TPTP Problem File: GRP667+1.p
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- Solve Problem
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% File : GRP667+1 : TPTP v8.2.0. Released v4.0.0.
% Domain : Group Theory (Quasigroups)
% Problem : 2-divisible ARIF loops are Moufang
% Version : Especial.
% English :
% Refs : [KKP02] Kinyon et al. (2002), A Generalization of Moufang and
% : [PS08] Phillips & Stanovsky (2008), Automated Theorem Proving
% : [Sta08] Stanovsky (2008), Email to G. Sutcliffe
% Source : [Sta08]
% Names : KKP02b [PS08]
% Status : Theorem
% Rating : 0.20 v8.2.0, 0.38 v8.1.0, 0.43 v7.5.0, 0.33 v7.4.0, 0.41 v7.3.0, 0.38 v7.2.0, 0.33 v7.1.0, 0.36 v7.0.0, 0.27 v6.4.0, 0.36 v6.3.0, 0.29 v6.2.0, 0.27 v6.1.0, 0.42 v6.0.0, 0.50 v5.5.0, 0.38 v5.4.0, 0.44 v5.3.0, 0.17 v5.2.0, 0.14 v5.1.0, 0.29 v5.0.0, 0.38 v4.1.0, 0.45 v4.0.1, 0.70 v4.0.0
% Syntax : Number of formulae : 13 ( 10 unt; 0 def)
% Number of atoms : 16 ( 16 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 3 ( 0 ~; 0 |; 0 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 25 ( 25 !; 0 ?)
% SPC : FOF_THM_RFO_PEQ
% Comments :
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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,
! [A] : mult(A,unit) = A ).
fof(f06,axiom,
! [A] : mult(unit,A) = A ).
fof(f07,axiom,
! [C,B,A] : mult(mult(A,B),mult(mult(C,B),C)) = mult(mult(A,mult(mult(B,C),B)),C) ).
fof(f08,axiom,
! [B,A] : mult(mult(A,B),A) = mult(A,mult(B,A)) ).
fof(f09,axiom,
! [A] : mult(f(A),f(A)) = A ).
fof(f10,axiom,
! [X0,X1,X2] :
( mult(X0,mult(X1,mult(X2,X1))) = mult(mult(mult(X0,X1),X2),X1)
=> mult(X1,mult(X0,mult(X1,X2))) = mult(mult(mult(X1,X0),X1),X2) ) ).
fof(f11,axiom,
! [X3,X4,X5] :
( mult(mult(X3,X4),mult(X5,X3)) = mult(mult(X3,mult(X4,X5)),X3)
=> mult(X3,mult(X4,mult(X3,X5))) = mult(mult(mult(X3,X4),X3),X5) ) ).
fof(f12,axiom,
! [X6,X7,X8] :
( mult(mult(X6,X7),mult(X8,X6)) = mult(X6,mult(mult(X7,X8),X6))
=> mult(X6,mult(X7,mult(X6,X8))) = mult(mult(mult(X6,X7),X6),X8) ) ).
fof(goals,conjecture,
mult(a,mult(b,mult(a,c))) = mult(mult(mult(a,b),a),c) ).
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