ITP001 Axioms: ITP005^5.ax
%------------------------------------------------------------------------------
% File : ITP005^5 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 set theory export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau20] Gauthier (2020), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : marker^2.ax [Gau20]
% : HL4005^5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 25 ( 0 unt; 7 typ; 0 def)
% Number of atoms : 196 ( 2 equ; 0 cnn)
% Maximal formula atoms : 34 ( 7 avg)
% Number of connectives : 320 ( 0 ~; 20 |; 29 &; 235 @)
% ( 17 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 avg; 235 nst)
% Number of types : 1 ( 0 usr)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 16 usr; 15 con; 0-2 aty)
% Number of variables : 24 ( 0 ^ 24 !; 0 ?; 24 :)
% SPC : TH0_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(tp_c_2Emarker_2E_3A_2D,type,
c_2Emarker_2E_3A_2D: $i ).
thf(mem_c_2Emarker_2E_3A_2D,axiom,
mem @ c_2Emarker_2E_3A_2D @ ( arr @ ind @ ( arr @ bool @ bool ) ) ).
thf(tp_c_2Emarker_2EAC,type,
c_2Emarker_2EAC: $i ).
thf(mem_c_2Emarker_2EAC,axiom,
mem @ c_2Emarker_2EAC @ ( arr @ bool @ ( arr @ bool @ bool ) ) ).
thf(tp_c_2Emarker_2EAbbrev,type,
c_2Emarker_2EAbbrev: $i ).
thf(mem_c_2Emarker_2EAbbrev,axiom,
mem @ c_2Emarker_2EAbbrev @ ( arr @ bool @ bool ) ).
thf(tp_c_2Emarker_2ECong,type,
c_2Emarker_2ECong: $i ).
thf(mem_c_2Emarker_2ECong,axiom,
mem @ c_2Emarker_2ECong @ ( arr @ bool @ bool ) ).
thf(tp_c_2Emarker_2EIfCases,type,
c_2Emarker_2EIfCases: $i ).
thf(mem_c_2Emarker_2EIfCases,axiom,
mem @ c_2Emarker_2EIfCases @ bool ).
thf(tp_c_2Emarker_2Estmarker,type,
c_2Emarker_2Estmarker: del > $i ).
thf(mem_c_2Emarker_2Estmarker,axiom,
! [A_27a: del] : ( mem @ ( c_2Emarker_2Estmarker @ A_27a ) @ ( arr @ A_27a @ A_27a ) ) ).
thf(tp_c_2Emarker_2Eunint,type,
c_2Emarker_2Eunint: del > $i ).
thf(mem_c_2Emarker_2Eunint,axiom,
! [A_27a: del] : ( mem @ ( c_2Emarker_2Eunint @ A_27a ) @ ( arr @ A_27a @ A_27a ) ) ).
thf(ax_thm_2Emarker_2Estmarker__def,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ A_27a )
=> ( ( ap @ ( c_2Emarker_2Estmarker @ A_27a ) @ V0x )
= V0x ) ) ).
thf(conj_thm_2Emarker_2Emove__left__conj,axiom,
! [V0p: $i] :
( ( mem @ V0p @ bool )
=> ! [V1q: $i] :
( ( mem @ V1q @ bool )
=> ! [V2m: $i] :
( ( mem @ V2m @ bool )
=> ( ( ( ( p @ V0p )
& ( p @ ( ap @ ( c_2Emarker_2Estmarker @ bool ) @ V2m ) ) )
<=> ( ( p @ ( ap @ ( c_2Emarker_2Estmarker @ bool ) @ V2m ) )
& ( p @ V0p ) ) )
& ( ( ( p @ ( ap @ ( c_2Emarker_2Estmarker @ bool ) @ V2m ) )
& ( p @ V0p )
& ( p @ V1q ) )
<=> ( ( p @ ( ap @ ( c_2Emarker_2Estmarker @ bool ) @ V2m ) )
& ( p @ V0p )
& ( p @ V1q ) ) )
& ( ( ( p @ V0p )
& ( p @ ( ap @ ( c_2Emarker_2Estmarker @ bool ) @ V2m ) )
& ( p @ V1q ) )
<=> ( ( p @ ( ap @ ( c_2Emarker_2Estmarker @ bool ) @ V2m ) )
& ( p @ V0p )
& ( p @ V1q ) ) ) ) ) ) ) ).
thf(conj_thm_2Emarker_2Emove__right__conj,axiom,
! [V0p: $i] :
( ( mem @ V0p @ bool )
=> ! [V1q: $i] :
( ( mem @ V1q @ bool )
=> ! [V2m: $i] :
( ( mem @ V2m @ bool )
=> ( ( ( ( p @ ( ap @ ( c_2Emarker_2Estmarker @ bool ) @ V2m ) )
& ( p @ V0p ) )
<=> ( ( p @ V0p )
& ( p @ ( ap @ ( c_2Emarker_2Estmarker @ bool ) @ V2m ) ) ) )
& ( ( ( p @ V0p )
& ( p @ V1q )
& ( p @ ( ap @ ( c_2Emarker_2Estmarker @ bool ) @ V2m ) ) )
<=> ( ( p @ V0p )
& ( p @ V1q )
& ( p @ ( ap @ ( c_2Emarker_2Estmarker @ bool ) @ V2m ) ) ) )
& ( ( ( p @ V0p )
& ( p @ ( ap @ ( c_2Emarker_2Estmarker @ bool ) @ V2m ) )
& ( p @ V1q ) )
<=> ( ( p @ V0p )
& ( p @ V1q )
& ( p @ ( ap @ ( c_2Emarker_2Estmarker @ bool ) @ V2m ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Emarker_2Emove__left__disj,axiom,
! [V0p: $i] :
( ( mem @ V0p @ bool )
=> ! [V1q: $i] :
( ( mem @ V1q @ bool )
=> ! [V2m: $i] :
( ( mem @ V2m @ bool )
=> ( ( ( ( p @ V0p )
| ( p @ ( ap @ ( c_2Emarker_2Estmarker @ bool ) @ V2m ) ) )
<=> ( ( p @ ( ap @ ( c_2Emarker_2Estmarker @ bool ) @ V2m ) )
| ( p @ V0p ) ) )
& ( ( ( p @ ( ap @ ( c_2Emarker_2Estmarker @ bool ) @ V2m ) )
| ( p @ V0p )
| ( p @ V1q ) )
<=> ( ( p @ ( ap @ ( c_2Emarker_2Estmarker @ bool ) @ V2m ) )
| ( p @ V0p )
| ( p @ V1q ) ) )
& ( ( ( p @ V0p )
| ( p @ ( ap @ ( c_2Emarker_2Estmarker @ bool ) @ V2m ) )
| ( p @ V1q ) )
<=> ( ( p @ ( ap @ ( c_2Emarker_2Estmarker @ bool ) @ V2m ) )
| ( p @ V0p )
| ( p @ V1q ) ) ) ) ) ) ) ).
thf(conj_thm_2Emarker_2Emove__right__disj,axiom,
! [V0p: $i] :
( ( mem @ V0p @ bool )
=> ! [V1q: $i] :
( ( mem @ V1q @ bool )
=> ! [V2m: $i] :
( ( mem @ V2m @ bool )
=> ( ( ( ( p @ ( ap @ ( c_2Emarker_2Estmarker @ bool ) @ V2m ) )
| ( p @ V0p ) )
<=> ( ( p @ V0p )
| ( p @ ( ap @ ( c_2Emarker_2Estmarker @ bool ) @ V2m ) ) ) )
& ( ( ( p @ V0p )
| ( p @ V1q )
| ( p @ ( ap @ ( c_2Emarker_2Estmarker @ bool ) @ V2m ) ) )
<=> ( ( p @ V0p )
| ( p @ V1q )
| ( p @ ( ap @ ( c_2Emarker_2Estmarker @ bool ) @ V2m ) ) ) )
& ( ( ( p @ V0p )
| ( p @ ( ap @ ( c_2Emarker_2Estmarker @ bool ) @ V2m ) )
| ( p @ V1q ) )
<=> ( ( p @ V0p )
| ( p @ V1q )
| ( p @ ( ap @ ( c_2Emarker_2Estmarker @ bool ) @ V2m ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Emarker_2Eunint__def,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ A_27a )
=> ( ( ap @ ( c_2Emarker_2Eunint @ A_27a ) @ V0x )
= V0x ) ) ).
thf(ax_thm_2Emarker_2EAbbrev__def,axiom,
! [V0x: $i] :
( ( mem @ V0x @ bool )
=> ( ( p @ ( ap @ c_2Emarker_2EAbbrev @ V0x ) )
<=> ( p @ V0x ) ) ) ).
thf(ax_thm_2Emarker_2EIfCases__def,axiom,
( ( p @ c_2Emarker_2EIfCases )
<=> $true ) ).
thf(ax_thm_2Emarker_2EAC__DEF,axiom,
! [V0b1: $i] :
( ( mem @ V0b1 @ bool )
=> ! [V1b2: $i] :
( ( mem @ V1b2 @ bool )
=> ( ( p @ ( ap @ ( ap @ c_2Emarker_2EAC @ V0b1 ) @ V1b2 ) )
<=> ( ( p @ V0b1 )
& ( p @ V1b2 ) ) ) ) ) ).
thf(ax_thm_2Emarker_2ECong__def,axiom,
! [V0x: $i] :
( ( mem @ V0x @ bool )
=> ( ( p @ ( ap @ c_2Emarker_2ECong @ V0x ) )
<=> ( p @ V0x ) ) ) ).
thf(ax_thm_2Emarker_2Elabel__def,axiom,
! [V0lab: tp__i,V1argument: $i] :
( ( mem @ V1argument @ bool )
=> ( ( p @ ( ap @ ( ap @ c_2Emarker_2E_3A_2D @ ( inj__i @ V0lab ) ) @ V1argument ) )
<=> ( p @ V1argument ) ) ) ).
%------------------------------------------------------------------------------