TPTP Problem File: GRP711+1.p
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% File : GRP711+1 : TPTP v8.2.0. Released v4.0.0.
% Domain : Group Theory (Quasigroups)
% Problem : A magma with 2-sided inverses satisfying the C-law is a loop - 1b
% Version : Especial.
% English :
% Refs : [PV08] Phillips & Vojtechovsky (2008), A Scoop from Groups: N
% : [PS08] Phillips & Stanovsky (2008), Automated Theorem Proving
% : [Sta08] Stanovsky (2008), Email to G. Sutcliffe
% Source : [Sta08]
% Names : PV08 [PS08]
% Status : Theorem
% Rating : 0.10 v8.2.0, 0.21 v8.1.0, 0.13 v7.5.0, 0.19 v7.4.0, 0.24 v7.3.0, 0.15 v7.2.0, 0.08 v7.1.0, 0.09 v7.0.0, 0.13 v6.4.0, 0.21 v6.3.0, 0.29 v6.2.0, 0.36 v6.1.0, 0.25 v6.0.0, 0.33 v5.5.0, 0.12 v5.4.0, 0.22 v5.3.0, 0.00 v5.1.0, 0.14 v5.0.0, 0.25 v4.1.0, 0.27 v4.0.1, 0.40 v4.0.0
% Syntax : Number of formulae : 6 ( 5 unt; 0 def)
% Number of atoms : 9 ( 9 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 3 ( 0 ~; 0 |; 1 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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; 1 con; 0-2 aty)
% Number of variables : 10 ( 10 !; 0 ?)
% SPC : FOF_THM_RFO_PEQ
% Comments :
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fof(f01,axiom,
! [A] : mult(A,unit) = A ).
fof(f02,axiom,
! [A] : mult(unit,A) = A ).
fof(f03,axiom,
! [C,B,A] : mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) ).
fof(f04,axiom,
! [A] : mult(A,i(A)) = unit ).
fof(f05,axiom,
! [A] : mult(i(A),A) = unit ).
fof(goals,conjecture,
! [X6,X7,X8] :
( ( mult(X6,X7) = mult(X6,X8)
=> X7 = X8 )
& ( mult(X7,X6) = mult(X8,X6)
=> X7 = X8 ) ) ).
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