## TPTP Problem File: COM001-1.p

View Solutions - Solve Problem

```%--------------------------------------------------------------------------
% File     : COM001-1 : TPTP v8.1.0. Released v1.0.0.
% Domain   : Computing Theory
% Problem  : A program correctness theorem
% Version  : Especial.
% English  : A simple computing state space, with four states - P3, P4,
%            P5, and P8 (the full version of this state space is in the
%            problem COM002-1). There is a branch at P3 such that the
%            following state is either P4 or P8. P8 has a loop back to P3,
%            while P4 leads to termination. The problem is to show that
%            there is a loop in the computation, passing through P3.

% Refs     : [RR+72] Reboh et al. (1972), Study of automatic theorem provin
%          : [WM76]  Wilson & Minker (1976), Resolution, Refinements, and S
% Source   : [SPRFN]
% Names    : SHORTBURST [RR+72]
%          : SHORTBURST [WM76]

% Status   : Unsatisfiable
% Rating   : 0.00 v5.4.0, 0.06 v5.3.0, 0.05 v5.2.0, 0.00 v2.0.0
% Syntax   : Number of clauses     :   11 (   7 unt;   0 nHn;  11 RR)
%            Number of literals    :   17 (   0 equ;   7 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   4 usr;   0 prp; 2-2 aty)
%            Number of functors    :   11 (  11 usr;   8 con; 0-2 aty)
%            Number of variables   :   11 (   1 sgn)
% SPC      : CNF_UNS_RFO_NEQ_HRN

% Comments : I suspect this problem was originally by R.M. Burstall.
%--------------------------------------------------------------------------
cnf(direct_success,axiom,
( succeeds(Goal_state,Start_state)
| ~ follows(Goal_state,Start_state) ) ).

cnf(transitivity_of_success,axiom,
( succeeds(Goal_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| ~ succeeds(Intermediate_state,Start_state) ) ).

cnf(goto_success,axiom,
( succeeds(Goal_state,Start_state)
| ~ has(Start_state,goto(Label))
| ~ labels(Label,Goal_state) ) ).

cnf(conditional_success,axiom,
( succeeds(Goal_state,Start_state)
| ~ has(Start_state,ifthen(Condition,Goal_state)) ) ).

cnf(label_state_3,hypothesis,
labels(loop,p3) ).

cnf(state_3,hypothesis,
has(p3,ifthen(equal_function(register_j,n),p4)) ).

cnf(state_4,hypothesis,
has(p4,goto(out)) ).

cnf(transition_4_to_5,hypothesis,
follows(p5,p4) ).

cnf(transition_3_to_8,hypothesis,
follows(p8,p3) ).

cnf(state_8,hypothesis,
has(p8,goto(loop)) ).

cnf(prove_there_is_a_loop_through_p3,negated_conjecture,
~ succeeds(p3,p3) ).

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