TPTP Problem File: GRP733+1.p
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% File : GRP733+1 : TPTP v8.2.0. Released v4.0.0.
% Domain : Group Theory (Quasigroups)
% Problem : Non-flexible non-commutative DTS loop.
% Version : Especial.
% English :
% Refs : [Sta08] Stanovsky (2008), Email to G. Sutcliffe
% Source : [Sta08]
% Names :
% Status : Satisfiable
% Rating : 0.00 v7.3.0, 0.67 v7.1.0, 0.00 v4.0.1, 0.50 v4.0.0
% Syntax : Number of formulae : 10 ( 9 unt; 0 def)
% Number of atoms : 16 ( 16 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 8 ( 2 ~; 2 |; 3 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 14 ( 14 !; 0 ?)
% SPC : FOF_SAT_RFO_PEQ
% Comments : Size 10
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fof(c01,axiom,
! [B,A] : mult(A,ld(A,B)) = B ).
fof(c02,axiom,
! [B,A] : ld(A,mult(A,B)) = B ).
fof(c03,axiom,
! [B,A] : mult(rd(A,B),B) = A ).
fof(c04,axiom,
! [B,A] : rd(mult(A,B),B) = A ).
fof(c05,axiom,
! [A] : mult(A,unit) = A ).
fof(c06,axiom,
! [A] : mult(unit,A) = A ).
fof(c07,axiom,
! [A] : mult(A,A) = unit ).
fof(c08,axiom,
mult(c,d) != mult(d,c) ).
fof(c09,axiom,
mult(mult(a,b),a) != mult(a,mult(b,a)) ).
fof(c10,axiom,
! [X0,X1,X2] :
( mult(X0,X1) = X2
=> ( ( mult(X0,X2) = X1
& mult(X1,X2) = X0 )
| ( mult(X0,X2) = X1
& mult(X2,X1) = X0 )
| ( mult(X2,X0) = X1
& mult(X2,X1) = X0 ) ) ) ).
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