%--------------------------------------------------------------------------
% File     : GRP316-1 : TPTP v8.2.0. Released v2.5.0.
% Domain   : Group Theory
% Problem  : An identity generated by HR, number 18432
% Version  : [MOW76] (equality) axioms.
% English  :

% Refs     : [CS02]  Colton & Sutcliffe (2002), Automatic Generation of Ben
%          : [Col01] Colton (2001), Email to G. Sutcliffe
%          : [CBW99] Colton et al. (1999), Automatic Concept Formation in P
% Source   : [Col01]
% Names    :

% Status   : Unsatisfiable
% Rating   : 0.40 v8.2.0, 0.38 v8.1.0, 0.32 v7.5.0, 0.35 v7.3.0, 0.38 v7.2.0, 0.33 v7.1.0, 0.36 v7.0.0, 0.31 v6.4.0, 0.36 v6.3.0, 0.30 v6.2.0, 0.50 v6.1.0, 0.55 v6.0.0, 0.71 v5.5.0, 0.62 v5.4.0, 0.56 v5.3.0, 0.60 v5.2.0, 0.38 v5.1.0, 0.56 v5.0.0, 0.50 v4.1.0, 0.67 v4.0.1, 0.62 v4.0.0, 0.57 v3.7.0, 0.29 v3.4.0, 0.17 v3.3.0, 0.22 v3.2.0, 0.33 v3.1.0, 0.00 v2.7.0, 0.38 v2.6.0, 0.40 v2.5.0
% Syntax   : Number of clauses     :   34 (   3 unt;  30 nHn;  31 RR)
%            Number of literals    :   74 (  74 equ;  11 neg)
%            Maximal clause size   :   11 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    1 (   0 usr;   0 prp; 2-2 aty)
%            Number of functors    :   11 (  11 usr;   9 con; 0-2 aty)
%            Number of variables   :   10 (   0 sgn)
% SPC      : CNF_UNS_RFO_PEQ_NUE

% Comments :
%--------------------------------------------------------------------------
include('Axioms/GRP004-0.ax').
%--------------------------------------------------------------------------
cnf(prove_this_1,negated_conjecture,
    ( multiply(sk_c7,sk_c8) = sk_c6
    | multiply(sk_c6,sk_c8) = sk_c7 ) ).

cnf(prove_this_2,negated_conjecture,
    ( multiply(sk_c7,sk_c8) = sk_c6
    | multiply(sk_c8,sk_c4) = sk_c7 ) ).

cnf(prove_this_3,negated_conjecture,
    ( multiply(sk_c7,sk_c8) = sk_c6
    | multiply(sk_c3,sk_c8) = sk_c4 ) ).

cnf(prove_this_4,negated_conjecture,
    ( multiply(sk_c7,sk_c8) = sk_c6
    | inverse(sk_c3) = sk_c8 ) ).

cnf(prove_this_5,negated_conjecture,
    ( multiply(sk_c7,sk_c8) = sk_c6
    | multiply(sk_c5,sk_c6) = sk_c8 ) ).

cnf(prove_this_6,negated_conjecture,
    ( multiply(sk_c7,sk_c8) = sk_c6
    | inverse(sk_c5) = sk_c6 ) ).

cnf(prove_this_7,negated_conjecture,
    ( multiply(sk_c1,sk_c8) = sk_c7
    | multiply(sk_c6,sk_c8) = sk_c7 ) ).

cnf(prove_this_8,negated_conjecture,
    ( multiply(sk_c1,sk_c8) = sk_c7
    | multiply(sk_c8,sk_c4) = sk_c7 ) ).

cnf(prove_this_9,negated_conjecture,
    ( multiply(sk_c1,sk_c8) = sk_c7
    | multiply(sk_c3,sk_c8) = sk_c4 ) ).

cnf(prove_this_10,negated_conjecture,
    ( multiply(sk_c1,sk_c8) = sk_c7
    | inverse(sk_c3) = sk_c8 ) ).

cnf(prove_this_11,negated_conjecture,
    ( multiply(sk_c1,sk_c8) = sk_c7
    | multiply(sk_c5,sk_c6) = sk_c8 ) ).

cnf(prove_this_12,negated_conjecture,
    ( multiply(sk_c1,sk_c8) = sk_c7
    | inverse(sk_c5) = sk_c6 ) ).

cnf(prove_this_13,negated_conjecture,
    ( inverse(sk_c1) = sk_c8
    | multiply(sk_c6,sk_c8) = sk_c7 ) ).

cnf(prove_this_14,negated_conjecture,
    ( inverse(sk_c1) = sk_c8
    | multiply(sk_c8,sk_c4) = sk_c7 ) ).

cnf(prove_this_15,negated_conjecture,
    ( inverse(sk_c1) = sk_c8
    | multiply(sk_c3,sk_c8) = sk_c4 ) ).

cnf(prove_this_16,negated_conjecture,
    ( inverse(sk_c1) = sk_c8
    | inverse(sk_c3) = sk_c8 ) ).

cnf(prove_this_17,negated_conjecture,
    ( inverse(sk_c1) = sk_c8
    | multiply(sk_c5,sk_c6) = sk_c8 ) ).

cnf(prove_this_18,negated_conjecture,
    ( inverse(sk_c1) = sk_c8
    | inverse(sk_c5) = sk_c6 ) ).

cnf(prove_this_19,negated_conjecture,
    ( multiply(sk_c2,sk_c7) = sk_c6
    | multiply(sk_c6,sk_c8) = sk_c7 ) ).

cnf(prove_this_20,negated_conjecture,
    ( multiply(sk_c2,sk_c7) = sk_c6
    | multiply(sk_c8,sk_c4) = sk_c7 ) ).

cnf(prove_this_21,negated_conjecture,
    ( multiply(sk_c2,sk_c7) = sk_c6
    | multiply(sk_c3,sk_c8) = sk_c4 ) ).

cnf(prove_this_22,negated_conjecture,
    ( multiply(sk_c2,sk_c7) = sk_c6
    | inverse(sk_c3) = sk_c8 ) ).

cnf(prove_this_23,negated_conjecture,
    ( multiply(sk_c2,sk_c7) = sk_c6
    | multiply(sk_c5,sk_c6) = sk_c8 ) ).

cnf(prove_this_24,negated_conjecture,
    ( multiply(sk_c2,sk_c7) = sk_c6
    | inverse(sk_c5) = sk_c6 ) ).

cnf(prove_this_25,negated_conjecture,
    ( inverse(sk_c2) = sk_c7
    | multiply(sk_c6,sk_c8) = sk_c7 ) ).

cnf(prove_this_26,negated_conjecture,
    ( inverse(sk_c2) = sk_c7
    | multiply(sk_c8,sk_c4) = sk_c7 ) ).

cnf(prove_this_27,negated_conjecture,
    ( inverse(sk_c2) = sk_c7
    | multiply(sk_c3,sk_c8) = sk_c4 ) ).

cnf(prove_this_28,negated_conjecture,
    ( inverse(sk_c2) = sk_c7
    | inverse(sk_c3) = sk_c8 ) ).

cnf(prove_this_29,negated_conjecture,
    ( inverse(sk_c2) = sk_c7
    | multiply(sk_c5,sk_c6) = sk_c8 ) ).

cnf(prove_this_30,negated_conjecture,
    ( inverse(sk_c2) = sk_c7
    | inverse(sk_c5) = sk_c6 ) ).

cnf(prove_this_31,negated_conjecture,
    ( multiply(sk_c7,sk_c8) != sk_c6
    | multiply(X3,sk_c8) != sk_c7
    | inverse(X3) != sk_c8
    | multiply(X4,sk_c7) != sk_c6
    | inverse(X4) != sk_c7
    | multiply(sk_c6,sk_c8) != sk_c7
    | multiply(sk_c8,X1) != sk_c7
    | multiply(X2,sk_c8) != X1
    | inverse(X2) != sk_c8
    | multiply(X5,sk_c6) != sk_c8
    | inverse(X5) != sk_c6 ) ).

%--------------------------------------------------------------------------