## TPTP Problem File: LCL042-1.p

View Solutions - Solve Problem

```%--------------------------------------------------------------------------
% File     : LCL042-1 : TPTP v8.1.2. Released v1.0.0.
% Domain   : Logic Calculi (Implication/Negation 2 valued sentential)
% Problem  : CN-35 depends on Hilbert's system
% Version  : [McC92] axioms.
% English  : Two axiomatisations of the Implication/Negation 2 valued
%            sentential calculus are {CN-18,CN-21,CN-35,CN-39,CN-39,
%            CN-40,CN-46} by Frege and {CN-3,CN-18,CN-21,CN-22,CN-30,
%            CN-54} by Hilbert. Show that CN-35 depends on the simplified
%            Hilbert system (without CN-30).

% Refs     : [MW92]  McCune & Wos (1992), Experiments in Automated Deductio
%          : [McC92] McCune (1992), Email to G. Sutcliffe
% Source   : [McC92]
% Names    : CN-3 [MW92]

% Status   : Unsatisfiable
% Rating   : 0.14 v8.1.0, 0.00 v7.4.0, 0.17 v7.3.0, 0.00 v6.1.0, 0.36 v6.0.0, 0.33 v5.5.0, 0.38 v5.4.0, 0.44 v5.3.0, 0.60 v5.2.0, 0.54 v5.1.0, 0.56 v5.0.0, 0.60 v4.1.0, 0.53 v4.0.1, 0.43 v3.4.0, 0.20 v3.3.0, 0.00 v3.1.0, 0.17 v2.7.0, 0.38 v2.6.0, 0.29 v2.5.0, 0.43 v2.4.0, 0.57 v2.3.0, 0.29 v2.2.1, 0.67 v2.1.0, 0.63 v2.0.0
% Syntax   : Number of clauses     :    7 (   6 unt;   0 nHn;   2 RR)
%            Number of literals    :    9 (   0 equ;   3 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    1 (   1 usr;   0 prp; 1-1 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   14 (   2 sgn)
% SPC      : CNF_UNS_RFO_NEQ_HRN

%--------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ) ).

cnf(cn_3,axiom,
is_a_theorem(implies(X,implies(not(X),Y))) ).

cnf(cn_18,axiom,
is_a_theorem(implies(X,implies(Y,X))) ).

cnf(cn_21,axiom,
is_a_theorem(implies(implies(X,implies(Y,Z)),implies(Y,implies(X,Z)))) ).

cnf(cn_22,axiom,
is_a_theorem(implies(implies(Y,Z),implies(implies(X,Y),implies(X,Z)))) ).

cnf(cn_54,axiom,
is_a_theorem(implies(implies(X,Y),implies(implies(not(X),Y),Y))) ).

cnf(prove_cn_35,negated_conjecture,
~ is_a_theorem(implies(implies(a,implies(b,c)),implies(implies(a,b),implies(a,c)))) ).

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