TPTP Problem File: GRP655+3.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : GRP655+3 : TPTP v9.0.0. Released v4.0.0.
% Domain : Group Theory (Quasigroups)
% Problem : A quasigroup satisfying Moufang 2 is a loop
% Version : Especial.
% English :
% Refs : [Kun96] Kunen (1996), Moufang Quasigroups
% : [PS08] Phillips & Stanovsky (2008), Automated Theorem Proving
% : [Sta08] Stanovsky (2008), Email to G. Sutcliffe
% Source : [Sta08]
% Names : Kun96a [PS08]
% Status : Theorem
% Rating : 0.29 v9.0.0, 0.45 v8.2.0, 0.50 v8.1.0, 0.52 v7.4.0, 0.53 v7.3.0, 0.38 v7.2.0, 0.42 v7.1.0, 0.36 v7.0.0, 0.53 v6.4.0, 0.50 v6.3.0, 0.57 v6.2.0, 0.55 v6.1.0, 0.50 v6.0.0, 0.58 v5.5.0, 0.38 v5.4.0, 0.56 v5.3.0, 0.17 v5.2.0, 0.29 v5.1.0, 0.43 v5.0.0, 0.50 v4.1.0, 0.55 v4.0.1, 0.80 v4.0.0
% Syntax : Number of formulae : 6 ( 5 unt; 0 def)
% Number of atoms : 7 ( 7 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 1 ( 0 ~; 0 |; 1 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% Number of functors : 3 ( 3 usr; 0 con; 2-2 aty)
% Number of variables : 13 ( 13 !; 0 ?)
% SPC : FOF_THM_RFO_PEQ
% Comments :
%------------------------------------------------------------------------------
fof(f01,axiom,
! [B,A] : mult(A,ld(A,B)) = B ).
fof(f02,axiom,
! [B,A] : ld(A,mult(A,B)) = B ).
fof(f03,axiom,
! [B,A] : mult(rd(A,B),B) = A ).
fof(f04,axiom,
! [B,A] : rd(mult(A,B),B) = A ).
fof(f05,axiom,
! [C,B,A] : mult(A,mult(B,mult(C,B))) = mult(mult(mult(A,B),C),B) ).
fof(goals,conjecture,
! [X0,X1] :
( mult(X0,ld(X1,X1)) = X0
& mult(ld(X1,X1),X0) = X0 ) ).
%------------------------------------------------------------------------------