TPTP Problem File: ITP014+2.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : ITP014+2 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Problem : HOL4 set theory export of thm_2Ebitstring_2Eword__1comp__v2w.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_2Ebitstring_2Eword__1comp__v2w.p [Gau19]
% : HL406501+2.p [TPAP]
% Status : Theorem
% Rating : 1.00 v8.1.0, 0.97 v7.5.0
% Syntax : Number of formulae : 131 ( 35 unt; 0 def)
% Number of atoms : 676 ( 89 equ)
% Maximal formula atoms : 94 ( 5 avg)
% Number of connectives : 595 ( 50 ~; 38 |; 116 &)
% ( 101 <=>; 290 =>; 0 <=; 0 <~>)
% Maximal formula depth : 38 ( 6 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 6 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 55 ( 55 usr; 31 con; 0-2 aty)
% Number of variables : 252 ( 252 !; 0 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments :
% Bugfixes : v7.5.0 - Bugfixes in axioms and export.
%------------------------------------------------------------------------------
include('Axioms/ITP001/ITP001+2.ax').
%------------------------------------------------------------------------------
fof(ne_ty_2Efcp_2Ecart,axiom,
! [A0] :
( ne(A0)
=> ! [A1] :
( ne(A1)
=> ne(ty_2Efcp_2Ecart(A0,A1)) ) ) ).
fof(ne_ty_2Elist_2Elist,axiom,
! [A0] :
( ne(A0)
=> ne(ty_2Elist_2Elist(A0)) ) ).
fof(mem_c_2Ebitstring_2Ev2w,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ebitstring_2Ev2w(A_27a),arr(ty_2Elist_2Elist(bool),ty_2Efcp_2Ecart(bool,A_27a))) ) ).
fof(mem_c_2Ebitstring_2Ebnot,axiom,
mem(c_2Ebitstring_2Ebnot,arr(ty_2Elist_2Elist(bool),ty_2Elist_2Elist(bool))) ).
fof(ne_ty_2Enum_2Enum,axiom,
ne(ty_2Enum_2Enum) ).
fof(mem_c_2Ebitstring_2Efixwidth,axiom,
mem(c_2Ebitstring_2Efixwidth,arr(ty_2Enum_2Enum,arr(ty_2Elist_2Elist(bool),ty_2Elist_2Elist(bool)))) ).
fof(mem_c_2Ebitstring_2Etestbit,axiom,
mem(c_2Ebitstring_2Etestbit,arr(ty_2Enum_2Enum,arr(ty_2Elist_2Elist(bool),bool))) ).
fof(mem_c_2Ebool_2ELET,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Ebool_2ELET(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) ) ) ).
fof(mem_c_2Ebool_2ECOND,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ebool_2ECOND(A_27a),arr(bool,arr(A_27a,arr(A_27a,A_27a)))) ) ).
fof(mem_c_2Ecombin_2EI,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ecombin_2EI(A_27a),arr(A_27a,A_27a)) ) ).
fof(mem_c_2Elist_2EMAP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Elist_2EMAP(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)))) ) ) ).
fof(mem_c_2Elist_2EEL,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elist_2EEL(A_27a),arr(ty_2Enum_2Enum,arr(ty_2Elist_2Elist(A_27a),A_27a))) ) ).
fof(mem_c_2Elist_2ELENGTH,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elist_2ELENGTH(A_27a),arr(ty_2Elist_2Elist(A_27a),ty_2Enum_2Enum)) ) ).
fof(mem_c_2Earithmetic_2EEVEN,axiom,
mem(c_2Earithmetic_2EEVEN,arr(ty_2Enum_2Enum,bool)) ).
fof(mem_c_2Earithmetic_2EODD,axiom,
mem(c_2Earithmetic_2EODD,arr(ty_2Enum_2Enum,bool)) ).
fof(mem_c_2Earithmetic_2E_3E_3D,axiom,
mem(c_2Earithmetic_2E_3E_3D,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool))) ).
fof(mem_c_2Earithmetic_2E_3E,axiom,
mem(c_2Earithmetic_2E_3E,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool))) ).
fof(mem_c_2Eprim__rec_2EPRE,axiom,
mem(c_2Eprim__rec_2EPRE,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) ).
fof(mem_c_2Earithmetic_2EEXP,axiom,
mem(c_2Earithmetic_2EEXP,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) ).
fof(mem_c_2Earithmetic_2E_2D,axiom,
mem(c_2Earithmetic_2E_2D,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) ).
fof(mem_c_2Earithmetic_2E_2A,axiom,
mem(c_2Earithmetic_2E_2A,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) ).
fof(mem_c_2Earithmetic_2ENUMERAL,axiom,
mem(c_2Earithmetic_2ENUMERAL,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) ).
fof(mem_c_2Enumeral_2EiiSUC,axiom,
mem(c_2Enumeral_2EiiSUC,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) ).
fof(mem_c_2Enum_2ESUC,axiom,
mem(c_2Enum_2ESUC,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) ).
fof(mem_c_2Earithmetic_2E_2B,axiom,
mem(c_2Earithmetic_2E_2B,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) ).
fof(mem_c_2Enumeral_2EiZ,axiom,
mem(c_2Enumeral_2EiZ,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) ).
fof(mem_c_2Earithmetic_2EBIT2,axiom,
mem(c_2Earithmetic_2EBIT2,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) ).
fof(mem_c_2Earithmetic_2EBIT1,axiom,
mem(c_2Earithmetic_2EBIT1,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) ).
fof(mem_c_2Ebool_2ET,axiom,
mem(c_2Ebool_2ET,bool) ).
fof(ax_true_p,axiom,
p(c_2Ebool_2ET) ).
fof(mem_c_2Earithmetic_2EZERO,axiom,
mem(c_2Earithmetic_2EZERO,ty_2Enum_2Enum) ).
fof(mem_c_2Earithmetic_2E_3C_3D,axiom,
mem(c_2Earithmetic_2E_3C_3D,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool))) ).
fof(mem_c_2Ebool_2EF,axiom,
mem(c_2Ebool_2EF,bool) ).
fof(ax_false_p,axiom,
~ p(c_2Ebool_2EF) ).
fof(mem_c_2Emin_2E_3D_3D_3E,axiom,
mem(c_2Emin_2E_3D_3D_3E,arr(bool,arr(bool,bool))) ).
fof(ax_imp_p,axiom,
! [Q] :
( mem(Q,bool)
=> ! [R] :
( mem(R,bool)
=> ( p(ap(ap(c_2Emin_2E_3D_3D_3E,Q),R))
<=> ( p(Q)
=> p(R) ) ) ) ) ).
fof(mem_c_2Ebool_2E_5C_2F,axiom,
mem(c_2Ebool_2E_5C_2F,arr(bool,arr(bool,bool))) ).
fof(ax_or_p,axiom,
! [Q] :
( mem(Q,bool)
=> ! [R] :
( mem(R,bool)
=> ( p(ap(ap(c_2Ebool_2E_5C_2F,Q),R))
<=> ( p(Q)
| p(R) ) ) ) ) ).
fof(mem_c_2Ebool_2E_2F_5C,axiom,
mem(c_2Ebool_2E_2F_5C,arr(bool,arr(bool,bool))) ).
fof(ax_and_p,axiom,
! [Q] :
( mem(Q,bool)
=> ! [R] :
( mem(R,bool)
=> ( p(ap(ap(c_2Ebool_2E_2F_5C,Q),R))
<=> ( p(Q)
& p(R) ) ) ) ) ).
fof(mem_c_2Efcp_2Efcp__index,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Efcp_2Efcp__index(A_27a,A_27b),arr(ty_2Efcp_2Ecart(A_27a,A_27b),arr(ty_2Enum_2Enum,A_27a))) ) ) ).
fof(mem_c_2Ebool_2E_7E,axiom,
mem(c_2Ebool_2E_7E,arr(bool,bool)) ).
fof(ax_neg_p,axiom,
! [Q] :
( mem(Q,bool)
=> ( p(ap(c_2Ebool_2E_7E,Q))
<=> ~ p(Q) ) ) ).
fof(mem_c_2Efcp_2EFCP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Efcp_2EFCP(A_27a,A_27b),arr(arr(ty_2Enum_2Enum,A_27a),ty_2Efcp_2Ecart(A_27a,A_27b))) ) ) ).
fof(mem_c_2Ewords_2Eword__1comp,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__1comp(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27a))) ) ).
fof(mem_c_2Emin_2E_3D,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Emin_2E_3D(A_27a),arr(A_27a,arr(A_27a,bool))) ) ).
fof(ax_eq_p,axiom,
! [A] :
( ne(A)
=> ! [X] :
( mem(X,A)
=> ! [Y] :
( mem(Y,A)
=> ( p(ap(ap(c_2Emin_2E_3D(A),X),Y))
<=> X = Y ) ) ) ) ).
fof(mem_c_2Ebool_2E_21,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ebool_2E_21(A_27a),arr(arr(A_27a,bool),bool)) ) ).
fof(ax_all_p,axiom,
! [A] :
( ne(A)
=> ! [Q] :
( mem(Q,arr(A,bool))
=> ( p(ap(c_2Ebool_2E_21(A),Q))
<=> ! [X] :
( mem(X,A)
=> p(ap(Q,X)) ) ) ) ) ).
fof(ne_ty_2Ebool_2Eitself,axiom,
! [A0] :
( ne(A0)
=> ne(ty_2Ebool_2Eitself(A0)) ) ).
fof(mem_c_2Ebool_2Ethe__value,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ebool_2Ethe__value(A_27a),ty_2Ebool_2Eitself(A_27a)) ) ).
fof(mem_c_2Efcp_2Edimindex,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Efcp_2Edimindex(A_27a),arr(ty_2Ebool_2Eitself(A_27a),ty_2Enum_2Enum)) ) ).
fof(mem_c_2Enum_2E0,axiom,
mem(c_2Enum_2E0,ty_2Enum_2Enum) ).
fof(mem_c_2Eprim__rec_2E_3C,axiom,
mem(c_2Eprim__rec_2E_3C,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool))) ).
fof(conj_thm_2Earithmetic_2EADD__CLAUSES,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( ap(ap(c_2Earithmetic_2E_2B,c_2Enum_2E0),V0m) = V0m
& ap(ap(c_2Earithmetic_2E_2B,V0m),c_2Enum_2E0) = V0m
& ap(ap(c_2Earithmetic_2E_2B,ap(c_2Enum_2ESUC,V0m)),V1n) = ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n))
& ap(ap(c_2Earithmetic_2E_2B,V0m),ap(c_2Enum_2ESUC,V1n)) = ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)) ) ) ) ).
fof(conj_thm_2Earithmetic_2EADD__SYM,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2E_2B,V0m),V1n) = ap(ap(c_2Earithmetic_2E_2B,V1n),V0m) ) ) ).
fof(conj_thm_2Earithmetic_2EADD__COMM,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2E_2B,V0m),V1n) = ap(ap(c_2Earithmetic_2E_2B,V1n),V0m) ) ) ).
fof(conj_thm_2Earithmetic_2EADD__ASSOC,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2E_2B,V0m),ap(ap(c_2Earithmetic_2E_2B,V1n),V2p)) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)),V2p) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELESS__EQ,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n))
<=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V0m)),V1n)) ) ) ) ).
fof(conj_thm_2Earithmetic_2EZERO__LESS__EQ,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> p(ap(ap(c_2Earithmetic_2E_3C_3D,c_2Enum_2E0),V0n)) ) ).
fof(conj_thm_2Earithmetic_2ENOT__LESS,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( ~ p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n))
<=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V0m)) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELESS__EQ__0,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),c_2Enum_2E0))
<=> V0n = c_2Enum_2E0 ) ) ).
fof(conj_thm_2Earithmetic_2EMULT__CLAUSES,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( ap(ap(c_2Earithmetic_2E_2A,c_2Enum_2E0),V0m) = c_2Enum_2E0
& ap(ap(c_2Earithmetic_2E_2A,V0m),c_2Enum_2E0) = c_2Enum_2E0
& ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0m) = V0m
& ap(ap(c_2Earithmetic_2E_2A,V0m),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = V0m
& ap(ap(c_2Earithmetic_2E_2A,ap(c_2Enum_2ESUC,V0m)),V1n) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)),V1n)
& ap(ap(c_2Earithmetic_2E_2A,V0m),ap(c_2Enum_2ESUC,V1n)) = ap(ap(c_2Earithmetic_2E_2B,V0m),ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)) ) ) ) ).
fof(conj_thm_2Earithmetic_2ELESS__EQ__TRANS,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n))
& p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V2p)) )
=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V2p)) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EEQ__LESS__EQ,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( V0m = V1n
<=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n))
& p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V0m)) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2EADD__MONO__LESS__EQ,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)),ap(ap(c_2Earithmetic_2E_2B,V0m),V2p)))
<=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V2p)) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ENOT__LEQ,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( ~ p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n))
<=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V1n)),V0m)) ) ) ) ).
fof(conj_thm_2Earithmetic_2ENOT__NUM__EQ,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( V0m != V1n
<=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V0m)),V1n))
| p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V1n)),V0m)) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ESUC__ONE__ADD,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(c_2Enum_2ESUC,V0n) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0n) ) ).
fof(conj_thm_2Earithmetic_2ESUB__RIGHT__SUB,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2D,V0m),V1n)),V2p) = ap(ap(c_2Earithmetic_2E_2D,V0m),ap(ap(c_2Earithmetic_2E_2B,V1n),V2p)) ) ) ) ).
fof(conj_thm_2Earithmetic_2ESUB__LEFT__LESS__EQ,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),ap(ap(c_2Earithmetic_2E_2D,V1n),V2p)))
<=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,V0m),V2p)),V1n))
| p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),c_2Enum_2E0)) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ESUB__RIGHT__LESS__EQ,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2D,V0m),V1n)),V2p))
<=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),ap(ap(c_2Earithmetic_2E_2B,V1n),V2p))) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ESUB__RIGHT__LESS,axiom,
! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2p] :
( mem(V2p,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2D,V0m),V1n)),V2p))
<=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0m),ap(ap(c_2Earithmetic_2E_2B,V1n),V2p)))
& p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2p)) ) ) ) ) ) ).
fof(conj_thm_2Earithmetic_2ESUB__ELIM__THM,axiom,
! [V0P] :
( mem(V0P,arr(ty_2Enum_2Enum,bool))
=> ! [V1a] :
( mem(V1a,ty_2Enum_2Enum)
=> ! [V2b] :
( mem(V2b,ty_2Enum_2Enum)
=> ( p(ap(V0P,ap(ap(c_2Earithmetic_2E_2D,V1a),V2b)))
<=> ! [V3d] :
( mem(V3d,ty_2Enum_2Enum)
=> ( ( V2b = ap(ap(c_2Earithmetic_2E_2B,V1a),V3d)
=> p(ap(V0P,c_2Enum_2E0)) )
& ( V1a = ap(ap(c_2Earithmetic_2E_2B,V2b),V3d)
=> p(ap(V0P,V3d)) ) ) ) ) ) ) ) ).
fof(ax_thm_2Ebitstring_2Ev2w__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Elist_2Elist(bool))
=> ap(c_2Ebitstring_2Ev2w(A_27a),V0v) = ap(c_2Efcp_2EFCP(bool,A_27a),f2293(V0v)) ) ) ).
fof(ax_thm_2Ebitstring_2Ebnot__def,axiom,
c_2Ebitstring_2Ebnot = ap(c_2Elist_2EMAP(bool,bool),c_2Ebool_2E_7E) ).
fof(conj_thm_2Ebitstring_2Elength__fixwidth,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1v] :
( mem(V1v,ty_2Elist_2Elist(bool))
=> ap(c_2Elist_2ELENGTH(bool),ap(ap(c_2Ebitstring_2Efixwidth,V0n),V1v)) = V0n ) ) ).
fof(conj_thm_2Ebitstring_2Eel__fixwidth,axiom,
! [V0i] :
( mem(V0i,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2w] :
( mem(V2w,ty_2Elist_2Elist(bool))
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0i),V1n))
=> ( p(ap(ap(c_2Elist_2EEL(bool),V0i),ap(ap(c_2Ebitstring_2Efixwidth,V1n),V2w)))
<=> p(ap(ap(ap(c_2Ebool_2ECOND(bool),ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Elist_2ELENGTH(bool),V2w)),V1n)),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2D,V1n),ap(c_2Elist_2ELENGTH(bool),V2w))),V0i)),ap(ap(c_2Elist_2EEL(bool),ap(ap(c_2Earithmetic_2E_2D,V0i),ap(ap(c_2Earithmetic_2E_2D,V1n),ap(c_2Elist_2ELENGTH(bool),V2w)))),V2w))),ap(ap(c_2Elist_2EEL(bool),ap(ap(c_2Earithmetic_2E_2B,V0i),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Elist_2ELENGTH(bool),V2w)),V1n))),V2w))) ) ) ) ) ) ).
fof(conj_thm_2Ebitstring_2Etestbit,axiom,
! [V0b] :
( mem(V0b,ty_2Enum_2Enum)
=> ! [V1v] :
( mem(V1v,ty_2Elist_2Elist(bool))
=> ( p(ap(ap(c_2Ebitstring_2Etestbit,V0b),V1v))
<=> p(ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,bool),f2305(V1v,V0b)),ap(c_2Elist_2ELENGTH(bool),V1v))) ) ) ) ).
fof(conj_thm_2Ebool_2ETRUTH,axiom,
$true ).
fof(conj_thm_2Ebool_2EIMP__ANTISYM__AX,axiom,
! [V0t1] :
( mem(V0t1,bool)
=> ! [V1t2] :
( mem(V1t2,bool)
=> ( ( p(V0t1)
=> p(V1t2) )
=> ( ( p(V1t2)
=> p(V0t1) )
=> ( p(V0t1)
<=> p(V1t2) ) ) ) ) ) ).
fof(conj_thm_2Ebool_2EFALSITY,axiom,
! [V0t] :
( mem(V0t,bool)
=> ( $false
=> p(V0t) ) ) ).
fof(conj_thm_2Ebool_2EEXCLUDED__MIDDLE,axiom,
! [V0t] :
( mem(V0t,bool)
=> ( p(V0t)
| ~ p(V0t) ) ) ).
fof(conj_thm_2Ebool_2ELET__THM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0f] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ap(ap(c_2Ebool_2ELET(A_27a,A_27b),V0f),V1x) = ap(V0f,V1x) ) ) ) ) ).
fof(conj_thm_2Ebool_2EFORALL__SIMP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0t] :
( mem(V0t,bool)
=> ( ! [V1x] :
( mem(V1x,A_27a)
=> p(V0t) )
<=> p(V0t) ) ) ) ).
fof(conj_thm_2Ebool_2ECONJ__ASSOC,axiom,
! [V0t1] :
( mem(V0t1,bool)
=> ! [V1t2] :
( mem(V1t2,bool)
=> ! [V2t3] :
( mem(V2t3,bool)
=> ( ( p(V0t1)
& p(V1t2)
& p(V2t3) )
<=> ( p(V0t1)
& p(V1t2)
& p(V2t3) ) ) ) ) ) ).
fof(conj_thm_2Ebool_2EAND__CLAUSES,axiom,
! [V0t] :
( mem(V0t,bool)
=> ( ( ( $true
& p(V0t) )
<=> p(V0t) )
& ( ( p(V0t)
& $true )
<=> p(V0t) )
& ( ( $false
& p(V0t) )
<=> $false )
& ( ( p(V0t)
& $false )
<=> $false )
& ( ( p(V0t)
& p(V0t) )
<=> p(V0t) ) ) ) ).
fof(conj_thm_2Ebool_2EOR__CLAUSES,axiom,
! [V0t] :
( mem(V0t,bool)
=> ( ( ( $true
| p(V0t) )
<=> $true )
& ( ( p(V0t)
| $true )
<=> $true )
& ( ( $false
| p(V0t) )
<=> p(V0t) )
& ( ( p(V0t)
| $false )
<=> p(V0t) )
& ( ( p(V0t)
| p(V0t) )
<=> p(V0t) ) ) ) ).
fof(conj_thm_2Ebool_2EIMP__CLAUSES,axiom,
! [V0t] :
( mem(V0t,bool)
=> ( ( ( $true
=> p(V0t) )
<=> p(V0t) )
& ( ( p(V0t)
=> $true )
<=> $true )
& ( ( $false
=> p(V0t) )
<=> $true )
& ( ( p(V0t)
=> p(V0t) )
<=> $true )
& ( ( p(V0t)
=> $false )
<=> ~ p(V0t) ) ) ) ).
fof(conj_thm_2Ebool_2ENOT__CLAUSES,axiom,
( ! [V0t] :
( mem(V0t,bool)
=> ( ~ ~ p(V0t)
<=> p(V0t) ) )
& ( ~ $true
<=> $false )
& ( ~ $false
<=> $true ) ) ).
fof(conj_thm_2Ebool_2EREFL__CLAUSE,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ( V0x = V0x
<=> $true ) ) ) ).
fof(conj_thm_2Ebool_2EEQ__SYM__EQ,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ! [V1y] :
( mem(V1y,A_27a)
=> ( V0x = V1y
<=> V1y = V0x ) ) ) ) ).
fof(conj_thm_2Ebool_2EEQ__CLAUSES,axiom,
! [V0t] :
( mem(V0t,bool)
=> ( ( ( $true
<=> p(V0t) )
<=> p(V0t) )
& ( ( p(V0t)
<=> $true )
<=> p(V0t) )
& ( ( $false
<=> p(V0t) )
<=> ~ p(V0t) )
& ( ( p(V0t)
<=> $false )
<=> ~ p(V0t) ) ) ) ).
fof(conj_thm_2Ebool_2ECOND__ID,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0b] :
( mem(V0b,bool)
=> ! [V1t] :
( mem(V1t,A_27a)
=> ap(ap(ap(c_2Ebool_2ECOND(A_27a),V0b),V1t),V1t) = V1t ) ) ) ).
fof(conj_thm_2Ebool_2EDISJ__ASSOC,axiom,
! [V0A] :
( mem(V0A,bool)
=> ! [V1B] :
( mem(V1B,bool)
=> ! [V2C] :
( mem(V2C,bool)
=> ( ( p(V0A)
| p(V1B)
| p(V2C) )
<=> ( p(V0A)
| p(V1B)
| p(V2C) ) ) ) ) ) ).
fof(conj_thm_2Ebool_2EDE__MORGAN__THM,axiom,
! [V0A] :
( mem(V0A,bool)
=> ! [V1B] :
( mem(V1B,bool)
=> ( ( ~ ( p(V0A)
& p(V1B) )
<=> ( ~ p(V0A)
| ~ p(V1B) ) )
& ( ~ ( p(V0A)
| p(V1B) )
<=> ( ~ p(V0A)
& ~ p(V1B) ) ) ) ) ) ).
fof(conj_thm_2Ebool_2EIMP__DISJ__THM,axiom,
! [V0A] :
( mem(V0A,bool)
=> ! [V1B] :
( mem(V1B,bool)
=> ( ( p(V0A)
=> p(V1B) )
<=> ( ~ p(V0A)
| p(V1B) ) ) ) ) ).
fof(conj_thm_2Ebool_2EIMP__F__EQ__F,axiom,
! [V0t] :
( mem(V0t,bool)
=> ( ( p(V0t)
=> $false )
<=> ( p(V0t)
<=> $false ) ) ) ).
fof(conj_thm_2Ebool_2EAND__IMP__INTRO,axiom,
! [V0t1] :
( mem(V0t1,bool)
=> ! [V1t2] :
( mem(V1t2,bool)
=> ! [V2t3] :
( mem(V2t3,bool)
=> ( ( p(V0t1)
=> ( p(V1t2)
=> p(V2t3) ) )
<=> ( ( p(V0t1)
& p(V1t2) )
=> p(V2t3) ) ) ) ) ) ).
fof(conj_thm_2Ebool_2EEQ__EXPAND,axiom,
! [V0t1] :
( mem(V0t1,bool)
=> ! [V1t2] :
( mem(V1t2,bool)
=> ( ( p(V0t1)
<=> p(V1t2) )
<=> ( ( p(V0t1)
& p(V1t2) )
| ( ~ p(V0t1)
& ~ p(V1t2) ) ) ) ) ) ).
fof(conj_thm_2Ebool_2EIMP__CONG,axiom,
! [V0x] :
( mem(V0x,bool)
=> ! [V1x_27] :
( mem(V1x_27,bool)
=> ! [V2y] :
( mem(V2y,bool)
=> ! [V3y_27] :
( mem(V3y_27,bool)
=> ( ( ( p(V0x)
<=> p(V1x_27) )
& ( p(V1x_27)
=> ( p(V2y)
<=> p(V3y_27) ) ) )
=> ( ( p(V0x)
=> p(V2y) )
<=> ( p(V1x_27)
=> p(V3y_27) ) ) ) ) ) ) ) ).
fof(conj_thm_2Ebool_2ECOND__CONG,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,bool)
=> ! [V1Q] :
( mem(V1Q,bool)
=> ! [V2x] :
( mem(V2x,A_27a)
=> ! [V3x_27] :
( mem(V3x_27,A_27a)
=> ! [V4y] :
( mem(V4y,A_27a)
=> ! [V5y_27] :
( mem(V5y_27,A_27a)
=> ( ( ( p(V0P)
<=> p(V1Q) )
& ( p(V1Q)
=> V2x = V3x_27 )
& ( ~ p(V1Q)
=> V4y = V5y_27 ) )
=> ap(ap(ap(c_2Ebool_2ECOND(A_27a),V0P),V2x),V4y) = ap(ap(ap(c_2Ebool_2ECOND(A_27a),V1Q),V3x_27),V5y_27) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Ebool_2Ebool__case__thm,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0t1] :
( mem(V0t1,A_27a)
=> ! [V1t2] :
( mem(V1t2,A_27a)
=> ap(ap(ap(c_2Ebool_2ECOND(A_27a),c_2Ebool_2ET),V0t1),V1t2) = V0t1 ) )
& ! [V2t1] :
( mem(V2t1,A_27a)
=> ! [V3t2] :
( mem(V3t2,A_27a)
=> ap(ap(ap(c_2Ebool_2ECOND(A_27a),c_2Ebool_2EF),V2t1),V3t2) = V3t2 ) ) ) ) ).
fof(conj_thm_2Ecombin_2EI__THM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ap(c_2Ecombin_2EI(A_27a),V0x) = V0x ) ) ).
fof(conj_thm_2Efcp_2ECART__EQ,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0x] :
( mem(V0x,ty_2Efcp_2Ecart(A_27a,A_27b))
=> ! [V1y] :
( mem(V1y,ty_2Efcp_2Ecart(A_27a,A_27b))
=> ( V0x = V1y
<=> ! [V2i] :
( mem(V2i,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V2i),ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))))
=> ap(ap(c_2Efcp_2Efcp__index(A_27a,A_27b),V0x),V2i) = ap(ap(c_2Efcp_2Efcp__index(A_27a,A_27b),V1y),V2i) ) ) ) ) ) ) ) ).
fof(conj_thm_2Efcp_2EFCP__BETA,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0g] :
( mem(V0g,arr(ty_2Enum_2Enum,A_27a))
=> ! [V1i] :
( mem(V1i,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V1i),ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b))))
=> ap(ap(c_2Efcp_2Efcp__index(A_27a,A_27b),ap(c_2Efcp_2EFCP(A_27a,A_27b),V0g)),V1i) = ap(V0g,V1i) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELENGTH__MAP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ! [V1f] :
( mem(V1f,arr(A_27a,A_27b))
=> ap(c_2Elist_2ELENGTH(A_27b),ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V1f),V0l)) = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) ) ) ) ).
fof(conj_thm_2Elist_2EEL__MAP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0n),ap(c_2Elist_2ELENGTH(A_27a),V1l)))
=> ! [V2f] :
( mem(V2f,arr(A_27a,A_27b))
=> ap(ap(c_2Elist_2EEL(A_27b),V0n),ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V2f),V1l)) = ap(V2f,ap(ap(c_2Elist_2EEL(A_27a),V0n),V1l)) ) ) ) ) ) ) ).
fof(conj_thm_2Enumeral_2Enumeral__distrib,axiom,
( ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2E_2B,c_2Enum_2E0),V0n) = V0n )
& ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2E_2B,V1n),c_2Enum_2E0) = V1n )
& ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ! [V3m] :
( mem(V3m,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,V2n)),ap(c_2Earithmetic_2ENUMERAL,V3m)) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,V2n),V3m))) ) )
& ! [V4n] :
( mem(V4n,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2E_2A,c_2Enum_2E0),V4n) = c_2Enum_2E0 )
& ! [V5n] :
( mem(V5n,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2E_2A,V5n),c_2Enum_2E0) = c_2Enum_2E0 )
& ! [V6n] :
( mem(V6n,ty_2Enum_2Enum)
=> ! [V7m] :
( mem(V7m,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,V6n)),ap(c_2Earithmetic_2ENUMERAL,V7m)) = ap(c_2Earithmetic_2ENUMERAL,ap(ap(c_2Earithmetic_2E_2A,V6n),V7m)) ) )
& ! [V8n] :
( mem(V8n,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2E_2D,c_2Enum_2E0),V8n) = c_2Enum_2E0 )
& ! [V9n] :
( mem(V9n,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2E_2D,V9n),c_2Enum_2E0) = V9n )
& ! [V10n] :
( mem(V10n,ty_2Enum_2Enum)
=> ! [V11m] :
( mem(V11m,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,V10n)),ap(c_2Earithmetic_2ENUMERAL,V11m)) = ap(c_2Earithmetic_2ENUMERAL,ap(ap(c_2Earithmetic_2E_2D,V10n),V11m)) ) )
& ! [V12n] :
( mem(V12n,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2EEXP,c_2Enum_2E0),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V12n))) = c_2Enum_2E0 )
& ! [V13n] :
( mem(V13n,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2EEXP,c_2Enum_2E0),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V13n))) = c_2Enum_2E0 )
& ! [V14n] :
( mem(V14n,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2EEXP,V14n),c_2Enum_2E0) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) )
& ! [V15n] :
( mem(V15n,ty_2Enum_2Enum)
=> ! [V16m] :
( mem(V16m,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,V15n)),ap(c_2Earithmetic_2ENUMERAL,V16m)) = ap(c_2Earithmetic_2ENUMERAL,ap(ap(c_2Earithmetic_2EEXP,V15n),V16m)) ) )
& ap(c_2Enum_2ESUC,c_2Enum_2E0) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))
& ! [V17n] :
( mem(V17n,ty_2Enum_2Enum)
=> ap(c_2Enum_2ESUC,ap(c_2Earithmetic_2ENUMERAL,V17n)) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Enum_2ESUC,V17n)) )
& ap(c_2Eprim__rec_2EPRE,c_2Enum_2E0) = c_2Enum_2E0
& ! [V18n] :
( mem(V18n,ty_2Enum_2Enum)
=> ap(c_2Eprim__rec_2EPRE,ap(c_2Earithmetic_2ENUMERAL,V18n)) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Eprim__rec_2EPRE,V18n)) )
& ! [V19n] :
( mem(V19n,ty_2Enum_2Enum)
=> ( ap(c_2Earithmetic_2ENUMERAL,V19n) = c_2Enum_2E0
<=> V19n = c_2Earithmetic_2EZERO ) )
& ! [V20n] :
( mem(V20n,ty_2Enum_2Enum)
=> ( c_2Enum_2E0 = ap(c_2Earithmetic_2ENUMERAL,V20n)
<=> V20n = c_2Earithmetic_2EZERO ) )
& ! [V21n] :
( mem(V21n,ty_2Enum_2Enum)
=> ! [V22m] :
( mem(V22m,ty_2Enum_2Enum)
=> ( ap(c_2Earithmetic_2ENUMERAL,V21n) = ap(c_2Earithmetic_2ENUMERAL,V22m)
<=> V21n = V22m ) ) )
& ! [V23n] :
( mem(V23n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V23n),c_2Enum_2E0))
<=> $false ) )
& ! [V24n] :
( mem(V24n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(c_2Earithmetic_2ENUMERAL,V24n)))
<=> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Earithmetic_2EZERO),V24n)) ) )
& ! [V25n] :
( mem(V25n,ty_2Enum_2Enum)
=> ! [V26m] :
( mem(V26m,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,V25n)),ap(c_2Earithmetic_2ENUMERAL,V26m)))
<=> p(ap(ap(c_2Eprim__rec_2E_3C,V25n),V26m)) ) ) )
& ! [V27n] :
( mem(V27n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3E,c_2Enum_2E0),V27n))
<=> $false ) )
& ! [V28n] :
( mem(V28n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3E,ap(c_2Earithmetic_2ENUMERAL,V28n)),c_2Enum_2E0))
<=> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Earithmetic_2EZERO),V28n)) ) )
& ! [V29n] :
( mem(V29n,ty_2Enum_2Enum)
=> ! [V30m] :
( mem(V30m,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3E,ap(c_2Earithmetic_2ENUMERAL,V29n)),ap(c_2Earithmetic_2ENUMERAL,V30m)))
<=> p(ap(ap(c_2Eprim__rec_2E_3C,V30m),V29n)) ) ) )
& ! [V31n] :
( mem(V31n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,c_2Enum_2E0),V31n))
<=> $true ) )
& ! [V32n] :
( mem(V32n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,V32n)),c_2Enum_2E0))
<=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V32n),c_2Earithmetic_2EZERO)) ) )
& ! [V33n] :
( mem(V33n,ty_2Enum_2Enum)
=> ! [V34m] :
( mem(V34m,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,V33n)),ap(c_2Earithmetic_2ENUMERAL,V34m)))
<=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V33n),V34m)) ) ) )
& ! [V35n] :
( mem(V35n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3E_3D,V35n),c_2Enum_2E0))
<=> $true ) )
& ! [V36n] :
( mem(V36n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3E_3D,c_2Enum_2E0),V36n))
<=> V36n = c_2Enum_2E0 ) )
& ! [V37n] :
( mem(V37n,ty_2Enum_2Enum)
=> ! [V38m] :
( mem(V38m,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Earithmetic_2ENUMERAL,V37n)),ap(c_2Earithmetic_2ENUMERAL,V38m)))
<=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V38m),V37n)) ) ) )
& ! [V39n] :
( mem(V39n,ty_2Enum_2Enum)
=> ( p(ap(c_2Earithmetic_2EODD,ap(c_2Earithmetic_2ENUMERAL,V39n)))
<=> p(ap(c_2Earithmetic_2EODD,V39n)) ) )
& ! [V40n] :
( mem(V40n,ty_2Enum_2Enum)
=> ( p(ap(c_2Earithmetic_2EEVEN,ap(c_2Earithmetic_2ENUMERAL,V40n)))
<=> p(ap(c_2Earithmetic_2EEVEN,V40n)) ) )
& ~ p(ap(c_2Earithmetic_2EODD,c_2Enum_2E0))
& p(ap(c_2Earithmetic_2EEVEN,c_2Enum_2E0)) ) ).
fof(conj_thm_2Enumeral_2Enumeral__add,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ( ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,c_2Earithmetic_2EZERO),V0n)) = V0n
& ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,V0n),c_2Earithmetic_2EZERO)) = V0n
& ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT1,V1m))) = ap(c_2Earithmetic_2EBIT2,ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m)))
& ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT2,V1m))) = ap(c_2Earithmetic_2EBIT1,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m)))
& ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT1,V1m))) = ap(c_2Earithmetic_2EBIT1,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m)))
& ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT2,V1m))) = ap(c_2Earithmetic_2EBIT2,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m)))
& ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,c_2Earithmetic_2EZERO),V0n)) = ap(c_2Enum_2ESUC,V0n)
& ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0n),c_2Earithmetic_2EZERO)) = ap(c_2Enum_2ESUC,V0n)
& ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT1,V1m))) = ap(c_2Earithmetic_2EBIT1,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m)))
& ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT2,V1m))) = ap(c_2Earithmetic_2EBIT2,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m)))
& ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT1,V1m))) = ap(c_2Earithmetic_2EBIT2,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m)))
& ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT2,V1m))) = ap(c_2Earithmetic_2EBIT1,ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m)))
& ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,c_2Earithmetic_2EZERO),V0n)) = ap(c_2Enumeral_2EiiSUC,V0n)
& ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,V0n),c_2Earithmetic_2EZERO)) = ap(c_2Enumeral_2EiiSUC,V0n)
& ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT1,V1m))) = ap(c_2Earithmetic_2EBIT2,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m)))
& ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT2,V1m))) = ap(c_2Earithmetic_2EBIT1,ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m)))
& ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT1,V1m))) = ap(c_2Earithmetic_2EBIT1,ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m)))
& ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT2,V1m))) = ap(c_2Earithmetic_2EBIT2,ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) ) ) ) ).
fof(conj_thm_2Enumeral_2Enumeral__lte,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,c_2Earithmetic_2EZERO),V0n))
<=> $true )
& ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2EBIT1,V0n)),c_2Earithmetic_2EZERO))
<=> $false )
& ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2EBIT2,V0n)),c_2Earithmetic_2EZERO))
<=> $false )
& ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT1,V1m)))
<=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),V1m)) )
& ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT2,V1m)))
<=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),V1m)) )
& ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT1,V1m)))
<=> ~ p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),V0n)) )
& ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT2,V1m)))
<=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),V1m)) ) ) ) ) ).
fof(conj_thm_2Esat_2ENOT__NOT,axiom,
! [V0t] :
( mem(V0t,bool)
=> ( ~ ~ p(V0t)
<=> p(V0t) ) ) ).
fof(conj_thm_2Esat_2EAND__INV__IMP,axiom,
! [V0A] :
( mem(V0A,bool)
=> ( p(V0A)
=> ( ~ p(V0A)
=> $false ) ) ) ).
fof(conj_thm_2Esat_2EOR__DUAL2,axiom,
! [V0A] :
( mem(V0A,bool)
=> ! [V1B] :
( mem(V1B,bool)
=> ( ( ~ ( p(V0A)
| p(V1B) )
=> $false )
<=> ( ( p(V0A)
=> $false )
=> ( ~ p(V1B)
=> $false ) ) ) ) ) ).
fof(conj_thm_2Esat_2EOR__DUAL3,axiom,
! [V0A] :
( mem(V0A,bool)
=> ! [V1B] :
( mem(V1B,bool)
=> ( ( ~ ( ~ p(V0A)
| p(V1B) )
=> $false )
<=> ( p(V0A)
=> ( ~ p(V1B)
=> $false ) ) ) ) ) ).
fof(conj_thm_2Esat_2EAND__INV2,axiom,
! [V0A] :
( mem(V0A,bool)
=> ( ( ~ p(V0A)
=> $false )
=> ( ( p(V0A)
=> $false )
=> $false ) ) ) ).
fof(conj_thm_2Esat_2Edc__eq,axiom,
! [V0p] :
( mem(V0p,bool)
=> ! [V1q] :
( mem(V1q,bool)
=> ! [V2r] :
( mem(V2r,bool)
=> ( ( p(V0p)
<=> ( p(V1q)
<=> p(V2r) ) )
<=> ( ( p(V0p)
| p(V1q)
| p(V2r) )
& ( p(V0p)
| ~ p(V2r)
| ~ p(V1q) )
& ( p(V1q)
| ~ p(V2r)
| ~ p(V0p) )
& ( p(V2r)
| ~ p(V1q)
| ~ p(V0p) ) ) ) ) ) ) ).
fof(conj_thm_2Esat_2Edc__conj,axiom,
! [V0p] :
( mem(V0p,bool)
=> ! [V1q] :
( mem(V1q,bool)
=> ! [V2r] :
( mem(V2r,bool)
=> ( ( p(V0p)
<=> ( p(V1q)
& p(V2r) ) )
<=> ( ( p(V0p)
| ~ p(V1q)
| ~ p(V2r) )
& ( p(V1q)
| ~ p(V0p) )
& ( p(V2r)
| ~ p(V0p) ) ) ) ) ) ) ).
fof(conj_thm_2Esat_2Edc__disj,axiom,
! [V0p] :
( mem(V0p,bool)
=> ! [V1q] :
( mem(V1q,bool)
=> ! [V2r] :
( mem(V2r,bool)
=> ( ( p(V0p)
<=> ( p(V1q)
| p(V2r) ) )
<=> ( ( p(V0p)
| ~ p(V1q) )
& ( p(V0p)
| ~ p(V2r) )
& ( p(V1q)
| p(V2r)
| ~ p(V0p) ) ) ) ) ) ) ).
fof(conj_thm_2Esat_2Edc__neg,axiom,
! [V0p] :
( mem(V0p,bool)
=> ! [V1q] :
( mem(V1q,bool)
=> ( ( p(V0p)
<=> ~ p(V1q) )
<=> ( ( p(V0p)
| p(V1q) )
& ( ~ p(V1q)
| ~ p(V0p) ) ) ) ) ) ).
fof(ax_thm_2Ewords_2Eword__1comp__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0w] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(c_2Ewords_2Eword__1comp(A_27a),V0w) = ap(c_2Efcp_2EFCP(bool,A_27a),f2161(A_27a,V0w)) ) ) ).
fof(conj_thm_2Ewords_2EDIMINDEX__GT__0,axiom,
! [A_27a] :
( ne(A_27a)
=> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a)))) ) ).
fof(conj_thm_2Ebitstring_2Eword__1comp__v2w,conjecture,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Elist_2Elist(bool))
=> ap(c_2Ewords_2Eword__1comp(A_27a),ap(c_2Ebitstring_2Ev2w(A_27a),V0v)) = ap(c_2Ebitstring_2Ev2w(A_27a),ap(c_2Ebitstring_2Ebnot,ap(ap(c_2Ebitstring_2Efixwidth,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),V0v))) ) ) ).
%------------------------------------------------------------------------------