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196 lines (147 loc) · 4.96 KB
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%--------------------------------------------------------------------------
% File : GRP132-2.005 : TPTP v3.7.0. Released v1.2.0.
% Domain : Group Theory (Quasigroups)
% Problem : (3,1,2) conjugate orthogonality, no idempotence
% Version : [Sla93] axioms : Augmented.
% English : Generate the multiplication table for the specified quasi-
% group with 5 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 : Satisfiable
% Rating : 0.00 v3.4.0, 0.40 v3.3.0, 0.00 v3.2.0, 0.50 v2.6.0, 0.67 v2.5.0, 0.60 v2.4.0, 0.67 v2.2.0, 1.00 v2.1.0
% Syntax : Number of clauses : 46 ( 1 non-Horn; 39 unit; 46 RR)
% Number of atoms : 68 ( 0 equality)
% Maximal clause size : 7 ( 1 average)
% Number of predicates : 5 ( 0 propositional; 1-3 arity)
% Number of functors : 5 ( 5 constant; 0-0 arity)
% Number of variables : 29 ( 0 singleton)
% Maximal term depth : 1 ( 1 average)
% Comments : Slaney's [1993] axiomatization has been modified for this.
% : Substitution axioms are not needed, as any positive equality
% literals should resolve on negative ones directly.
% : As in GRP130-1, either one of qg2_1 or qg2_2 may be used, as
% each implies the other in this scenario, with the help of
% cancellation. The dependence cannot be proved, so both have
% been left in here.
% : This version adds a simple isomorphism avoidance clause,
% mentioned in [FSB93].
% : tptp2X: -f tptp -s5 GRP132-2.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_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_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_4_greater_e_3,axiom,
( greater(e_4,e_3) )).
cnf(e_5_greater_e_3,axiom,
( greater(e_5,e_3) )).
cnf(e_5_greater_e_4,axiom,
( greater(e_5,e_4) )).
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(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_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_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_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_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(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) )).
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(qg2_1,negated_conjecture,
( ~ product(X1,Y1,Z1)
| ~ product(X2,Y2,Z1)
| ~ product(Z2,X1,Y1)
| ~ product(Z2,X2,Y2)
| equalish(X1,X2) )).
cnf(qg2_2,negated_conjecture,
( ~ product(X1,Y1,Z1)
| ~ product(X2,Y2,Z1)
| ~ product(Z2,X1,Y1)
| ~ product(Z2,X2,Y2)
| equalish(Y1,Y2) )).
%--------------------------------------------------------------------------