%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : PUZ016-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n028.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Mon Jul 18 18:20:26 EDT 2022

% Result   : Unsatisfiable 0.19s 0.39s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   29
%            Number of leaves      :  148
% Syntax   : Number of clauses     :  450 ( 192 unt;   0 nHn; 449 RR)
%            Number of literals    :  828 ( 712 equ; 379 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   15 (  15 usr;  11 con; 0-8 aty)
%            Number of variables   :   34 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(cover_columns_2_and_3,axiom,
    ( ~ achievable(row(X),squares(Y1,not_covered,not_covered,Y4,Y5,Y6,Y7,Y8))
    | achievable(row(X),squares(Y1,covered,covered,Y4,Y5,Y6,Y7,Y8)) ) ).

cnf(cover_columns_6_and_7,axiom,
    ( ~ achievable(row(X),squares(Y1,Y2,Y3,Y4,Y5,not_covered,not_covered,Y8))
    | achievable(row(X),squares(Y1,Y2,Y3,Y4,Y5,covered,covered,Y8)) ) ).

cnf(place_vertical_pieces,axiom,
    ( ~ achievable(row(X),squares(Y1,Y2,Y3,Y4,Y5,Y6,Y7,Y8))
    | achievable(row(successor(X)),squares(complement(Y1),complement(Y2),complement(Y3),complement(Y4),complement(Y5),complement(Y6),complement(Y7),complement(Y8))) ) ).

cnf(successor_of_1_is_2,axiom,
    successor(n1) = n2 ).

cnf(successor_of_2_is_3,axiom,
    successor(n2) = n3 ).

cnf(successor_of_3_is_4,axiom,
    successor(n3) = n4 ).

cnf(successor_of_4_is_5,axiom,
    successor(n4) = n5 ).

cnf(successor_of_5_is_6,axiom,
    successor(n5) = n6 ).

cnf(successor_of_6_is_7,axiom,
    successor(n6) = n7 ).

cnf(successor_of_7_is_8,axiom,
    successor(n7) = n8 ).

cnf(complement_of_covered_is_not_covered,axiom,
    complement(covered) = not_covered ).

cnf(complement_of_not_covered_is_covered,axiom,
    complement(not_covered) = covered ).

cnf(complement_of_removed_is_not_covered,axiom,
    complement(removed) = not_covered ).

cnf(first_row_initially,hypothesis,
    achievable(row(n1),squares(not_covered,removed,removed,not_covered,not_covered,not_covered,not_covered,not_covered)) ).

cnf(prove_row_8_can_be_covered,negated_conjecture,
    ~ achievable(row(n8),squares(covered,covered,covered,covered,covered,covered,covered,covered)) ).

cnf(refute_0_0,plain,
    ( ~ achievable(row(n7),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered))
    | achievable(row(successor(n7)),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))) ),
    inference(subst,[],[place_vertical_pieces:[bind(X,$fot(n7)),bind(Y1,$fot(not_covered)),bind(Y2,$fot(not_covered)),bind(Y3,$fot(not_covered)),bind(Y4,$fot(not_covered)),bind(Y5,$fot(not_covered)),bind(Y6,$fot(not_covered)),bind(Y7,$fot(not_covered)),bind(Y8,$fot(not_covered))]]) ).

cnf(refute_0_1,plain,
    ( ~ achievable(row(n6),squares(covered,covered,covered,covered,covered,covered,covered,covered))
    | achievable(row(successor(n6)),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered))) ),
    inference(subst,[],[place_vertical_pieces:[bind(X,$fot(n6)),bind(Y1,$fot(covered)),bind(Y2,$fot(covered)),bind(Y3,$fot(covered)),bind(Y4,$fot(covered)),bind(Y5,$fot(covered)),bind(Y6,$fot(covered)),bind(Y7,$fot(covered)),bind(Y8,$fot(covered))]]) ).

cnf(refute_0_2,plain,
    ( ~ achievable(row(n6),squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered))
    | achievable(row(n6),squares(covered,covered,covered,covered,covered,covered,covered,covered)) ),
    inference(subst,[],[cover_columns_6_and_7:[bind(X,$fot(n6)),bind(Y1,$fot(covered)),bind(Y2,$fot(covered)),bind(Y3,$fot(covered)),bind(Y4,$fot(covered)),bind(Y5,$fot(covered)),bind(Y8,$fot(covered))]]) ).

cnf(refute_0_3,plain,
    ( ~ achievable(row(n5),squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered))
    | achievable(row(successor(n5)),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))) ),
    inference(subst,[],[place_vertical_pieces:[bind(X,$fot(n5)),bind(Y1,$fot(not_covered)),bind(Y2,$fot(not_covered)),bind(Y3,$fot(not_covered)),bind(Y4,$fot(not_covered)),bind(Y5,$fot(not_covered)),bind(Y6,$fot(covered)),bind(Y7,$fot(covered)),bind(Y8,$fot(not_covered))]]) ).

cnf(refute_0_4,plain,
    ( ~ achievable(row(n4),squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered))
    | achievable(row(successor(n4)),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered))) ),
    inference(subst,[],[place_vertical_pieces:[bind(X,$fot(n4)),bind(Y1,$fot(covered)),bind(Y2,$fot(covered)),bind(Y3,$fot(covered)),bind(Y4,$fot(covered)),bind(Y5,$fot(covered)),bind(Y6,$fot(not_covered)),bind(Y7,$fot(not_covered)),bind(Y8,$fot(covered))]]) ).

cnf(refute_0_5,plain,
    ( ~ achievable(row(n4),squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered))
    | achievable(row(n4),squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered)) ),
    inference(subst,[],[cover_columns_2_and_3:[bind(X,$fot(n4)),bind(Y1,$fot(covered)),bind(Y4,$fot(covered)),bind(Y5,$fot(covered)),bind(Y6,$fot(not_covered)),bind(Y7,$fot(not_covered)),bind(Y8,$fot(covered))]]) ).

cnf(refute_0_6,plain,
    ( ~ achievable(row(n3),squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered))
    | achievable(row(successor(n3)),squares(complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))) ),
    inference(subst,[],[place_vertical_pieces:[bind(X,$fot(n3)),bind(Y1,$fot(not_covered)),bind(Y2,$fot(covered)),bind(Y3,$fot(covered)),bind(Y4,$fot(not_covered)),bind(Y5,$fot(not_covered)),bind(Y6,$fot(covered)),bind(Y7,$fot(covered)),bind(Y8,$fot(not_covered))]]) ).

cnf(refute_0_7,plain,
    ( ~ achievable(row(n2),squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered))
    | achievable(row(successor(n2)),squares(complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered))) ),
    inference(subst,[],[place_vertical_pieces:[bind(X,$fot(n2)),bind(Y1,$fot(covered)),bind(Y2,$fot(not_covered)),bind(Y3,$fot(not_covered)),bind(Y4,$fot(covered)),bind(Y5,$fot(covered)),bind(Y6,$fot(not_covered)),bind(Y7,$fot(not_covered)),bind(Y8,$fot(covered))]]) ).

cnf(refute_0_8,plain,
    ( ~ achievable(row(n1),squares(not_covered,removed,removed,not_covered,not_covered,not_covered,not_covered,not_covered))
    | achievable(row(n1),squares(not_covered,removed,removed,not_covered,not_covered,covered,covered,not_covered)) ),
    inference(subst,[],[cover_columns_6_and_7:[bind(X,$fot(n1)),bind(Y1,$fot(not_covered)),bind(Y2,$fot(removed)),bind(Y3,$fot(removed)),bind(Y4,$fot(not_covered)),bind(Y5,$fot(not_covered)),bind(Y8,$fot(not_covered))]]) ).

cnf(refute_0_9,plain,
    achievable(row(n1),squares(not_covered,removed,removed,not_covered,not_covered,covered,covered,not_covered)),
    inference(resolve,[$cnf( achievable(row(n1),squares(not_covered,removed,removed,not_covered,not_covered,not_covered,not_covered,not_covered)) )],[first_row_initially,refute_0_8]) ).

cnf(refute_0_10,plain,
    ( ~ achievable(row(n1),squares(not_covered,removed,removed,not_covered,not_covered,covered,covered,not_covered))
    | achievable(row(successor(n1)),squares(complement(not_covered),complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))) ),
    inference(subst,[],[place_vertical_pieces:[bind(X,$fot(n1)),bind(Y1,$fot(not_covered)),bind(Y2,$fot(removed)),bind(Y3,$fot(removed)),bind(Y4,$fot(not_covered)),bind(Y5,$fot(not_covered)),bind(Y6,$fot(covered)),bind(Y7,$fot(covered)),bind(Y8,$fot(not_covered))]]) ).

cnf(refute_0_11,plain,
    achievable(row(successor(n1)),squares(complement(not_covered),complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))),
    inference(resolve,[$cnf( achievable(row(n1),squares(not_covered,removed,removed,not_covered,not_covered,covered,covered,not_covered)) )],[refute_0_9,refute_0_10]) ).

cnf(refute_0_12,plain,
    row(successor(n1)) = row(successor(n1)),
    introduced(tautology,[refl,[$fot(row(successor(n1)))]]) ).

cnf(refute_0_13,plain,
    ( row(successor(n1)) != row(successor(n1))
    | successor(n1) != n2
    | row(successor(n1)) = row(n2) ),
    introduced(tautology,[equality,[$cnf( $equal(row(successor(n1)),row(successor(n1))) ),[1,0],$fot(n2)]]) ).

cnf(refute_0_14,plain,
    ( successor(n1) != n2
    | row(successor(n1)) = row(n2) ),
    inference(resolve,[$cnf( $equal(row(successor(n1)),row(successor(n1))) )],[refute_0_12,refute_0_13]) ).

cnf(refute_0_15,plain,
    row(successor(n1)) = row(n2),
    inference(resolve,[$cnf( $equal(successor(n1),n2) )],[successor_of_1_is_2,refute_0_14]) ).

cnf(refute_0_16,plain,
    ( row(successor(n1)) != row(n2)
    | ~ achievable(row(successor(n1)),squares(complement(not_covered),complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)))
    | achievable(row(n2),squares(complement(not_covered),complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))) ),
    introduced(tautology,[equality,[$cnf( achievable(row(successor(n1)),squares(complement(not_covered),complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))) ),[0],$fot(row(n2))]]) ).

cnf(refute_0_17,plain,
    ( ~ achievable(row(successor(n1)),squares(complement(not_covered),complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)))
    | achievable(row(n2),squares(complement(not_covered),complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))) ),
    inference(resolve,[$cnf( $equal(row(successor(n1)),row(n2)) )],[refute_0_15,refute_0_16]) ).

cnf(refute_0_18,plain,
    squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,complement(not_covered)) = squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,complement(not_covered)),
    introduced(tautology,[refl,[$fot(squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,complement(not_covered)))]]) ).

cnf(refute_0_19,plain,
    ( complement(not_covered) != covered
    | squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,complement(not_covered)) != squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,complement(not_covered))
    | squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,complement(not_covered)) = squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered) ),
    introduced(tautology,[equality,[$cnf( $equal(squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,complement(not_covered)),squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,complement(not_covered))) ),[1,7],$fot(covered)]]) ).

cnf(refute_0_20,plain,
    ( complement(not_covered) != covered
    | squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,complement(not_covered)) = squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered) ),
    inference(resolve,[$cnf( $equal(squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,complement(not_covered)),squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,complement(not_covered))) )],[refute_0_18,refute_0_19]) ).

cnf(refute_0_21,plain,
    squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,complement(not_covered)) = squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered),
    inference(resolve,[$cnf( $equal(complement(not_covered),covered) )],[complement_of_not_covered_is_covered,refute_0_20]) ).

cnf(refute_0_22,plain,
    squares(covered,not_covered,not_covered,covered,covered,not_covered,complement(covered),complement(not_covered)) = squares(covered,not_covered,not_covered,covered,covered,not_covered,complement(covered),complement(not_covered)),
    introduced(tautology,[refl,[$fot(squares(covered,not_covered,not_covered,covered,covered,not_covered,complement(covered),complement(not_covered)))]]) ).

cnf(refute_0_23,plain,
    ( complement(covered) != not_covered
    | squares(covered,not_covered,not_covered,covered,covered,not_covered,complement(covered),complement(not_covered)) != squares(covered,not_covered,not_covered,covered,covered,not_covered,complement(covered),complement(not_covered))
    | squares(covered,not_covered,not_covered,covered,covered,not_covered,complement(covered),complement(not_covered)) = squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,complement(not_covered)) ),
    introduced(tautology,[equality,[$cnf( $equal(squares(covered,not_covered,not_covered,covered,covered,not_covered,complement(covered),complement(not_covered)),squares(covered,not_covered,not_covered,covered,covered,not_covered,complement(covered),complement(not_covered))) ),[1,6],$fot(not_covered)]]) ).

cnf(refute_0_24,plain,
    ( complement(covered) != not_covered
    | squares(covered,not_covered,not_covered,covered,covered,not_covered,complement(covered),complement(not_covered)) = squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,complement(not_covered)) ),
    inference(resolve,[$cnf( $equal(squares(covered,not_covered,not_covered,covered,covered,not_covered,complement(covered),complement(not_covered)),squares(covered,not_covered,not_covered,covered,covered,not_covered,complement(covered),complement(not_covered))) )],[refute_0_22,refute_0_23]) ).

cnf(refute_0_25,plain,
    squares(covered,not_covered,not_covered,covered,covered,not_covered,complement(covered),complement(not_covered)) = squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,complement(not_covered)),
    inference(resolve,[$cnf( $equal(complement(covered),not_covered) )],[complement_of_covered_is_not_covered,refute_0_24]) ).

cnf(refute_0_26,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_27,plain,
    ( X0 != X0
    | X0 != Y
    | Y = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y)]]) ).

cnf(refute_0_28,plain,
    ( X0 != Y
    | Y = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_26,refute_0_27]) ).

cnf(refute_0_29,plain,
    ( Y != X0
    | Y != Z
    | X0 = Z ),
    introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X0)]]) ).

cnf(refute_0_30,plain,
    ( X0 != Y
    | Y != Z
    | X0 = Z ),
    inference(resolve,[$cnf( $equal(Y,X0) )],[refute_0_28,refute_0_29]) ).

cnf(refute_0_31,plain,
    ( squares(covered,not_covered,not_covered,covered,covered,not_covered,complement(covered),complement(not_covered)) != squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,complement(not_covered))
    | squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,complement(not_covered)) != squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)
    | squares(covered,not_covered,not_covered,covered,covered,not_covered,complement(covered),complement(not_covered)) = squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered) ),
    inference(subst,[],[refute_0_30:[bind(X0,$fot(squares(covered,not_covered,not_covered,covered,covered,not_covered,complement(covered),complement(not_covered)))),bind(Y,$fot(squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,complement(not_covered)))),bind(Z,$fot(squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)))]]) ).

cnf(refute_0_32,plain,
    ( squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,complement(not_covered)) != squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)
    | squares(covered,not_covered,not_covered,covered,covered,not_covered,complement(covered),complement(not_covered)) = squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered) ),
    inference(resolve,[$cnf( $equal(squares(covered,not_covered,not_covered,covered,covered,not_covered,complement(covered),complement(not_covered)),squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,complement(not_covered))) )],[refute_0_25,refute_0_31]) ).

cnf(refute_0_33,plain,
    squares(covered,not_covered,not_covered,covered,covered,not_covered,complement(covered),complement(not_covered)) = squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered),
    inference(resolve,[$cnf( $equal(squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,complement(not_covered)),squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)) )],[refute_0_21,refute_0_32]) ).

cnf(refute_0_34,plain,
    squares(covered,not_covered,not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered)) = squares(covered,not_covered,not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered)),
    introduced(tautology,[refl,[$fot(squares(covered,not_covered,not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered)))]]) ).

cnf(refute_0_35,plain,
    ( complement(covered) != not_covered
    | squares(covered,not_covered,not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered)) != squares(covered,not_covered,not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered))
    | squares(covered,not_covered,not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered)) = squares(covered,not_covered,not_covered,covered,covered,not_covered,complement(covered),complement(not_covered)) ),
    introduced(tautology,[equality,[$cnf( $equal(squares(covered,not_covered,not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered)),squares(covered,not_covered,not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered))) ),[1,5],$fot(not_covered)]]) ).

cnf(refute_0_36,plain,
    ( complement(covered) != not_covered
    | squares(covered,not_covered,not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered)) = squares(covered,not_covered,not_covered,covered,covered,not_covered,complement(covered),complement(not_covered)) ),
    inference(resolve,[$cnf( $equal(squares(covered,not_covered,not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered)),squares(covered,not_covered,not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered))) )],[refute_0_34,refute_0_35]) ).

cnf(refute_0_37,plain,
    squares(covered,not_covered,not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered)) = squares(covered,not_covered,not_covered,covered,covered,not_covered,complement(covered),complement(not_covered)),
    inference(resolve,[$cnf( $equal(complement(covered),not_covered) )],[complement_of_covered_is_not_covered,refute_0_36]) ).

cnf(refute_0_38,plain,
    ( squares(covered,not_covered,not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered)) != squares(covered,not_covered,not_covered,covered,covered,not_covered,complement(covered),complement(not_covered))
    | squares(covered,not_covered,not_covered,covered,covered,not_covered,complement(covered),complement(not_covered)) != squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)
    | squares(covered,not_covered,not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered)) = squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered) ),
    inference(subst,[],[refute_0_30:[bind(X0,$fot(squares(covered,not_covered,not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered)))),bind(Y,$fot(squares(covered,not_covered,not_covered,covered,covered,not_covered,complement(covered),complement(not_covered)))),bind(Z,$fot(squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)))]]) ).

cnf(refute_0_39,plain,
    ( squares(covered,not_covered,not_covered,covered,covered,not_covered,complement(covered),complement(not_covered)) != squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)
    | squares(covered,not_covered,not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered)) = squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered) ),
    inference(resolve,[$cnf( $equal(squares(covered,not_covered,not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered)),squares(covered,not_covered,not_covered,covered,covered,not_covered,complement(covered),complement(not_covered))) )],[refute_0_37,refute_0_38]) ).

cnf(refute_0_40,plain,
    squares(covered,not_covered,not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered)) = squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered),
    inference(resolve,[$cnf( $equal(squares(covered,not_covered,not_covered,covered,covered,not_covered,complement(covered),complement(not_covered)),squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)) )],[refute_0_33,refute_0_39]) ).

cnf(refute_0_41,plain,
    squares(covered,not_covered,not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,not_covered,not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered)),
    introduced(tautology,[refl,[$fot(squares(covered,not_covered,not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered)))]]) ).

cnf(refute_0_42,plain,
    ( complement(not_covered) != covered
    | squares(covered,not_covered,not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered)) != squares(covered,not_covered,not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered))
    | squares(covered,not_covered,not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,not_covered,not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered)) ),
    introduced(tautology,[equality,[$cnf( $equal(squares(covered,not_covered,not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered)),squares(covered,not_covered,not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered))) ),[1,4],$fot(covered)]]) ).

cnf(refute_0_43,plain,
    ( complement(not_covered) != covered
    | squares(covered,not_covered,not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,not_covered,not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered)) ),
    inference(resolve,[$cnf( $equal(squares(covered,not_covered,not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered)),squares(covered,not_covered,not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered))) )],[refute_0_41,refute_0_42]) ).

cnf(refute_0_44,plain,
    squares(covered,not_covered,not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,not_covered,not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered)),
    inference(resolve,[$cnf( $equal(complement(not_covered),covered) )],[complement_of_not_covered_is_covered,refute_0_43]) ).

cnf(refute_0_45,plain,
    ( squares(covered,not_covered,not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered)) != squares(covered,not_covered,not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered))
    | squares(covered,not_covered,not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered)) != squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)
    | squares(covered,not_covered,not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered) ),
    inference(subst,[],[refute_0_30:[bind(X0,$fot(squares(covered,not_covered,not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered)))),bind(Y,$fot(squares(covered,not_covered,not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered)))),bind(Z,$fot(squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)))]]) ).

cnf(refute_0_46,plain,
    ( squares(covered,not_covered,not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered)) != squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)
    | squares(covered,not_covered,not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered) ),
    inference(resolve,[$cnf( $equal(squares(covered,not_covered,not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered)),squares(covered,not_covered,not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered))) )],[refute_0_44,refute_0_45]) ).

cnf(refute_0_47,plain,
    squares(covered,not_covered,not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered),
    inference(resolve,[$cnf( $equal(squares(covered,not_covered,not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered)),squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)) )],[refute_0_40,refute_0_46]) ).

cnf(refute_0_48,plain,
    squares(covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),
    introduced(tautology,[refl,[$fot(squares(covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)))]]) ).

cnf(refute_0_49,plain,
    ( complement(not_covered) != covered
    | squares(covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) != squares(covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))
    | squares(covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,not_covered,not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered)) ),
    introduced(tautology,[equality,[$cnf( $equal(squares(covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),squares(covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))) ),[1,3],$fot(covered)]]) ).

cnf(refute_0_50,plain,
    ( complement(not_covered) != covered
    | squares(covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,not_covered,not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered)) ),
    inference(resolve,[$cnf( $equal(squares(covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),squares(covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))) )],[refute_0_48,refute_0_49]) ).

cnf(refute_0_51,plain,
    squares(covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,not_covered,not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered)),
    inference(resolve,[$cnf( $equal(complement(not_covered),covered) )],[complement_of_not_covered_is_covered,refute_0_50]) ).

cnf(refute_0_52,plain,
    ( squares(covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) != squares(covered,not_covered,not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered))
    | squares(covered,not_covered,not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered)) != squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)
    | squares(covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered) ),
    inference(subst,[],[refute_0_30:[bind(X0,$fot(squares(covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)))),bind(Y,$fot(squares(covered,not_covered,not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered)))),bind(Z,$fot(squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)))]]) ).

cnf(refute_0_53,plain,
    ( squares(covered,not_covered,not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered)) != squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)
    | squares(covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered) ),
    inference(resolve,[$cnf( $equal(squares(covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),squares(covered,not_covered,not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered))) )],[refute_0_51,refute_0_52]) ).

cnf(refute_0_54,plain,
    squares(covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered),
    inference(resolve,[$cnf( $equal(squares(covered,not_covered,not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered)),squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)) )],[refute_0_47,refute_0_53]) ).

cnf(refute_0_55,plain,
    squares(covered,not_covered,complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,not_covered,complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),
    introduced(tautology,[refl,[$fot(squares(covered,not_covered,complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)))]]) ).

cnf(refute_0_56,plain,
    ( complement(removed) != not_covered
    | squares(covered,not_covered,complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) != squares(covered,not_covered,complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))
    | squares(covered,not_covered,complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) ),
    introduced(tautology,[equality,[$cnf( $equal(squares(covered,not_covered,complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),squares(covered,not_covered,complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))) ),[1,2],$fot(not_covered)]]) ).

cnf(refute_0_57,plain,
    ( complement(removed) != not_covered
    | squares(covered,not_covered,complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) ),
    inference(resolve,[$cnf( $equal(squares(covered,not_covered,complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),squares(covered,not_covered,complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))) )],[refute_0_55,refute_0_56]) ).

cnf(refute_0_58,plain,
    squares(covered,not_covered,complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),
    inference(resolve,[$cnf( $equal(complement(removed),not_covered) )],[complement_of_removed_is_not_covered,refute_0_57]) ).

cnf(refute_0_59,plain,
    ( squares(covered,not_covered,complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) != squares(covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))
    | squares(covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) != squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)
    | squares(covered,not_covered,complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered) ),
    inference(subst,[],[refute_0_30:[bind(X0,$fot(squares(covered,not_covered,complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)))),bind(Y,$fot(squares(covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)))),bind(Z,$fot(squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)))]]) ).

cnf(refute_0_60,plain,
    ( squares(covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) != squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)
    | squares(covered,not_covered,complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered) ),
    inference(resolve,[$cnf( $equal(squares(covered,not_covered,complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),squares(covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))) )],[refute_0_58,refute_0_59]) ).

cnf(refute_0_61,plain,
    squares(covered,not_covered,complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered),
    inference(resolve,[$cnf( $equal(squares(covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)) )],[refute_0_54,refute_0_60]) ).

cnf(refute_0_62,plain,
    squares(covered,complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),
    introduced(tautology,[refl,[$fot(squares(covered,complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)))]]) ).

cnf(refute_0_63,plain,
    ( complement(removed) != not_covered
    | squares(covered,complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) != squares(covered,complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))
    | squares(covered,complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,not_covered,complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) ),
    introduced(tautology,[equality,[$cnf( $equal(squares(covered,complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),squares(covered,complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))) ),[1,1],$fot(not_covered)]]) ).

cnf(refute_0_64,plain,
    ( complement(removed) != not_covered
    | squares(covered,complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,not_covered,complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) ),
    inference(resolve,[$cnf( $equal(squares(covered,complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),squares(covered,complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))) )],[refute_0_62,refute_0_63]) ).

cnf(refute_0_65,plain,
    squares(covered,complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,not_covered,complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),
    inference(resolve,[$cnf( $equal(complement(removed),not_covered) )],[complement_of_removed_is_not_covered,refute_0_64]) ).

cnf(refute_0_66,plain,
    ( squares(covered,complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) != squares(covered,not_covered,complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))
    | squares(covered,not_covered,complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) != squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)
    | squares(covered,complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered) ),
    inference(subst,[],[refute_0_30:[bind(X0,$fot(squares(covered,complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)))),bind(Y,$fot(squares(covered,not_covered,complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)))),bind(Z,$fot(squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)))]]) ).

cnf(refute_0_67,plain,
    ( squares(covered,not_covered,complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) != squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)
    | squares(covered,complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered) ),
    inference(resolve,[$cnf( $equal(squares(covered,complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),squares(covered,not_covered,complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))) )],[refute_0_65,refute_0_66]) ).

cnf(refute_0_68,plain,
    squares(covered,complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered),
    inference(resolve,[$cnf( $equal(squares(covered,not_covered,complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)) )],[refute_0_61,refute_0_67]) ).

cnf(refute_0_69,plain,
    squares(complement(not_covered),complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(complement(not_covered),complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),
    introduced(tautology,[refl,[$fot(squares(complement(not_covered),complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)))]]) ).

cnf(refute_0_70,plain,
    ( complement(not_covered) != covered
    | squares(complement(not_covered),complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) != squares(complement(not_covered),complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))
    | squares(complement(not_covered),complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) ),
    introduced(tautology,[equality,[$cnf( $equal(squares(complement(not_covered),complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),squares(complement(not_covered),complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))) ),[1,0],$fot(covered)]]) ).

cnf(refute_0_71,plain,
    ( complement(not_covered) != covered
    | squares(complement(not_covered),complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) ),
    inference(resolve,[$cnf( $equal(squares(complement(not_covered),complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),squares(complement(not_covered),complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))) )],[refute_0_69,refute_0_70]) ).

cnf(refute_0_72,plain,
    squares(complement(not_covered),complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),
    inference(resolve,[$cnf( $equal(complement(not_covered),covered) )],[complement_of_not_covered_is_covered,refute_0_71]) ).

cnf(refute_0_73,plain,
    ( squares(complement(not_covered),complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) != squares(covered,complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))
    | squares(covered,complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) != squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)
    | squares(complement(not_covered),complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered) ),
    inference(subst,[],[refute_0_30:[bind(X0,$fot(squares(complement(not_covered),complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)))),bind(Y,$fot(squares(covered,complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)))),bind(Z,$fot(squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)))]]) ).

cnf(refute_0_74,plain,
    ( squares(covered,complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) != squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)
    | squares(complement(not_covered),complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered) ),
    inference(resolve,[$cnf( $equal(squares(complement(not_covered),complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),squares(covered,complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))) )],[refute_0_72,refute_0_73]) ).

cnf(refute_0_75,plain,
    squares(complement(not_covered),complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered),
    inference(resolve,[$cnf( $equal(squares(covered,complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)) )],[refute_0_68,refute_0_74]) ).

cnf(refute_0_76,plain,
    ( squares(complement(not_covered),complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) != squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)
    | ~ achievable(row(n2),squares(complement(not_covered),complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)))
    | achievable(row(n2),squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)) ),
    introduced(tautology,[equality,[$cnf( achievable(row(n2),squares(complement(not_covered),complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))) ),[1],$fot(squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered))]]) ).

cnf(refute_0_77,plain,
    ( ~ achievable(row(n2),squares(complement(not_covered),complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)))
    | achievable(row(n2),squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)) ),
    inference(resolve,[$cnf( $equal(squares(complement(not_covered),complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)) )],[refute_0_75,refute_0_76]) ).

cnf(refute_0_78,plain,
    ( ~ achievable(row(successor(n1)),squares(complement(not_covered),complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)))
    | achievable(row(n2),squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)) ),
    inference(resolve,[$cnf( achievable(row(n2),squares(complement(not_covered),complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))) )],[refute_0_17,refute_0_77]) ).

cnf(refute_0_79,plain,
    achievable(row(n2),squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)),
    inference(resolve,[$cnf( achievable(row(successor(n1)),squares(complement(not_covered),complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))) )],[refute_0_11,refute_0_78]) ).

cnf(refute_0_80,plain,
    achievable(row(successor(n2)),squares(complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered))),
    inference(resolve,[$cnf( achievable(row(n2),squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)) )],[refute_0_79,refute_0_7]) ).

cnf(refute_0_81,plain,
    row(successor(n2)) = row(successor(n2)),
    introduced(tautology,[refl,[$fot(row(successor(n2)))]]) ).

cnf(refute_0_82,plain,
    ( row(successor(n2)) != row(successor(n2))
    | successor(n2) != n3
    | row(successor(n2)) = row(n3) ),
    introduced(tautology,[equality,[$cnf( $equal(row(successor(n2)),row(successor(n2))) ),[1,0],$fot(n3)]]) ).

cnf(refute_0_83,plain,
    ( successor(n2) != n3
    | row(successor(n2)) = row(n3) ),
    inference(resolve,[$cnf( $equal(row(successor(n2)),row(successor(n2))) )],[refute_0_81,refute_0_82]) ).

cnf(refute_0_84,plain,
    row(successor(n2)) = row(n3),
    inference(resolve,[$cnf( $equal(successor(n2),n3) )],[successor_of_2_is_3,refute_0_83]) ).

cnf(refute_0_85,plain,
    ( row(successor(n2)) != row(n3)
    | ~ achievable(row(successor(n2)),squares(complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)))
    | achievable(row(n3),squares(complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered))) ),
    introduced(tautology,[equality,[$cnf( achievable(row(successor(n2)),squares(complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered))) ),[0],$fot(row(n3))]]) ).

cnf(refute_0_86,plain,
    ( ~ achievable(row(successor(n2)),squares(complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)))
    | achievable(row(n3),squares(complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered))) ),
    inference(resolve,[$cnf( $equal(row(successor(n2)),row(n3)) )],[refute_0_84,refute_0_85]) ).

cnf(refute_0_87,plain,
    squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,complement(covered)) = squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,complement(covered)),
    introduced(tautology,[refl,[$fot(squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,complement(covered)))]]) ).

cnf(refute_0_88,plain,
    ( complement(covered) != not_covered
    | squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,complement(covered)) != squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,complement(covered))
    | squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,complement(covered)) = squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered) ),
    introduced(tautology,[equality,[$cnf( $equal(squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,complement(covered)),squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,complement(covered))) ),[1,7],$fot(not_covered)]]) ).

cnf(refute_0_89,plain,
    ( complement(covered) != not_covered
    | squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,complement(covered)) = squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered) ),
    inference(resolve,[$cnf( $equal(squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,complement(covered)),squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,complement(covered))) )],[refute_0_87,refute_0_88]) ).

cnf(refute_0_90,plain,
    squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,complement(covered)) = squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered),
    inference(resolve,[$cnf( $equal(complement(covered),not_covered) )],[complement_of_covered_is_not_covered,refute_0_89]) ).

cnf(refute_0_91,plain,
    squares(not_covered,covered,covered,not_covered,not_covered,covered,complement(not_covered),complement(covered)) = squares(not_covered,covered,covered,not_covered,not_covered,covered,complement(not_covered),complement(covered)),
    introduced(tautology,[refl,[$fot(squares(not_covered,covered,covered,not_covered,not_covered,covered,complement(not_covered),complement(covered)))]]) ).

cnf(refute_0_92,plain,
    ( complement(not_covered) != covered
    | squares(not_covered,covered,covered,not_covered,not_covered,covered,complement(not_covered),complement(covered)) != squares(not_covered,covered,covered,not_covered,not_covered,covered,complement(not_covered),complement(covered))
    | squares(not_covered,covered,covered,not_covered,not_covered,covered,complement(not_covered),complement(covered)) = squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,complement(covered)) ),
    introduced(tautology,[equality,[$cnf( $equal(squares(not_covered,covered,covered,not_covered,not_covered,covered,complement(not_covered),complement(covered)),squares(not_covered,covered,covered,not_covered,not_covered,covered,complement(not_covered),complement(covered))) ),[1,6],$fot(covered)]]) ).

cnf(refute_0_93,plain,
    ( complement(not_covered) != covered
    | squares(not_covered,covered,covered,not_covered,not_covered,covered,complement(not_covered),complement(covered)) = squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,complement(covered)) ),
    inference(resolve,[$cnf( $equal(squares(not_covered,covered,covered,not_covered,not_covered,covered,complement(not_covered),complement(covered)),squares(not_covered,covered,covered,not_covered,not_covered,covered,complement(not_covered),complement(covered))) )],[refute_0_91,refute_0_92]) ).

cnf(refute_0_94,plain,
    squares(not_covered,covered,covered,not_covered,not_covered,covered,complement(not_covered),complement(covered)) = squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,complement(covered)),
    inference(resolve,[$cnf( $equal(complement(not_covered),covered) )],[complement_of_not_covered_is_covered,refute_0_93]) ).

cnf(refute_0_95,plain,
    ( squares(not_covered,covered,covered,not_covered,not_covered,covered,complement(not_covered),complement(covered)) != squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,complement(covered))
    | squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,complement(covered)) != squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered)
    | squares(not_covered,covered,covered,not_covered,not_covered,covered,complement(not_covered),complement(covered)) = squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered) ),
    inference(subst,[],[refute_0_30:[bind(X0,$fot(squares(not_covered,covered,covered,not_covered,not_covered,covered,complement(not_covered),complement(covered)))),bind(Y,$fot(squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,complement(covered)))),bind(Z,$fot(squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered)))]]) ).

cnf(refute_0_96,plain,
    ( squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,complement(covered)) != squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered)
    | squares(not_covered,covered,covered,not_covered,not_covered,covered,complement(not_covered),complement(covered)) = squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered) ),
    inference(resolve,[$cnf( $equal(squares(not_covered,covered,covered,not_covered,not_covered,covered,complement(not_covered),complement(covered)),squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,complement(covered))) )],[refute_0_94,refute_0_95]) ).

cnf(refute_0_97,plain,
    squares(not_covered,covered,covered,not_covered,not_covered,covered,complement(not_covered),complement(covered)) = squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered),
    inference(resolve,[$cnf( $equal(squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,complement(covered)),squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered)) )],[refute_0_90,refute_0_96]) ).

cnf(refute_0_98,plain,
    squares(not_covered,covered,covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,covered,covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered)),
    introduced(tautology,[refl,[$fot(squares(not_covered,covered,covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered)))]]) ).

cnf(refute_0_99,plain,
    ( complement(not_covered) != covered
    | squares(not_covered,covered,covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered)) != squares(not_covered,covered,covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered))
    | squares(not_covered,covered,covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,covered,covered,not_covered,not_covered,covered,complement(not_covered),complement(covered)) ),
    introduced(tautology,[equality,[$cnf( $equal(squares(not_covered,covered,covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered)),squares(not_covered,covered,covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered))) ),[1,5],$fot(covered)]]) ).

cnf(refute_0_100,plain,
    ( complement(not_covered) != covered
    | squares(not_covered,covered,covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,covered,covered,not_covered,not_covered,covered,complement(not_covered),complement(covered)) ),
    inference(resolve,[$cnf( $equal(squares(not_covered,covered,covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered)),squares(not_covered,covered,covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered))) )],[refute_0_98,refute_0_99]) ).

cnf(refute_0_101,plain,
    squares(not_covered,covered,covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,covered,covered,not_covered,not_covered,covered,complement(not_covered),complement(covered)),
    inference(resolve,[$cnf( $equal(complement(not_covered),covered) )],[complement_of_not_covered_is_covered,refute_0_100]) ).

cnf(refute_0_102,plain,
    ( squares(not_covered,covered,covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered)) != squares(not_covered,covered,covered,not_covered,not_covered,covered,complement(not_covered),complement(covered))
    | squares(not_covered,covered,covered,not_covered,not_covered,covered,complement(not_covered),complement(covered)) != squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered)
    | squares(not_covered,covered,covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered) ),
    inference(subst,[],[refute_0_30:[bind(X0,$fot(squares(not_covered,covered,covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered)))),bind(Y,$fot(squares(not_covered,covered,covered,not_covered,not_covered,covered,complement(not_covered),complement(covered)))),bind(Z,$fot(squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered)))]]) ).

cnf(refute_0_103,plain,
    ( squares(not_covered,covered,covered,not_covered,not_covered,covered,complement(not_covered),complement(covered)) != squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered)
    | squares(not_covered,covered,covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered) ),
    inference(resolve,[$cnf( $equal(squares(not_covered,covered,covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered)),squares(not_covered,covered,covered,not_covered,not_covered,covered,complement(not_covered),complement(covered))) )],[refute_0_101,refute_0_102]) ).

cnf(refute_0_104,plain,
    squares(not_covered,covered,covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered),
    inference(resolve,[$cnf( $equal(squares(not_covered,covered,covered,not_covered,not_covered,covered,complement(not_covered),complement(covered)),squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered)) )],[refute_0_97,refute_0_103]) ).

cnf(refute_0_105,plain,
    squares(not_covered,covered,covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,covered,covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered)),
    introduced(tautology,[refl,[$fot(squares(not_covered,covered,covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered)))]]) ).

cnf(refute_0_106,plain,
    ( complement(covered) != not_covered
    | squares(not_covered,covered,covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered)) != squares(not_covered,covered,covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered))
    | squares(not_covered,covered,covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,covered,covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered)) ),
    introduced(tautology,[equality,[$cnf( $equal(squares(not_covered,covered,covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered)),squares(not_covered,covered,covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered))) ),[1,4],$fot(not_covered)]]) ).

cnf(refute_0_107,plain,
    ( complement(covered) != not_covered
    | squares(not_covered,covered,covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,covered,covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered)) ),
    inference(resolve,[$cnf( $equal(squares(not_covered,covered,covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered)),squares(not_covered,covered,covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered))) )],[refute_0_105,refute_0_106]) ).

cnf(refute_0_108,plain,
    squares(not_covered,covered,covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,covered,covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered)),
    inference(resolve,[$cnf( $equal(complement(covered),not_covered) )],[complement_of_covered_is_not_covered,refute_0_107]) ).

cnf(refute_0_109,plain,
    ( squares(not_covered,covered,covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered)) != squares(not_covered,covered,covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered))
    | squares(not_covered,covered,covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered)) != squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered)
    | squares(not_covered,covered,covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered) ),
    inference(subst,[],[refute_0_30:[bind(X0,$fot(squares(not_covered,covered,covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered)))),bind(Y,$fot(squares(not_covered,covered,covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered)))),bind(Z,$fot(squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered)))]]) ).

cnf(refute_0_110,plain,
    ( squares(not_covered,covered,covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered)) != squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered)
    | squares(not_covered,covered,covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered) ),
    inference(resolve,[$cnf( $equal(squares(not_covered,covered,covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered)),squares(not_covered,covered,covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered))) )],[refute_0_108,refute_0_109]) ).

cnf(refute_0_111,plain,
    squares(not_covered,covered,covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered),
    inference(resolve,[$cnf( $equal(squares(not_covered,covered,covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered)),squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered)) )],[refute_0_104,refute_0_110]) ).

cnf(refute_0_112,plain,
    squares(not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)),
    introduced(tautology,[refl,[$fot(squares(not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)))]]) ).

cnf(refute_0_113,plain,
    ( complement(covered) != not_covered
    | squares(not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) != squares(not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered))
    | squares(not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,covered,covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered)) ),
    introduced(tautology,[equality,[$cnf( $equal(squares(not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)),squares(not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered))) ),[1,3],$fot(not_covered)]]) ).

cnf(refute_0_114,plain,
    ( complement(covered) != not_covered
    | squares(not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,covered,covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered)) ),
    inference(resolve,[$cnf( $equal(squares(not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)),squares(not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered))) )],[refute_0_112,refute_0_113]) ).

cnf(refute_0_115,plain,
    squares(not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,covered,covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered)),
    inference(resolve,[$cnf( $equal(complement(covered),not_covered) )],[complement_of_covered_is_not_covered,refute_0_114]) ).

cnf(refute_0_116,plain,
    ( squares(not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) != squares(not_covered,covered,covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered))
    | squares(not_covered,covered,covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered)) != squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered)
    | squares(not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered) ),
    inference(subst,[],[refute_0_30:[bind(X0,$fot(squares(not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)))),bind(Y,$fot(squares(not_covered,covered,covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered)))),bind(Z,$fot(squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered)))]]) ).

cnf(refute_0_117,plain,
    ( squares(not_covered,covered,covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered)) != squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered)
    | squares(not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered) ),
    inference(resolve,[$cnf( $equal(squares(not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)),squares(not_covered,covered,covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered))) )],[refute_0_115,refute_0_116]) ).

cnf(refute_0_118,plain,
    squares(not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered),
    inference(resolve,[$cnf( $equal(squares(not_covered,covered,covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered)),squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered)) )],[refute_0_111,refute_0_117]) ).

cnf(refute_0_119,plain,
    squares(not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)),
    introduced(tautology,[refl,[$fot(squares(not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)))]]) ).

cnf(refute_0_120,plain,
    ( complement(not_covered) != covered
    | squares(not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) != squares(not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered))
    | squares(not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) ),
    introduced(tautology,[equality,[$cnf( $equal(squares(not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)),squares(not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered))) ),[1,2],$fot(covered)]]) ).

cnf(refute_0_121,plain,
    ( complement(not_covered) != covered
    | squares(not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) ),
    inference(resolve,[$cnf( $equal(squares(not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)),squares(not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered))) )],[refute_0_119,refute_0_120]) ).

cnf(refute_0_122,plain,
    squares(not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)),
    inference(resolve,[$cnf( $equal(complement(not_covered),covered) )],[complement_of_not_covered_is_covered,refute_0_121]) ).

cnf(refute_0_123,plain,
    ( squares(not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) != squares(not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered))
    | squares(not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) != squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered)
    | squares(not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered) ),
    inference(subst,[],[refute_0_30:[bind(X0,$fot(squares(not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)))),bind(Y,$fot(squares(not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)))),bind(Z,$fot(squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered)))]]) ).

cnf(refute_0_124,plain,
    ( squares(not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) != squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered)
    | squares(not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered) ),
    inference(resolve,[$cnf( $equal(squares(not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)),squares(not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered))) )],[refute_0_122,refute_0_123]) ).

cnf(refute_0_125,plain,
    squares(not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered),
    inference(resolve,[$cnf( $equal(squares(not_covered,covered,covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)),squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered)) )],[refute_0_118,refute_0_124]) ).

cnf(refute_0_126,plain,
    squares(not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)),
    introduced(tautology,[refl,[$fot(squares(not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)))]]) ).

cnf(refute_0_127,plain,
    ( complement(not_covered) != covered
    | squares(not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) != squares(not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered))
    | squares(not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) ),
    introduced(tautology,[equality,[$cnf( $equal(squares(not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)),squares(not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered))) ),[1,1],$fot(covered)]]) ).

cnf(refute_0_128,plain,
    ( complement(not_covered) != covered
    | squares(not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) ),
    inference(resolve,[$cnf( $equal(squares(not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)),squares(not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered))) )],[refute_0_126,refute_0_127]) ).

cnf(refute_0_129,plain,
    squares(not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)),
    inference(resolve,[$cnf( $equal(complement(not_covered),covered) )],[complement_of_not_covered_is_covered,refute_0_128]) ).

cnf(refute_0_130,plain,
    ( squares(not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) != squares(not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered))
    | squares(not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) != squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered)
    | squares(not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered) ),
    inference(subst,[],[refute_0_30:[bind(X0,$fot(squares(not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)))),bind(Y,$fot(squares(not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)))),bind(Z,$fot(squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered)))]]) ).

cnf(refute_0_131,plain,
    ( squares(not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) != squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered)
    | squares(not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered) ),
    inference(resolve,[$cnf( $equal(squares(not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)),squares(not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered))) )],[refute_0_129,refute_0_130]) ).

cnf(refute_0_132,plain,
    squares(not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered),
    inference(resolve,[$cnf( $equal(squares(not_covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)),squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered)) )],[refute_0_125,refute_0_131]) ).

cnf(refute_0_133,plain,
    squares(complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)),
    introduced(tautology,[refl,[$fot(squares(complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)))]]) ).

cnf(refute_0_134,plain,
    ( complement(covered) != not_covered
    | squares(complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) != squares(complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered))
    | squares(complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) ),
    introduced(tautology,[equality,[$cnf( $equal(squares(complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)),squares(complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered))) ),[1,0],$fot(not_covered)]]) ).

cnf(refute_0_135,plain,
    ( complement(covered) != not_covered
    | squares(complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) ),
    inference(resolve,[$cnf( $equal(squares(complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)),squares(complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered))) )],[refute_0_133,refute_0_134]) ).

cnf(refute_0_136,plain,
    squares(complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)),
    inference(resolve,[$cnf( $equal(complement(covered),not_covered) )],[complement_of_covered_is_not_covered,refute_0_135]) ).

cnf(refute_0_137,plain,
    ( squares(complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) != squares(not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered))
    | squares(not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) != squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered)
    | squares(complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered) ),
    inference(subst,[],[refute_0_30:[bind(X0,$fot(squares(complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)))),bind(Y,$fot(squares(not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)))),bind(Z,$fot(squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered)))]]) ).

cnf(refute_0_138,plain,
    ( squares(not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) != squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered)
    | squares(complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered) ),
    inference(resolve,[$cnf( $equal(squares(complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)),squares(not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered))) )],[refute_0_136,refute_0_137]) ).

cnf(refute_0_139,plain,
    squares(complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered),
    inference(resolve,[$cnf( $equal(squares(not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)),squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered)) )],[refute_0_132,refute_0_138]) ).

cnf(refute_0_140,plain,
    ( squares(complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) != squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered)
    | ~ achievable(row(n3),squares(complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)))
    | achievable(row(n3),squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered)) ),
    introduced(tautology,[equality,[$cnf( achievable(row(n3),squares(complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered))) ),[1],$fot(squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered))]]) ).

cnf(refute_0_141,plain,
    ( ~ achievable(row(n3),squares(complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)))
    | achievable(row(n3),squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered)) ),
    inference(resolve,[$cnf( $equal(squares(complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)),squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered)) )],[refute_0_139,refute_0_140]) ).

cnf(refute_0_142,plain,
    ( ~ achievable(row(successor(n2)),squares(complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)))
    | achievable(row(n3),squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered)) ),
    inference(resolve,[$cnf( achievable(row(n3),squares(complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered))) )],[refute_0_86,refute_0_141]) ).

cnf(refute_0_143,plain,
    achievable(row(n3),squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered)),
    inference(resolve,[$cnf( achievable(row(successor(n2)),squares(complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered))) )],[refute_0_80,refute_0_142]) ).

cnf(refute_0_144,plain,
    achievable(row(successor(n3)),squares(complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))),
    inference(resolve,[$cnf( achievable(row(n3),squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered)) )],[refute_0_143,refute_0_6]) ).

cnf(refute_0_145,plain,
    row(successor(n3)) = row(successor(n3)),
    introduced(tautology,[refl,[$fot(row(successor(n3)))]]) ).

cnf(refute_0_146,plain,
    ( row(successor(n3)) != row(successor(n3))
    | successor(n3) != n4
    | row(successor(n3)) = row(n4) ),
    introduced(tautology,[equality,[$cnf( $equal(row(successor(n3)),row(successor(n3))) ),[1,0],$fot(n4)]]) ).

cnf(refute_0_147,plain,
    ( successor(n3) != n4
    | row(successor(n3)) = row(n4) ),
    inference(resolve,[$cnf( $equal(row(successor(n3)),row(successor(n3))) )],[refute_0_145,refute_0_146]) ).

cnf(refute_0_148,plain,
    row(successor(n3)) = row(n4),
    inference(resolve,[$cnf( $equal(successor(n3),n4) )],[successor_of_3_is_4,refute_0_147]) ).

cnf(refute_0_149,plain,
    ( row(successor(n3)) != row(n4)
    | ~ achievable(row(successor(n3)),squares(complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)))
    | achievable(row(n4),squares(complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))) ),
    introduced(tautology,[equality,[$cnf( achievable(row(successor(n3)),squares(complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))) ),[0],$fot(row(n4))]]) ).

cnf(refute_0_150,plain,
    ( ~ achievable(row(successor(n3)),squares(complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)))
    | achievable(row(n4),squares(complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))) ),
    inference(resolve,[$cnf( $equal(row(successor(n3)),row(n4)) )],[refute_0_148,refute_0_149]) ).

cnf(refute_0_151,plain,
    squares(covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),
    introduced(tautology,[refl,[$fot(squares(covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)))]]) ).

cnf(refute_0_152,plain,
    ( complement(covered) != not_covered
    | squares(covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) != squares(covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))
    | squares(covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) ),
    introduced(tautology,[equality,[$cnf( $equal(squares(covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),squares(covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))) ),[1,2],$fot(not_covered)]]) ).

cnf(refute_0_153,plain,
    ( complement(covered) != not_covered
    | squares(covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) ),
    inference(resolve,[$cnf( $equal(squares(covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),squares(covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))) )],[refute_0_151,refute_0_152]) ).

cnf(refute_0_154,plain,
    squares(covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),
    inference(resolve,[$cnf( $equal(complement(covered),not_covered) )],[complement_of_covered_is_not_covered,refute_0_153]) ).

cnf(refute_0_155,plain,
    ( squares(covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) != squares(covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))
    | squares(covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) != squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)
    | squares(covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered) ),
    inference(subst,[],[refute_0_30:[bind(X0,$fot(squares(covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)))),bind(Y,$fot(squares(covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)))),bind(Z,$fot(squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)))]]) ).

cnf(refute_0_156,plain,
    ( squares(covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) != squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)
    | squares(covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered) ),
    inference(resolve,[$cnf( $equal(squares(covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),squares(covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))) )],[refute_0_154,refute_0_155]) ).

cnf(refute_0_157,plain,
    squares(covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered),
    inference(resolve,[$cnf( $equal(squares(covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)) )],[refute_0_54,refute_0_156]) ).

cnf(refute_0_158,plain,
    squares(covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),
    introduced(tautology,[refl,[$fot(squares(covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)))]]) ).

cnf(refute_0_159,plain,
    ( complement(covered) != not_covered
    | squares(covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) != squares(covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))
    | squares(covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) ),
    introduced(tautology,[equality,[$cnf( $equal(squares(covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),squares(covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))) ),[1,1],$fot(not_covered)]]) ).

cnf(refute_0_160,plain,
    ( complement(covered) != not_covered
    | squares(covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) ),
    inference(resolve,[$cnf( $equal(squares(covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),squares(covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))) )],[refute_0_158,refute_0_159]) ).

cnf(refute_0_161,plain,
    squares(covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),
    inference(resolve,[$cnf( $equal(complement(covered),not_covered) )],[complement_of_covered_is_not_covered,refute_0_160]) ).

cnf(refute_0_162,plain,
    ( squares(covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) != squares(covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))
    | squares(covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) != squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)
    | squares(covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered) ),
    inference(subst,[],[refute_0_30:[bind(X0,$fot(squares(covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)))),bind(Y,$fot(squares(covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)))),bind(Z,$fot(squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)))]]) ).

cnf(refute_0_163,plain,
    ( squares(covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) != squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)
    | squares(covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered) ),
    inference(resolve,[$cnf( $equal(squares(covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),squares(covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))) )],[refute_0_161,refute_0_162]) ).

cnf(refute_0_164,plain,
    squares(covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered),
    inference(resolve,[$cnf( $equal(squares(covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)) )],[refute_0_157,refute_0_163]) ).

cnf(refute_0_165,plain,
    squares(complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),
    introduced(tautology,[refl,[$fot(squares(complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)))]]) ).

cnf(refute_0_166,plain,
    ( complement(not_covered) != covered
    | squares(complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) != squares(complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))
    | squares(complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) ),
    introduced(tautology,[equality,[$cnf( $equal(squares(complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),squares(complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))) ),[1,0],$fot(covered)]]) ).

cnf(refute_0_167,plain,
    ( complement(not_covered) != covered
    | squares(complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) ),
    inference(resolve,[$cnf( $equal(squares(complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),squares(complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))) )],[refute_0_165,refute_0_166]) ).

cnf(refute_0_168,plain,
    squares(complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),
    inference(resolve,[$cnf( $equal(complement(not_covered),covered) )],[complement_of_not_covered_is_covered,refute_0_167]) ).

cnf(refute_0_169,plain,
    ( squares(complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) != squares(covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))
    | squares(covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) != squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)
    | squares(complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered) ),
    inference(subst,[],[refute_0_30:[bind(X0,$fot(squares(complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)))),bind(Y,$fot(squares(covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)))),bind(Z,$fot(squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)))]]) ).

cnf(refute_0_170,plain,
    ( squares(covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) != squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)
    | squares(complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered) ),
    inference(resolve,[$cnf( $equal(squares(complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),squares(covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))) )],[refute_0_168,refute_0_169]) ).

cnf(refute_0_171,plain,
    squares(complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered),
    inference(resolve,[$cnf( $equal(squares(covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)) )],[refute_0_164,refute_0_170]) ).

cnf(refute_0_172,plain,
    ( squares(complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) != squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)
    | ~ achievable(row(n4),squares(complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)))
    | achievable(row(n4),squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)) ),
    introduced(tautology,[equality,[$cnf( achievable(row(n4),squares(complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))) ),[1],$fot(squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered))]]) ).

cnf(refute_0_173,plain,
    ( ~ achievable(row(n4),squares(complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)))
    | achievable(row(n4),squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)) ),
    inference(resolve,[$cnf( $equal(squares(complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)) )],[refute_0_171,refute_0_172]) ).

cnf(refute_0_174,plain,
    ( ~ achievable(row(successor(n3)),squares(complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)))
    | achievable(row(n4),squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)) ),
    inference(resolve,[$cnf( achievable(row(n4),squares(complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))) )],[refute_0_150,refute_0_173]) ).

cnf(refute_0_175,plain,
    achievable(row(n4),squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)),
    inference(resolve,[$cnf( achievable(row(successor(n3)),squares(complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))) )],[refute_0_144,refute_0_174]) ).

cnf(refute_0_176,plain,
    achievable(row(n4),squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered)),
    inference(resolve,[$cnf( achievable(row(n4),squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)) )],[refute_0_175,refute_0_5]) ).

cnf(refute_0_177,plain,
    achievable(row(successor(n4)),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered))),
    inference(resolve,[$cnf( achievable(row(n4),squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered)) )],[refute_0_176,refute_0_4]) ).

cnf(refute_0_178,plain,
    row(successor(n4)) = row(successor(n4)),
    introduced(tautology,[refl,[$fot(row(successor(n4)))]]) ).

cnf(refute_0_179,plain,
    ( row(successor(n4)) != row(successor(n4))
    | successor(n4) != n5
    | row(successor(n4)) = row(n5) ),
    introduced(tautology,[equality,[$cnf( $equal(row(successor(n4)),row(successor(n4))) ),[1,0],$fot(n5)]]) ).

cnf(refute_0_180,plain,
    ( successor(n4) != n5
    | row(successor(n4)) = row(n5) ),
    inference(resolve,[$cnf( $equal(row(successor(n4)),row(successor(n4))) )],[refute_0_178,refute_0_179]) ).

cnf(refute_0_181,plain,
    row(successor(n4)) = row(n5),
    inference(resolve,[$cnf( $equal(successor(n4),n5) )],[successor_of_4_is_5,refute_0_180]) ).

cnf(refute_0_182,plain,
    ( row(successor(n4)) != row(n5)
    | ~ achievable(row(successor(n4)),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)))
    | achievable(row(n5),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered))) ),
    introduced(tautology,[equality,[$cnf( achievable(row(successor(n4)),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered))) ),[0],$fot(row(n5))]]) ).

cnf(refute_0_183,plain,
    ( ~ achievable(row(successor(n4)),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)))
    | achievable(row(n5),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered))) ),
    inference(resolve,[$cnf( $equal(row(successor(n4)),row(n5)) )],[refute_0_181,refute_0_182]) ).

cnf(refute_0_184,plain,
    squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,complement(covered)),
    introduced(tautology,[refl,[$fot(squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,complement(covered)))]]) ).

cnf(refute_0_185,plain,
    ( complement(covered) != not_covered
    | squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,complement(covered)) != squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,complement(covered))
    | squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered) ),
    introduced(tautology,[equality,[$cnf( $equal(squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,complement(covered)),squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,complement(covered))) ),[1,7],$fot(not_covered)]]) ).

cnf(refute_0_186,plain,
    ( complement(covered) != not_covered
    | squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered) ),
    inference(resolve,[$cnf( $equal(squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,complement(covered)),squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,complement(covered))) )],[refute_0_184,refute_0_185]) ).

cnf(refute_0_187,plain,
    squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered),
    inference(resolve,[$cnf( $equal(complement(covered),not_covered) )],[complement_of_covered_is_not_covered,refute_0_186]) ).

cnf(refute_0_188,plain,
    squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,complement(not_covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,complement(not_covered),complement(covered)),
    introduced(tautology,[refl,[$fot(squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,complement(not_covered),complement(covered)))]]) ).

cnf(refute_0_189,plain,
    ( complement(not_covered) != covered
    | squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,complement(not_covered),complement(covered)) != squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,complement(not_covered),complement(covered))
    | squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,complement(not_covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,complement(covered)) ),
    introduced(tautology,[equality,[$cnf( $equal(squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,complement(not_covered),complement(covered)),squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,complement(not_covered),complement(covered))) ),[1,6],$fot(covered)]]) ).

cnf(refute_0_190,plain,
    ( complement(not_covered) != covered
    | squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,complement(not_covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,complement(covered)) ),
    inference(resolve,[$cnf( $equal(squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,complement(not_covered),complement(covered)),squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,complement(not_covered),complement(covered))) )],[refute_0_188,refute_0_189]) ).

cnf(refute_0_191,plain,
    squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,complement(not_covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,complement(covered)),
    inference(resolve,[$cnf( $equal(complement(not_covered),covered) )],[complement_of_not_covered_is_covered,refute_0_190]) ).

cnf(refute_0_192,plain,
    ( squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,complement(not_covered),complement(covered)) != squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,complement(covered))
    | squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,complement(covered)) != squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered)
    | squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,complement(not_covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered) ),
    inference(subst,[],[refute_0_30:[bind(X0,$fot(squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,complement(not_covered),complement(covered)))),bind(Y,$fot(squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,complement(covered)))),bind(Z,$fot(squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered)))]]) ).

cnf(refute_0_193,plain,
    ( squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,complement(covered)) != squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered)
    | squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,complement(not_covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered) ),
    inference(resolve,[$cnf( $equal(squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,complement(not_covered),complement(covered)),squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,complement(covered))) )],[refute_0_191,refute_0_192]) ).

cnf(refute_0_194,plain,
    squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,complement(not_covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered),
    inference(resolve,[$cnf( $equal(squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,complement(covered)),squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered)) )],[refute_0_187,refute_0_193]) ).

cnf(refute_0_195,plain,
    squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered)),
    introduced(tautology,[refl,[$fot(squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered)))]]) ).

cnf(refute_0_196,plain,
    ( complement(not_covered) != covered
    | squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered)) != squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered))
    | squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,complement(not_covered),complement(covered)) ),
    introduced(tautology,[equality,[$cnf( $equal(squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered)),squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered))) ),[1,5],$fot(covered)]]) ).

cnf(refute_0_197,plain,
    ( complement(not_covered) != covered
    | squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,complement(not_covered),complement(covered)) ),
    inference(resolve,[$cnf( $equal(squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered)),squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered))) )],[refute_0_195,refute_0_196]) ).

cnf(refute_0_198,plain,
    squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,complement(not_covered),complement(covered)),
    inference(resolve,[$cnf( $equal(complement(not_covered),covered) )],[complement_of_not_covered_is_covered,refute_0_197]) ).

cnf(refute_0_199,plain,
    ( squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered)) != squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,complement(not_covered),complement(covered))
    | squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,complement(not_covered),complement(covered)) != squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered)
    | squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered) ),
    inference(subst,[],[refute_0_30:[bind(X0,$fot(squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered)))),bind(Y,$fot(squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,complement(not_covered),complement(covered)))),bind(Z,$fot(squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered)))]]) ).

cnf(refute_0_200,plain,
    ( squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,complement(not_covered),complement(covered)) != squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered)
    | squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered) ),
    inference(resolve,[$cnf( $equal(squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered)),squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,complement(not_covered),complement(covered))) )],[refute_0_198,refute_0_199]) ).

cnf(refute_0_201,plain,
    squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered),
    inference(resolve,[$cnf( $equal(squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,complement(not_covered),complement(covered)),squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered)) )],[refute_0_194,refute_0_200]) ).

cnf(refute_0_202,plain,
    squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered)),
    introduced(tautology,[refl,[$fot(squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered)))]]) ).

cnf(refute_0_203,plain,
    ( complement(covered) != not_covered
    | squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered)) != squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered))
    | squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered)) ),
    introduced(tautology,[equality,[$cnf( $equal(squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered)),squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered))) ),[1,4],$fot(not_covered)]]) ).

cnf(refute_0_204,plain,
    ( complement(covered) != not_covered
    | squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered)) ),
    inference(resolve,[$cnf( $equal(squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered)),squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered))) )],[refute_0_202,refute_0_203]) ).

cnf(refute_0_205,plain,
    squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered)),
    inference(resolve,[$cnf( $equal(complement(covered),not_covered) )],[complement_of_covered_is_not_covered,refute_0_204]) ).

cnf(refute_0_206,plain,
    ( squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered)) != squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered))
    | squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered)) != squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered)
    | squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered) ),
    inference(subst,[],[refute_0_30:[bind(X0,$fot(squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered)))),bind(Y,$fot(squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered)))),bind(Z,$fot(squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered)))]]) ).

cnf(refute_0_207,plain,
    ( squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered)) != squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered)
    | squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered) ),
    inference(resolve,[$cnf( $equal(squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered)),squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered))) )],[refute_0_205,refute_0_206]) ).

cnf(refute_0_208,plain,
    squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered),
    inference(resolve,[$cnf( $equal(squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(not_covered),complement(not_covered),complement(covered)),squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered)) )],[refute_0_201,refute_0_207]) ).

cnf(refute_0_209,plain,
    squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)),
    introduced(tautology,[refl,[$fot(squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)))]]) ).

cnf(refute_0_210,plain,
    ( complement(covered) != not_covered
    | squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) != squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered))
    | squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered)) ),
    introduced(tautology,[equality,[$cnf( $equal(squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)),squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered))) ),[1,3],$fot(not_covered)]]) ).

cnf(refute_0_211,plain,
    ( complement(covered) != not_covered
    | squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered)) ),
    inference(resolve,[$cnf( $equal(squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)),squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered))) )],[refute_0_209,refute_0_210]) ).

cnf(refute_0_212,plain,
    squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered)),
    inference(resolve,[$cnf( $equal(complement(covered),not_covered) )],[complement_of_covered_is_not_covered,refute_0_211]) ).

cnf(refute_0_213,plain,
    ( squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) != squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered))
    | squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered)) != squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered)
    | squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered) ),
    inference(subst,[],[refute_0_30:[bind(X0,$fot(squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)))),bind(Y,$fot(squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered)))),bind(Z,$fot(squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered)))]]) ).

cnf(refute_0_214,plain,
    ( squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered)) != squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered)
    | squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered) ),
    inference(resolve,[$cnf( $equal(squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)),squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered))) )],[refute_0_212,refute_0_213]) ).

cnf(refute_0_215,plain,
    squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered),
    inference(resolve,[$cnf( $equal(squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(not_covered),complement(not_covered),complement(covered)),squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered)) )],[refute_0_208,refute_0_214]) ).

cnf(refute_0_216,plain,
    squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)),
    introduced(tautology,[refl,[$fot(squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)))]]) ).

cnf(refute_0_217,plain,
    ( complement(covered) != not_covered
    | squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) != squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered))
    | squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) ),
    introduced(tautology,[equality,[$cnf( $equal(squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)),squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered))) ),[1,2],$fot(not_covered)]]) ).

cnf(refute_0_218,plain,
    ( complement(covered) != not_covered
    | squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) ),
    inference(resolve,[$cnf( $equal(squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)),squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered))) )],[refute_0_216,refute_0_217]) ).

cnf(refute_0_219,plain,
    squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)),
    inference(resolve,[$cnf( $equal(complement(covered),not_covered) )],[complement_of_covered_is_not_covered,refute_0_218]) ).

cnf(refute_0_220,plain,
    ( squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) != squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered))
    | squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) != squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered)
    | squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered) ),
    inference(subst,[],[refute_0_30:[bind(X0,$fot(squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)))),bind(Y,$fot(squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)))),bind(Z,$fot(squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered)))]]) ).

cnf(refute_0_221,plain,
    ( squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) != squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered)
    | squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered) ),
    inference(resolve,[$cnf( $equal(squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)),squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered))) )],[refute_0_219,refute_0_220]) ).

cnf(refute_0_222,plain,
    squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered),
    inference(resolve,[$cnf( $equal(squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)),squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered)) )],[refute_0_215,refute_0_221]) ).

cnf(refute_0_223,plain,
    squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)),
    introduced(tautology,[refl,[$fot(squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)))]]) ).

cnf(refute_0_224,plain,
    ( complement(covered) != not_covered
    | squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) != squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered))
    | squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) ),
    introduced(tautology,[equality,[$cnf( $equal(squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)),squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered))) ),[1,1],$fot(not_covered)]]) ).

cnf(refute_0_225,plain,
    ( complement(covered) != not_covered
    | squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) ),
    inference(resolve,[$cnf( $equal(squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)),squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered))) )],[refute_0_223,refute_0_224]) ).

cnf(refute_0_226,plain,
    squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)),
    inference(resolve,[$cnf( $equal(complement(covered),not_covered) )],[complement_of_covered_is_not_covered,refute_0_225]) ).

cnf(refute_0_227,plain,
    ( squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) != squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered))
    | squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) != squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered)
    | squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered) ),
    inference(subst,[],[refute_0_30:[bind(X0,$fot(squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)))),bind(Y,$fot(squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)))),bind(Z,$fot(squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered)))]]) ).

cnf(refute_0_228,plain,
    ( squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) != squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered)
    | squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered) ),
    inference(resolve,[$cnf( $equal(squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)),squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered))) )],[refute_0_226,refute_0_227]) ).

cnf(refute_0_229,plain,
    squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered),
    inference(resolve,[$cnf( $equal(squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)),squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered)) )],[refute_0_222,refute_0_228]) ).

cnf(refute_0_230,plain,
    squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)),
    introduced(tautology,[refl,[$fot(squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)))]]) ).

cnf(refute_0_231,plain,
    ( complement(covered) != not_covered
    | squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) != squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered))
    | squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) ),
    introduced(tautology,[equality,[$cnf( $equal(squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered))) ),[1,0],$fot(not_covered)]]) ).

cnf(refute_0_232,plain,
    ( complement(covered) != not_covered
    | squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) ),
    inference(resolve,[$cnf( $equal(squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered))) )],[refute_0_230,refute_0_231]) ).

cnf(refute_0_233,plain,
    squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)),
    inference(resolve,[$cnf( $equal(complement(covered),not_covered) )],[complement_of_covered_is_not_covered,refute_0_232]) ).

cnf(refute_0_234,plain,
    ( squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) != squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered))
    | squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) != squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered)
    | squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered) ),
    inference(subst,[],[refute_0_30:[bind(X0,$fot(squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)))),bind(Y,$fot(squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)))),bind(Z,$fot(squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered)))]]) ).

cnf(refute_0_235,plain,
    ( squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) != squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered)
    | squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered) ),
    inference(resolve,[$cnf( $equal(squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)),squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered))) )],[refute_0_233,refute_0_234]) ).

cnf(refute_0_236,plain,
    squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered),
    inference(resolve,[$cnf( $equal(squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)),squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered)) )],[refute_0_229,refute_0_235]) ).

cnf(refute_0_237,plain,
    ( squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)) != squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered)
    | ~ achievable(row(n5),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)))
    | achievable(row(n5),squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered)) ),
    introduced(tautology,[equality,[$cnf( achievable(row(n5),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered))) ),[1],$fot(squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered))]]) ).

cnf(refute_0_238,plain,
    ( ~ achievable(row(n5),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)))
    | achievable(row(n5),squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered)) ),
    inference(resolve,[$cnf( $equal(squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)),squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered)) )],[refute_0_236,refute_0_237]) ).

cnf(refute_0_239,plain,
    ( ~ achievable(row(successor(n4)),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered)))
    | achievable(row(n5),squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered)) ),
    inference(resolve,[$cnf( achievable(row(n5),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered))) )],[refute_0_183,refute_0_238]) ).

cnf(refute_0_240,plain,
    achievable(row(n5),squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered)),
    inference(resolve,[$cnf( achievable(row(successor(n4)),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(covered))) )],[refute_0_177,refute_0_239]) ).

cnf(refute_0_241,plain,
    achievable(row(successor(n5)),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))),
    inference(resolve,[$cnf( achievable(row(n5),squares(not_covered,not_covered,not_covered,not_covered,not_covered,covered,covered,not_covered)) )],[refute_0_240,refute_0_3]) ).

cnf(refute_0_242,plain,
    row(successor(n5)) = row(successor(n5)),
    introduced(tautology,[refl,[$fot(row(successor(n5)))]]) ).

cnf(refute_0_243,plain,
    ( row(successor(n5)) != row(successor(n5))
    | successor(n5) != n6
    | row(successor(n5)) = row(n6) ),
    introduced(tautology,[equality,[$cnf( $equal(row(successor(n5)),row(successor(n5))) ),[1,0],$fot(n6)]]) ).

cnf(refute_0_244,plain,
    ( successor(n5) != n6
    | row(successor(n5)) = row(n6) ),
    inference(resolve,[$cnf( $equal(row(successor(n5)),row(successor(n5))) )],[refute_0_242,refute_0_243]) ).

cnf(refute_0_245,plain,
    row(successor(n5)) = row(n6),
    inference(resolve,[$cnf( $equal(successor(n5),n6) )],[successor_of_5_is_6,refute_0_244]) ).

cnf(refute_0_246,plain,
    ( row(successor(n5)) != row(n6)
    | ~ achievable(row(successor(n5)),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)))
    | achievable(row(n6),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))) ),
    introduced(tautology,[equality,[$cnf( achievable(row(successor(n5)),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))) ),[0],$fot(row(n6))]]) ).

cnf(refute_0_247,plain,
    ( ~ achievable(row(successor(n5)),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)))
    | achievable(row(n6),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))) ),
    inference(resolve,[$cnf( $equal(row(successor(n5)),row(n6)) )],[refute_0_245,refute_0_246]) ).

cnf(refute_0_248,plain,
    squares(covered,covered,covered,covered,covered,not_covered,not_covered,complement(not_covered)) = squares(covered,covered,covered,covered,covered,not_covered,not_covered,complement(not_covered)),
    introduced(tautology,[refl,[$fot(squares(covered,covered,covered,covered,covered,not_covered,not_covered,complement(not_covered)))]]) ).

cnf(refute_0_249,plain,
    ( complement(not_covered) != covered
    | squares(covered,covered,covered,covered,covered,not_covered,not_covered,complement(not_covered)) != squares(covered,covered,covered,covered,covered,not_covered,not_covered,complement(not_covered))
    | squares(covered,covered,covered,covered,covered,not_covered,not_covered,complement(not_covered)) = squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered) ),
    introduced(tautology,[equality,[$cnf( $equal(squares(covered,covered,covered,covered,covered,not_covered,not_covered,complement(not_covered)),squares(covered,covered,covered,covered,covered,not_covered,not_covered,complement(not_covered))) ),[1,7],$fot(covered)]]) ).

cnf(refute_0_250,plain,
    ( complement(not_covered) != covered
    | squares(covered,covered,covered,covered,covered,not_covered,not_covered,complement(not_covered)) = squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered) ),
    inference(resolve,[$cnf( $equal(squares(covered,covered,covered,covered,covered,not_covered,not_covered,complement(not_covered)),squares(covered,covered,covered,covered,covered,not_covered,not_covered,complement(not_covered))) )],[refute_0_248,refute_0_249]) ).

cnf(refute_0_251,plain,
    squares(covered,covered,covered,covered,covered,not_covered,not_covered,complement(not_covered)) = squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered),
    inference(resolve,[$cnf( $equal(complement(not_covered),covered) )],[complement_of_not_covered_is_covered,refute_0_250]) ).

cnf(refute_0_252,plain,
    squares(covered,covered,covered,covered,covered,not_covered,complement(covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,not_covered,complement(covered),complement(not_covered)),
    introduced(tautology,[refl,[$fot(squares(covered,covered,covered,covered,covered,not_covered,complement(covered),complement(not_covered)))]]) ).

cnf(refute_0_253,plain,
    ( complement(covered) != not_covered
    | squares(covered,covered,covered,covered,covered,not_covered,complement(covered),complement(not_covered)) != squares(covered,covered,covered,covered,covered,not_covered,complement(covered),complement(not_covered))
    | squares(covered,covered,covered,covered,covered,not_covered,complement(covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,not_covered,not_covered,complement(not_covered)) ),
    introduced(tautology,[equality,[$cnf( $equal(squares(covered,covered,covered,covered,covered,not_covered,complement(covered),complement(not_covered)),squares(covered,covered,covered,covered,covered,not_covered,complement(covered),complement(not_covered))) ),[1,6],$fot(not_covered)]]) ).

cnf(refute_0_254,plain,
    ( complement(covered) != not_covered
    | squares(covered,covered,covered,covered,covered,not_covered,complement(covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,not_covered,not_covered,complement(not_covered)) ),
    inference(resolve,[$cnf( $equal(squares(covered,covered,covered,covered,covered,not_covered,complement(covered),complement(not_covered)),squares(covered,covered,covered,covered,covered,not_covered,complement(covered),complement(not_covered))) )],[refute_0_252,refute_0_253]) ).

cnf(refute_0_255,plain,
    squares(covered,covered,covered,covered,covered,not_covered,complement(covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,not_covered,not_covered,complement(not_covered)),
    inference(resolve,[$cnf( $equal(complement(covered),not_covered) )],[complement_of_covered_is_not_covered,refute_0_254]) ).

cnf(refute_0_256,plain,
    ( squares(covered,covered,covered,covered,covered,not_covered,complement(covered),complement(not_covered)) != squares(covered,covered,covered,covered,covered,not_covered,not_covered,complement(not_covered))
    | squares(covered,covered,covered,covered,covered,not_covered,not_covered,complement(not_covered)) != squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered)
    | squares(covered,covered,covered,covered,covered,not_covered,complement(covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered) ),
    inference(subst,[],[refute_0_30:[bind(X0,$fot(squares(covered,covered,covered,covered,covered,not_covered,complement(covered),complement(not_covered)))),bind(Y,$fot(squares(covered,covered,covered,covered,covered,not_covered,not_covered,complement(not_covered)))),bind(Z,$fot(squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered)))]]) ).

cnf(refute_0_257,plain,
    ( squares(covered,covered,covered,covered,covered,not_covered,not_covered,complement(not_covered)) != squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered)
    | squares(covered,covered,covered,covered,covered,not_covered,complement(covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered) ),
    inference(resolve,[$cnf( $equal(squares(covered,covered,covered,covered,covered,not_covered,complement(covered),complement(not_covered)),squares(covered,covered,covered,covered,covered,not_covered,not_covered,complement(not_covered))) )],[refute_0_255,refute_0_256]) ).

cnf(refute_0_258,plain,
    squares(covered,covered,covered,covered,covered,not_covered,complement(covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered),
    inference(resolve,[$cnf( $equal(squares(covered,covered,covered,covered,covered,not_covered,not_covered,complement(not_covered)),squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered)) )],[refute_0_251,refute_0_257]) ).

cnf(refute_0_259,plain,
    squares(covered,covered,covered,covered,covered,complement(covered),complement(covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,complement(covered),complement(covered),complement(not_covered)),
    introduced(tautology,[refl,[$fot(squares(covered,covered,covered,covered,covered,complement(covered),complement(covered),complement(not_covered)))]]) ).

cnf(refute_0_260,plain,
    ( complement(covered) != not_covered
    | squares(covered,covered,covered,covered,covered,complement(covered),complement(covered),complement(not_covered)) != squares(covered,covered,covered,covered,covered,complement(covered),complement(covered),complement(not_covered))
    | squares(covered,covered,covered,covered,covered,complement(covered),complement(covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,not_covered,complement(covered),complement(not_covered)) ),
    introduced(tautology,[equality,[$cnf( $equal(squares(covered,covered,covered,covered,covered,complement(covered),complement(covered),complement(not_covered)),squares(covered,covered,covered,covered,covered,complement(covered),complement(covered),complement(not_covered))) ),[1,5],$fot(not_covered)]]) ).

cnf(refute_0_261,plain,
    ( complement(covered) != not_covered
    | squares(covered,covered,covered,covered,covered,complement(covered),complement(covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,not_covered,complement(covered),complement(not_covered)) ),
    inference(resolve,[$cnf( $equal(squares(covered,covered,covered,covered,covered,complement(covered),complement(covered),complement(not_covered)),squares(covered,covered,covered,covered,covered,complement(covered),complement(covered),complement(not_covered))) )],[refute_0_259,refute_0_260]) ).

cnf(refute_0_262,plain,
    squares(covered,covered,covered,covered,covered,complement(covered),complement(covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,not_covered,complement(covered),complement(not_covered)),
    inference(resolve,[$cnf( $equal(complement(covered),not_covered) )],[complement_of_covered_is_not_covered,refute_0_261]) ).

cnf(refute_0_263,plain,
    ( squares(covered,covered,covered,covered,covered,complement(covered),complement(covered),complement(not_covered)) != squares(covered,covered,covered,covered,covered,not_covered,complement(covered),complement(not_covered))
    | squares(covered,covered,covered,covered,covered,not_covered,complement(covered),complement(not_covered)) != squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered)
    | squares(covered,covered,covered,covered,covered,complement(covered),complement(covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered) ),
    inference(subst,[],[refute_0_30:[bind(X0,$fot(squares(covered,covered,covered,covered,covered,complement(covered),complement(covered),complement(not_covered)))),bind(Y,$fot(squares(covered,covered,covered,covered,covered,not_covered,complement(covered),complement(not_covered)))),bind(Z,$fot(squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered)))]]) ).

cnf(refute_0_264,plain,
    ( squares(covered,covered,covered,covered,covered,not_covered,complement(covered),complement(not_covered)) != squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered)
    | squares(covered,covered,covered,covered,covered,complement(covered),complement(covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered) ),
    inference(resolve,[$cnf( $equal(squares(covered,covered,covered,covered,covered,complement(covered),complement(covered),complement(not_covered)),squares(covered,covered,covered,covered,covered,not_covered,complement(covered),complement(not_covered))) )],[refute_0_262,refute_0_263]) ).

cnf(refute_0_265,plain,
    squares(covered,covered,covered,covered,covered,complement(covered),complement(covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered),
    inference(resolve,[$cnf( $equal(squares(covered,covered,covered,covered,covered,not_covered,complement(covered),complement(not_covered)),squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered)) )],[refute_0_258,refute_0_264]) ).

cnf(refute_0_266,plain,
    squares(covered,covered,covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,covered,covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered)),
    introduced(tautology,[refl,[$fot(squares(covered,covered,covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered)))]]) ).

cnf(refute_0_267,plain,
    ( complement(not_covered) != covered
    | squares(covered,covered,covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered)) != squares(covered,covered,covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered))
    | squares(covered,covered,covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,complement(covered),complement(covered),complement(not_covered)) ),
    introduced(tautology,[equality,[$cnf( $equal(squares(covered,covered,covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered)),squares(covered,covered,covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered))) ),[1,4],$fot(covered)]]) ).

cnf(refute_0_268,plain,
    ( complement(not_covered) != covered
    | squares(covered,covered,covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,complement(covered),complement(covered),complement(not_covered)) ),
    inference(resolve,[$cnf( $equal(squares(covered,covered,covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered)),squares(covered,covered,covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered))) )],[refute_0_266,refute_0_267]) ).

cnf(refute_0_269,plain,
    squares(covered,covered,covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,complement(covered),complement(covered),complement(not_covered)),
    inference(resolve,[$cnf( $equal(complement(not_covered),covered) )],[complement_of_not_covered_is_covered,refute_0_268]) ).

cnf(refute_0_270,plain,
    ( squares(covered,covered,covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered)) != squares(covered,covered,covered,covered,covered,complement(covered),complement(covered),complement(not_covered))
    | squares(covered,covered,covered,covered,covered,complement(covered),complement(covered),complement(not_covered)) != squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered)
    | squares(covered,covered,covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered) ),
    inference(subst,[],[refute_0_30:[bind(X0,$fot(squares(covered,covered,covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered)))),bind(Y,$fot(squares(covered,covered,covered,covered,covered,complement(covered),complement(covered),complement(not_covered)))),bind(Z,$fot(squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered)))]]) ).

cnf(refute_0_271,plain,
    ( squares(covered,covered,covered,covered,covered,complement(covered),complement(covered),complement(not_covered)) != squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered)
    | squares(covered,covered,covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered) ),
    inference(resolve,[$cnf( $equal(squares(covered,covered,covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered)),squares(covered,covered,covered,covered,covered,complement(covered),complement(covered),complement(not_covered))) )],[refute_0_269,refute_0_270]) ).

cnf(refute_0_272,plain,
    squares(covered,covered,covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered),
    inference(resolve,[$cnf( $equal(squares(covered,covered,covered,covered,covered,complement(covered),complement(covered),complement(not_covered)),squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered)) )],[refute_0_265,refute_0_271]) ).

cnf(refute_0_273,plain,
    squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),
    introduced(tautology,[refl,[$fot(squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)))]]) ).

cnf(refute_0_274,plain,
    ( complement(not_covered) != covered
    | squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) != squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))
    | squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,covered,covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered)) ),
    introduced(tautology,[equality,[$cnf( $equal(squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))) ),[1,3],$fot(covered)]]) ).

cnf(refute_0_275,plain,
    ( complement(not_covered) != covered
    | squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,covered,covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered)) ),
    inference(resolve,[$cnf( $equal(squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))) )],[refute_0_273,refute_0_274]) ).

cnf(refute_0_276,plain,
    squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,covered,covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered)),
    inference(resolve,[$cnf( $equal(complement(not_covered),covered) )],[complement_of_not_covered_is_covered,refute_0_275]) ).

cnf(refute_0_277,plain,
    ( squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) != squares(covered,covered,covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered))
    | squares(covered,covered,covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered)) != squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered)
    | squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered) ),
    inference(subst,[],[refute_0_30:[bind(X0,$fot(squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)))),bind(Y,$fot(squares(covered,covered,covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered)))),bind(Z,$fot(squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered)))]]) ).

cnf(refute_0_278,plain,
    ( squares(covered,covered,covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered)) != squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered)
    | squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered) ),
    inference(resolve,[$cnf( $equal(squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),squares(covered,covered,covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered))) )],[refute_0_276,refute_0_277]) ).

cnf(refute_0_279,plain,
    squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered),
    inference(resolve,[$cnf( $equal(squares(covered,covered,covered,covered,complement(not_covered),complement(covered),complement(covered),complement(not_covered)),squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered)) )],[refute_0_272,refute_0_278]) ).

cnf(refute_0_280,plain,
    squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),
    introduced(tautology,[refl,[$fot(squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)))]]) ).

cnf(refute_0_281,plain,
    ( complement(not_covered) != covered
    | squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) != squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))
    | squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) ),
    introduced(tautology,[equality,[$cnf( $equal(squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))) ),[1,2],$fot(covered)]]) ).

cnf(refute_0_282,plain,
    ( complement(not_covered) != covered
    | squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) ),
    inference(resolve,[$cnf( $equal(squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))) )],[refute_0_280,refute_0_281]) ).

cnf(refute_0_283,plain,
    squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),
    inference(resolve,[$cnf( $equal(complement(not_covered),covered) )],[complement_of_not_covered_is_covered,refute_0_282]) ).

cnf(refute_0_284,plain,
    ( squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) != squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))
    | squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) != squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered)
    | squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered) ),
    inference(subst,[],[refute_0_30:[bind(X0,$fot(squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)))),bind(Y,$fot(squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)))),bind(Z,$fot(squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered)))]]) ).

cnf(refute_0_285,plain,
    ( squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) != squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered)
    | squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered) ),
    inference(resolve,[$cnf( $equal(squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))) )],[refute_0_283,refute_0_284]) ).

cnf(refute_0_286,plain,
    squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered),
    inference(resolve,[$cnf( $equal(squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered)) )],[refute_0_279,refute_0_285]) ).

cnf(refute_0_287,plain,
    squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),
    introduced(tautology,[refl,[$fot(squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)))]]) ).

cnf(refute_0_288,plain,
    ( complement(not_covered) != covered
    | squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) != squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))
    | squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) ),
    introduced(tautology,[equality,[$cnf( $equal(squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))) ),[1,1],$fot(covered)]]) ).

cnf(refute_0_289,plain,
    ( complement(not_covered) != covered
    | squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) ),
    inference(resolve,[$cnf( $equal(squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))) )],[refute_0_287,refute_0_288]) ).

cnf(refute_0_290,plain,
    squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),
    inference(resolve,[$cnf( $equal(complement(not_covered),covered) )],[complement_of_not_covered_is_covered,refute_0_289]) ).

cnf(refute_0_291,plain,
    ( squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) != squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))
    | squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) != squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered)
    | squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered) ),
    inference(subst,[],[refute_0_30:[bind(X0,$fot(squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)))),bind(Y,$fot(squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)))),bind(Z,$fot(squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered)))]]) ).

cnf(refute_0_292,plain,
    ( squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) != squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered)
    | squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered) ),
    inference(resolve,[$cnf( $equal(squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))) )],[refute_0_290,refute_0_291]) ).

cnf(refute_0_293,plain,
    squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered),
    inference(resolve,[$cnf( $equal(squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered)) )],[refute_0_286,refute_0_292]) ).

cnf(refute_0_294,plain,
    squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),
    introduced(tautology,[refl,[$fot(squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)))]]) ).

cnf(refute_0_295,plain,
    ( complement(not_covered) != covered
    | squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) != squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))
    | squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) ),
    introduced(tautology,[equality,[$cnf( $equal(squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))) ),[1,0],$fot(covered)]]) ).

cnf(refute_0_296,plain,
    ( complement(not_covered) != covered
    | squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) ),
    inference(resolve,[$cnf( $equal(squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))) )],[refute_0_294,refute_0_295]) ).

cnf(refute_0_297,plain,
    squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),
    inference(resolve,[$cnf( $equal(complement(not_covered),covered) )],[complement_of_not_covered_is_covered,refute_0_296]) ).

cnf(refute_0_298,plain,
    ( squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) != squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))
    | squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) != squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered)
    | squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered) ),
    inference(subst,[],[refute_0_30:[bind(X0,$fot(squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)))),bind(Y,$fot(squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)))),bind(Z,$fot(squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered)))]]) ).

cnf(refute_0_299,plain,
    ( squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) != squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered)
    | squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered) ),
    inference(resolve,[$cnf( $equal(squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))) )],[refute_0_297,refute_0_298]) ).

cnf(refute_0_300,plain,
    squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered),
    inference(resolve,[$cnf( $equal(squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered)) )],[refute_0_293,refute_0_299]) ).

cnf(refute_0_301,plain,
    ( squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)) != squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered)
    | ~ achievable(row(n6),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)))
    | achievable(row(n6),squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered)) ),
    introduced(tautology,[equality,[$cnf( achievable(row(n6),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))) ),[1],$fot(squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered))]]) ).

cnf(refute_0_302,plain,
    ( ~ achievable(row(n6),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)))
    | achievable(row(n6),squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered)) ),
    inference(resolve,[$cnf( $equal(squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)),squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered)) )],[refute_0_300,refute_0_301]) ).

cnf(refute_0_303,plain,
    ( ~ achievable(row(successor(n5)),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered)))
    | achievable(row(n6),squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered)) ),
    inference(resolve,[$cnf( achievable(row(n6),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))) )],[refute_0_247,refute_0_302]) ).

cnf(refute_0_304,plain,
    achievable(row(n6),squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered)),
    inference(resolve,[$cnf( achievable(row(successor(n5)),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(covered),complement(covered),complement(not_covered))) )],[refute_0_241,refute_0_303]) ).

cnf(refute_0_305,plain,
    achievable(row(n6),squares(covered,covered,covered,covered,covered,covered,covered,covered)),
    inference(resolve,[$cnf( achievable(row(n6),squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered)) )],[refute_0_304,refute_0_2]) ).

cnf(refute_0_306,plain,
    achievable(row(successor(n6)),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered))),
    inference(resolve,[$cnf( achievable(row(n6),squares(covered,covered,covered,covered,covered,covered,covered,covered)) )],[refute_0_305,refute_0_1]) ).

cnf(refute_0_307,plain,
    row(successor(n6)) = row(successor(n6)),
    introduced(tautology,[refl,[$fot(row(successor(n6)))]]) ).

cnf(refute_0_308,plain,
    ( row(successor(n6)) != row(successor(n6))
    | successor(n6) != n7
    | row(successor(n6)) = row(n7) ),
    introduced(tautology,[equality,[$cnf( $equal(row(successor(n6)),row(successor(n6))) ),[1,0],$fot(n7)]]) ).

cnf(refute_0_309,plain,
    ( successor(n6) != n7
    | row(successor(n6)) = row(n7) ),
    inference(resolve,[$cnf( $equal(row(successor(n6)),row(successor(n6))) )],[refute_0_307,refute_0_308]) ).

cnf(refute_0_310,plain,
    row(successor(n6)) = row(n7),
    inference(resolve,[$cnf( $equal(successor(n6),n7) )],[successor_of_6_is_7,refute_0_309]) ).

cnf(refute_0_311,plain,
    ( row(successor(n6)) != row(n7)
    | ~ achievable(row(successor(n6)),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)))
    | achievable(row(n7),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered))) ),
    introduced(tautology,[equality,[$cnf( achievable(row(successor(n6)),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered))) ),[0],$fot(row(n7))]]) ).

cnf(refute_0_312,plain,
    ( ~ achievable(row(successor(n6)),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)))
    | achievable(row(n7),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered))) ),
    inference(resolve,[$cnf( $equal(row(successor(n6)),row(n7)) )],[refute_0_310,refute_0_311]) ).

cnf(refute_0_313,plain,
    squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered)),
    introduced(tautology,[refl,[$fot(squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered)))]]) ).

cnf(refute_0_314,plain,
    ( complement(covered) != not_covered
    | squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered)) != squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered))
    | squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered) ),
    introduced(tautology,[equality,[$cnf( $equal(squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered)),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered))) ),[1,7],$fot(not_covered)]]) ).

cnf(refute_0_315,plain,
    ( complement(covered) != not_covered
    | squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered) ),
    inference(resolve,[$cnf( $equal(squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered)),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered))) )],[refute_0_313,refute_0_314]) ).

cnf(refute_0_316,plain,
    squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered),
    inference(resolve,[$cnf( $equal(complement(covered),not_covered) )],[complement_of_covered_is_not_covered,refute_0_315]) ).

cnf(refute_0_317,plain,
    squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered)),
    introduced(tautology,[refl,[$fot(squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered)))]]) ).

cnf(refute_0_318,plain,
    ( complement(covered) != not_covered
    | squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered)) != squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered))
    | squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered)) ),
    introduced(tautology,[equality,[$cnf( $equal(squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered)),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered))) ),[1,6],$fot(not_covered)]]) ).

cnf(refute_0_319,plain,
    ( complement(covered) != not_covered
    | squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered)) ),
    inference(resolve,[$cnf( $equal(squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered)),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered))) )],[refute_0_317,refute_0_318]) ).

cnf(refute_0_320,plain,
    squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered)),
    inference(resolve,[$cnf( $equal(complement(covered),not_covered) )],[complement_of_covered_is_not_covered,refute_0_319]) ).

cnf(refute_0_321,plain,
    ( squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered)) != squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered))
    | squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered)) != squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered)
    | squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered) ),
    inference(subst,[],[refute_0_30:[bind(X0,$fot(squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered)))),bind(Y,$fot(squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered)))),bind(Z,$fot(squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered)))]]) ).

cnf(refute_0_322,plain,
    ( squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered)) != squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered)
    | squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered) ),
    inference(resolve,[$cnf( $equal(squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered)),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered))) )],[refute_0_320,refute_0_321]) ).

cnf(refute_0_323,plain,
    squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered),
    inference(resolve,[$cnf( $equal(squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered)),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered)) )],[refute_0_316,refute_0_322]) ).

cnf(refute_0_324,plain,
    squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered)),
    introduced(tautology,[refl,[$fot(squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered)))]]) ).

cnf(refute_0_325,plain,
    ( complement(covered) != not_covered
    | squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered)) != squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered))
    | squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered)) ),
    introduced(tautology,[equality,[$cnf( $equal(squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered)),squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered))) ),[1,5],$fot(not_covered)]]) ).

cnf(refute_0_326,plain,
    ( complement(covered) != not_covered
    | squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered)) ),
    inference(resolve,[$cnf( $equal(squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered)),squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered))) )],[refute_0_324,refute_0_325]) ).

cnf(refute_0_327,plain,
    squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered)),
    inference(resolve,[$cnf( $equal(complement(covered),not_covered) )],[complement_of_covered_is_not_covered,refute_0_326]) ).

cnf(refute_0_328,plain,
    ( squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered)) != squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered))
    | squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered)) != squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered)
    | squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered) ),
    inference(subst,[],[refute_0_30:[bind(X0,$fot(squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered)))),bind(Y,$fot(squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered)))),bind(Z,$fot(squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered)))]]) ).

cnf(refute_0_329,plain,
    ( squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered)) != squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered)
    | squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered) ),
    inference(resolve,[$cnf( $equal(squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered)),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered))) )],[refute_0_327,refute_0_328]) ).

cnf(refute_0_330,plain,
    squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered),
    inference(resolve,[$cnf( $equal(squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered)),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered)) )],[refute_0_323,refute_0_329]) ).

cnf(refute_0_331,plain,
    squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered)),
    introduced(tautology,[refl,[$fot(squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered)))]]) ).

cnf(refute_0_332,plain,
    ( complement(covered) != not_covered
    | squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered)) != squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered))
    | squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered)) ),
    introduced(tautology,[equality,[$cnf( $equal(squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered)),squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered))) ),[1,4],$fot(not_covered)]]) ).

cnf(refute_0_333,plain,
    ( complement(covered) != not_covered
    | squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered)) ),
    inference(resolve,[$cnf( $equal(squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered)),squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered))) )],[refute_0_331,refute_0_332]) ).

cnf(refute_0_334,plain,
    squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered)),
    inference(resolve,[$cnf( $equal(complement(covered),not_covered) )],[complement_of_covered_is_not_covered,refute_0_333]) ).

cnf(refute_0_335,plain,
    ( squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered)) != squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered))
    | squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered)) != squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered)
    | squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered) ),
    inference(subst,[],[refute_0_30:[bind(X0,$fot(squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered)))),bind(Y,$fot(squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered)))),bind(Z,$fot(squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered)))]]) ).

cnf(refute_0_336,plain,
    ( squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered)) != squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered)
    | squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered) ),
    inference(resolve,[$cnf( $equal(squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered)),squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered))) )],[refute_0_334,refute_0_335]) ).

cnf(refute_0_337,plain,
    squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered),
    inference(resolve,[$cnf( $equal(squares(not_covered,not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered)),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered)) )],[refute_0_330,refute_0_336]) ).

cnf(refute_0_338,plain,
    squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)) = squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)),
    introduced(tautology,[refl,[$fot(squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)))]]) ).

cnf(refute_0_339,plain,
    ( complement(covered) != not_covered
    | squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)) != squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered))
    | squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered)) ),
    introduced(tautology,[equality,[$cnf( $equal(squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)),squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered))) ),[1,3],$fot(not_covered)]]) ).

cnf(refute_0_340,plain,
    ( complement(covered) != not_covered
    | squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered)) ),
    inference(resolve,[$cnf( $equal(squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)),squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered))) )],[refute_0_338,refute_0_339]) ).

cnf(refute_0_341,plain,
    squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered)),
    inference(resolve,[$cnf( $equal(complement(covered),not_covered) )],[complement_of_covered_is_not_covered,refute_0_340]) ).

cnf(refute_0_342,plain,
    ( squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)) != squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered))
    | squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered)) != squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered)
    | squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered) ),
    inference(subst,[],[refute_0_30:[bind(X0,$fot(squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)))),bind(Y,$fot(squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered)))),bind(Z,$fot(squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered)))]]) ).

cnf(refute_0_343,plain,
    ( squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered)) != squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered)
    | squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered) ),
    inference(resolve,[$cnf( $equal(squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)),squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered))) )],[refute_0_341,refute_0_342]) ).

cnf(refute_0_344,plain,
    squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered),
    inference(resolve,[$cnf( $equal(squares(not_covered,not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered)),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered)) )],[refute_0_337,refute_0_343]) ).

cnf(refute_0_345,plain,
    squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)) = squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)),
    introduced(tautology,[refl,[$fot(squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)))]]) ).

cnf(refute_0_346,plain,
    ( complement(covered) != not_covered
    | squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)) != squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered))
    | squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)) = squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)) ),
    introduced(tautology,[equality,[$cnf( $equal(squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)),squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered))) ),[1,2],$fot(not_covered)]]) ).

cnf(refute_0_347,plain,
    ( complement(covered) != not_covered
    | squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)) = squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)) ),
    inference(resolve,[$cnf( $equal(squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)),squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered))) )],[refute_0_345,refute_0_346]) ).

cnf(refute_0_348,plain,
    squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)) = squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)),
    inference(resolve,[$cnf( $equal(complement(covered),not_covered) )],[complement_of_covered_is_not_covered,refute_0_347]) ).

cnf(refute_0_349,plain,
    ( squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)) != squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered))
    | squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)) != squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered)
    | squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered) ),
    inference(subst,[],[refute_0_30:[bind(X0,$fot(squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)))),bind(Y,$fot(squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)))),bind(Z,$fot(squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered)))]]) ).

cnf(refute_0_350,plain,
    ( squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)) != squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered)
    | squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered) ),
    inference(resolve,[$cnf( $equal(squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)),squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered))) )],[refute_0_348,refute_0_349]) ).

cnf(refute_0_351,plain,
    squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered),
    inference(resolve,[$cnf( $equal(squares(not_covered,not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered)) )],[refute_0_344,refute_0_350]) ).

cnf(refute_0_352,plain,
    squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)) = squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)),
    introduced(tautology,[refl,[$fot(squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)))]]) ).

cnf(refute_0_353,plain,
    ( complement(covered) != not_covered
    | squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)) != squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered))
    | squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)) = squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)) ),
    introduced(tautology,[equality,[$cnf( $equal(squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)),squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered))) ),[1,1],$fot(not_covered)]]) ).

cnf(refute_0_354,plain,
    ( complement(covered) != not_covered
    | squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)) = squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)) ),
    inference(resolve,[$cnf( $equal(squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)),squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered))) )],[refute_0_352,refute_0_353]) ).

cnf(refute_0_355,plain,
    squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)) = squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)),
    inference(resolve,[$cnf( $equal(complement(covered),not_covered) )],[complement_of_covered_is_not_covered,refute_0_354]) ).

cnf(refute_0_356,plain,
    ( squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)) != squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered))
    | squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)) != squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered)
    | squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered) ),
    inference(subst,[],[refute_0_30:[bind(X0,$fot(squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)))),bind(Y,$fot(squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)))),bind(Z,$fot(squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered)))]]) ).

cnf(refute_0_357,plain,
    ( squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)) != squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered)
    | squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered) ),
    inference(resolve,[$cnf( $equal(squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)),squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered))) )],[refute_0_355,refute_0_356]) ).

cnf(refute_0_358,plain,
    squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered),
    inference(resolve,[$cnf( $equal(squares(not_covered,not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered)) )],[refute_0_351,refute_0_357]) ).

cnf(refute_0_359,plain,
    squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)) = squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)),
    introduced(tautology,[refl,[$fot(squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)))]]) ).

cnf(refute_0_360,plain,
    ( complement(covered) != not_covered
    | squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)) != squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered))
    | squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)) = squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)) ),
    introduced(tautology,[equality,[$cnf( $equal(squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered))) ),[1,0],$fot(not_covered)]]) ).

cnf(refute_0_361,plain,
    ( complement(covered) != not_covered
    | squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)) = squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)) ),
    inference(resolve,[$cnf( $equal(squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered))) )],[refute_0_359,refute_0_360]) ).

cnf(refute_0_362,plain,
    squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)) = squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)),
    inference(resolve,[$cnf( $equal(complement(covered),not_covered) )],[complement_of_covered_is_not_covered,refute_0_361]) ).

cnf(refute_0_363,plain,
    ( squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)) != squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered))
    | squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)) != squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered)
    | squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered) ),
    inference(subst,[],[refute_0_30:[bind(X0,$fot(squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)))),bind(Y,$fot(squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)))),bind(Z,$fot(squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered)))]]) ).

cnf(refute_0_364,plain,
    ( squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)) != squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered)
    | squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered) ),
    inference(resolve,[$cnf( $equal(squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)),squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered))) )],[refute_0_362,refute_0_363]) ).

cnf(refute_0_365,plain,
    squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)) = squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered),
    inference(resolve,[$cnf( $equal(squares(not_covered,complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered)) )],[refute_0_358,refute_0_364]) ).

cnf(refute_0_366,plain,
    ( squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)) != squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered)
    | ~ achievable(row(n7),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)))
    | achievable(row(n7),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered)) ),
    introduced(tautology,[equality,[$cnf( achievable(row(n7),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered))) ),[1],$fot(squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered))]]) ).

cnf(refute_0_367,plain,
    ( ~ achievable(row(n7),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)))
    | achievable(row(n7),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered)) ),
    inference(resolve,[$cnf( $equal(squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered)) )],[refute_0_365,refute_0_366]) ).

cnf(refute_0_368,plain,
    ( ~ achievable(row(successor(n6)),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)))
    | achievable(row(n7),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered)) ),
    inference(resolve,[$cnf( achievable(row(n7),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered))) )],[refute_0_312,refute_0_367]) ).

cnf(refute_0_369,plain,
    achievable(row(n7),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered)),
    inference(resolve,[$cnf( achievable(row(successor(n6)),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered))) )],[refute_0_306,refute_0_368]) ).

cnf(refute_0_370,plain,
    achievable(row(successor(n7)),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))),
    inference(resolve,[$cnf( achievable(row(n7),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered)) )],[refute_0_369,refute_0_0]) ).

cnf(refute_0_371,plain,
    row(successor(n7)) = row(successor(n7)),
    introduced(tautology,[refl,[$fot(row(successor(n7)))]]) ).

cnf(refute_0_372,plain,
    ( row(successor(n7)) != row(successor(n7))
    | successor(n7) != n8
    | row(successor(n7)) = row(n8) ),
    introduced(tautology,[equality,[$cnf( $equal(row(successor(n7)),row(successor(n7))) ),[1,0],$fot(n8)]]) ).

cnf(refute_0_373,plain,
    ( successor(n7) != n8
    | row(successor(n7)) = row(n8) ),
    inference(resolve,[$cnf( $equal(row(successor(n7)),row(successor(n7))) )],[refute_0_371,refute_0_372]) ).

cnf(refute_0_374,plain,
    row(successor(n7)) = row(n8),
    inference(resolve,[$cnf( $equal(successor(n7),n8) )],[successor_of_7_is_8,refute_0_373]) ).

cnf(refute_0_375,plain,
    ( row(successor(n7)) != row(n8)
    | ~ achievable(row(successor(n7)),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)))
    | achievable(row(n8),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))) ),
    introduced(tautology,[equality,[$cnf( achievable(row(successor(n7)),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))) ),[0],$fot(row(n8))]]) ).

cnf(refute_0_376,plain,
    ( ~ achievable(row(successor(n7)),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)))
    | achievable(row(n8),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))) ),
    inference(resolve,[$cnf( $equal(row(successor(n7)),row(n8)) )],[refute_0_374,refute_0_375]) ).

cnf(refute_0_377,plain,
    squares(covered,covered,covered,covered,covered,covered,covered,complement(not_covered)) = squares(covered,covered,covered,covered,covered,covered,covered,complement(not_covered)),
    introduced(tautology,[refl,[$fot(squares(covered,covered,covered,covered,covered,covered,covered,complement(not_covered)))]]) ).

cnf(refute_0_378,plain,
    ( complement(not_covered) != covered
    | squares(covered,covered,covered,covered,covered,covered,covered,complement(not_covered)) != squares(covered,covered,covered,covered,covered,covered,covered,complement(not_covered))
    | squares(covered,covered,covered,covered,covered,covered,covered,complement(not_covered)) = squares(covered,covered,covered,covered,covered,covered,covered,covered) ),
    introduced(tautology,[equality,[$cnf( $equal(squares(covered,covered,covered,covered,covered,covered,covered,complement(not_covered)),squares(covered,covered,covered,covered,covered,covered,covered,complement(not_covered))) ),[1,7],$fot(covered)]]) ).

cnf(refute_0_379,plain,
    ( complement(not_covered) != covered
    | squares(covered,covered,covered,covered,covered,covered,covered,complement(not_covered)) = squares(covered,covered,covered,covered,covered,covered,covered,covered) ),
    inference(resolve,[$cnf( $equal(squares(covered,covered,covered,covered,covered,covered,covered,complement(not_covered)),squares(covered,covered,covered,covered,covered,covered,covered,complement(not_covered))) )],[refute_0_377,refute_0_378]) ).

cnf(refute_0_380,plain,
    squares(covered,covered,covered,covered,covered,covered,covered,complement(not_covered)) = squares(covered,covered,covered,covered,covered,covered,covered,covered),
    inference(resolve,[$cnf( $equal(complement(not_covered),covered) )],[complement_of_not_covered_is_covered,refute_0_379]) ).

cnf(refute_0_381,plain,
    squares(covered,covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered)),
    introduced(tautology,[refl,[$fot(squares(covered,covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered)))]]) ).

cnf(refute_0_382,plain,
    ( complement(not_covered) != covered
    | squares(covered,covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered)) != squares(covered,covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered))
    | squares(covered,covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,covered,covered,complement(not_covered)) ),
    introduced(tautology,[equality,[$cnf( $equal(squares(covered,covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered)),squares(covered,covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered))) ),[1,6],$fot(covered)]]) ).

cnf(refute_0_383,plain,
    ( complement(not_covered) != covered
    | squares(covered,covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,covered,covered,complement(not_covered)) ),
    inference(resolve,[$cnf( $equal(squares(covered,covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered)),squares(covered,covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered))) )],[refute_0_381,refute_0_382]) ).

cnf(refute_0_384,plain,
    squares(covered,covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,covered,covered,complement(not_covered)),
    inference(resolve,[$cnf( $equal(complement(not_covered),covered) )],[complement_of_not_covered_is_covered,refute_0_383]) ).

cnf(refute_0_385,plain,
    ( squares(covered,covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered)) != squares(covered,covered,covered,covered,covered,covered,covered,complement(not_covered))
    | squares(covered,covered,covered,covered,covered,covered,covered,complement(not_covered)) != squares(covered,covered,covered,covered,covered,covered,covered,covered)
    | squares(covered,covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,covered,covered,covered) ),
    inference(subst,[],[refute_0_30:[bind(X0,$fot(squares(covered,covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered)))),bind(Y,$fot(squares(covered,covered,covered,covered,covered,covered,covered,complement(not_covered)))),bind(Z,$fot(squares(covered,covered,covered,covered,covered,covered,covered,covered)))]]) ).

cnf(refute_0_386,plain,
    ( squares(covered,covered,covered,covered,covered,covered,covered,complement(not_covered)) != squares(covered,covered,covered,covered,covered,covered,covered,covered)
    | squares(covered,covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,covered,covered,covered) ),
    inference(resolve,[$cnf( $equal(squares(covered,covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered)),squares(covered,covered,covered,covered,covered,covered,covered,complement(not_covered))) )],[refute_0_384,refute_0_385]) ).

cnf(refute_0_387,plain,
    squares(covered,covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,covered,covered,covered),
    inference(resolve,[$cnf( $equal(squares(covered,covered,covered,covered,covered,covered,covered,complement(not_covered)),squares(covered,covered,covered,covered,covered,covered,covered,covered)) )],[refute_0_380,refute_0_386]) ).

cnf(refute_0_388,plain,
    squares(covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered)),
    introduced(tautology,[refl,[$fot(squares(covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered)))]]) ).

cnf(refute_0_389,plain,
    ( complement(not_covered) != covered
    | squares(covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered)) != squares(covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered))
    | squares(covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered)) ),
    introduced(tautology,[equality,[$cnf( $equal(squares(covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered)),squares(covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered))) ),[1,5],$fot(covered)]]) ).

cnf(refute_0_390,plain,
    ( complement(not_covered) != covered
    | squares(covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered)) ),
    inference(resolve,[$cnf( $equal(squares(covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered)),squares(covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered))) )],[refute_0_388,refute_0_389]) ).

cnf(refute_0_391,plain,
    squares(covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered)),
    inference(resolve,[$cnf( $equal(complement(not_covered),covered) )],[complement_of_not_covered_is_covered,refute_0_390]) ).

cnf(refute_0_392,plain,
    ( squares(covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered)) != squares(covered,covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered))
    | squares(covered,covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered)) != squares(covered,covered,covered,covered,covered,covered,covered,covered)
    | squares(covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,covered,covered,covered) ),
    inference(subst,[],[refute_0_30:[bind(X0,$fot(squares(covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered)))),bind(Y,$fot(squares(covered,covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered)))),bind(Z,$fot(squares(covered,covered,covered,covered,covered,covered,covered,covered)))]]) ).

cnf(refute_0_393,plain,
    ( squares(covered,covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered)) != squares(covered,covered,covered,covered,covered,covered,covered,covered)
    | squares(covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,covered,covered,covered) ),
    inference(resolve,[$cnf( $equal(squares(covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered)),squares(covered,covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered))) )],[refute_0_391,refute_0_392]) ).

cnf(refute_0_394,plain,
    squares(covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,covered,covered,covered),
    inference(resolve,[$cnf( $equal(squares(covered,covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered)),squares(covered,covered,covered,covered,covered,covered,covered,covered)) )],[refute_0_387,refute_0_393]) ).

cnf(refute_0_395,plain,
    squares(covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) = squares(covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)),
    introduced(tautology,[refl,[$fot(squares(covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)))]]) ).

cnf(refute_0_396,plain,
    ( complement(not_covered) != covered
    | squares(covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) != squares(covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))
    | squares(covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered)) ),
    introduced(tautology,[equality,[$cnf( $equal(squares(covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)),squares(covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))) ),[1,4],$fot(covered)]]) ).

cnf(refute_0_397,plain,
    ( complement(not_covered) != covered
    | squares(covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered)) ),
    inference(resolve,[$cnf( $equal(squares(covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)),squares(covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))) )],[refute_0_395,refute_0_396]) ).

cnf(refute_0_398,plain,
    squares(covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered)),
    inference(resolve,[$cnf( $equal(complement(not_covered),covered) )],[complement_of_not_covered_is_covered,refute_0_397]) ).

cnf(refute_0_399,plain,
    ( squares(covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) != squares(covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered))
    | squares(covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered)) != squares(covered,covered,covered,covered,covered,covered,covered,covered)
    | squares(covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,covered,covered,covered) ),
    inference(subst,[],[refute_0_30:[bind(X0,$fot(squares(covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)))),bind(Y,$fot(squares(covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered)))),bind(Z,$fot(squares(covered,covered,covered,covered,covered,covered,covered,covered)))]]) ).

cnf(refute_0_400,plain,
    ( squares(covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered)) != squares(covered,covered,covered,covered,covered,covered,covered,covered)
    | squares(covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,covered,covered,covered) ),
    inference(resolve,[$cnf( $equal(squares(covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)),squares(covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered))) )],[refute_0_398,refute_0_399]) ).

cnf(refute_0_401,plain,
    squares(covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,covered,covered,covered),
    inference(resolve,[$cnf( $equal(squares(covered,covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered)),squares(covered,covered,covered,covered,covered,covered,covered,covered)) )],[refute_0_394,refute_0_400]) ).

cnf(refute_0_402,plain,
    squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) = squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)),
    introduced(tautology,[refl,[$fot(squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)))]]) ).

cnf(refute_0_403,plain,
    ( complement(not_covered) != covered
    | squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) != squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))
    | squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) = squares(covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) ),
    introduced(tautology,[equality,[$cnf( $equal(squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)),squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))) ),[1,3],$fot(covered)]]) ).

cnf(refute_0_404,plain,
    ( complement(not_covered) != covered
    | squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) = squares(covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) ),
    inference(resolve,[$cnf( $equal(squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)),squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))) )],[refute_0_402,refute_0_403]) ).

cnf(refute_0_405,plain,
    squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) = squares(covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)),
    inference(resolve,[$cnf( $equal(complement(not_covered),covered) )],[complement_of_not_covered_is_covered,refute_0_404]) ).

cnf(refute_0_406,plain,
    ( squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) != squares(covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))
    | squares(covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) != squares(covered,covered,covered,covered,covered,covered,covered,covered)
    | squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,covered,covered,covered) ),
    inference(subst,[],[refute_0_30:[bind(X0,$fot(squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)))),bind(Y,$fot(squares(covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)))),bind(Z,$fot(squares(covered,covered,covered,covered,covered,covered,covered,covered)))]]) ).

cnf(refute_0_407,plain,
    ( squares(covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) != squares(covered,covered,covered,covered,covered,covered,covered,covered)
    | squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,covered,covered,covered) ),
    inference(resolve,[$cnf( $equal(squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)),squares(covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))) )],[refute_0_405,refute_0_406]) ).

cnf(refute_0_408,plain,
    squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,covered,covered,covered),
    inference(resolve,[$cnf( $equal(squares(covered,covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)),squares(covered,covered,covered,covered,covered,covered,covered,covered)) )],[refute_0_401,refute_0_407]) ).

cnf(refute_0_409,plain,
    squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) = squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)),
    introduced(tautology,[refl,[$fot(squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)))]]) ).

cnf(refute_0_410,plain,
    ( complement(not_covered) != covered
    | squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) != squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))
    | squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) = squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) ),
    introduced(tautology,[equality,[$cnf( $equal(squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)),squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))) ),[1,2],$fot(covered)]]) ).

cnf(refute_0_411,plain,
    ( complement(not_covered) != covered
    | squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) = squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) ),
    inference(resolve,[$cnf( $equal(squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)),squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))) )],[refute_0_409,refute_0_410]) ).

cnf(refute_0_412,plain,
    squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) = squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)),
    inference(resolve,[$cnf( $equal(complement(not_covered),covered) )],[complement_of_not_covered_is_covered,refute_0_411]) ).

cnf(refute_0_413,plain,
    ( squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) != squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))
    | squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) != squares(covered,covered,covered,covered,covered,covered,covered,covered)
    | squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,covered,covered,covered) ),
    inference(subst,[],[refute_0_30:[bind(X0,$fot(squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)))),bind(Y,$fot(squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)))),bind(Z,$fot(squares(covered,covered,covered,covered,covered,covered,covered,covered)))]]) ).

cnf(refute_0_414,plain,
    ( squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) != squares(covered,covered,covered,covered,covered,covered,covered,covered)
    | squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,covered,covered,covered) ),
    inference(resolve,[$cnf( $equal(squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)),squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))) )],[refute_0_412,refute_0_413]) ).

cnf(refute_0_415,plain,
    squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,covered,covered,covered),
    inference(resolve,[$cnf( $equal(squares(covered,covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)),squares(covered,covered,covered,covered,covered,covered,covered,covered)) )],[refute_0_408,refute_0_414]) ).

cnf(refute_0_416,plain,
    squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) = squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)),
    introduced(tautology,[refl,[$fot(squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)))]]) ).

cnf(refute_0_417,plain,
    ( complement(not_covered) != covered
    | squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) != squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))
    | squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) = squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) ),
    introduced(tautology,[equality,[$cnf( $equal(squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)),squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))) ),[1,1],$fot(covered)]]) ).

cnf(refute_0_418,plain,
    ( complement(not_covered) != covered
    | squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) = squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) ),
    inference(resolve,[$cnf( $equal(squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)),squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))) )],[refute_0_416,refute_0_417]) ).

cnf(refute_0_419,plain,
    squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) = squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)),
    inference(resolve,[$cnf( $equal(complement(not_covered),covered) )],[complement_of_not_covered_is_covered,refute_0_418]) ).

cnf(refute_0_420,plain,
    ( squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) != squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))
    | squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) != squares(covered,covered,covered,covered,covered,covered,covered,covered)
    | squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,covered,covered,covered) ),
    inference(subst,[],[refute_0_30:[bind(X0,$fot(squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)))),bind(Y,$fot(squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)))),bind(Z,$fot(squares(covered,covered,covered,covered,covered,covered,covered,covered)))]]) ).

cnf(refute_0_421,plain,
    ( squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) != squares(covered,covered,covered,covered,covered,covered,covered,covered)
    | squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,covered,covered,covered) ),
    inference(resolve,[$cnf( $equal(squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)),squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))) )],[refute_0_419,refute_0_420]) ).

cnf(refute_0_422,plain,
    squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,covered,covered,covered),
    inference(resolve,[$cnf( $equal(squares(covered,covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)),squares(covered,covered,covered,covered,covered,covered,covered,covered)) )],[refute_0_415,refute_0_421]) ).

cnf(refute_0_423,plain,
    squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) = squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)),
    introduced(tautology,[refl,[$fot(squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)))]]) ).

cnf(refute_0_424,plain,
    ( complement(not_covered) != covered
    | squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) != squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))
    | squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) = squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) ),
    introduced(tautology,[equality,[$cnf( $equal(squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))) ),[1,0],$fot(covered)]]) ).

cnf(refute_0_425,plain,
    ( complement(not_covered) != covered
    | squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) = squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) ),
    inference(resolve,[$cnf( $equal(squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))) )],[refute_0_423,refute_0_424]) ).

cnf(refute_0_426,plain,
    squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) = squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)),
    inference(resolve,[$cnf( $equal(complement(not_covered),covered) )],[complement_of_not_covered_is_covered,refute_0_425]) ).

cnf(refute_0_427,plain,
    ( squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) != squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))
    | squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) != squares(covered,covered,covered,covered,covered,covered,covered,covered)
    | squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,covered,covered,covered) ),
    inference(subst,[],[refute_0_30:[bind(X0,$fot(squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)))),bind(Y,$fot(squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)))),bind(Z,$fot(squares(covered,covered,covered,covered,covered,covered,covered,covered)))]]) ).

cnf(refute_0_428,plain,
    ( squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) != squares(covered,covered,covered,covered,covered,covered,covered,covered)
    | squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,covered,covered,covered) ),
    inference(resolve,[$cnf( $equal(squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)),squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))) )],[refute_0_426,refute_0_427]) ).

cnf(refute_0_429,plain,
    squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,covered,covered,covered),
    inference(resolve,[$cnf( $equal(squares(covered,complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)),squares(covered,covered,covered,covered,covered,covered,covered,covered)) )],[refute_0_422,refute_0_428]) ).

cnf(refute_0_430,plain,
    ( squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) != squares(covered,covered,covered,covered,covered,covered,covered,covered)
    | ~ achievable(row(n8),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)))
    | achievable(row(n8),squares(covered,covered,covered,covered,covered,covered,covered,covered)) ),
    introduced(tautology,[equality,[$cnf( achievable(row(n8),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))) ),[1],$fot(squares(covered,covered,covered,covered,covered,covered,covered,covered))]]) ).

cnf(refute_0_431,plain,
    ( ~ achievable(row(n8),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)))
    | achievable(row(n8),squares(covered,covered,covered,covered,covered,covered,covered,covered)) ),
    inference(resolve,[$cnf( $equal(squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)),squares(covered,covered,covered,covered,covered,covered,covered,covered)) )],[refute_0_429,refute_0_430]) ).

cnf(refute_0_432,plain,
    ( ~ achievable(row(successor(n7)),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)))
    | achievable(row(n8),squares(covered,covered,covered,covered,covered,covered,covered,covered)) ),
    inference(resolve,[$cnf( achievable(row(n8),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))) )],[refute_0_376,refute_0_431]) ).

cnf(refute_0_433,plain,
    achievable(row(n8),squares(covered,covered,covered,covered,covered,covered,covered,covered)),
    inference(resolve,[$cnf( achievable(row(successor(n7)),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))) )],[refute_0_370,refute_0_432]) ).

cnf(refute_0_434,plain,
    $false,
    inference(resolve,[$cnf( achievable(row(n8),squares(covered,covered,covered,covered,covered,covered,covered,covered)) )],[refute_0_433,prove_row_8_can_be_covered]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : PUZ016-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n028.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Sat May 28 22:37:17 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.39  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.39  
% 0.19/0.39  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.49  
%------------------------------------------------------------------------------