## TPTP Problem File: SWV491+4.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SWV491+4 : TPTP v8.1.2. Released v4.0.0.
% Domain   : Software Verification
% Problem  : Matrix is identity
% Version  : Especial.
% English  :

% Refs     : [KV09]  Kovacs (2009), Email to Geoff Sutcliffe
% Source   : [KV09]
% Names    : Id7 [KV09]

% Status   : Theorem
% Rating   : 0.64 v7.5.0, 0.69 v7.4.0, 0.57 v7.3.0, 0.66 v7.1.0, 0.65 v7.0.0, 0.73 v6.3.0, 0.62 v6.2.0, 0.72 v6.1.0, 0.77 v6.0.0, 0.78 v5.5.0, 0.85 v5.4.0, 0.89 v5.3.0, 0.93 v5.2.0, 0.85 v5.1.0, 0.90 v5.0.0, 0.96 v4.1.0, 1.00 v4.0.1, 0.87 v4.0.0
% Syntax   : Number of formulae    :   13 (   4 unt;   0 def)
%            Number of atoms       :   47 (  15 equ)
%            Maximal formula atoms :   17 (   3 avg)
%            Number of connectives :   37 (   3   ~;   2   |;  17   &)
%                                         (   3 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   0 prp; 2-2 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :   29 (  28   !;   1   ?)
% SPC      : FOF_THM_RFO_SEQ

%------------------------------------------------------------------------------
fof(int_leq,axiom,
! [I,J] :
( int_leq(I,J)
<=> ( int_less(I,J)
| I = J ) ) ).

fof(int_less_transitive,axiom,
! [I,J,K] :
( ( int_less(I,J)
& int_less(J,K) )
=> int_less(I,K) ) ).

fof(int_less_irreflexive,axiom,
! [I,J] :
( int_less(I,J)
=> I != J ) ).

fof(int_less_total,axiom,
! [I,J] :
( int_less(I,J)
| int_leq(J,I) ) ).

fof(int_zero_one,axiom,
int_less(int_zero,int_one) ).

fof(plus_commutative,axiom,
! [I,J] : plus(I,J) = plus(J,I) ).

fof(plus_zero,axiom,
! [I] : plus(I,int_zero) = I ).

fof(plus_and_order1,axiom,
! [I1,J1,I2,J2] :
( ( int_less(I1,J1)
& int_leq(I2,J2) )
=> int_leq(plus(I1,I2),plus(J1,J2)) ) ).

fof(plus_and_inverse,axiom,
! [I,J] :
( int_less(I,J)
<=> ? [K] :
( plus(I,K) = J
& int_less(int_zero,K) ) ) ).

fof(one_successor_of_zero,axiom,
! [I] :
( int_less(int_zero,I)
<=> int_leq(int_one,I) ) ).

fof(real_constants,axiom,
real_zero != real_one ).

fof(qii,hypothesis,
! [I,J] :
( ( int_leq(int_one,I)
& int_leq(I,n)
& int_leq(int_one,J)
& int_leq(J,n) )
=> ( ! [C] :
( ( int_less(int_zero,C)
& I = plus(J,C) )
=> ! [K] :
( ( int_leq(int_one,K)
& int_leq(K,J) )
=> a(plus(K,C),K) = real_zero ) )
& ! [K] :
( ( int_leq(int_one,K)
& int_leq(K,J) )
=> a(K,K) = real_one )
& ! [C] :
( ( int_less(int_zero,C)
& J = plus(I,C) )
=> ! [K] :
( ( int_leq(int_one,K)
& int_leq(K,I) )
=> a(K,plus(K,C)) = real_zero ) ) ) ) ).

fof(id,conjecture,
! [I,J] :
( ( int_leq(int_one,I)
& int_leq(I,n)
& int_leq(int_one,J)
& int_leq(J,n) )
=> ( ( I != J
=> a(I,J) = real_zero )
& ( I = J
=> a(I,J) = real_one ) ) ) ).

%------------------------------------------------------------------------------
```