=> ( p(s(tyop_2Emin_2Ebool,V1x_27_2E0))
& p(s(tyop_2Emin_2Ebool,V3y_27_2E0)) ) ) ) ).
fof(thm_2EConseqConv_2EAND__CLAUSES__TX,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)) ) ).
fof(thm_2EConseqConv_2EAND__CLAUSES__XT,axiom,
! [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)) ) ).
fof(thm_2EConseqConv_2EAND__CLAUSES__FX,axiom,
! [V0t_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))
& p(s(tyop_2Emin_2Ebool,V0t_2E0)) )
<=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) ) ).
fof(thm_2EConseqConv_2EAND__CLAUSES__XF,axiom,
! [V0t_2E0] :
( ( p(s(tyop_2Emin_2Ebool,V0t_2E0))
& p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) )
<=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) ) ).
fof(thm_2EConseqConv_2EAND__CLAUSES__XX,axiom,
! [V0t_2E0] :
( ( p(s(tyop_2Emin_2Ebool,V0t_2E0))
& p(s(tyop_2Emin_2Ebool,V0t_2E0)) )
<=> p(s(tyop_2Emin_2Ebool,V0t_2E0)) ) ).
fof(thm_2EConseqConv_2EIMP__CONG__disj__strengthen,axiom,
! [V0x_2E0,V1x_27_2E0,V2y_2E0,V3y_27_2E0] :
( ( ( ~ p(s(tyop_2Emin_2Ebool,V2y_2E0))
=> ( p(s(tyop_2Emin_2Ebool,V1x_27_2E0))
=> p(s(tyop_2Emin_2Ebool,V0x_2E0)) ) )
& ( ~ p(s(tyop_2Emin_2Ebool,V1x_27_2E0))
=> ( p(s(tyop_2Emin_2Ebool,V3y_27_2E0))
=> p(s(tyop_2Emin_2Ebool,V2y_2E0)) ) ) )
=> ( ( p(s(tyop_2Emin_2Ebool,V1x_27_2E0))
| p(s(tyop_2Emin_2Ebool,V3y_27_2E0)) )
=> ( p(s(tyop_2Emin_2Ebool,V0x_2E0))
| p(s(tyop_2Emin_2Ebool,V2y_2E0)) ) ) ) ).
fof(thm_2EConseqConv_2EIMP__CONG__disj__weaken,axiom,
! [V0x_2E0,V1x_27_2E0,V2y_2E0,V3y_27_2E0] :
( ( ( ~ p(s(tyop_2Emin_2Ebool,V2y_2E0))
=> ( p(s(tyop_2Emin_2Ebool,V0x_2E0))
=> p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) ) )
& ( ~ p(s(tyop_2Emin_2Ebool,V1x_27_2E0))
=> ( p(s(tyop_2Emin_2Ebool,V2y_2E0))
=> p(s(tyop_2Emin_2Ebool,V3y_27_2E0)) ) ) )
=> ( ( p(s(tyop_2Emin_2Ebool,V0x_2E0))
| p(s(tyop_2Emin_2Ebool,V2y_2E0)) )
=> ( p(s(tyop_2Emin_2Ebool,V1x_27_2E0))
| p(s(tyop_2Emin_2Ebool,V3y_27_2E0)) ) ) ) ).
fof(thm_2EConseqConv_2EOR__CLAUSES__TX,axiom,
! [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_2ET_2E0)) ) ).
fof(thm_2EConseqConv_2EOR__CLAUSES__XT,axiom,
! [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)) ) ).
fof(thm_2EConseqConv_2EOR__CLAUSES__FX,axiom,
! [V0t_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))
| p(s(tyop_2Emin_2Ebool,V0t_2E0)) )
<=> p(s(tyop_2Emin_2Ebool,V0t_2E0)) ) ).
fof(thm_2EConseqConv_2EOR__CLAUSES__XF,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_2EConseqConv_2EOR__CLAUSES__XX,axiom,
! [V0t_2E0] :
( ( p(s(tyop_2Emin_2Ebool,V0t_2E0))
| p(s(tyop_2Emin_2Ebool,V0t_2E0)) )
<=> p(s(tyop_2Emin_2Ebool,V0t_2E0)) ) ).
fof(thm_2EConseqConv_2EIMP__CONG__imp__strengthen,axiom,
! [V0x_2E0,V1x_27_2E0,V2y_2E0,V3y_27_2E0] :
( ( ( p(s(tyop_2Emin_2Ebool,V0x_2E0))
=> ( p(s(tyop_2Emin_2Ebool,V3y_27_2E0))
=> p(s(tyop_2Emin_2Ebool,V2y_2E0)) ) )
& ( ~ p(s(tyop_2Emin_2Ebool,V3y_27_2E0))
=> ( p(s(tyop_2Emin_2Ebool,V0x_2E0))
=> p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) ) ) )
=> ( ( p(s(tyop_2Emin_2Ebool,V1x_27_2E0))
=> p(s(tyop_2Emin_2Ebool,V3y_27_2E0)) )
=> ( p(s(tyop_2Emin_2Ebool,V0x_2E0))
=> p(s(tyop_2Emin_2Ebool,V2y_2E0)) ) ) ) ).
fof(thm_2EConseqConv_2EIMP__CONG__imp__weaken,axiom,
! [V0x_2E0,V1x_27_2E0,V2y_2E0,V3y_27_2E0] :
( ( ( p(s(tyop_2Emin_2Ebool,V0x_2E0))
=> ( p(s(tyop_2Emin_2Ebool,V2y_2E0))
=> p(s(tyop_2Emin_2Ebool,V3y_27_2E0)) ) )
& ( ~ p(s(tyop_2Emin_2Ebool,V3y_27_2E0))
=> ( p(s(tyop_2Emin_2Ebool,V1x_27_2E0))
=> p(s(tyop_2Emin_2Ebool,V0x_2E0)) ) ) )
=> ( ( p(s(tyop_2Emin_2Ebool,V0x_2E0))
=> p(s(tyop_2Emin_2Ebool,V2y_2E0)) )
=> ( p(s(tyop_2Emin_2Ebool,V1x_27_2E0))
=> p(s(tyop_2Emin_2Ebool,V3y_27_2E0)) ) ) ) ).
fof(thm_2EConseqConv_2EIMP__CONG__simple__imp__strengthen,axiom,
! [V0x_2E0,V1x_27_2E0,V2y_2E0,V3y_27_2E0] :
( ( ( p(s(tyop_2Emin_2Ebool,V0x_2E0))
=> p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) )
& ( p(s(tyop_2Emin_2Ebool,V1x_27_2E0))
=> ( p(s(tyop_2Emin_2Ebool,V3y_27_2E0))
=> p(s(tyop_2Emin_2Ebool,V2y_2E0)) ) ) )
=> ( ( p(s(tyop_2Emin_2Ebool,V1x_27_2E0))
=> p(s(tyop_2Emin_2Ebool,V3y_27_2E0)) )
=> ( p(s(tyop_2Emin_2Ebool,V0x_2E0))
=> p(s(tyop_2Emin_2Ebool,V2y_2E0)) ) ) ) ).
fof(thm_2EConseqConv_2EIMP__CONG__simple__imp__weaken,axiom,
! [V0x_2E0,V1x_27_2E0,V2y_2E0,V3y_27_2E0] :
( ( ( p(s(tyop_2Emin_2Ebool,V1x_27_2E0))
=> p(s(tyop_2Emin_2Ebool,V0x_2E0)) )
& ( p(s(tyop_2Emin_2Ebool,V1x_27_2E0))
=> ( p(s(tyop_2Emin_2Ebool,V2y_2E0))
=> p(s(tyop_2Emin_2Ebool,V3y_27_2E0)) ) ) )
=> ( ( p(s(tyop_2Emin_2Ebool,V0x_2E0))
=> p(s(tyop_2Emin_2Ebool,V2y_2E0)) )
=> ( p(s(tyop_2Emin_2Ebool,V1x_27_2E0))
=> p(s(tyop_2Emin_2Ebool,V3y_27_2E0)) ) ) ) ).
fof(thm_2EConseqConv_2EIMP__CLAUSES__TX,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)) ) ).
fof(thm_2EConseqConv_2EIMP__CLAUSES__XT,axiom,
! [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)) ) ).
fof(thm_2EConseqConv_2EIMP__CLAUSES__FX,axiom,
! [V0t_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)) ) ).
fof(thm_2EConseqConv_2EIMP__CLAUSES__XX,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)) ) ).
fof(thm_2EConseqConv_2EIMP__CLAUSES__XF,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_2EConseqConv_2EIMP__CONG__cond__simple,axiom,
! [V0c_2E0,V1x_2E0,V2x_27_2E0,V3y_2E0,V4y_27_2E0] :
( ( ( p(s(tyop_2Emin_2Ebool,V2x_27_2E0))
=> p(s(tyop_2Emin_2Ebool,V1x_2E0)) )
& ( p(s(tyop_2Emin_2Ebool,V4y_27_2E0))
=> p(s(tyop_2Emin_2Ebool,V3y_2E0)) ) )
=> ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0c_2E0),s(tyop_2Emin_2Ebool,V2x_27_2E0),s(tyop_2Emin_2Ebool,V4y_27_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0c_2E0),s(tyop_2Emin_2Ebool,V1x_2E0),s(tyop_2Emin_2Ebool,V3y_2E0)))) ) ) ).
fof(thm_2EConseqConv_2EIMP__CONG__cond,axiom,
! [V0c_2E0,V1x_2E0,V2x_27_2E0,V3y_2E0,V4y_27_2E0] :
( ( ( p(s(tyop_2Emin_2Ebool,V0c_2E0))
=> ( p(s(tyop_2Emin_2Ebool,V2x_27_2E0))
=> p(s(tyop_2Emin_2Ebool,V1x_2E0)) ) )
& ( ~ p(s(tyop_2Emin_2Ebool,V0c_2E0))
=> ( p(s(tyop_2Emin_2Ebool,V4y_27_2E0))
=> p(s(tyop_2Emin_2Ebool,V3y_2E0)) ) ) )
=> ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0c_2E0),s(tyop_2Emin_2Ebool,V2x_27_2E0),s(tyop_2Emin_2Ebool,V4y_27_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0c_2E0),s(tyop_2Emin_2Ebool,V1x_2E0),s(tyop_2Emin_2Ebool,V3y_2E0)))) ) ) ).
fof(thm_2EConseqConv_2ECOND__CLAUSES__CT,axiom,
! [A_27a,V0t1_2E0,V1t2_2E0] : s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(A_27a,V0t1_2E0),s(A_27a,V1t2_2E0))) = s(A_27a,V0t1_2E0) ).
fof(thm_2EConseqConv_2ECOND__CLAUSES__CF,axiom,
! [A_27a,V0t1_2E0,V1t2_2E0] : s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(A_27a,V0t1_2E0),s(A_27a,V1t2_2E0))) = s(A_27a,V1t2_2E0) ).
fof(thm_2EConseqConv_2ECOND__CLAUSES__ID,axiom,
! [A_27a,V0b_2E0,V1t_2E0] : s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0b_2E0),s(A_27a,V1t_2E0),s(A_27a,V1t_2E0))) = s(A_27a,V1t_2E0) ).
fof(thm_2EConseqConv_2ECOND__CLAUSES__TT,axiom,
! [V0c_2E0,V1x_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0c_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Emin_2Ebool,V1x_2E0))))
<=> ( ~ p(s(tyop_2Emin_2Ebool,V0c_2E0))
=> p(s(tyop_2Emin_2Ebool,V1x_2E0)) ) ) ).
fof(thm_2EConseqConv_2ECOND__CLAUSES__FT,axiom,
! [V0c_2E0,V1x_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0c_2E0),s(tyop_2Emin_2Ebool,V1x_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,V0c_2E0))
=> p(s(tyop_2Emin_2Ebool,V1x_2E0)) ) ) ).
fof(thm_2EConseqConv_2ECOND__CLAUSES__TF,axiom,
! [V0c_2E0,V1x_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0c_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Emin_2Ebool,V1x_2E0))))
<=> ( ~ p(s(tyop_2Emin_2Ebool,V0c_2E0))
& p(s(tyop_2Emin_2Ebool,V1x_2E0)) ) ) ).
fof(thm_2EConseqConv_2ECOND__CLAUSES__FF,axiom,
! [V0c_2E0,V1x_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0c_2E0),s(tyop_2Emin_2Ebool,V1x_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,V0c_2E0))
& p(s(tyop_2Emin_2Ebool,V1x_2E0)) ) ) ).
fof(thm_2EConseqConv_2EASM__MARKER__THM,axiom,
! [V0y_2E0,V1x_2E0] : s(tyop_2Emin_2Ebool,c_2EConseqConv_2EASM__MARKER_2E2(s(tyop_2Emin_2Ebool,V0y_2E0),s(tyop_2Emin_2Ebool,V1x_2E0))) = s(tyop_2Emin_2Ebool,V1x_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) ) ).
%------------------------------------------------------------------------------