TPTP Problem File: ITP002+2.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : ITP002+2 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Problem : HOL4 set theory export of thm_2Eoption_2EOPTION__MAP2__THM.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_2Eoption_2EOPTION__MAP2__THM.p [Gau19]
% : HL400501+2.p [TPAP]
% Status : Theorem
% Rating : 0.89 v8.1.0, 0.86 v7.5.0
% Syntax : Number of formulae : 34 ( 8 unt; 0 def)
% Number of atoms : 119 ( 17 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 86 ( 1 ~; 0 |; 15 &)
% ( 13 <=>; 57 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 6 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 5 con; 0-3 aty)
% Number of variables : 62 ( 62 !; 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_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_2Eoption_2Eoption,axiom,
! [A0] :
( ne(A0)
=> ne(ty_2Eoption_2Eoption(A0)) ) ).
fof(mem_c_2Eoption_2ENONE,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Eoption_2ENONE(A_27a),ty_2Eoption_2Eoption(A_27a)) ) ).
fof(mem_c_2Eoption_2ETHE,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Eoption_2ETHE(A_27a),arr(ty_2Eoption_2Eoption(A_27a),A_27a)) ) ).
fof(mem_c_2Eoption_2ESOME,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Eoption_2ESOME(A_27a),arr(A_27a,ty_2Eoption_2Eoption(A_27a))) ) ).
fof(mem_c_2Eoption_2EIS__SOME,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Eoption_2EIS__SOME(A_27a),arr(ty_2Eoption_2Eoption(A_27a),bool)) ) ).
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_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_2Eoption_2EOPTION__MAP2,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> mem(c_2Eoption_2EOPTION__MAP2(A_27a,A_27b,A_27c),arr(arr(A_27b,arr(A_27c,A_27a)),arr(ty_2Eoption_2Eoption(A_27b),arr(ty_2Eoption_2Eoption(A_27c),ty_2Eoption_2Eoption(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(conj_thm_2Ebool_2ETRUTH,axiom,
$true ).
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_2EREFL__CLAUSE,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ( V0x = V0x
<=> $true ) ) ) ).
fof(conj_thm_2Ebool_2ECOND__CLAUSES,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
& ap(ap(ap(c_2Ebool_2ECOND(A_27a),c_2Ebool_2EF),V0t1),V1t2) = V1t2 ) ) ) ) ).
fof(conj_thm_2Eoption_2ESOME__11,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ! [V1y] :
( mem(V1y,A_27a)
=> ( ap(c_2Eoption_2ESOME(A_27a),V0x) = ap(c_2Eoption_2ESOME(A_27a),V1y)
<=> V0x = V1y ) ) ) ) ).
fof(ax_thm_2Eoption_2EIS__SOME__DEF,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0x] :
( mem(V0x,A_27a)
=> ( p(ap(c_2Eoption_2EIS__SOME(A_27a),ap(c_2Eoption_2ESOME(A_27a),V0x)))
<=> $true ) )
& ( p(ap(c_2Eoption_2EIS__SOME(A_27a),c_2Eoption_2ENONE(A_27a)))
<=> $false ) ) ) ).
fof(ax_thm_2Eoption_2ETHE__DEF,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ap(c_2Eoption_2ETHE(A_27a),ap(c_2Eoption_2ESOME(A_27a),V0x)) = V0x ) ) ).
fof(ax_thm_2Eoption_2EOPTION__MAP2__DEF,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0f] :
( mem(V0f,arr(A_27b,arr(A_27c,A_27a)))
=> ! [V1x] :
( mem(V1x,ty_2Eoption_2Eoption(A_27b))
=> ! [V2y] :
( mem(V2y,ty_2Eoption_2Eoption(A_27c))
=> ap(ap(ap(c_2Eoption_2EOPTION__MAP2(A_27a,A_27b,A_27c),V0f),V1x),V2y) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(A_27b),V1x)),ap(c_2Eoption_2EIS__SOME(A_27c),V2y))),ap(c_2Eoption_2ESOME(A_27a),ap(ap(V0f,ap(c_2Eoption_2ETHE(A_27b),V1x)),ap(c_2Eoption_2ETHE(A_27c),V2y)))),c_2Eoption_2ENONE(A_27a)) ) ) ) ) ) ) ).
fof(conj_thm_2Eoption_2EOPTION__MAP2__THM,conjecture,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0f] :
( mem(V0f,arr(A_27b,arr(A_27c,A_27a)))
=> ! [V1x] :
( mem(V1x,A_27b)
=> ! [V2y] :
( mem(V2y,A_27c)
=> ( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(A_27a,A_27b,A_27c),V0f),ap(c_2Eoption_2ESOME(A_27b),V1x)),ap(c_2Eoption_2ESOME(A_27c),V2y)) = ap(c_2Eoption_2ESOME(A_27a),ap(ap(V0f,V1x),V2y))
& ap(ap(ap(c_2Eoption_2EOPTION__MAP2(A_27a,A_27b,A_27c),V0f),ap(c_2Eoption_2ESOME(A_27b),V1x)),c_2Eoption_2ENONE(A_27c)) = c_2Eoption_2ENONE(A_27a)
& ap(ap(ap(c_2Eoption_2EOPTION__MAP2(A_27a,A_27b,A_27c),V0f),c_2Eoption_2ENONE(A_27b)),ap(c_2Eoption_2ESOME(A_27c),V2y)) = c_2Eoption_2ENONE(A_27a)
& ap(ap(ap(c_2Eoption_2EOPTION__MAP2(A_27a,A_27b,A_27c),V0f),c_2Eoption_2ENONE(A_27b)),c_2Eoption_2ENONE(A_27c)) = c_2Eoption_2ENONE(A_27a) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------