TPTP Problem File: ITP013+2.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : ITP013+2 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Problem : HOL4 set theory export of thm_2Ewords_2En2w__sub.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_2Ewords_2En2w__sub.p [Gau19]
% : HL406001+2.p [TPAP]
% Status : Theorem
% Rating : 0.92 v8.1.0, 0.94 v7.5.0
% Syntax : Number of formulae : 44 ( 14 unt; 0 def)
% Number of atoms : 172 ( 18 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 134 ( 6 ~; 0 |; 14 &)
% ( 26 <=>; 88 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 6 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 11 con; 0-2 aty)
% Number of variables : 76 ( 76 !; 0 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments :
% Bugfixes : v7.5.0 - Bugfixes in axioms and export.
%------------------------------------------------------------------------------
include('Axioms/ITP001/ITP001+2.ax').
%------------------------------------------------------------------------------
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_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_2EF,axiom,
mem(c_2Ebool_2EF,bool) ).
fof(ax_false_p,axiom,
~ p(c_2Ebool_2EF) ).
fof(mem_c_2Ebool_2ET,axiom,
mem(c_2Ebool_2ET,bool) ).
fof(ax_true_p,axiom,
p(c_2Ebool_2ET) ).
fof(ne_ty_2Efcp_2Ecart,axiom,
! [A0] :
( ne(A0)
=> ! [A1] :
( ne(A1)
=> ne(ty_2Efcp_2Ecart(A0,A1)) ) ) ).
fof(mem_c_2Ewords_2Eword__sub,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__sub(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27a)))) ) ).
fof(ne_ty_2Enum_2Enum,axiom,
ne(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_3C_3D,axiom,
mem(c_2Earithmetic_2E_3C_3D,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool))) ).
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_2Earithmetic_2E_2B,axiom,
mem(c_2Earithmetic_2E_2B,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) ).
fof(mem_c_2Ewords_2En2w,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2En2w(A_27a),arr(ty_2Enum_2Enum,ty_2Efcp_2Ecart(bool,A_27a))) ) ).
fof(mem_c_2Ewords_2Eword__2comp,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__2comp(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27a))) ) ).
fof(mem_c_2Ewords_2Eword__add,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ewords_2Eword__add(A_27a),arr(ty_2Efcp_2Ecart(bool,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(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(conj_thm_2Ebool_2ETRUTH,axiom,
$true ).
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_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_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_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(ax_thm_2Ewords_2Eword__sub__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1w] :
( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a))
=> ap(ap(c_2Ewords_2Eword__sub(A_27a),V0v),V1w) = ap(ap(c_2Ewords_2Eword__add(A_27a),V0v),ap(c_2Ewords_2Eword__2comp(A_27a),V1w)) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__LITERAL__ADD,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( ! [V0m] :
( mem(V0m,ty_2Enum_2Enum)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(ap(c_2Ewords_2Eword__add(A_27a),ap(c_2Ewords_2Eword__2comp(A_27a),ap(c_2Ewords_2En2w(A_27a),V0m))),ap(c_2Ewords_2Eword__2comp(A_27a),ap(c_2Ewords_2En2w(A_27a),V1n))) = ap(c_2Ewords_2Eword__2comp(A_27a),ap(c_2Ewords_2En2w(A_27a),ap(ap(c_2Earithmetic_2E_2B,V0m),V1n))) ) )
& ! [V2m] :
( mem(V2m,ty_2Enum_2Enum)
=> ! [V3n] :
( mem(V3n,ty_2Enum_2Enum)
=> ap(ap(c_2Ewords_2Eword__add(A_27b),ap(c_2Ewords_2En2w(A_27b),V2m)),ap(c_2Ewords_2Eword__2comp(A_27b),ap(c_2Ewords_2En2w(A_27b),V3n))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,A_27b)),ap(ap(c_2Earithmetic_2E_3C_3D,V3n),V2m)),ap(c_2Ewords_2En2w(A_27b),ap(ap(c_2Earithmetic_2E_2D,V2m),V3n))),ap(c_2Ewords_2Eword__2comp(A_27b),ap(c_2Ewords_2En2w(A_27b),ap(ap(c_2Earithmetic_2E_2D,V3n),V2m)))) ) ) ) ) ) ).
fof(conj_thm_2Ewords_2En2w__sub,conjecture,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Enum_2Enum)
=> ! [V1b] :
( mem(V1b,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1b),V0a))
=> ap(c_2Ewords_2En2w(A_27a),ap(ap(c_2Earithmetic_2E_2D,V0a),V1b)) = ap(ap(c_2Ewords_2Eword__sub(A_27a),ap(c_2Ewords_2En2w(A_27a),V0a)),ap(c_2Ewords_2En2w(A_27a),V1b)) ) ) ) ) ).
%------------------------------------------------------------------------------