TPTP Problem File: ITP002^3.p
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%------------------------------------------------------------------------------
% File : ITP002^3 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Problem : HOL4 syntactic 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]
% : HL400501^3.p [TPAP]
% Status : Theorem
% Rating : 0.67 v8.1.0, 0.75 v7.5.0
% Syntax : Number of formulae : 34 ( 8 unt; 18 typ; 0 def)
% Number of atoms : 39 ( 14 equ; 1 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 150 ( 1 ~; 1 |; 15 &; 118 @)
% ( 14 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 33 ( 33 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 17 usr; 3 con; 0-6 aty)
% Number of variables : 52 ( 0 ^; 40 !; 1 ?; 52 :)
% ( 11 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_THM_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Bugfixes in axioms and export.
%------------------------------------------------------------------------------
thf(tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: $tType ).
thf(tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: $tType > $tType > $tType ).
thf(tyop_2Eoption_2Eoption,type,
tyop_2Eoption_2Eoption: $tType > $tType ).
thf(c_2Ebool_2E_21,type,
c_2Ebool_2E_21:
!>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
thf(c_2Ebool_2E_2F_5C,type,
c_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(c_2Emin_2E_3D,type,
c_2Emin_2E_3D:
!>[A_27a: $tType] : ( A_27a > A_27a > $o ) ).
thf(c_2Emin_2E_3D_3D_3E,type,
c_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(c_2Ebool_2E_3F,type,
c_2Ebool_2E_3F:
!>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
thf(c_2Ebool_2ECOND,type,
c_2Ebool_2ECOND:
!>[A_27a: $tType] : ( $o > A_27a > A_27a > A_27a ) ).
thf(c_2Ebool_2EF,type,
c_2Ebool_2EF: $o ).
thf(c_2Eoption_2EIS__SOME,type,
c_2Eoption_2EIS__SOME:
!>[A_27a: $tType] : ( ( tyop_2Eoption_2Eoption @ A_27a ) > $o ) ).
thf(c_2Eoption_2ENONE,type,
c_2Eoption_2ENONE:
!>[A_27a: $tType] : ( tyop_2Eoption_2Eoption @ A_27a ) ).
thf(c_2Eoption_2EOPTION__MAP2,type,
c_2Eoption_2EOPTION__MAP2:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( A_27b > A_27c > A_27a ) > ( tyop_2Eoption_2Eoption @ A_27b ) > ( tyop_2Eoption_2Eoption @ A_27c ) > ( tyop_2Eoption_2Eoption @ A_27a ) ) ).
thf(c_2Eoption_2ESOME,type,
c_2Eoption_2ESOME:
!>[A_27a: $tType] : ( A_27a > ( tyop_2Eoption_2Eoption @ A_27a ) ) ).
thf(c_2Ebool_2ET,type,
c_2Ebool_2ET: $o ).
thf(c_2Eoption_2ETHE,type,
c_2Eoption_2ETHE:
!>[A_27a: $tType] : ( ( tyop_2Eoption_2Eoption @ A_27a ) > A_27a ) ).
thf(c_2Ebool_2E_5C_2F,type,
c_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(c_2Ebool_2E_7E,type,
c_2Ebool_2E_7E: $o > $o ).
thf(logicdef_2E_2F_5C,axiom,
! [V0: $o,V1: $o] :
( ( c_2Ebool_2E_2F_5C @ V0 @ V1 )
<=> ( V0
& V1 ) ) ).
thf(logicdef_2E_5C_2F,axiom,
! [V0: $o,V1: $o] :
( ( c_2Ebool_2E_5C_2F @ V0 @ V1 )
<=> ( V0
| V1 ) ) ).
thf(logicdef_2E_7E,axiom,
! [V0: $o] :
( ( c_2Ebool_2E_7E @ V0 )
<=> ( (~) @ V0 ) ) ).
thf(logicdef_2E_3D_3D_3E,axiom,
! [V0: $o,V1: $o] :
( ( c_2Emin_2E_3D_3D_3E @ V0 @ V1 )
<=> ( V0
=> V1 ) ) ).
thf(logicdef_2E_3D,axiom,
! [A_27a: $tType,V0: A_27a,V1: A_27a] :
( ( c_2Emin_2E_3D @ A_27a @ V0 @ V1 )
<=> ( V0 = V1 ) ) ).
thf(quantdef_2E_21,axiom,
! [A_27a: $tType,V0f: A_27a > $o] :
( ( c_2Ebool_2E_21 @ A_27a @ V0f )
<=> ! [V1x: A_27a] : ( V0f @ V1x ) ) ).
thf(quantdef_2E_3F,axiom,
! [A_27a: $tType,V0f: A_27a > $o] :
( ( c_2Ebool_2E_3F @ A_27a @ V0f )
<=> ? [V1x: A_27a] : ( V0f @ V1x ) ) ).
thf(thm_2Ebool_2ETRUTH,axiom,
c_2Ebool_2ET ).
thf(thm_2Ebool_2EAND__CLAUSES,axiom,
! [V0t: $o] :
( ( ( c_2Ebool_2ET
& V0t )
<=> V0t )
& ( ( V0t
& c_2Ebool_2ET )
<=> V0t )
& ( ( c_2Ebool_2EF
& V0t )
<=> c_2Ebool_2EF )
& ( ( V0t
& c_2Ebool_2EF )
<=> c_2Ebool_2EF )
& ( ( V0t
& V0t )
<=> V0t ) ) ).
thf(thm_2Ebool_2EREFL__CLAUSE,axiom,
! [A_27a: $tType,V0x: A_27a] :
( ( V0x = V0x )
<=> c_2Ebool_2ET ) ).
thf(thm_2Ebool_2ECOND__CLAUSES,axiom,
! [A_27a: $tType,V0t1: A_27a,V1t2: A_27a] :
( ( ( c_2Ebool_2ECOND @ A_27a @ c_2Ebool_2ET @ V0t1 @ V1t2 )
= V0t1 )
& ( ( c_2Ebool_2ECOND @ A_27a @ c_2Ebool_2EF @ V0t1 @ V1t2 )
= V1t2 ) ) ).
thf(thm_2Eoption_2ESOME__11,axiom,
! [A_27a: $tType,V0x: A_27a,V1y: A_27a] :
( ( ( c_2Eoption_2ESOME @ A_27a @ V0x )
= ( c_2Eoption_2ESOME @ A_27a @ V1y ) )
<=> ( V0x = V1y ) ) ).
thf(thm_2Eoption_2EIS__SOME__DEF,axiom,
! [A_27a: $tType] :
( ! [V0x: A_27a] :
( ( c_2Eoption_2EIS__SOME @ A_27a @ ( c_2Eoption_2ESOME @ A_27a @ V0x ) )
= c_2Ebool_2ET )
& ( ( c_2Eoption_2EIS__SOME @ A_27a @ ( c_2Eoption_2ENONE @ A_27a ) )
= c_2Ebool_2EF ) ) ).
thf(thm_2Eoption_2ETHE__DEF,axiom,
! [A_27a: $tType,V0x: A_27a] :
( ( c_2Eoption_2ETHE @ A_27a @ ( c_2Eoption_2ESOME @ A_27a @ V0x ) )
= V0x ) ).
thf(thm_2Eoption_2EOPTION__MAP2__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f: A_27b > A_27c > A_27a,V1x: tyop_2Eoption_2Eoption @ A_27b,V2y: tyop_2Eoption_2Eoption @ A_27c] :
( ( c_2Eoption_2EOPTION__MAP2 @ A_27a @ A_27b @ A_27c @ V0f @ V1x @ V2y )
= ( c_2Ebool_2ECOND @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Eoption_2EIS__SOME @ A_27b @ V1x ) @ ( c_2Eoption_2EIS__SOME @ A_27c @ V2y ) ) @ ( c_2Eoption_2ESOME @ A_27a @ ( V0f @ ( c_2Eoption_2ETHE @ A_27b @ V1x ) @ ( c_2Eoption_2ETHE @ A_27c @ V2y ) ) ) @ ( c_2Eoption_2ENONE @ A_27a ) ) ) ).
thf(thm_2Eoption_2EOPTION__MAP2__THM,conjecture,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0y: A_27c,V1x: A_27b,V2f: A_27b > A_27c > A_27a] :
( ( ( c_2Eoption_2EOPTION__MAP2 @ A_27a @ A_27b @ A_27c @ V2f @ ( c_2Eoption_2ESOME @ A_27b @ V1x ) @ ( c_2Eoption_2ESOME @ A_27c @ V0y ) )
= ( c_2Eoption_2ESOME @ A_27a @ ( V2f @ V1x @ V0y ) ) )
& ( ( c_2Eoption_2EOPTION__MAP2 @ A_27a @ A_27b @ A_27c @ V2f @ ( c_2Eoption_2ESOME @ A_27b @ V1x ) @ ( c_2Eoption_2ENONE @ A_27c ) )
= ( c_2Eoption_2ENONE @ A_27a ) )
& ( ( c_2Eoption_2EOPTION__MAP2 @ A_27a @ A_27b @ A_27c @ V2f @ ( c_2Eoption_2ENONE @ A_27b ) @ ( c_2Eoption_2ESOME @ A_27c @ V0y ) )
= ( c_2Eoption_2ENONE @ A_27a ) )
& ( ( c_2Eoption_2EOPTION__MAP2 @ A_27a @ A_27b @ A_27c @ V2f @ ( c_2Eoption_2ENONE @ A_27b ) @ ( c_2Eoption_2ENONE @ A_27c ) )
= ( c_2Eoption_2ENONE @ A_27a ) ) ) ).
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