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 def)
% Number of atoms : 182 ( 0 equ)
% Maximal formula atoms : 21 ( 7 avg)
% Number of connectives : 209 ( 51 ~; 38 |; 19 &)
% ( 22 <=>; 79 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 9 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 47 ( 47 !; 0 ?)
% SPC : FOF_SAT_RFO_NEQ
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
fof(conj_thm_2Esat_2EAND__IMP,axiom,
! [V0A] :
( mem(V0A,bool)
=> ! [V1B] :
( mem(V1B,bool)
=> ! [V2C] :
( mem(V2C,bool)
=> ( ( ( p(V0A)
& p(V1B) )
=> p(V2C) )
<=> ( p(V0A)
=> ( p(V1B)
=> p(V2C) ) ) ) ) ) ) ).
fof(conj_thm_2Esat_2ENOT__NOT,axiom,
! [V0t] :
( mem(V0t,bool)
=> ( ~ ~ p(V0t)
<=> p(V0t) ) ) ).
fof(conj_thm_2Esat_2EAND__INV,axiom,
! [V0A] :
( mem(V0A,bool)
=> ( ( ~ p(V0A)
& p(V0A) )
<=> $false ) ) ).
fof(conj_thm_2Esat_2EAND__INV__IMP,axiom,
! [V0A] :
( mem(V0A,bool)
=> ( p(V0A)
=> ( ~ p(V0A)
=> $false ) ) ) ).
fof(conj_thm_2Esat_2EOR__DUAL,axiom,
! [V0A] :
( mem(V0A,bool)
=> ! [V1B] :
( mem(V1B,bool)
=> ( ( ~ ( p(V0A)
| p(V1B) )
=> $false )
<=> ( ~ p(V0A)
=> ( ~ p(V1B)
=> $false ) ) ) ) ) ).
fof(conj_thm_2Esat_2EOR__DUAL2,axiom,
! [V0A] :
( mem(V0A,bool)
=> ! [V1B] :
( mem(V1B,bool)
=> ( ( ~ ( p(V0A)
| p(V1B) )
=> $false )
<=> ( ( p(V0A)
=> $false )
=> ( ~ p(V1B)
=> $false ) ) ) ) ) ).
fof(conj_thm_2Esat_2EOR__DUAL3,axiom,
! [V0A] :
( mem(V0A,bool)
=> ! [V1B] :
( mem(V1B,bool)
=> ( ( ~ ( ~ p(V0A)
| p(V1B) )
=> $false )
<=> ( p(V0A)
=> ( ~ p(V1B)
=> $false ) ) ) ) ) ).
fof(conj_thm_2Esat_2EAND__INV2,axiom,
! [V0A] :
( mem(V0A,bool)
=> ( ( ~ p(V0A)
=> $false )
=> ( ( p(V0A)
=> $false )
=> $false ) ) ) ).
fof(conj_thm_2Esat_2ENOT__ELIM2,axiom,
! [V0A] :
( mem(V0A,bool)
=> ( ( ~ p(V0A)
=> $false )
<=> p(V0A) ) ) ).
fof(conj_thm_2Esat_2EEQT__Imp1,axiom,
! [V0b] :
( mem(V0b,bool)
=> ( p(V0b)
=> ( p(V0b)
<=> $true ) ) ) ).
fof(conj_thm_2Esat_2EEQF__Imp1,axiom,
! [V0b] :
( mem(V0b,bool)
=> ( ~ p(V0b)
=> ( p(V0b)
<=> $false ) ) ) ).
fof(conj_thm_2Esat_2Edc__eq,axiom,
! [V0p] :
( mem(V0p,bool)
=> ! [V1q] :
( mem(V1q,bool)
=> ! [V2r] :
( mem(V2r,bool)
=> ( ( p(V0p)
<=> ( p(V1q)
<=> p(V2r) ) )
<=> ( ( p(V0p)
| p(V1q)
| p(V2r) )
& ( p(V0p)
| ~ p(V2r)
| ~ p(V1q) )
& ( p(V1q)
| ~ p(V2r)
| ~ p(V0p) )
& ( p(V2r)
| ~ p(V1q)
| ~ p(V0p) ) ) ) ) ) ) ).
fof(conj_thm_2Esat_2Edc__conj,axiom,
! [V0p] :
( mem(V0p,bool)
=> ! [V1q] :
( mem(V1q,bool)
=> ! [V2r] :
( mem(V2r,bool)
=> ( ( p(V0p)
<=> ( p(V1q)
& p(V2r) ) )
<=> ( ( p(V0p)
| ~ p(V1q)
| ~ p(V2r) )
& ( p(V1q)
| ~ p(V0p) )
& ( p(V2r)
| ~ p(V0p) ) ) ) ) ) ) ).
fof(conj_thm_2Esat_2Edc__disj,axiom,
! [V0p] :
( mem(V0p,bool)
=> ! [V1q] :
( mem(V1q,bool)
=> ! [V2r] :
( mem(V2r,bool)
=> ( ( p(V0p)
<=> ( p(V1q)
| p(V2r) ) )
<=> ( ( p(V0p)
| ~ p(V1q) )
& ( p(V0p)
| ~ p(V2r) )
& ( p(V1q)
| p(V2r)
| ~ p(V0p) ) ) ) ) ) ) ).
fof(conj_thm_2Esat_2Edc__imp,axiom,
! [V0p] :
( mem(V0p,bool)
=> ! [V1q] :
( mem(V1q,bool)
=> ! [V2r] :
( mem(V2r,bool)
=> ( ( p(V0p)
<=> ( p(V1q)
=> p(V2r) ) )
<=> ( ( p(V0p)
| p(V1q) )
& ( p(V0p)
| ~ p(V2r) )
& ( ~ p(V1q)
| p(V2r)
| ~ p(V0p) ) ) ) ) ) ) ).
fof(conj_thm_2Esat_2Edc__neg,axiom,
! [V0p] :
( mem(V0p,bool)
=> ! [V1q] :
( mem(V1q,bool)
=> ( ( p(V0p)
<=> ~ p(V1q) )
<=> ( ( p(V0p)
| p(V1q) )
& ( ~ p(V1q)
| ~ p(V0p) ) ) ) ) ) ).
fof(conj_thm_2Esat_2Edc__cond,axiom,
! [V0p] :
( mem(V0p,bool)
=> ! [V1q] :
( mem(V1q,bool)
=> ! [V2r] :
( mem(V2r,bool)
=> ! [V3s] :
( mem(V3s,bool)
=> ( ( p(V0p)
<=> p(ap(ap(ap(c_2Ebool_2ECOND(bool),V1q),V2r),V3s)) )
<=> ( ( p(V0p)
| p(V1q)
| ~ p(V3s) )
& ( p(V0p)
| ~ p(V2r)
| ~ p(V1q) )
& ( p(V0p)
| ~ p(V2r)
| ~ p(V3s) )
& ( ~ p(V1q)
| p(V2r)
| ~ p(V0p) )
& ( p(V1q)
| p(V3s)
| ~ p(V0p) ) ) ) ) ) ) ) ).
fof(conj_thm_2Esat_2Epth__ni1,axiom,
! [V0p] :
( mem(V0p,bool)
=> ! [V1q] :
( mem(V1q,bool)
=> ( ~ ( p(V0p)
=> p(V1q) )
=> p(V0p) ) ) ) ).
fof(conj_thm_2Esat_2Epth__ni2,axiom,
! [V0p] :
( mem(V0p,bool)
=> ! [V1q] :
( mem(V1q,bool)
=> ( ~ ( p(V0p)
=> p(V1q) )
=> ~ p(V1q) ) ) ) ).
fof(conj_thm_2Esat_2Epth__no1,axiom,
! [V0p] :
( mem(V0p,bool)
=> ! [V1q] :
( mem(V1q,bool)
=> ( ~ ( p(V0p)
| p(V1q) )
=> ~ p(V0p) ) ) ) ).
fof(conj_thm_2Esat_2Epth__no2,axiom,
! [V0p] :
( mem(V0p,bool)
=> ! [V1q] :
( mem(V1q,bool)
=> ( ~ ( p(V0p)
| p(V1q) )
=> ~ p(V1q) ) ) ) ).
fof(conj_thm_2Esat_2Epth__an1,axiom,
! [V0p] :
( mem(V0p,bool)
=> ! [V1q] :
( mem(V1q,bool)
=> ( ( p(V0p)
& p(V1q) )
=> p(V0p) ) ) ) ).
fof(conj_thm_2Esat_2Epth__an2,axiom,
! [V0p] :
( mem(V0p,bool)
=> ! [V1q] :
( mem(V1q,bool)
=> ( ( p(V0p)
& p(V1q) )
=> p(V1q) ) ) ) ).
fof(conj_thm_2Esat_2Epth__nn,axiom,
! [V0p] :
( mem(V0p,bool)
=> ( ~ ~ p(V0p)
=> p(V0p) ) ) ).
%------------------------------------------------------------------------------