TPTP Problem File: GRP124-7.005.p
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- Solve Problem
%--------------------------------------------------------------------------
% File : GRP124-7.005 : TPTP v8.2.0. Released v1.2.0.
% Domain : Group Theory (Quasigroups)
% Problem : (3,1,2) conjugate orthogonality
% Version : [Sla93] axioms : Augmented.
% Theorem formulation : Uses a second group.
% English : If ab=xy and a*b = x*y then a=x and b=y, where c*a=b iff ab=c.
% 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 v7.3.0, 0.25 v7.0.0, 0.00 v6.2.0, 0.33 v6.1.0, 0.20 v6.0.0, 0.00 v5.0.0, 0.29 v4.1.0, 0.25 v4.0.1, 0.00 v3.4.0, 0.20 v3.3.0, 0.00 v3.2.0, 0.33 v3.1.0, 0.50 v2.5.0, 0.40 v2.4.0, 0.67 v2.2.0, 1.00 v2.1.0
% Syntax : Number of clauses : 51 ( 41 unt; 2 nHn; 49 RR)
% Number of literals : 79 ( 0 equ; 41 neg)
% Maximal clause size : 7 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 7 usr; 0 prp; 1-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 37 ( 0 sgn)
% SPC : CNF_SAT_EPR_NEQ
% 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 7 has simple isomorphism avoidance (as mentioned in
% [FSB93])
% : tptp2X: -f tptp -s5 GRP124-7.g
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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(product1_total_function1,axiom,
( ~ group_element(X)
| ~ group_element(Y)
| product1(X,Y,e_1)
| product1(X,Y,e_2)
| product1(X,Y,e_3)
| product1(X,Y,e_4)
| product1(X,Y,e_5) ) ).
cnf(product1_total_function2,axiom,
( ~ product1(X,Y,W)
| ~ product1(X,Y,Z)
| equalish(W,Z) ) ).
cnf(product1_right_cancellation,axiom,
( ~ product1(X,W,Y)
| ~ product1(X,Z,Y)
| equalish(W,Z) ) ).
cnf(product1_left_cancellation,axiom,
( ~ product1(W,Y,X)
| ~ product1(Z,Y,X)
| equalish(W,Z) ) ).
cnf(product1_idempotence,axiom,
product1(X,X,X) ).
cnf(product2_total_function1,axiom,
( ~ group_element(X)
| ~ group_element(Y)
| product2(X,Y,e_1)
| product2(X,Y,e_2)
| product2(X,Y,e_3)
| product2(X,Y,e_4)
| product2(X,Y,e_5) ) ).
cnf(product2_total_function2,axiom,
( ~ product2(X,Y,W)
| ~ product2(X,Y,Z)
| equalish(W,Z) ) ).
cnf(product2_right_cancellation,axiom,
( ~ product2(X,W,Y)
| ~ product2(X,Z,Y)
| equalish(W,Z) ) ).
cnf(product2_left_cancellation,axiom,
( ~ product2(W,Y,X)
| ~ product2(Z,Y,X)
| equalish(W,Z) ) ).
cnf(product2_idempotence,axiom,
product2(X,X,X) ).
cnf(qg2a,negated_conjecture,
( ~ product1(X,Y,Z1)
| ~ product1(Z1,X,Z2)
| product2(Z2,Y,X) ) ).
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