## TPTP Problem File: SYN098-1.002.p

View Solutions - Solve Problem

```%--------------------------------------------------------------------------
% File     : SYN098-1.002 : TPTP v8.1.0. Bugfixed v1.2.1.
% Domain   : Syntactic
% Problem  : Plaisted problem sym(u(t(3,2)))
% Version  : Biased.
% English  :

% Refs     : [Pla94] Plaisted (1994), The Search Efficiency of Theorem Prov
% Source   : [Pla94]
% Names    : Sym(U(T3n)) [Pla94]

% Status   : Unsatisfiable
% Rating   : 0.33 v5.5.0, 0.00 v4.1.0, 0.20 v4.0.1, 0.00 v2.1.0
% Syntax   : Number of clauses     :   68 (   2 unt;  25 nHn;  68 RR)
%            Number of literals    :  176 (   0 equ;  88 neg)
%            Maximal clause size   :    4 (   2 avg)
%            Maximal term depth    :    0 (   0 avg)
%            Number of predicates  :   54 (  54 usr;  54 prp; 0-0 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :    0 (   0 sgn)
% SPC      : CNF_UNS_PRP

% Comments : Biased away from various calculi.
%          : tptp2X: -f tptp -s2 SYN098-1.g
% Bugfixes : v1.2.0 - Bugfix in SYN086-1.
%          : v1.2.1 - Bugfix in SYN086-1.
%--------------------------------------------------------------------------
cnf(u_s3_goal_1,negated_conjecture,
( u_1
| ~ p_0
| ~ q_0 ) ).

cnf(u_1_s3_goal_1,axiom,
~ u_1 ).

cnf(u_s3_type11_1,axiom,
( u_2
| p_0
| ~ p_1
| ~ p_2 ) ).

cnf(u_2_s3_type11_1,axiom,
( p_0
| ~ u_2 ) ).

cnf(u_s3_type11_2,axiom,
( u_3
| p_0
| ~ q_1
| ~ q_2 ) ).

cnf(u_3_s3_type11_2,axiom,
( p_0
| ~ u_3 ) ).

cnf(u_s3_type11_3,axiom,
( u_4
| p_1
| ~ p_2
| ~ p_3 ) ).

cnf(u_4_s3_type11_3,axiom,
( p_1
| ~ u_4 ) ).

cnf(u_s3_type11_4,axiom,
( u_5
| p_1
| ~ q_2
| ~ q_3 ) ).

cnf(u_5_s3_type11_4,axiom,
( p_1
| ~ u_5 ) ).

cnf(u_s3_type12_1,axiom,
( u_6
| q_0
| ~ p_1
| ~ q_2 ) ).

cnf(u_6_s3_type12_1,axiom,
( q_0
| ~ u_6 ) ).

cnf(u_s3_type12_2,axiom,
( u_7
| q_0
| ~ q_1
| ~ p_2 ) ).

cnf(u_7_s3_type12_2,axiom,
( q_0
| ~ u_7 ) ).

cnf(u_s3_type12_3,axiom,
( u_8
| q_1
| ~ p_2
| ~ q_3 ) ).

cnf(u_8_s3_type12_3,axiom,
( q_1
| ~ u_8 ) ).

cnf(u_s3_type12_4,axiom,
( u_9
| q_1
| ~ q_2
| ~ p_3 ) ).

cnf(u_9_s3_type12_4,axiom,
( q_1
| ~ u_9 ) ).

cnf(u_s3_type2_1,axiom,
( u_10
| p_3
| ~ p_1 ) ).

cnf(u_10_s3_type2_1,axiom,
( p_3
| ~ u_10 ) ).

cnf(u_s3_type2_2,axiom,
( u_11
| p_4
| ~ p_2 ) ).

cnf(u_11_s3_type2_2,axiom,
( p_4
| ~ u_11 ) ).

cnf(u_s3_type2_3,axiom,
( u_12
| q_3
| ~ q_1 ) ).

cnf(u_12_s3_type2_3,axiom,
( q_3
| ~ u_12 ) ).

cnf(u_s3_type2_4,axiom,
( u_13
| q_4
| ~ q_2 ) ).

cnf(u_13_s3_type2_4,axiom,
( q_4
| ~ u_13 ) ).

cnf(u_t3_1,axiom,
( u_14
| p_2 ) ).

cnf(u_14_t3_1,axiom,
( p_2
| ~ u_14 ) ).

cnf(u_t3_2,axiom,
( u_15
| p_3 ) ).

cnf(u_15_t3_2,axiom,
( p_3
| ~ u_15 ) ).

cnf(u_t3_3,axiom,
( u_16
| q_2 ) ).

cnf(u_16_t3_3,axiom,
( q_2
| ~ u_16 ) ).

cnf(u_t3_4,axiom,
( u_17
| q_3 ) ).

cnf(u_17_t3_4,axiom,
( q_3
| ~ u_17 ) ).

cnf(sym_u_s3_goal_1,axiom,
( ~ sym_u_1
| sym_p_0
| sym_q_0 ) ).

cnf(sym_u_1_s3_goal_1,axiom,
sym_u_1 ).

cnf(sym_u_s3_type11_1,axiom,
( ~ sym_u_2
| ~ sym_p_0
| sym_p_1
| sym_p_2 ) ).

cnf(sym_u_2_s3_type11_1,axiom,
( ~ sym_p_0
| sym_u_2 ) ).

cnf(sym_u_s3_type11_2,axiom,
( ~ sym_u_3
| ~ sym_p_0
| sym_q_1
| sym_q_2 ) ).

cnf(sym_u_3_s3_type11_2,axiom,
( ~ sym_p_0
| sym_u_3 ) ).

cnf(sym_u_s3_type11_3,axiom,
( ~ sym_u_4
| ~ sym_p_1
| sym_p_2
| sym_p_3 ) ).

cnf(sym_u_4_s3_type11_3,axiom,
( ~ sym_p_1
| sym_u_4 ) ).

cnf(sym_u_s3_type11_4,axiom,
( ~ sym_u_5
| ~ sym_p_1
| sym_q_2
| sym_q_3 ) ).

cnf(sym_u_5_s3_type11_4,axiom,
( ~ sym_p_1
| sym_u_5 ) ).

cnf(sym_u_s3_type12_1,axiom,
( ~ sym_u_6
| ~ sym_q_0
| sym_p_1
| sym_q_2 ) ).

cnf(sym_u_6_s3_type12_1,axiom,
( ~ sym_q_0
| sym_u_6 ) ).

cnf(sym_u_s3_type12_2,axiom,
( ~ sym_u_7
| ~ sym_q_0
| sym_q_1
| sym_p_2 ) ).

cnf(sym_u_7_s3_type12_2,axiom,
( ~ sym_q_0
| sym_u_7 ) ).

cnf(sym_u_s3_type12_3,axiom,
( ~ sym_u_8
| ~ sym_q_1
| sym_p_2
| sym_q_3 ) ).

cnf(sym_u_8_s3_type12_3,axiom,
( ~ sym_q_1
| sym_u_8 ) ).

cnf(sym_u_s3_type12_4,axiom,
( ~ sym_u_9
| ~ sym_q_1
| sym_q_2
| sym_p_3 ) ).

cnf(sym_u_9_s3_type12_4,axiom,
( ~ sym_q_1
| sym_u_9 ) ).

cnf(sym_u_s3_type2_1,axiom,
( ~ sym_u_10
| ~ sym_p_3
| sym_p_1 ) ).

cnf(sym_u_10_s3_type2_1,axiom,
( ~ sym_p_3
| sym_u_10 ) ).

cnf(sym_u_s3_type2_2,axiom,
( ~ sym_u_11
| ~ sym_p_4
| sym_p_2 ) ).

cnf(sym_u_11_s3_type2_2,axiom,
( ~ sym_p_4
| sym_u_11 ) ).

cnf(sym_u_s3_type2_3,axiom,
( ~ sym_u_12
| ~ sym_q_3
| sym_q_1 ) ).

cnf(sym_u_12_s3_type2_3,axiom,
( ~ sym_q_3
| sym_u_12 ) ).

cnf(sym_u_s3_type2_4,axiom,
( ~ sym_u_13
| ~ sym_q_4
| sym_q_2 ) ).

cnf(sym_u_13_s3_type2_4,axiom,
( ~ sym_q_4
| sym_u_13 ) ).

cnf(sym_u_t3_1,axiom,
( ~ sym_u_14
| ~ sym_p_2 ) ).

cnf(sym_u_14_t3_1,axiom,
( ~ sym_p_2
| sym_u_14 ) ).

cnf(sym_u_t3_2,axiom,
( ~ sym_u_15
| ~ sym_p_3 ) ).

cnf(sym_u_15_t3_2,axiom,
( ~ sym_p_3
| sym_u_15 ) ).

cnf(sym_u_t3_3,axiom,
( ~ sym_u_16
| ~ sym_q_2 ) ).

cnf(sym_u_16_t3_3,axiom,
( ~ sym_q_2
| sym_u_16 ) ).

cnf(sym_u_t3_4,axiom,
( ~ sym_u_17
| ~ sym_q_3 ) ).

cnf(sym_u_17_t3_4,axiom,
( ~ sym_q_3
| sym_u_17 ) ).

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