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 : 35 ( 12 unt; 12 typ; 0 def)
% Number of atoms : 259 ( 7 equ)
% Maximal formula atoms : 16 ( 7 avg)
% Number of connectives : 68 ( 0 ~; 20 |; 29 &)
% ( 17 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 168 ( 168 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 8 ( 6 >; 2 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 6 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 30 ( 30 !; 0 ?; 30 :)
% SPC : TF0_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(tp_c_2Emarker_2E_3A_2D,type,
c_2Emarker_2E_3A_2D: $i ).
tff(mem_c_2Emarker_2E_3A_2D,axiom,
mem(c_2Emarker_2E_3A_2D,arr(ind,arr(bool,bool))) ).
tff(stp_fo_c_2Emarker_2E_3A_2D,type,
fo__c_2Emarker_2E_3A_2D: ( tp__i * tp__o ) > tp__o ).
tff(stp_eq_fo_c_2Emarker_2E_3A_2D,axiom,
! [X0: tp__i,X1: tp__o] : ( inj__o(fo__c_2Emarker_2E_3A_2D(X0,X1)) = ap(ap(c_2Emarker_2E_3A_2D,inj__i(X0)),inj__o(X1)) ) ).
tff(tp_c_2Emarker_2EAC,type,
c_2Emarker_2EAC: $i ).
tff(mem_c_2Emarker_2EAC,axiom,
mem(c_2Emarker_2EAC,arr(bool,arr(bool,bool))) ).
tff(stp_fo_c_2Emarker_2EAC,type,
fo__c_2Emarker_2EAC: ( tp__o * tp__o ) > tp__o ).
tff(stp_eq_fo_c_2Emarker_2EAC,axiom,
! [X0: tp__o,X1: tp__o] : ( inj__o(fo__c_2Emarker_2EAC(X0,X1)) = ap(ap(c_2Emarker_2EAC,inj__o(X0)),inj__o(X1)) ) ).
tff(tp_c_2Emarker_2EAbbrev,type,
c_2Emarker_2EAbbrev: $i ).
tff(mem_c_2Emarker_2EAbbrev,axiom,
mem(c_2Emarker_2EAbbrev,arr(bool,bool)) ).
tff(stp_fo_c_2Emarker_2EAbbrev,type,
fo__c_2Emarker_2EAbbrev: tp__o > tp__o ).
tff(stp_eq_fo_c_2Emarker_2EAbbrev,axiom,
! [X0: tp__o] : ( inj__o(fo__c_2Emarker_2EAbbrev(X0)) = ap(c_2Emarker_2EAbbrev,inj__o(X0)) ) ).
tff(tp_c_2Emarker_2ECong,type,
c_2Emarker_2ECong: $i ).
tff(mem_c_2Emarker_2ECong,axiom,
mem(c_2Emarker_2ECong,arr(bool,bool)) ).
tff(stp_fo_c_2Emarker_2ECong,type,
fo__c_2Emarker_2ECong: tp__o > tp__o ).
tff(stp_eq_fo_c_2Emarker_2ECong,axiom,
! [X0: tp__o] : ( inj__o(fo__c_2Emarker_2ECong(X0)) = ap(c_2Emarker_2ECong,inj__o(X0)) ) ).
tff(tp_c_2Emarker_2EIfCases,type,
c_2Emarker_2EIfCases: $i ).
tff(mem_c_2Emarker_2EIfCases,axiom,
mem(c_2Emarker_2EIfCases,bool) ).
tff(stp_fo_c_2Emarker_2EIfCases,type,
fo__c_2Emarker_2EIfCases: tp__o ).
tff(stp_eq_fo_c_2Emarker_2EIfCases,axiom,
inj__o(fo__c_2Emarker_2EIfCases) = c_2Emarker_2EIfCases ).
tff(tp_c_2Emarker_2Estmarker,type,
c_2Emarker_2Estmarker: del > $i ).
tff(mem_c_2Emarker_2Estmarker,axiom,
! [A_27a: del] : mem(c_2Emarker_2Estmarker(A_27a),arr(A_27a,A_27a)) ).
tff(tp_c_2Emarker_2Eunint,type,
c_2Emarker_2Eunint: del > $i ).
tff(mem_c_2Emarker_2Eunint,axiom,
! [A_27a: del] : mem(c_2Emarker_2Eunint(A_27a),arr(A_27a,A_27a)) ).
tff(ax_thm_2Emarker_2Estmarker__def,axiom,
! [A_27a: del,V0x: $i] :
( mem(V0x,A_27a)
=> ( ap(c_2Emarker_2Estmarker(A_27a),V0x) = V0x ) ) ).
tff(conj_thm_2Emarker_2Emove__left__conj,axiom,
! [V0p: tp__o,V1q: tp__o,V2m: tp__o] :
( ( ( p(inj__o(V0p))
& p(ap(c_2Emarker_2Estmarker(bool),inj__o(V2m))) )
<=> ( p(ap(c_2Emarker_2Estmarker(bool),inj__o(V2m)))
& p(inj__o(V0p)) ) )
& ( ( p(ap(c_2Emarker_2Estmarker(bool),inj__o(V2m)))
& p(inj__o(V0p))
& p(inj__o(V1q)) )
<=> ( p(ap(c_2Emarker_2Estmarker(bool),inj__o(V2m)))
& p(inj__o(V0p))
& p(inj__o(V1q)) ) )
& ( ( p(inj__o(V0p))
& p(ap(c_2Emarker_2Estmarker(bool),inj__o(V2m)))
& p(inj__o(V1q)) )
<=> ( p(ap(c_2Emarker_2Estmarker(bool),inj__o(V2m)))
& p(inj__o(V0p))
& p(inj__o(V1q)) ) ) ) ).
tff(conj_thm_2Emarker_2Emove__right__conj,axiom,
! [V0p: tp__o,V1q: tp__o,V2m: tp__o] :
( ( ( p(ap(c_2Emarker_2Estmarker(bool),inj__o(V2m)))
& p(inj__o(V0p)) )
<=> ( p(inj__o(V0p))
& p(ap(c_2Emarker_2Estmarker(bool),inj__o(V2m))) ) )
& ( ( p(inj__o(V0p))
& p(inj__o(V1q))
& p(ap(c_2Emarker_2Estmarker(bool),inj__o(V2m))) )
<=> ( p(inj__o(V0p))
& p(inj__o(V1q))
& p(ap(c_2Emarker_2Estmarker(bool),inj__o(V2m))) ) )
& ( ( p(inj__o(V0p))
& p(ap(c_2Emarker_2Estmarker(bool),inj__o(V2m)))
& p(inj__o(V1q)) )
<=> ( p(inj__o(V0p))
& p(inj__o(V1q))
& p(ap(c_2Emarker_2Estmarker(bool),inj__o(V2m))) ) ) ) ).
tff(conj_thm_2Emarker_2Emove__left__disj,axiom,
! [V0p: tp__o,V1q: tp__o,V2m: tp__o] :
( ( ( p(inj__o(V0p))
| p(ap(c_2Emarker_2Estmarker(bool),inj__o(V2m))) )
<=> ( p(ap(c_2Emarker_2Estmarker(bool),inj__o(V2m)))
| p(inj__o(V0p)) ) )
& ( ( p(ap(c_2Emarker_2Estmarker(bool),inj__o(V2m)))
| p(inj__o(V0p))
| p(inj__o(V1q)) )
<=> ( p(ap(c_2Emarker_2Estmarker(bool),inj__o(V2m)))
| p(inj__o(V0p))
| p(inj__o(V1q)) ) )
& ( ( p(inj__o(V0p))
| p(ap(c_2Emarker_2Estmarker(bool),inj__o(V2m)))
| p(inj__o(V1q)) )
<=> ( p(ap(c_2Emarker_2Estmarker(bool),inj__o(V2m)))
| p(inj__o(V0p))
| p(inj__o(V1q)) ) ) ) ).
tff(conj_thm_2Emarker_2Emove__right__disj,axiom,
! [V0p: tp__o,V1q: tp__o,V2m: tp__o] :
( ( ( p(ap(c_2Emarker_2Estmarker(bool),inj__o(V2m)))
| p(inj__o(V0p)) )
<=> ( p(inj__o(V0p))
| p(ap(c_2Emarker_2Estmarker(bool),inj__o(V2m))) ) )
& ( ( p(inj__o(V0p))
| p(inj__o(V1q))
| p(ap(c_2Emarker_2Estmarker(bool),inj__o(V2m))) )
<=> ( p(inj__o(V0p))
| p(inj__o(V1q))
| p(ap(c_2Emarker_2Estmarker(bool),inj__o(V2m))) ) )
& ( ( p(inj__o(V0p))
| p(ap(c_2Emarker_2Estmarker(bool),inj__o(V2m)))
| p(inj__o(V1q)) )
<=> ( p(inj__o(V0p))
| p(inj__o(V1q))
| p(ap(c_2Emarker_2Estmarker(bool),inj__o(V2m))) ) ) ) ).
tff(ax_thm_2Emarker_2Eunint__def,axiom,
! [A_27a: del,V0x: $i] :
( mem(V0x,A_27a)
=> ( ap(c_2Emarker_2Eunint(A_27a),V0x) = V0x ) ) ).
tff(ax_thm_2Emarker_2EAbbrev__def,axiom,
! [V0x: tp__o] :
( p(ap(c_2Emarker_2EAbbrev,inj__o(V0x)))
<=> p(inj__o(V0x)) ) ).
tff(ax_thm_2Emarker_2EIfCases__def,axiom,
( p(inj__o(fo__c_2Emarker_2EIfCases))
<=> $true ) ).
tff(ax_thm_2Emarker_2EAC__DEF,axiom,
! [V0b1: tp__o,V1b2: tp__o] :
( p(ap(ap(c_2Emarker_2EAC,inj__o(V0b1)),inj__o(V1b2)))
<=> ( p(inj__o(V0b1))
& p(inj__o(V1b2)) ) ) ).
tff(ax_thm_2Emarker_2ECong__def,axiom,
! [V0x: tp__o] :
( p(ap(c_2Emarker_2ECong,inj__o(V0x)))
<=> p(inj__o(V0x)) ) ).
tff(ax_thm_2Emarker_2Elabel__def,axiom,
! [V0lab: tp__i,V1argument: tp__o] :
( p(ap(ap(c_2Emarker_2E_3A_2D,inj__i(V0lab)),inj__o(V1argument)))
<=> p(inj__o(V1argument)) ) ).
%------------------------------------------------------------------------------