TPTP Problem File: GRP129-1.003.p
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% File : GRP129-1.003 : TPTP v9.0.0. Released v1.2.0.
% Domain : Group Theory (Quasigroups)
% Problem : a.(b.a) = (b.a).b
% Version : [Sla93] axioms.
% English : Generate the multiplication table for the specified quasi-
% group with 3 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 : [Sla93]
% Names : QG7 [Sla93]
% : QG7 [FSB93]
% : QG7 [SFS95]
% : Bennett QG7 [TPTP]
% Status : Unsatisfiable
% Rating : 0.00 v2.1.0
% Syntax : Number of clauses : 14 ( 9 unt; 1 nHn; 14 RR)
% Number of literals : 26 ( 0 equ; 16 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 3 usr; 0 prp; 1-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 18 ( 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.
% : tptp2X: -f tptp -s3 GRP129-1.g
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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(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_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_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(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) ) ).
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(Y,X,Z1)
| ~ product(X,Z1,Z2)
| product(Z1,Y,Z2) ) ).
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