%------------------------------------------------------------------------------
% File     : TOP051-1 : TPTP v9.0.0. Released v8.1.0.
% Domain   : Topology (Knot theory)
% Problem  : Goerlitz unknot
% Version  : [FL14] axioms.
% English  :

% Refs     : [FL14]  Fish & Lisitsa (2014), Detecting Unknots via Equationa
%          : [Sma21] Smallbone (2021), Email to Geoff Sutcliffe
% Source   : [Sma21]
% Names    : goerlitz.p [WM89]

% Status   : Unsatisfiable
% Rating   : 0.05 v8.2.0, 0.08 v8.1.0
% Syntax   : Number of clauses     :   14 (  14 unt;   0 nHn;  11 RR)
%            Number of literals    :   14 (  14 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    1 (   0 usr;   0 prp; 2-2 aty)
%            Number of functors    :   13 (  13 usr;  11 con; 0-10 aty)
%            Number of variables   :    6 (   0 sgn)
% SPC      : CNF_UNS_RFO_PEQ_UEQ

% Comments : See https://cgi.csc.liv.ac.uk/~alexei/Unknot/
%------------------------------------------------------------------------------
cnf(involutory_quandle,axiom,
    product(X,X) = X ).

cnf(involutory_quandle_01,axiom,
    product(product(X,Y),Y) = X ).

cnf(involutory_quandle_02,axiom,
    product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) ).

cnf(knot,axiom,
    product(a1,a6) = a2 ).

cnf(knot_03,axiom,
    product(a2,a7) = a3 ).

cnf(knot_04,axiom,
    product(a3,a1) = a4 ).

cnf(knot_05,axiom,
    product(a4,a10) = a5 ).

cnf(knot_06,axiom,
    product(a5,a9) = a6 ).

cnf(knot_07,axiom,
    product(a6,a2) = a7 ).

cnf(knot_08,axiom,
    product(a7,a3) = a8 ).

cnf(knot_09,axiom,
    product(a8,a6) = a9 ).

cnf(knot_10,axiom,
    product(a9,a4) = a10 ).

cnf(knot_11,axiom,
    product(a10,a5) = a11 ).

cnf(goal,negated_conjecture,
    tuple(a1,a6,a5,a2,a7,a3,a4,a9,a10,a8) != tuple(a2,a7,a6,a3,a8,a4,a5,a10,a11,a9) ).

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