TPTP Problem File: GRP128-2.006.p
View Solutions
- Solve Problem
%--------------------------------------------------------------------------
% File : GRP128-2.006 : TPTP v9.0.0. Released v1.2.0.
% Domain : Group Theory (Quasigroups)
% Problem : (a.b).b = a.(a.b)
% Version : [Sla93] axioms : Augmented.
% English : Generate the multiplication table for the specified quasi-
% group with 6 elements.
% Refs : [FSB93] Fujita et al. (1993), Automatic Generation of Some Res
% : [Sla93] Slaney (1993), Email to G. Sutcliffe
% : [SFS95] Slaney et al. (1995), Automated Reasoning and Exhausti
% Source : [TPTP]
% Names :
% Status : Unsatisfiable
% Rating : 0.00 v6.2.0, 0.25 v6.1.0, 0.12 v6.0.0, 0.00 v3.5.0, 0.33 v3.3.0, 0.00 v3.2.0, 0.33 v3.1.0, 0.22 v2.7.0, 0.67 v2.6.0, 0.44 v2.5.0, 0.50 v2.4.0, 0.25 v2.3.0, 0.00 v2.2.1, 1.00 v2.1.0
% Syntax : Number of clauses : 62 ( 56 unt; 1 nHn; 62 RR)
% Number of literals : 79 ( 0 equ; 43 neg)
% Maximal clause size : 8 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 5 usr; 0 prp; 1-3 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 21 ( 0 sgn)
% SPC : CNF_UNS_EPR_NEQ_NHN
% Comments : [SFS93]'s axiomatization has been modified for this.
% : Substitution axioms are not needed, as any positive equality
% literals should resolve on negative ones directly.
% : Version 2 has simple isomorphism avoidance (as mentioned in
% [FSB93])
% : tptp2X: -f tptp -s6 GRP128-2.g
%--------------------------------------------------------------------------
cnf(e_1_then_e_2,axiom,
next(e_1,e_2) ).
cnf(e_2_then_e_3,axiom,
next(e_2,e_3) ).
cnf(e_3_then_e_4,axiom,
next(e_3,e_4) ).
cnf(e_4_then_e_5,axiom,
next(e_4,e_5) ).
cnf(e_5_then_e_6,axiom,
next(e_5,e_6) ).
cnf(e_2_greater_e_1,axiom,
greater(e_2,e_1) ).
cnf(e_3_greater_e_1,axiom,
greater(e_3,e_1) ).
cnf(e_4_greater_e_1,axiom,
greater(e_4,e_1) ).
cnf(e_5_greater_e_1,axiom,
greater(e_5,e_1) ).
cnf(e_6_greater_e_1,axiom,
greater(e_6,e_1) ).
cnf(e_3_greater_e_2,axiom,
greater(e_3,e_2) ).
cnf(e_4_greater_e_2,axiom,
greater(e_4,e_2) ).
cnf(e_5_greater_e_2,axiom,
greater(e_5,e_2) ).
cnf(e_6_greater_e_2,axiom,
greater(e_6,e_2) ).
cnf(e_4_greater_e_3,axiom,
greater(e_4,e_3) ).
cnf(e_5_greater_e_3,axiom,
greater(e_5,e_3) ).
cnf(e_6_greater_e_3,axiom,
greater(e_6,e_3) ).
cnf(e_5_greater_e_4,axiom,
greater(e_5,e_4) ).
cnf(e_6_greater_e_4,axiom,
greater(e_6,e_4) ).
cnf(e_6_greater_e_5,axiom,
greater(e_6,e_5) ).
cnf(no_redundancy,axiom,
( ~ product(X,e_1,Y)
| ~ next(X,X1)
| ~ greater(Y,X1) ) ).
cnf(element_1,axiom,
group_element(e_1) ).
cnf(element_2,axiom,
group_element(e_2) ).
cnf(element_3,axiom,
group_element(e_3) ).
cnf(element_4,axiom,
group_element(e_4) ).
cnf(element_5,axiom,
group_element(e_5) ).
cnf(element_6,axiom,
group_element(e_6) ).
cnf(e_1_is_not_e_2,axiom,
~ equalish(e_1,e_2) ).
cnf(e_1_is_not_e_3,axiom,
~ equalish(e_1,e_3) ).
cnf(e_1_is_not_e_4,axiom,
~ equalish(e_1,e_4) ).
cnf(e_1_is_not_e_5,axiom,
~ equalish(e_1,e_5) ).
cnf(e_1_is_not_e_6,axiom,
~ equalish(e_1,e_6) ).
cnf(e_2_is_not_e_1,axiom,
~ equalish(e_2,e_1) ).
cnf(e_2_is_not_e_3,axiom,
~ equalish(e_2,e_3) ).
cnf(e_2_is_not_e_4,axiom,
~ equalish(e_2,e_4) ).
cnf(e_2_is_not_e_5,axiom,
~ equalish(e_2,e_5) ).
cnf(e_2_is_not_e_6,axiom,
~ equalish(e_2,e_6) ).
cnf(e_3_is_not_e_1,axiom,
~ equalish(e_3,e_1) ).
cnf(e_3_is_not_e_2,axiom,
~ equalish(e_3,e_2) ).
cnf(e_3_is_not_e_4,axiom,
~ equalish(e_3,e_4) ).
cnf(e_3_is_not_e_5,axiom,
~ equalish(e_3,e_5) ).
cnf(e_3_is_not_e_6,axiom,
~ equalish(e_3,e_6) ).
cnf(e_4_is_not_e_1,axiom,
~ equalish(e_4,e_1) ).
cnf(e_4_is_not_e_2,axiom,
~ equalish(e_4,e_2) ).
cnf(e_4_is_not_e_3,axiom,
~ equalish(e_4,e_3) ).
cnf(e_4_is_not_e_5,axiom,
~ equalish(e_4,e_5) ).
cnf(e_4_is_not_e_6,axiom,
~ equalish(e_4,e_6) ).
cnf(e_5_is_not_e_1,axiom,
~ equalish(e_5,e_1) ).
cnf(e_5_is_not_e_2,axiom,
~ equalish(e_5,e_2) ).
cnf(e_5_is_not_e_3,axiom,
~ equalish(e_5,e_3) ).
cnf(e_5_is_not_e_4,axiom,
~ equalish(e_5,e_4) ).
cnf(e_5_is_not_e_6,axiom,
~ equalish(e_5,e_6) ).
cnf(e_6_is_not_e_1,axiom,
~ equalish(e_6,e_1) ).
cnf(e_6_is_not_e_2,axiom,
~ equalish(e_6,e_2) ).
cnf(e_6_is_not_e_3,axiom,
~ equalish(e_6,e_3) ).
cnf(e_6_is_not_e_4,axiom,
~ equalish(e_6,e_4) ).
cnf(e_6_is_not_e_5,axiom,
~ equalish(e_6,e_5) ).
cnf(product_total_function1,axiom,
( ~ group_element(X)
| ~ group_element(Y)
| product(X,Y,e_1)
| product(X,Y,e_2)
| product(X,Y,e_3)
| product(X,Y,e_4)
| product(X,Y,e_5)
| product(X,Y,e_6) ) ).
cnf(product_total_function2,axiom,
( ~ product(X,Y,W)
| ~ product(X,Y,Z)
| equalish(W,Z) ) ).
cnf(product_right_cancellation,axiom,
( ~ product(X,W,Y)
| ~ product(X,Z,Y)
| equalish(W,Z) ) ).
cnf(product_left_cancellation,axiom,
( ~ product(W,Y,X)
| ~ product(Z,Y,X)
| equalish(W,Z) ) ).
cnf(qg3,negated_conjecture,
( ~ product(X,Y,Z1)
| ~ product(Z1,Y,Z2)
| product(X,Z1,Z2) ) ).
%--------------------------------------------------------------------------