TPTP Problem File: ITP015^3.p
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%------------------------------------------------------------------------------
% File : ITP015^3 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Problem : HOL4 syntactic export of thm_2Einteger__word_2Ei2w__0.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_2Einteger__word_2Ei2w__0.p [Gau19]
% : HL407001^3.p [TPAP]
% Status : Theorem
% Rating : 0.33 v8.1.0, 0.25 v7.5.0
% Syntax : Number of formulae : 51 ( 13 unt; 28 typ; 0 def)
% Number of atoms : 49 ( 23 equ; 5 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 162 ( 5 ~; 2 |; 8 &; 123 @)
% ( 12 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 36 ( 36 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 25 usr; 4 con; 0-4 aty)
% Number of variables : 59 ( 0 ^; 49 !; 1 ?; 59 :)
% ( 9 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_THM_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Bugfixes in axioms and export.
%------------------------------------------------------------------------------
thf(tyop_2Ebool_2Eitself,type,
tyop_2Ebool_2Eitself: $tType > $tType ).
thf(tyop_2Efcp_2Ecart,type,
tyop_2Efcp_2Ecart: $tType > $tType > $tType ).
thf(tyop_2Einteger_2Eint,type,
tyop_2Einteger_2Eint: $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_2Ebool_2E_2F_5C,type,
c_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(c_2Enum_2E0,type,
c_2Enum_2E0: tyop_2Enum_2Enum ).
thf(c_2Eprim__rec_2E_3C,type,
c_2Eprim__rec_2E_3C: 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_2Earithmetic_2EMOD,type,
c_2Earithmetic_2EMOD: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Einteger_2ENum,type,
c_2Einteger_2ENum: tyop_2Einteger_2Eint > tyop_2Enum_2Enum ).
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_2Edimword,type,
c_2Ewords_2Edimword:
!>[A_27a: $tType] : ( ( tyop_2Ebool_2Eitself @ A_27a ) > tyop_2Enum_2Enum ) ).
thf(c_2Einteger__word_2Ei2w,type,
c_2Einteger__word_2Ei2w:
!>[A_27a: $tType] : ( tyop_2Einteger_2Eint > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
thf(c_2Einteger_2Eint__lt,type,
c_2Einteger_2Eint__lt: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > $o ).
thf(c_2Einteger_2Eint__neg,type,
c_2Einteger_2Eint__neg: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).
thf(c_2Einteger_2Eint__of__num,type,
c_2Einteger_2Eint__of__num: tyop_2Enum_2Enum > tyop_2Einteger_2Eint ).
thf(c_2Ewords_2En2w,type,
c_2Ewords_2En2w:
!>[A_27a: $tType] : ( tyop_2Enum_2Enum > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
thf(c_2Ebool_2Ethe__value,type,
c_2Ebool_2Ethe__value:
!>[A_27a: $tType] : ( tyop_2Ebool_2Eitself @ 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_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__ANTISYM__AX,axiom,
! [V0t1: $o,V1t2: $o] :
( ( V0t1
=> V1t2 )
=> ( ( V1t2
=> V0t1 )
=> ( V0t1 = V1t2 ) ) ) ).
thf(thm_2Ebool_2EFALSITY,axiom,
! [V0t: $o] :
( 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_2EAND__IMP__INTRO,axiom,
! [V0t1: $o,V1t2: $o,V2t3: $o] :
( ( V0t1
=> ( V1t2
=> V2t3 ) )
<=> ( ( V0t1
& V1t2 )
=> V2t3 ) ) ).
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_2Einteger_2EINT__NEG__0,axiom,
( ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ).
thf(thm_2Einteger_2EINT__LT__CALCULATE,axiom,
! [V0n: tyop_2Enum_2Enum,V1m: tyop_2Enum_2Enum] :
( ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ V0n ) @ ( c_2Einteger_2Eint__of__num @ V1m ) )
= ( c_2Eprim__rec_2E_3C @ V0n @ V1m ) )
& ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ V0n ) ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ V1m ) ) )
= ( c_2Eprim__rec_2E_3C @ V1m @ V0n ) )
& ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ V0n ) ) @ ( c_2Einteger_2Eint__of__num @ V1m ) )
<=> ( ( (~) @ ( V0n = c_2Enum_2E0 ) )
| ( (~) @ ( V1m = c_2Enum_2E0 ) ) ) )
& ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ V0n ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ V1m ) ) )
= c_2Ebool_2EF ) ) ).
thf(thm_2Einteger_2ENUM__OF__INT,axiom,
! [V0n: tyop_2Enum_2Enum] :
( ( c_2Einteger_2ENum @ ( c_2Einteger_2Eint__of__num @ V0n ) )
= V0n ) ).
thf(thm_2Einteger__word_2Ei2w__def,axiom,
! [A_27a: $tType,V0i: tyop_2Einteger_2Eint] :
( ( c_2Einteger__word_2Ei2w @ A_27a @ V0i )
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( c_2Einteger_2Eint__lt @ V0i @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( c_2Ewords_2Eword__2comp @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Einteger_2ENum @ ( c_2Einteger_2Eint__neg @ V0i ) ) ) ) @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Einteger_2ENum @ V0i ) ) ) ) ).
thf(thm_2Eprim__rec_2ENOT__LESS__0,axiom,
! [V0n: tyop_2Enum_2Enum] : ( (~) @ ( c_2Eprim__rec_2E_3C @ V0n @ c_2Enum_2E0 ) ) ).
thf(thm_2Ewords_2En2w__11,axiom,
! [A_27a: $tType,V0m: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum] :
( ( ( c_2Ewords_2En2w @ A_27a @ V0m )
= ( c_2Ewords_2En2w @ A_27a @ V1n ) )
<=> ( ( c_2Earithmetic_2EMOD @ V0m @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
= ( c_2Earithmetic_2EMOD @ V1n @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ).
thf(thm_2Ewords_2EWORD__NEG__0,axiom,
! [A_27a: $tType] :
( ( c_2Ewords_2Eword__2comp @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) )
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) ).
thf(thm_2Einteger__word_2Ei2w__0,conjecture,
! [A_27a: $tType] :
( ( c_2Einteger__word_2Ei2w @ A_27a @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) ) ).
%------------------------------------------------------------------------------