TPTP Problem File: ITP013^3.p
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%------------------------------------------------------------------------------
% File : ITP013^3 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Problem : HOL4 syntactic 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]
% : HL406001^3.p [TPAP]
% Status : Theorem
% Rating : 0.33 v8.1.0, 0.25 v7.5.0
% Syntax : Number of formulae : 40 ( 7 unt; 21 typ; 0 def)
% Number of atoms : 49 ( 20 equ; 5 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 181 ( 5 ~; 1 |; 14 &; 124 @)
% ( 20 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 34 ( 34 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 19 usr; 3 con; 0-4 aty)
% Number of variables : 62 ( 0 ^; 53 !; 1 ?; 62 :)
% ( 8 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_THM_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Bugfixes in axioms and export.
%------------------------------------------------------------------------------
thf(tyop_2Efcp_2Ecart,type,
tyop_2Efcp_2Ecart: $tType > $tType > $tType ).
thf(tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: $tType ).
thf(tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: $tType > $tType > $tType ).
thf(tyop_2Enum_2Enum,type,
tyop_2Enum_2Enum: $tType ).
thf(c_2Ebool_2E_21,type,
c_2Ebool_2E_21:
!>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
thf(c_2Earithmetic_2E_2B,type,
c_2Earithmetic_2E_2B: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Earithmetic_2E_2D,type,
c_2Earithmetic_2E_2D: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Ebool_2E_2F_5C,type,
c_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(c_2Earithmetic_2E_3C_3D,type,
c_2Earithmetic_2E_3C_3D: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $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_2Ebool_2ET,type,
c_2Ebool_2ET: $o ).
thf(c_2Ebool_2E_5C_2F,type,
c_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(c_2Ewords_2En2w,type,
c_2Ewords_2En2w:
!>[A_27a: $tType] : ( tyop_2Enum_2Enum > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
thf(c_2Ewords_2Eword__2comp,type,
c_2Ewords_2Eword__2comp:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
thf(c_2Ewords_2Eword__add,type,
c_2Ewords_2Eword__add:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
thf(c_2Ewords_2Eword__sub,type,
c_2Ewords_2Eword__sub:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
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_2EIMP__CLAUSES,axiom,
! [V0t: $o] :
( ( ( c_2Ebool_2ET
=> V0t )
<=> V0t )
& ( ( V0t
=> c_2Ebool_2ET )
<=> c_2Ebool_2ET )
& ( ( c_2Ebool_2EF
=> V0t )
<=> c_2Ebool_2ET )
& ( ( V0t
=> V0t )
<=> c_2Ebool_2ET )
& ( ( V0t
=> c_2Ebool_2EF )
<=> ( (~) @ V0t ) ) ) ).
thf(thm_2Ebool_2EREFL__CLAUSE,axiom,
! [A_27a: $tType,V0x: A_27a] :
( ( V0x = V0x )
<=> c_2Ebool_2ET ) ).
thf(thm_2Ebool_2EEQ__SYM__EQ,axiom,
! [A_27a: $tType,V0x: A_27a,V1y: A_27a] :
( ( V0x = V1y )
<=> ( V1y = V0x ) ) ).
thf(thm_2Ebool_2EEQ__CLAUSES,axiom,
! [V0t: $o] :
( ( ( c_2Ebool_2ET = V0t )
<=> V0t )
& ( ( V0t = c_2Ebool_2ET )
<=> V0t )
& ( ( c_2Ebool_2EF = V0t )
<=> ( (~) @ V0t ) )
& ( ( V0t = c_2Ebool_2EF )
<=> ( (~) @ V0t ) ) ) ).
thf(thm_2Ebool_2EAND__IMP__INTRO,axiom,
! [V0t1: $o,V1t2: $o,V2t3: $o] :
( ( V0t1
=> ( V1t2
=> V2t3 ) )
<=> ( ( V0t1
& V1t2 )
=> V2t3 ) ) ).
thf(thm_2Ebool_2EIMP__CONG,axiom,
! [V0x: $o,V1x_27: $o,V2y: $o,V3y_27: $o] :
( ( ( V0x = V1x_27 )
& ( V1x_27
=> ( V2y = V3y_27 ) ) )
=> ( ( V0x
=> V2y )
<=> ( V1x_27
=> V3y_27 ) ) ) ).
thf(thm_2Ebool_2ECOND__CONG,axiom,
! [A_27a: $tType,V0P: $o,V1Q: $o,V2x: A_27a,V3x_27: A_27a,V4y: A_27a,V5y_27: A_27a] :
( ( ( V0P = V1Q )
& ( V1Q
=> ( V2x = V3x_27 ) )
& ( ( (~) @ V1Q )
=> ( V4y = V5y_27 ) ) )
=> ( ( c_2Ebool_2ECOND @ A_27a @ V0P @ V2x @ V4y )
= ( c_2Ebool_2ECOND @ A_27a @ V1Q @ V3x_27 @ V5y_27 ) ) ) ).
thf(thm_2Ebool_2Ebool__case__thm,axiom,
! [A_27a: $tType] :
( ! [V0t1: A_27a,V1t2: A_27a] :
( ( c_2Ebool_2ECOND @ A_27a @ c_2Ebool_2ET @ V0t1 @ V1t2 )
= V0t1 )
& ! [V2t1: A_27a,V3t2: A_27a] :
( ( c_2Ebool_2ECOND @ A_27a @ c_2Ebool_2EF @ V2t1 @ V3t2 )
= V3t2 ) ) ).
thf(thm_2Ewords_2Eword__sub__def,axiom,
! [A_27a: $tType,V0v: tyop_2Efcp_2Ecart @ $o @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__sub @ A_27a @ V0v @ V1w )
= ( c_2Ewords_2Eword__add @ A_27a @ V0v @ ( c_2Ewords_2Eword__2comp @ A_27a @ V1w ) ) ) ).
thf(thm_2Ewords_2EWORD__LITERAL__ADD,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ! [V0m: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__add @ A_27a @ ( c_2Ewords_2Eword__2comp @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V0m ) ) @ ( c_2Ewords_2Eword__2comp @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V1n ) ) )
= ( c_2Ewords_2Eword__2comp @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2E_2B @ V0m @ V1n ) ) ) )
& ! [V2m: tyop_2Enum_2Enum,V3n: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__add @ A_27b @ ( c_2Ewords_2En2w @ A_27b @ V2m ) @ ( c_2Ewords_2Eword__2comp @ A_27b @ ( c_2Ewords_2En2w @ A_27b @ V3n ) ) )
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ A_27b ) @ ( c_2Earithmetic_2E_3C_3D @ V3n @ V2m ) @ ( c_2Ewords_2En2w @ A_27b @ ( c_2Earithmetic_2E_2D @ V2m @ V3n ) ) @ ( c_2Ewords_2Eword__2comp @ A_27b @ ( c_2Ewords_2En2w @ A_27b @ ( c_2Earithmetic_2E_2D @ V3n @ V2m ) ) ) ) ) ) ).
thf(thm_2Ewords_2En2w__sub,conjecture,
! [A_27a: $tType,V0a: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ V1b @ V0a )
=> ( ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2E_2D @ V0a @ V1b ) )
= ( c_2Ewords_2Eword__sub @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ V0a ) @ ( c_2Ewords_2En2w @ A_27a @ V1b ) ) ) ) ).
%------------------------------------------------------------------------------