TPTP Problem File: ALG074+1.p
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- Solve Problem
%--------------------------------------------------------------------------
% File : ALG074+1 : TPTP v8.2.0. Released v2.7.0.
% Domain : General Algebra
% Problem : Loops 5: CPROPS-SORTED-DISCRIMINANT-PROBLEM-6
% Version : Especial.
% English :
% Refs : [Mei03] Meier (2003), Email to G.Sutcliffe
% : [CM+04] Colton et al. (2004), Automatic Generation of Classifi
% Source : [Mei03]
% Names :
% Status : Theorem
% Rating : 0.39 v7.5.0, 0.44 v7.4.0, 0.27 v7.3.0, 0.35 v7.0.0, 0.30 v6.4.0, 0.35 v6.3.0, 0.38 v6.2.0, 0.43 v6.0.0, 0.35 v5.5.0, 0.52 v5.4.0, 0.57 v5.3.0, 0.63 v5.2.0, 0.48 v5.0.0, 0.48 v4.0.0, 0.46 v3.7.0, 0.40 v3.5.0, 0.37 v3.4.0, 0.42 v3.3.0, 0.43 v3.2.0, 0.44 v2.7.0
% Syntax : Number of formulae : 5 ( 0 unt; 0 def)
% Number of atoms : 30 ( 10 equ)
% Maximal formula atoms : 14 ( 6 avg)
% Number of connectives : 31 ( 6 ~; 0 |; 12 &)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty)
% Number of functors : 4 ( 4 usr; 0 con; 1-2 aty)
% Number of variables : 16 ( 12 !; 4 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments :
%--------------------------------------------------------------------------
fof(ax1,axiom,
! [U] :
( sorti1(U)
=> ! [V] :
( sorti1(V)
=> sorti1(op1(U,V)) ) ) ).
fof(ax2,axiom,
! [U] :
( sorti2(U)
=> ! [V] :
( sorti2(V)
=> sorti2(op2(U,V)) ) ) ).
fof(ax3,axiom,
? [U] :
( sorti1(U)
& ? [V] :
( sorti1(V)
& op1(V,U) != op1(U,V)
& op1(op1(U,V),V) = U
& op1(op1(U,V),U) != V ) ) ).
fof(ax4,axiom,
~ ? [U] :
( sorti2(U)
& ? [V] :
( sorti2(V)
& op2(V,U) != op2(U,V)
& op2(op2(U,V),V) = U
& op2(op2(U,V),U) != V ) ) ).
fof(co1,conjecture,
( ( ! [U] :
( sorti1(U)
=> sorti2(h(U)) )
& ! [V] :
( sorti2(V)
=> sorti1(j(V)) ) )
=> ~ ( ! [W] :
( sorti1(W)
=> ! [X] :
( sorti1(X)
=> h(op1(W,X)) = op2(h(W),h(X)) ) )
& ! [Y] :
( sorti2(Y)
=> ! [Z] :
( sorti2(Z)
=> j(op2(Y,Z)) = op1(j(Y),j(Z)) ) )
& ! [X1] :
( sorti2(X1)
=> h(j(X1)) = X1 )
& ! [X2] :
( sorti1(X2)
=> j(h(X2)) = X2 ) ) ) ).
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