## TPTP Problem File: SYN101-1.002.002.p

View Solutions - Solve Problem

```%--------------------------------------------------------------------------
% File     : SYN101-1.002.002 : TPTP v8.1.0. Bugfixed v1.2.1.
% Domain   : Syntactic
% Problem  : Plaisted problem n(t(2,2),2)
% Version  : Biased.
% English  :

% Refs     : [Pla94] Plaisted (1994), The Search Efficiency of Theorem Prov
% Source   : [Pla94]
% Names    : N(T2n)) [Pla94]

% Status   : Unsatisfiable
% Rating   : 0.00 v2.1.0
% Syntax   : Number of clauses     :   17 (   5 unt;   0 nHn;  17 RR)
%            Number of literals    :   37 (   0 equ;  21 neg)
%            Maximal clause size   :    3 (   2 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    8 (   8 usr;   0 prp; 1-2 aty)
%            Number of functors    :    2 (   2 usr;   2 con; 0-0 aty)
%            Number of variables   :   24 (   0 sgn)
% SPC      : CNF_UNS_EPR_NEQ_HRN

% Comments : Biased away from various calculi.
%          : tptp2X: -f tptp -s2:2 SYN101-1.g
% Bugfixes : v1.2.0 - Bugfix in SYN086-1.
%          : v1.2.1 - Bugfix in SYN086-1.
%--------------------------------------------------------------------------
cnf(n_s2_goal_1,negated_conjecture,
~ p_1_2(a,a) ).

cnf(n_s2_type11_1,axiom,
( p_1_2(X_1,X_2)
| ~ p_2_2(X_1,X_2)
| ~ p_1_1(X_1,X_2) ) ).

cnf(n_s2_type11_2,axiom,
( p_1_2(X_1,X_2)
| ~ q_2_2(X_1,X_2)
| ~ q_1_1(X_1,X_2) ) ).

cnf(n_s2_type12_1,axiom,
( q_1_2(X_1,X_2)
| ~ p_2_2(X_1,X_2)
| ~ q_1_1(X_1,X_2) ) ).

cnf(n_s2_type12_2,axiom,
( q_1_2(X_1,X_2)
| ~ q_2_2(X_1,X_2)
| ~ p_1_1(X_1,X_2) ) ).

cnf(n_s2_type21_1,axiom,
( p_1_1(X_1,X_2)
| ~ p_1_2(X_1,X_2) ) ).

cnf(n_s2_type21_2,axiom,
( q_1_1(X_1,X_2)
| ~ q_1_2(X_1,X_2) ) ).

cnf(n_s2_type22_1,axiom,
( p_2_2(X_1,X_2)
| ~ p_1_2(X_1,X_2) ) ).

cnf(n_s2_type22_2,axiom,
( q_2_2(X_1,X_2)
| ~ q_1_2(X_1,X_2) ) ).

cnf(n_t2_1,axiom,
( p_1_1(X_1,X_2)
| ~ nq_1(X_1)
| ~ nq_2(X_2) ) ).

cnf(n_t2_2,axiom,
( q_1_1(X_1,X_2)
| ~ nq_1(X_1)
| ~ nq_2(X_2) ) ).

cnf(n_t2_3,axiom,
( p_2_2(X_1,X_2)
| ~ nq_1(X_1)
| ~ nq_2(X_2) ) ).

cnf(n_t2_4,axiom,
( q_2_2(X_1,X_2)
| ~ nq_1(X_1)
| ~ nq_2(X_2) ) ).

cnf(n_1,axiom,
nq_1(a) ).

cnf(n_2,axiom,
nq_1(b) ).

cnf(n_3,axiom,
nq_2(a) ).

cnf(n_4,axiom,
nq_2(b) ).

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