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 : 18 ( 5 unt; 0 def)
% Number of atoms : 108 ( 2 equ)
% Maximal formula atoms : 19 ( 6 avg)
% Number of connectives : 90 ( 0 ~; 20 |; 29 &)
% ( 17 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 24 ( 24 !; 0 ?)
% SPC : FOF_SAT_RFO_SEQ
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
fof(mem_c_2Emarker_2E_3A_2D,axiom,
mem(c_2Emarker_2E_3A_2D,arr(ind,arr(bool,bool))) ).
fof(mem_c_2Emarker_2EAC,axiom,
mem(c_2Emarker_2EAC,arr(bool,arr(bool,bool))) ).
fof(mem_c_2Emarker_2EAbbrev,axiom,
mem(c_2Emarker_2EAbbrev,arr(bool,bool)) ).
fof(mem_c_2Emarker_2ECong,axiom,
mem(c_2Emarker_2ECong,arr(bool,bool)) ).
fof(mem_c_2Emarker_2EIfCases,axiom,
mem(c_2Emarker_2EIfCases,bool) ).
fof(mem_c_2Emarker_2Estmarker,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Emarker_2Estmarker(A_27a),arr(A_27a,A_27a)) ) ).
fof(mem_c_2Emarker_2Eunint,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Emarker_2Eunint(A_27a),arr(A_27a,A_27a)) ) ).
fof(ax_thm_2Emarker_2Estmarker__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ap(c_2Emarker_2Estmarker(A_27a),V0x) = V0x ) ) ).
fof(conj_thm_2Emarker_2Emove__left__conj,axiom,
! [V0p] :
( mem(V0p,bool)
=> ! [V1q] :
( mem(V1q,bool)
=> ! [V2m] :
( 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) ) ) ) ) ) ) ).
fof(conj_thm_2Emarker_2Emove__right__conj,axiom,
! [V0p] :
( mem(V0p,bool)
=> ! [V1q] :
( mem(V1q,bool)
=> ! [V2m] :
( 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)) ) ) ) ) ) ) ).
fof(conj_thm_2Emarker_2Emove__left__disj,axiom,
! [V0p] :
( mem(V0p,bool)
=> ! [V1q] :
( mem(V1q,bool)
=> ! [V2m] :
( 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) ) ) ) ) ) ) ).
fof(conj_thm_2Emarker_2Emove__right__disj,axiom,
! [V0p] :
( mem(V0p,bool)
=> ! [V1q] :
( mem(V1q,bool)
=> ! [V2m] :
( 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)) ) ) ) ) ) ) ).
fof(ax_thm_2Emarker_2Eunint__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ap(c_2Emarker_2Eunint(A_27a),V0x) = V0x ) ) ).
fof(ax_thm_2Emarker_2EAbbrev__def,axiom,
! [V0x] :
( mem(V0x,bool)
=> ( p(ap(c_2Emarker_2EAbbrev,V0x))
<=> p(V0x) ) ) ).
fof(ax_thm_2Emarker_2EIfCases__def,axiom,
( p(c_2Emarker_2EIfCases)
<=> $true ) ).
fof(ax_thm_2Emarker_2EAC__DEF,axiom,
! [V0b1] :
( mem(V0b1,bool)
=> ! [V1b2] :
( mem(V1b2,bool)
=> ( p(ap(ap(c_2Emarker_2EAC,V0b1),V1b2))
<=> ( p(V0b1)
& p(V1b2) ) ) ) ) ).
fof(ax_thm_2Emarker_2ECong__def,axiom,
! [V0x] :
( mem(V0x,bool)
=> ( p(ap(c_2Emarker_2ECong,V0x))
<=> p(V0x) ) ) ).
fof(ax_thm_2Emarker_2Elabel__def,axiom,
! [V0lab] :
( mem(V0lab,ind)
=> ! [V1argument] :
( mem(V1argument,bool)
=> ( p(ap(ap(c_2Emarker_2E_3A_2D,V0lab),V1argument))
<=> p(V1argument) ) ) ) ).
%------------------------------------------------------------------------------