ITP001 Axioms: ITP007_5.ax
%------------------------------------------------------------------------------
% File : ITP007_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 : sat_2.ax [Gau20]
% : HL4007_5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 24 ( 0 unt; 0 typ; 0 def)
% Number of atoms : 262 ( 0 equ)
% Maximal formula atoms : 17 ( 10 avg)
% Number of connectives : 162 ( 51 ~; 38 |; 19 &)
% ( 22 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 127 ( 127 fml; 0 var)
% Number of types : 0 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 47 ( 47 !; 0 ?; 47 :)
% SPC : TF0_SAT_NEQ_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(conj_thm_2Esat_2EAND__IMP,axiom,
! [V0A: tp__o,V1B: tp__o,V2C: tp__o] :
( ( ( p(inj__o(V0A))
& p(inj__o(V1B)) )
=> p(inj__o(V2C)) )
<=> ( p(inj__o(V0A))
=> ( p(inj__o(V1B))
=> p(inj__o(V2C)) ) ) ) ).
tff(conj_thm_2Esat_2ENOT__NOT,axiom,
! [V0t: tp__o] :
( ~ ~ p(inj__o(V0t))
<=> p(inj__o(V0t)) ) ).
tff(conj_thm_2Esat_2EAND__INV,axiom,
! [V0A: tp__o] :
( ( ~ p(inj__o(V0A))
& p(inj__o(V0A)) )
<=> $false ) ).
tff(conj_thm_2Esat_2EAND__INV__IMP,axiom,
! [V0A: tp__o] :
( p(inj__o(V0A))
=> ( ~ p(inj__o(V0A))
=> $false ) ) ).
tff(conj_thm_2Esat_2EOR__DUAL,axiom,
! [V0A: tp__o,V1B: tp__o] :
( ( ~ ( p(inj__o(V0A))
| p(inj__o(V1B)) )
=> $false )
<=> ( ~ p(inj__o(V0A))
=> ( ~ p(inj__o(V1B))
=> $false ) ) ) ).
tff(conj_thm_2Esat_2EOR__DUAL2,axiom,
! [V0A: tp__o,V1B: tp__o] :
( ( ~ ( p(inj__o(V0A))
| p(inj__o(V1B)) )
=> $false )
<=> ( ( p(inj__o(V0A))
=> $false )
=> ( ~ p(inj__o(V1B))
=> $false ) ) ) ).
tff(conj_thm_2Esat_2EOR__DUAL3,axiom,
! [V0A: tp__o,V1B: tp__o] :
( ( ~ ( ~ p(inj__o(V0A))
| p(inj__o(V1B)) )
=> $false )
<=> ( p(inj__o(V0A))
=> ( ~ p(inj__o(V1B))
=> $false ) ) ) ).
tff(conj_thm_2Esat_2EAND__INV2,axiom,
! [V0A: tp__o] :
( ( ~ p(inj__o(V0A))
=> $false )
=> ( ( p(inj__o(V0A))
=> $false )
=> $false ) ) ).
tff(conj_thm_2Esat_2ENOT__ELIM2,axiom,
! [V0A: tp__o] :
( ( ~ p(inj__o(V0A))
=> $false )
<=> p(inj__o(V0A)) ) ).
tff(conj_thm_2Esat_2EEQT__Imp1,axiom,
! [V0b: tp__o] :
( p(inj__o(V0b))
=> ( p(inj__o(V0b))
<=> $true ) ) ).
tff(conj_thm_2Esat_2EEQF__Imp1,axiom,
! [V0b: tp__o] :
( ~ p(inj__o(V0b))
=> ( p(inj__o(V0b))
<=> $false ) ) ).
tff(conj_thm_2Esat_2Edc__eq,axiom,
! [V0p: tp__o,V1q: tp__o,V2r: tp__o] :
( ( p(inj__o(V0p))
<=> ( p(inj__o(V1q))
<=> p(inj__o(V2r)) ) )
<=> ( ( p(inj__o(V0p))
| p(inj__o(V1q))
| p(inj__o(V2r)) )
& ( p(inj__o(V0p))
| ~ p(inj__o(V2r))
| ~ p(inj__o(V1q)) )
& ( p(inj__o(V1q))
| ~ p(inj__o(V2r))
| ~ p(inj__o(V0p)) )
& ( p(inj__o(V2r))
| ~ p(inj__o(V1q))
| ~ p(inj__o(V0p)) ) ) ) ).
tff(conj_thm_2Esat_2Edc__conj,axiom,
! [V0p: tp__o,V1q: tp__o,V2r: tp__o] :
( ( p(inj__o(V0p))
<=> ( p(inj__o(V1q))
& p(inj__o(V2r)) ) )
<=> ( ( p(inj__o(V0p))
| ~ p(inj__o(V1q))
| ~ p(inj__o(V2r)) )
& ( p(inj__o(V1q))
| ~ p(inj__o(V0p)) )
& ( p(inj__o(V2r))
| ~ p(inj__o(V0p)) ) ) ) ).
tff(conj_thm_2Esat_2Edc__disj,axiom,
! [V0p: tp__o,V1q: tp__o,V2r: tp__o] :
( ( p(inj__o(V0p))
<=> ( p(inj__o(V1q))
| p(inj__o(V2r)) ) )
<=> ( ( p(inj__o(V0p))
| ~ p(inj__o(V1q)) )
& ( p(inj__o(V0p))
| ~ p(inj__o(V2r)) )
& ( p(inj__o(V1q))
| p(inj__o(V2r))
| ~ p(inj__o(V0p)) ) ) ) ).
tff(conj_thm_2Esat_2Edc__imp,axiom,
! [V0p: tp__o,V1q: tp__o,V2r: tp__o] :
( ( p(inj__o(V0p))
<=> ( p(inj__o(V1q))
=> p(inj__o(V2r)) ) )
<=> ( ( p(inj__o(V0p))
| p(inj__o(V1q)) )
& ( p(inj__o(V0p))
| ~ p(inj__o(V2r)) )
& ( ~ p(inj__o(V1q))
| p(inj__o(V2r))
| ~ p(inj__o(V0p)) ) ) ) ).
tff(conj_thm_2Esat_2Edc__neg,axiom,
! [V0p: tp__o,V1q: tp__o] :
( ( p(inj__o(V0p))
<=> ~ p(inj__o(V1q)) )
<=> ( ( p(inj__o(V0p))
| p(inj__o(V1q)) )
& ( ~ p(inj__o(V1q))
| ~ p(inj__o(V0p)) ) ) ) ).
tff(conj_thm_2Esat_2Edc__cond,axiom,
! [V0p: tp__o,V1q: tp__o,V2r: tp__o,V3s: tp__o] :
( ( p(inj__o(V0p))
<=> p(ap(ap(ap(c_2Ebool_2ECOND(bool),inj__o(V1q)),inj__o(V2r)),inj__o(V3s))) )
<=> ( ( p(inj__o(V0p))
| p(inj__o(V1q))
| ~ p(inj__o(V3s)) )
& ( p(inj__o(V0p))
| ~ p(inj__o(V2r))
| ~ p(inj__o(V1q)) )
& ( p(inj__o(V0p))
| ~ p(inj__o(V2r))
| ~ p(inj__o(V3s)) )
& ( ~ p(inj__o(V1q))
| p(inj__o(V2r))
| ~ p(inj__o(V0p)) )
& ( p(inj__o(V1q))
| p(inj__o(V3s))
| ~ p(inj__o(V0p)) ) ) ) ).
tff(conj_thm_2Esat_2Epth__ni1,axiom,
! [V0p: tp__o,V1q: tp__o] :
( ~ ( p(inj__o(V0p))
=> p(inj__o(V1q)) )
=> p(inj__o(V0p)) ) ).
tff(conj_thm_2Esat_2Epth__ni2,axiom,
! [V0p: tp__o,V1q: tp__o] :
( ~ ( p(inj__o(V0p))
=> p(inj__o(V1q)) )
=> ~ p(inj__o(V1q)) ) ).
tff(conj_thm_2Esat_2Epth__no1,axiom,
! [V0p: tp__o,V1q: tp__o] :
( ~ ( p(inj__o(V0p))
| p(inj__o(V1q)) )
=> ~ p(inj__o(V0p)) ) ).
tff(conj_thm_2Esat_2Epth__no2,axiom,
! [V0p: tp__o,V1q: tp__o] :
( ~ ( p(inj__o(V0p))
| p(inj__o(V1q)) )
=> ~ p(inj__o(V1q)) ) ).
tff(conj_thm_2Esat_2Epth__an1,axiom,
! [V0p: tp__o,V1q: tp__o] :
( ( p(inj__o(V0p))
& p(inj__o(V1q)) )
=> p(inj__o(V0p)) ) ).
tff(conj_thm_2Esat_2Epth__an2,axiom,
! [V0p: tp__o,V1q: tp__o] :
( ( p(inj__o(V0p))
& p(inj__o(V1q)) )
=> p(inj__o(V1q)) ) ).
tff(conj_thm_2Esat_2Epth__nn,axiom,
! [V0p: tp__o] :
( ~ ~ p(inj__o(V0p))
=> p(inj__o(V0p)) ) ).
%------------------------------------------------------------------------------