TSTP Solution File: REL013+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : REL013+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n015.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 19:43:22 EDT 2022
% Result : Theorem 1.95s 2.13s
% Output : CNFRefutation 2.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 176
% Number of leaves : 692
% Syntax : Number of formulae : 2988 (1506 unt; 0 def)
% Number of atoms : 5118 (5116 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 4266 (2136 ~;2125 |; 3 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 2701 ( 94 sgn 124 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(maddux1_join_commutativity,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0) ).
fof(maddux2_join_associativity,axiom,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2) ).
fof(maddux3_a_kind_of_de_Morgan,axiom,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) ).
fof(maddux4_definiton_of_meet,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))) ).
fof(composition_associativity,axiom,
! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2) ).
fof(composition_identity,axiom,
! [X0] : composition(X0,one) = X0 ).
fof(composition_distributivity,axiom,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)) ).
fof(converse_idempotence,axiom,
! [X0] : converse(converse(X0)) = X0 ).
fof(converse_additivity,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)) ).
fof(converse_multiplicativity,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)) ).
fof(converse_cancellativity,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1) ).
fof(def_top,axiom,
! [X0] : top = join(X0,complement(X0)) ).
fof(def_zero,axiom,
! [X0] : zero = meet(X0,complement(X0)) ).
fof(goals,conjecture,
! [X0] :
( composition(X0,zero) = zero
& composition(zero,X0) = zero ) ).
fof(subgoal_0,plain,
! [X0] : composition(X0,zero) = zero,
inference(strip,[],[goals]) ).
fof(subgoal_1,plain,
! [X0] :
( composition(X0,zero) = zero
=> composition(zero,X0) = zero ),
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ! [X0] : composition(X0,zero) = zero,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X0] : composition(X0,zero) != zero,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
composition(skolemFOFtoCNF_X0,zero) != zero,
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(canonicalize,[],[composition_distributivity]) ).
fof(normalize_0_3,plain,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(canonicalize,[],[converse_cancellativity]) ).
fof(normalize_0_5,plain,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(canonicalize,[],[maddux1_join_commutativity]) ).
fof(normalize_0_7,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(canonicalize,[],[converse_multiplicativity]) ).
fof(normalize_0_9,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X0] : converse(converse(X0)) = X0,
inference(canonicalize,[],[converse_idempotence]) ).
fof(normalize_0_11,plain,
! [X0] : converse(converse(X0)) = X0,
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [X0] : composition(X0,one) = X0,
inference(canonicalize,[],[composition_identity]) ).
fof(normalize_0_13,plain,
! [X0] : composition(X0,one) = X0,
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [X0] : top = join(X0,complement(X0)),
inference(canonicalize,[],[def_top]) ).
fof(normalize_0_15,plain,
! [X0] : top = join(X0,complement(X0)),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(canonicalize,[],[maddux4_definiton_of_meet]) ).
fof(normalize_0_17,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(specialize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(canonicalize,[],[maddux2_join_associativity]) ).
fof(normalize_0_19,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(specialize,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(canonicalize,[],[def_zero]) ).
fof(normalize_0_21,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(specialize,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(canonicalize,[],[maddux3_a_kind_of_de_Morgan]) ).
fof(normalize_0_23,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(specialize,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(canonicalize,[],[converse_additivity]) ).
fof(normalize_0_25,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(specialize,[],[normalize_0_24]) ).
cnf(refute_0_0,plain,
composition(skolemFOFtoCNF_X0,zero) != zero,
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
composition(join(top,X1),zero) = join(composition(top,zero),composition(X1,zero)),
inference(subst,[],[refute_0_1:[bind(X0,$fot(top)),bind(X2,$fot(zero))]]) ).
cnf(refute_0_3,plain,
join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_4,plain,
join(X0,X1) = join(X1,X0),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_6,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_7,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( join(X0,X1) != join(X1,X0)
| join(X1,X0) = join(X0,X1) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(X0,X1))),bind(Y,$fot(join(X1,X0)))]]) ).
cnf(refute_0_9,plain,
join(X1,X0) = join(X0,X1),
inference(resolve,[$cnf( $equal(join(X0,X1),join(X1,X0)) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))),
inference(subst,[],[refute_0_9:[bind(X0,$fot(complement(X1))),bind(X1,$fot(composition(converse(X0),complement(composition(X0,X1)))))]]) ).
cnf(refute_0_11,plain,
( join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) != complement(X1)
| join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) != join(complement(X1),composition(converse(X0),complement(composition(X0,X1))))
| join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))) = complement(X1) ),
introduced(tautology,[equality,[$cnf( $equal(join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),complement(X1)) ),[0],$fot(join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))))]]) ).
cnf(refute_0_12,plain,
( join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) != complement(X1)
| join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))) = complement(X1) ),
inference(resolve,[$cnf( $equal(join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),join(complement(X1),composition(converse(X0),complement(composition(X0,X1))))) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))) = complement(X1),
inference(resolve,[$cnf( $equal(join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),complement(X1)) )],[refute_0_3,refute_0_12]) ).
cnf(refute_0_14,plain,
join(complement(top),composition(converse(top),complement(composition(top,top)))) = complement(top),
inference(subst,[],[refute_0_13:[bind(X0,$fot(top)),bind(X1,$fot(top))]]) ).
cnf(refute_0_15,plain,
composition(join(X_87,one),X_89) = join(composition(X_87,X_89),composition(one,X_89)),
inference(subst,[],[refute_0_1:[bind(X0,$fot(X_87)),bind(X1,$fot(one)),bind(X2,$fot(X_89))]]) ).
cnf(refute_0_16,plain,
converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_17,plain,
converse(composition(converse(X0),X_25)) = composition(converse(X_25),converse(converse(X0))),
inference(subst,[],[refute_0_16:[bind(X0,$fot(converse(X0))),bind(X1,$fot(X_25))]]) ).
cnf(refute_0_18,plain,
converse(converse(X0)) = X0,
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_19,plain,
( converse(composition(converse(X0),X_25)) != composition(converse(X_25),converse(converse(X0)))
| converse(converse(X0)) != X0
| converse(composition(converse(X0),X_25)) = composition(converse(X_25),X0) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(X0),X_25)),composition(converse(X_25),converse(converse(X0)))) ),[1,1],$fot(X0)]]) ).
cnf(refute_0_20,plain,
( converse(composition(converse(X0),X_25)) != composition(converse(X_25),converse(converse(X0)))
| converse(composition(converse(X0),X_25)) = composition(converse(X_25),X0) ),
inference(resolve,[$cnf( $equal(converse(converse(X0)),X0) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
converse(composition(converse(X0),X_25)) = composition(converse(X_25),X0),
inference(resolve,[$cnf( $equal(converse(composition(converse(X0),X_25)),composition(converse(X_25),converse(converse(X0)))) )],[refute_0_17,refute_0_20]) ).
cnf(refute_0_22,plain,
converse(composition(converse(X_26),one)) = composition(converse(one),X_26),
inference(subst,[],[refute_0_21:[bind(X0,$fot(X_26)),bind(X_25,$fot(one))]]) ).
cnf(refute_0_23,plain,
composition(X0,one) = X0,
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_24,plain,
composition(converse(X_26),one) = converse(X_26),
inference(subst,[],[refute_0_23:[bind(X0,$fot(converse(X_26)))]]) ).
cnf(refute_0_25,plain,
( composition(converse(X_26),one) != converse(X_26)
| converse(composition(converse(X_26),one)) != composition(converse(one),X_26)
| converse(converse(X_26)) = composition(converse(one),X_26) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(X_26),one)),composition(converse(one),X_26)) ),[0,0],$fot(converse(X_26))]]) ).
cnf(refute_0_26,plain,
( converse(composition(converse(X_26),one)) != composition(converse(one),X_26)
| converse(converse(X_26)) = composition(converse(one),X_26) ),
inference(resolve,[$cnf( $equal(composition(converse(X_26),one),converse(X_26)) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
converse(converse(X_26)) = composition(converse(one),X_26),
inference(resolve,[$cnf( $equal(converse(composition(converse(X_26),one)),composition(converse(one),X_26)) )],[refute_0_22,refute_0_26]) ).
cnf(refute_0_28,plain,
converse(converse(X_26)) = X_26,
inference(subst,[],[refute_0_18:[bind(X0,$fot(X_26))]]) ).
cnf(refute_0_29,plain,
( converse(converse(X_26)) != X_26
| converse(converse(X_26)) != composition(converse(one),X_26)
| X_26 = composition(converse(one),X_26) ),
introduced(tautology,[equality,[$cnf( $equal(converse(converse(X_26)),composition(converse(one),X_26)) ),[0],$fot(X_26)]]) ).
cnf(refute_0_30,plain,
( converse(converse(X_26)) != composition(converse(one),X_26)
| X_26 = composition(converse(one),X_26) ),
inference(resolve,[$cnf( $equal(converse(converse(X_26)),X_26) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
X_26 = composition(converse(one),X_26),
inference(resolve,[$cnf( $equal(converse(converse(X_26)),composition(converse(one),X_26)) )],[refute_0_27,refute_0_30]) ).
cnf(refute_0_32,plain,
composition(converse(one),one) = converse(one),
inference(subst,[],[refute_0_23:[bind(X0,$fot(converse(one)))]]) ).
cnf(refute_0_33,plain,
one = composition(converse(one),one),
inference(subst,[],[refute_0_31:[bind(X_26,$fot(one))]]) ).
cnf(refute_0_34,plain,
( one != composition(converse(one),one)
| composition(converse(one),one) = one ),
inference(subst,[],[refute_0_7:[bind(X,$fot(one)),bind(Y,$fot(composition(converse(one),one)))]]) ).
cnf(refute_0_35,plain,
composition(converse(one),one) = one,
inference(resolve,[$cnf( $equal(one,composition(converse(one),one)) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
( composition(converse(one),one) != converse(one)
| composition(converse(one),one) != one
| one = converse(one) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(one),one),converse(one)) ),[0],$fot(one)]]) ).
cnf(refute_0_37,plain,
( composition(converse(one),one) != converse(one)
| one = converse(one) ),
inference(resolve,[$cnf( $equal(composition(converse(one),one),one) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
one = converse(one),
inference(resolve,[$cnf( $equal(composition(converse(one),one),converse(one)) )],[refute_0_32,refute_0_37]) ).
cnf(refute_0_39,plain,
( one != converse(one)
| converse(one) = one ),
inference(subst,[],[refute_0_7:[bind(X,$fot(one)),bind(Y,$fot(converse(one)))]]) ).
cnf(refute_0_40,plain,
converse(one) = one,
inference(resolve,[$cnf( $equal(one,converse(one)) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
composition(converse(one),X_26) = composition(converse(one),X_26),
introduced(tautology,[refl,[$fot(composition(converse(one),X_26))]]) ).
cnf(refute_0_42,plain,
( composition(converse(one),X_26) != composition(converse(one),X_26)
| converse(one) != one
| composition(converse(one),X_26) = composition(one,X_26) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(one),X_26),composition(converse(one),X_26)) ),[1,0],$fot(one)]]) ).
cnf(refute_0_43,plain,
( converse(one) != one
| composition(converse(one),X_26) = composition(one,X_26) ),
inference(resolve,[$cnf( $equal(composition(converse(one),X_26),composition(converse(one),X_26)) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
composition(converse(one),X_26) = composition(one,X_26),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_40,refute_0_43]) ).
cnf(refute_0_45,plain,
( X_26 != composition(converse(one),X_26)
| composition(converse(one),X_26) != composition(one,X_26)
| X_26 = composition(one,X_26) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_26,composition(one,X_26)) ),[0],$fot(composition(converse(one),X_26))]]) ).
cnf(refute_0_46,plain,
( X_26 != composition(converse(one),X_26)
| X_26 = composition(one,X_26) ),
inference(resolve,[$cnf( $equal(composition(converse(one),X_26),composition(one,X_26)) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
X_26 = composition(one,X_26),
inference(resolve,[$cnf( $equal(X_26,composition(converse(one),X_26)) )],[refute_0_31,refute_0_46]) ).
cnf(refute_0_48,plain,
X_89 = composition(one,X_89),
inference(subst,[],[refute_0_47:[bind(X_26,$fot(X_89))]]) ).
cnf(refute_0_49,plain,
( X_89 != composition(one,X_89)
| composition(one,X_89) = X_89 ),
inference(subst,[],[refute_0_7:[bind(X,$fot(X_89)),bind(Y,$fot(composition(one,X_89)))]]) ).
cnf(refute_0_50,plain,
composition(one,X_89) = X_89,
inference(resolve,[$cnf( $equal(X_89,composition(one,X_89)) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
( composition(join(X_87,one),X_89) != join(composition(X_87,X_89),composition(one,X_89))
| composition(one,X_89) != X_89
| composition(join(X_87,one),X_89) = join(composition(X_87,X_89),X_89) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(X_87,one),X_89),join(composition(X_87,X_89),composition(one,X_89))) ),[1,1],$fot(X_89)]]) ).
cnf(refute_0_52,plain,
( composition(join(X_87,one),X_89) != join(composition(X_87,X_89),composition(one,X_89))
| composition(join(X_87,one),X_89) = join(composition(X_87,X_89),X_89) ),
inference(resolve,[$cnf( $equal(composition(one,X_89),X_89) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
composition(join(X_87,one),X_89) = join(composition(X_87,X_89),X_89),
inference(resolve,[$cnf( $equal(composition(join(X_87,one),X_89),join(composition(X_87,X_89),composition(one,X_89))) )],[refute_0_15,refute_0_52]) ).
cnf(refute_0_54,plain,
join(composition(X_87,X_89),X_89) = join(X_89,composition(X_87,X_89)),
inference(subst,[],[refute_0_9:[bind(X0,$fot(X_89)),bind(X1,$fot(composition(X_87,X_89)))]]) ).
cnf(refute_0_55,plain,
( composition(join(X_87,one),X_89) != join(composition(X_87,X_89),X_89)
| join(composition(X_87,X_89),X_89) != join(X_89,composition(X_87,X_89))
| composition(join(X_87,one),X_89) = join(X_89,composition(X_87,X_89)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(join(X_87,one),X_89),join(X_89,composition(X_87,X_89))) ),[0],$fot(join(composition(X_87,X_89),X_89))]]) ).
cnf(refute_0_56,plain,
( composition(join(X_87,one),X_89) != join(composition(X_87,X_89),X_89)
| composition(join(X_87,one),X_89) = join(X_89,composition(X_87,X_89)) ),
inference(resolve,[$cnf( $equal(join(composition(X_87,X_89),X_89),join(X_89,composition(X_87,X_89))) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
composition(join(X_87,one),X_89) = join(X_89,composition(X_87,X_89)),
inference(resolve,[$cnf( $equal(composition(join(X_87,one),X_89),join(composition(X_87,X_89),X_89)) )],[refute_0_53,refute_0_56]) ).
cnf(refute_0_58,plain,
composition(join(X_87,one),top) = join(top,composition(X_87,top)),
inference(subst,[],[refute_0_57:[bind(X_89,$fot(top))]]) ).
cnf(refute_0_59,plain,
top = join(X0,complement(X0)),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_60,plain,
top = join(join(complement(X_8),complement(X_9)),complement(join(complement(X_8),complement(X_9)))),
inference(subst,[],[refute_0_59:[bind(X0,$fot(join(complement(X_8),complement(X_9))))]]) ).
cnf(refute_0_61,plain,
meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_62,plain,
meet(X_8,X_9) = complement(join(complement(X_8),complement(X_9))),
inference(subst,[],[refute_0_61:[bind(X0,$fot(X_8)),bind(X1,$fot(X_9))]]) ).
cnf(refute_0_63,plain,
( meet(X_8,X_9) != complement(join(complement(X_8),complement(X_9)))
| complement(join(complement(X_8),complement(X_9))) = meet(X_8,X_9) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(meet(X_8,X_9))),bind(Y,$fot(complement(join(complement(X_8),complement(X_9)))))]]) ).
cnf(refute_0_64,plain,
complement(join(complement(X_8),complement(X_9))) = meet(X_8,X_9),
inference(resolve,[$cnf( $equal(meet(X_8,X_9),complement(join(complement(X_8),complement(X_9)))) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
( complement(join(complement(X_8),complement(X_9))) != meet(X_8,X_9)
| top != join(join(complement(X_8),complement(X_9)),complement(join(complement(X_8),complement(X_9))))
| top = join(join(complement(X_8),complement(X_9)),meet(X_8,X_9)) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(join(complement(X_8),complement(X_9)),complement(join(complement(X_8),complement(X_9))))) ),[1,1],$fot(meet(X_8,X_9))]]) ).
cnf(refute_0_66,plain,
( top != join(join(complement(X_8),complement(X_9)),complement(join(complement(X_8),complement(X_9))))
| top = join(join(complement(X_8),complement(X_9)),meet(X_8,X_9)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_8),complement(X_9))),meet(X_8,X_9)) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
top = join(join(complement(X_8),complement(X_9)),meet(X_8,X_9)),
inference(resolve,[$cnf( $equal(top,join(join(complement(X_8),complement(X_9)),complement(join(complement(X_8),complement(X_9))))) )],[refute_0_60,refute_0_66]) ).
cnf(refute_0_68,plain,
join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_69,plain,
( join(X0,join(X1,X2)) != join(join(X0,X1),X2)
| join(join(X0,X1),X2) = join(X0,join(X1,X2)) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(X0,join(X1,X2)))),bind(Y,$fot(join(join(X0,X1),X2)))]]) ).
cnf(refute_0_70,plain,
join(join(X0,X1),X2) = join(X0,join(X1,X2)),
inference(resolve,[$cnf( $equal(join(X0,join(X1,X2)),join(join(X0,X1),X2)) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
join(join(complement(X_8),complement(X_9)),meet(X_8,X_9)) = join(complement(X_8),join(complement(X_9),meet(X_8,X_9))),
inference(subst,[],[refute_0_70:[bind(X0,$fot(complement(X_8))),bind(X1,$fot(complement(X_9))),bind(X2,$fot(meet(X_8,X_9)))]]) ).
cnf(refute_0_72,plain,
( join(join(complement(X_8),complement(X_9)),meet(X_8,X_9)) != join(complement(X_8),join(complement(X_9),meet(X_8,X_9)))
| top != join(join(complement(X_8),complement(X_9)),meet(X_8,X_9))
| top = join(complement(X_8),join(complement(X_9),meet(X_8,X_9))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(join(complement(X_8),complement(X_9)),meet(X_8,X_9))) ),[1],$fot(join(complement(X_8),join(complement(X_9),meet(X_8,X_9))))]]) ).
cnf(refute_0_73,plain,
( top != join(join(complement(X_8),complement(X_9)),meet(X_8,X_9))
| top = join(complement(X_8),join(complement(X_9),meet(X_8,X_9))) ),
inference(resolve,[$cnf( $equal(join(join(complement(X_8),complement(X_9)),meet(X_8,X_9)),join(complement(X_8),join(complement(X_9),meet(X_8,X_9)))) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
top = join(complement(X_8),join(complement(X_9),meet(X_8,X_9))),
inference(resolve,[$cnf( $equal(top,join(join(complement(X_8),complement(X_9)),meet(X_8,X_9))) )],[refute_0_67,refute_0_73]) ).
cnf(refute_0_75,plain,
top = join(complement(X_96),join(complement(X_96),meet(X_96,X_96))),
inference(subst,[],[refute_0_74:[bind(X_8,$fot(X_96)),bind(X_9,$fot(X_96))]]) ).
cnf(refute_0_76,plain,
join(zero,join(zero,X_77)) = join(join(zero,zero),X_77),
inference(subst,[],[refute_0_68:[bind(X0,$fot(zero)),bind(X1,$fot(zero)),bind(X2,$fot(X_77))]]) ).
cnf(refute_0_77,plain,
join(complement(X_5),composition(converse(converse(X0)),complement(composition(converse(X0),X_5)))) = complement(X_5),
inference(subst,[],[refute_0_13:[bind(X0,$fot(converse(X0))),bind(X1,$fot(X_5))]]) ).
cnf(refute_0_78,plain,
( converse(converse(X0)) != X0
| join(complement(X_5),composition(converse(converse(X0)),complement(composition(converse(X0),X_5)))) != complement(X_5)
| join(complement(X_5),composition(X0,complement(composition(converse(X0),X_5)))) = complement(X_5) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_5),composition(converse(converse(X0)),complement(composition(converse(X0),X_5)))),complement(X_5)) ),[0,1,0],$fot(X0)]]) ).
cnf(refute_0_79,plain,
( join(complement(X_5),composition(converse(converse(X0)),complement(composition(converse(X0),X_5)))) != complement(X_5)
| join(complement(X_5),composition(X0,complement(composition(converse(X0),X_5)))) = complement(X_5) ),
inference(resolve,[$cnf( $equal(converse(converse(X0)),X0) )],[refute_0_18,refute_0_78]) ).
cnf(refute_0_80,plain,
join(complement(X_5),composition(X0,complement(composition(converse(X0),X_5)))) = complement(X_5),
inference(resolve,[$cnf( $equal(join(complement(X_5),composition(converse(converse(X0)),complement(composition(converse(X0),X_5)))),complement(X_5)) )],[refute_0_77,refute_0_79]) ).
cnf(refute_0_81,plain,
join(complement(top),composition(X_21,complement(composition(converse(X_21),top)))) = complement(top),
inference(subst,[],[refute_0_80:[bind(X0,$fot(X_21)),bind(X_5,$fot(top))]]) ).
cnf(refute_0_82,plain,
zero = meet(X0,complement(X0)),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_83,plain,
zero = meet(join(complement(X_8),complement(X_9)),complement(join(complement(X_8),complement(X_9)))),
inference(subst,[],[refute_0_82:[bind(X0,$fot(join(complement(X_8),complement(X_9))))]]) ).
cnf(refute_0_84,plain,
( complement(join(complement(X_8),complement(X_9))) != meet(X_8,X_9)
| zero != meet(join(complement(X_8),complement(X_9)),complement(join(complement(X_8),complement(X_9))))
| zero = meet(join(complement(X_8),complement(X_9)),meet(X_8,X_9)) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(join(complement(X_8),complement(X_9)),complement(join(complement(X_8),complement(X_9))))) ),[1,1],$fot(meet(X_8,X_9))]]) ).
cnf(refute_0_85,plain,
( zero != meet(join(complement(X_8),complement(X_9)),complement(join(complement(X_8),complement(X_9))))
| zero = meet(join(complement(X_8),complement(X_9)),meet(X_8,X_9)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_8),complement(X_9))),meet(X_8,X_9)) )],[refute_0_64,refute_0_84]) ).
cnf(refute_0_86,plain,
zero = meet(join(complement(X_8),complement(X_9)),meet(X_8,X_9)),
inference(resolve,[$cnf( $equal(zero,meet(join(complement(X_8),complement(X_9)),complement(join(complement(X_8),complement(X_9))))) )],[refute_0_83,refute_0_85]) ).
cnf(refute_0_87,plain,
( top != join(X0,complement(X0))
| join(X0,complement(X0)) = top ),
inference(subst,[],[refute_0_7:[bind(X,$fot(top)),bind(Y,$fot(join(X0,complement(X0))))]]) ).
cnf(refute_0_88,plain,
join(X0,complement(X0)) = top,
inference(resolve,[$cnf( $equal(top,join(X0,complement(X0))) )],[refute_0_59,refute_0_87]) ).
cnf(refute_0_89,plain,
join(meet(X_8,X_9),complement(meet(X_8,X_9))) = top,
inference(subst,[],[refute_0_88:[bind(X0,$fot(meet(X_8,X_9)))]]) ).
cnf(refute_0_90,plain,
complement(join(meet(X_8,X_9),complement(meet(X_8,X_9)))) = complement(join(meet(X_8,X_9),complement(meet(X_8,X_9)))),
introduced(tautology,[refl,[$fot(complement(join(meet(X_8,X_9),complement(meet(X_8,X_9)))))]]) ).
cnf(refute_0_91,plain,
( complement(join(meet(X_8,X_9),complement(meet(X_8,X_9)))) != complement(join(meet(X_8,X_9),complement(meet(X_8,X_9))))
| join(meet(X_8,X_9),complement(meet(X_8,X_9))) != top
| complement(join(meet(X_8,X_9),complement(meet(X_8,X_9)))) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(meet(X_8,X_9),complement(meet(X_8,X_9)))),complement(join(meet(X_8,X_9),complement(meet(X_8,X_9))))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_92,plain,
( join(meet(X_8,X_9),complement(meet(X_8,X_9))) != top
| complement(join(meet(X_8,X_9),complement(meet(X_8,X_9)))) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(join(meet(X_8,X_9),complement(meet(X_8,X_9)))),complement(join(meet(X_8,X_9),complement(meet(X_8,X_9))))) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
complement(join(meet(X_8,X_9),complement(meet(X_8,X_9)))) = complement(top),
inference(resolve,[$cnf( $equal(join(meet(X_8,X_9),complement(meet(X_8,X_9))),top) )],[refute_0_89,refute_0_92]) ).
cnf(refute_0_94,plain,
meet(join(complement(X_8),complement(X_9)),X1) = complement(join(complement(join(complement(X_8),complement(X_9))),complement(X1))),
inference(subst,[],[refute_0_61:[bind(X0,$fot(join(complement(X_8),complement(X_9))))]]) ).
cnf(refute_0_95,plain,
( complement(join(complement(X_8),complement(X_9))) != meet(X_8,X_9)
| meet(join(complement(X_8),complement(X_9)),X1) != complement(join(complement(join(complement(X_8),complement(X_9))),complement(X1)))
| meet(join(complement(X_8),complement(X_9)),X1) = complement(join(meet(X_8,X_9),complement(X1))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(complement(X_8),complement(X_9)),X1),complement(join(complement(join(complement(X_8),complement(X_9))),complement(X1)))) ),[1,0,0],$fot(meet(X_8,X_9))]]) ).
cnf(refute_0_96,plain,
( meet(join(complement(X_8),complement(X_9)),X1) != complement(join(complement(join(complement(X_8),complement(X_9))),complement(X1)))
| meet(join(complement(X_8),complement(X_9)),X1) = complement(join(meet(X_8,X_9),complement(X1))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_8),complement(X_9))),meet(X_8,X_9)) )],[refute_0_64,refute_0_95]) ).
cnf(refute_0_97,plain,
meet(join(complement(X_8),complement(X_9)),X1) = complement(join(meet(X_8,X_9),complement(X1))),
inference(resolve,[$cnf( $equal(meet(join(complement(X_8),complement(X_9)),X1),complement(join(complement(join(complement(X_8),complement(X_9))),complement(X1)))) )],[refute_0_94,refute_0_96]) ).
cnf(refute_0_98,plain,
meet(join(complement(X_8),complement(X_9)),meet(X_8,X_9)) = complement(join(meet(X_8,X_9),complement(meet(X_8,X_9)))),
inference(subst,[],[refute_0_97:[bind(X1,$fot(meet(X_8,X_9)))]]) ).
cnf(refute_0_99,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_100,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_7,refute_0_99]) ).
cnf(refute_0_101,plain,
( complement(join(meet(X_8,X_9),complement(meet(X_8,X_9)))) != complement(top)
| meet(join(complement(X_8),complement(X_9)),meet(X_8,X_9)) != complement(join(meet(X_8,X_9),complement(meet(X_8,X_9))))
| meet(join(complement(X_8),complement(X_9)),meet(X_8,X_9)) = complement(top) ),
inference(subst,[],[refute_0_100:[bind(X,$fot(meet(join(complement(X_8),complement(X_9)),meet(X_8,X_9)))),bind(Y,$fot(complement(join(meet(X_8,X_9),complement(meet(X_8,X_9)))))),bind(Z,$fot(complement(top)))]]) ).
cnf(refute_0_102,plain,
( complement(join(meet(X_8,X_9),complement(meet(X_8,X_9)))) != complement(top)
| meet(join(complement(X_8),complement(X_9)),meet(X_8,X_9)) = complement(top) ),
inference(resolve,[$cnf( $equal(meet(join(complement(X_8),complement(X_9)),meet(X_8,X_9)),complement(join(meet(X_8,X_9),complement(meet(X_8,X_9))))) )],[refute_0_98,refute_0_101]) ).
cnf(refute_0_103,plain,
meet(join(complement(X_8),complement(X_9)),meet(X_8,X_9)) = complement(top),
inference(resolve,[$cnf( $equal(complement(join(meet(X_8,X_9),complement(meet(X_8,X_9)))),complement(top)) )],[refute_0_93,refute_0_102]) ).
cnf(refute_0_104,plain,
( meet(join(complement(X_8),complement(X_9)),meet(X_8,X_9)) != complement(top)
| zero != meet(join(complement(X_8),complement(X_9)),meet(X_8,X_9))
| zero = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(join(complement(X_8),complement(X_9)),meet(X_8,X_9))) ),[1],$fot(complement(top))]]) ).
cnf(refute_0_105,plain,
( zero != meet(join(complement(X_8),complement(X_9)),meet(X_8,X_9))
| zero = complement(top) ),
inference(resolve,[$cnf( $equal(meet(join(complement(X_8),complement(X_9)),meet(X_8,X_9)),complement(top)) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
zero = complement(top),
inference(resolve,[$cnf( $equal(zero,meet(join(complement(X_8),complement(X_9)),meet(X_8,X_9))) )],[refute_0_86,refute_0_105]) ).
cnf(refute_0_107,plain,
( zero != complement(top)
| complement(top) = zero ),
inference(subst,[],[refute_0_7:[bind(X,$fot(zero)),bind(Y,$fot(complement(top)))]]) ).
cnf(refute_0_108,plain,
complement(top) = zero,
inference(resolve,[$cnf( $equal(zero,complement(top)) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
( complement(top) != zero
| join(complement(top),composition(X_21,complement(composition(converse(X_21),top)))) != complement(top)
| join(zero,composition(X_21,complement(composition(converse(X_21),top)))) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),composition(X_21,complement(composition(converse(X_21),top)))),complement(top)) ),[0,0],$fot(zero)]]) ).
cnf(refute_0_110,plain,
( join(complement(top),composition(X_21,complement(composition(converse(X_21),top)))) != complement(top)
| join(zero,composition(X_21,complement(composition(converse(X_21),top)))) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_108,refute_0_109]) ).
cnf(refute_0_111,plain,
join(zero,composition(X_21,complement(composition(converse(X_21),top)))) = complement(top),
inference(resolve,[$cnf( $equal(join(complement(top),composition(X_21,complement(composition(converse(X_21),top)))),complement(top)) )],[refute_0_81,refute_0_110]) ).
cnf(refute_0_112,plain,
( complement(top) != zero
| join(zero,composition(X_21,complement(composition(converse(X_21),top)))) != complement(top)
| join(zero,composition(X_21,complement(composition(converse(X_21),top)))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,composition(X_21,complement(composition(converse(X_21),top)))),complement(top)) ),[1],$fot(zero)]]) ).
cnf(refute_0_113,plain,
( join(zero,composition(X_21,complement(composition(converse(X_21),top)))) != complement(top)
| join(zero,composition(X_21,complement(composition(converse(X_21),top)))) = zero ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_108,refute_0_112]) ).
cnf(refute_0_114,plain,
join(zero,composition(X_21,complement(composition(converse(X_21),top)))) = zero,
inference(resolve,[$cnf( $equal(join(zero,composition(X_21,complement(composition(converse(X_21),top)))),complement(top)) )],[refute_0_111,refute_0_113]) ).
cnf(refute_0_115,plain,
join(zero,composition(converse(one),complement(composition(converse(converse(one)),top)))) = zero,
inference(subst,[],[refute_0_114:[bind(X_21,$fot(converse(one)))]]) ).
cnf(refute_0_116,plain,
complement(composition(converse(converse(one)),top)) = composition(converse(one),complement(composition(converse(converse(one)),top))),
inference(subst,[],[refute_0_31:[bind(X_26,$fot(complement(composition(converse(converse(one)),top))))]]) ).
cnf(refute_0_117,plain,
( complement(composition(converse(converse(one)),top)) != composition(converse(one),complement(composition(converse(converse(one)),top)))
| composition(converse(one),complement(composition(converse(converse(one)),top))) = complement(composition(converse(converse(one)),top)) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(complement(composition(converse(converse(one)),top)))),bind(Y,$fot(composition(converse(one),complement(composition(converse(converse(one)),top)))))]]) ).
cnf(refute_0_118,plain,
composition(converse(one),complement(composition(converse(converse(one)),top))) = complement(composition(converse(converse(one)),top)),
inference(resolve,[$cnf( $equal(complement(composition(converse(converse(one)),top)),composition(converse(one),complement(composition(converse(converse(one)),top)))) )],[refute_0_116,refute_0_117]) ).
cnf(refute_0_119,plain,
( composition(converse(one),complement(composition(converse(converse(one)),top))) != complement(composition(converse(converse(one)),top))
| join(zero,composition(converse(one),complement(composition(converse(converse(one)),top)))) != zero
| join(zero,complement(composition(converse(converse(one)),top))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,composition(converse(one),complement(composition(converse(converse(one)),top)))),zero) ),[0,1],$fot(complement(composition(converse(converse(one)),top)))]]) ).
cnf(refute_0_120,plain,
( join(zero,composition(converse(one),complement(composition(converse(converse(one)),top)))) != zero
| join(zero,complement(composition(converse(converse(one)),top))) = zero ),
inference(resolve,[$cnf( $equal(composition(converse(one),complement(composition(converse(converse(one)),top))),complement(composition(converse(converse(one)),top))) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
join(zero,complement(composition(converse(converse(one)),top))) = zero,
inference(resolve,[$cnf( $equal(join(zero,composition(converse(one),complement(composition(converse(converse(one)),top)))),zero) )],[refute_0_115,refute_0_120]) ).
cnf(refute_0_122,plain,
converse(converse(one)) = one,
inference(subst,[],[refute_0_18:[bind(X0,$fot(one))]]) ).
cnf(refute_0_123,plain,
composition(converse(converse(one)),top) = composition(converse(converse(one)),top),
introduced(tautology,[refl,[$fot(composition(converse(converse(one)),top))]]) ).
cnf(refute_0_124,plain,
( composition(converse(converse(one)),top) != composition(converse(converse(one)),top)
| converse(converse(one)) != one
| composition(converse(converse(one)),top) = composition(one,top) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(converse(one)),top),composition(converse(converse(one)),top)) ),[1,0],$fot(one)]]) ).
cnf(refute_0_125,plain,
( converse(converse(one)) != one
| composition(converse(converse(one)),top) = composition(one,top) ),
inference(resolve,[$cnf( $equal(composition(converse(converse(one)),top),composition(converse(converse(one)),top)) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
composition(converse(converse(one)),top) = composition(one,top),
inference(resolve,[$cnf( $equal(converse(converse(one)),one) )],[refute_0_122,refute_0_125]) ).
cnf(refute_0_127,plain,
complement(composition(converse(converse(one)),top)) = complement(composition(converse(converse(one)),top)),
introduced(tautology,[refl,[$fot(complement(composition(converse(converse(one)),top)))]]) ).
cnf(refute_0_128,plain,
( complement(composition(converse(converse(one)),top)) != complement(composition(converse(converse(one)),top))
| composition(converse(converse(one)),top) != composition(one,top)
| complement(composition(converse(converse(one)),top)) = complement(composition(one,top)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(composition(converse(converse(one)),top)),complement(composition(converse(converse(one)),top))) ),[1,0],$fot(composition(one,top))]]) ).
cnf(refute_0_129,plain,
( composition(converse(converse(one)),top) != composition(one,top)
| complement(composition(converse(converse(one)),top)) = complement(composition(one,top)) ),
inference(resolve,[$cnf( $equal(complement(composition(converse(converse(one)),top)),complement(composition(converse(converse(one)),top))) )],[refute_0_127,refute_0_128]) ).
cnf(refute_0_130,plain,
complement(composition(converse(converse(one)),top)) = complement(composition(one,top)),
inference(resolve,[$cnf( $equal(composition(converse(converse(one)),top),composition(one,top)) )],[refute_0_126,refute_0_129]) ).
cnf(refute_0_131,plain,
join(zero,complement(composition(converse(converse(one)),top))) = join(zero,complement(composition(converse(converse(one)),top))),
introduced(tautology,[refl,[$fot(join(zero,complement(composition(converse(converse(one)),top))))]]) ).
cnf(refute_0_132,plain,
( complement(composition(converse(converse(one)),top)) != complement(composition(one,top))
| join(zero,complement(composition(converse(converse(one)),top))) != join(zero,complement(composition(converse(converse(one)),top)))
| join(zero,complement(composition(converse(converse(one)),top))) = join(zero,complement(composition(one,top))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(composition(converse(converse(one)),top))),join(zero,complement(composition(converse(converse(one)),top)))) ),[1,1],$fot(complement(composition(one,top)))]]) ).
cnf(refute_0_133,plain,
( complement(composition(converse(converse(one)),top)) != complement(composition(one,top))
| join(zero,complement(composition(converse(converse(one)),top))) = join(zero,complement(composition(one,top))) ),
inference(resolve,[$cnf( $equal(join(zero,complement(composition(converse(converse(one)),top))),join(zero,complement(composition(converse(converse(one)),top)))) )],[refute_0_131,refute_0_132]) ).
cnf(refute_0_134,plain,
join(zero,complement(composition(converse(converse(one)),top))) = join(zero,complement(composition(one,top))),
inference(resolve,[$cnf( $equal(complement(composition(converse(converse(one)),top)),complement(composition(one,top))) )],[refute_0_130,refute_0_133]) ).
cnf(refute_0_135,plain,
( join(zero,complement(composition(converse(converse(one)),top))) != join(zero,complement(composition(one,top)))
| join(zero,complement(composition(converse(converse(one)),top))) != zero
| join(zero,complement(composition(one,top))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(composition(converse(converse(one)),top))),zero) ),[0],$fot(join(zero,complement(composition(one,top))))]]) ).
cnf(refute_0_136,plain,
( join(zero,complement(composition(converse(converse(one)),top))) != zero
| join(zero,complement(composition(one,top))) = zero ),
inference(resolve,[$cnf( $equal(join(zero,complement(composition(converse(converse(one)),top))),join(zero,complement(composition(one,top)))) )],[refute_0_134,refute_0_135]) ).
cnf(refute_0_137,plain,
join(zero,complement(composition(one,top))) = zero,
inference(resolve,[$cnf( $equal(join(zero,complement(composition(converse(converse(one)),top))),zero) )],[refute_0_121,refute_0_136]) ).
cnf(refute_0_138,plain,
( X_26 != composition(one,X_26)
| composition(one,X_26) = X_26 ),
inference(subst,[],[refute_0_7:[bind(X,$fot(X_26)),bind(Y,$fot(composition(one,X_26)))]]) ).
cnf(refute_0_139,plain,
composition(one,X_26) = X_26,
inference(resolve,[$cnf( $equal(X_26,composition(one,X_26)) )],[refute_0_47,refute_0_138]) ).
cnf(refute_0_140,plain,
composition(one,top) = top,
inference(subst,[],[refute_0_139:[bind(X_26,$fot(top))]]) ).
cnf(refute_0_141,plain,
complement(composition(one,top)) = complement(composition(one,top)),
introduced(tautology,[refl,[$fot(complement(composition(one,top)))]]) ).
cnf(refute_0_142,plain,
( complement(composition(one,top)) != complement(composition(one,top))
| composition(one,top) != top
| complement(composition(one,top)) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(complement(composition(one,top)),complement(composition(one,top))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_143,plain,
( composition(one,top) != top
| complement(composition(one,top)) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(composition(one,top)),complement(composition(one,top))) )],[refute_0_141,refute_0_142]) ).
cnf(refute_0_144,plain,
complement(composition(one,top)) = complement(top),
inference(resolve,[$cnf( $equal(composition(one,top),top) )],[refute_0_140,refute_0_143]) ).
cnf(refute_0_145,plain,
( complement(composition(one,top)) != complement(top)
| complement(top) != zero
| complement(composition(one,top)) = zero ),
inference(subst,[],[refute_0_100:[bind(X,$fot(complement(composition(one,top)))),bind(Y,$fot(complement(top))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_146,plain,
( complement(top) != zero
| complement(composition(one,top)) = zero ),
inference(resolve,[$cnf( $equal(complement(composition(one,top)),complement(top)) )],[refute_0_144,refute_0_145]) ).
cnf(refute_0_147,plain,
complement(composition(one,top)) = zero,
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_108,refute_0_146]) ).
cnf(refute_0_148,plain,
join(zero,complement(composition(one,top))) = join(zero,complement(composition(one,top))),
introduced(tautology,[refl,[$fot(join(zero,complement(composition(one,top))))]]) ).
cnf(refute_0_149,plain,
( complement(composition(one,top)) != zero
| join(zero,complement(composition(one,top))) != join(zero,complement(composition(one,top)))
| join(zero,complement(composition(one,top))) = join(zero,zero) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(composition(one,top))),join(zero,complement(composition(one,top)))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_150,plain,
( complement(composition(one,top)) != zero
| join(zero,complement(composition(one,top))) = join(zero,zero) ),
inference(resolve,[$cnf( $equal(join(zero,complement(composition(one,top))),join(zero,complement(composition(one,top)))) )],[refute_0_148,refute_0_149]) ).
cnf(refute_0_151,plain,
join(zero,complement(composition(one,top))) = join(zero,zero),
inference(resolve,[$cnf( $equal(complement(composition(one,top)),zero) )],[refute_0_147,refute_0_150]) ).
cnf(refute_0_152,plain,
( join(zero,complement(composition(one,top))) != join(zero,zero)
| join(zero,complement(composition(one,top))) != zero
| join(zero,zero) = zero ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(composition(one,top))),zero) ),[0],$fot(join(zero,zero))]]) ).
cnf(refute_0_153,plain,
( join(zero,complement(composition(one,top))) != zero
| join(zero,zero) = zero ),
inference(resolve,[$cnf( $equal(join(zero,complement(composition(one,top))),join(zero,zero)) )],[refute_0_151,refute_0_152]) ).
cnf(refute_0_154,plain,
join(zero,zero) = zero,
inference(resolve,[$cnf( $equal(join(zero,complement(composition(one,top))),zero) )],[refute_0_137,refute_0_153]) ).
cnf(refute_0_155,plain,
( join(zero,join(zero,X_77)) != join(join(zero,zero),X_77)
| join(zero,zero) != zero
| join(zero,join(zero,X_77)) = join(zero,X_77) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(zero,X_77)),join(join(zero,zero),X_77)) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_156,plain,
( join(zero,join(zero,X_77)) != join(join(zero,zero),X_77)
| join(zero,join(zero,X_77)) = join(zero,X_77) ),
inference(resolve,[$cnf( $equal(join(zero,zero),zero) )],[refute_0_154,refute_0_155]) ).
cnf(refute_0_157,plain,
join(zero,join(zero,X_77)) = join(zero,X_77),
inference(resolve,[$cnf( $equal(join(zero,join(zero,X_77)),join(join(zero,zero),X_77)) )],[refute_0_76,refute_0_156]) ).
cnf(refute_0_158,plain,
join(zero,join(zero,meet(X_31,X_31))) = join(zero,meet(X_31,X_31)),
inference(subst,[],[refute_0_157:[bind(X_77,$fot(meet(X_31,X_31)))]]) ).
cnf(refute_0_159,plain,
X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_160,plain,
join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),
inference(subst,[],[refute_0_9:[bind(X0,$fot(complement(join(complement(X0),X1)))),bind(X1,$fot(complement(join(complement(X0),complement(X1)))))]]) ).
cnf(refute_0_161,plain,
( X0 != join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1)))
| join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) != join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))
| X0 = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X0,join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))) ),[0],$fot(join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))))]]) ).
cnf(refute_0_162,plain,
( X0 != join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1)))
| X0 = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) ),
inference(resolve,[$cnf( $equal(join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))) )],[refute_0_160,refute_0_161]) ).
cnf(refute_0_163,plain,
X0 = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),
inference(resolve,[$cnf( $equal(X0,join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1)))) )],[refute_0_159,refute_0_162]) ).
cnf(refute_0_164,plain,
join(complement(join(complement(X0),X1)),meet(X0,X1)) = join(meet(X0,X1),complement(join(complement(X0),X1))),
inference(subst,[],[refute_0_9:[bind(X0,$fot(meet(X0,X1))),bind(X1,$fot(complement(join(complement(X0),X1))))]]) ).
cnf(refute_0_165,plain,
( meet(X0,X1) != complement(join(complement(X0),complement(X1)))
| complement(join(complement(X0),complement(X1))) = meet(X0,X1) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(meet(X0,X1))),bind(Y,$fot(complement(join(complement(X0),complement(X1)))))]]) ).
cnf(refute_0_166,plain,
complement(join(complement(X0),complement(X1))) = meet(X0,X1),
inference(resolve,[$cnf( $equal(meet(X0,X1),complement(join(complement(X0),complement(X1)))) )],[refute_0_61,refute_0_165]) ).
cnf(refute_0_167,plain,
join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),
introduced(tautology,[refl,[$fot(join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))))]]) ).
cnf(refute_0_168,plain,
( complement(join(complement(X0),complement(X1))) != meet(X0,X1)
| join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) != join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))
| join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(complement(join(complement(X0),X1)),meet(X0,X1)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))) ),[1,1],$fot(meet(X0,X1))]]) ).
cnf(refute_0_169,plain,
( complement(join(complement(X0),complement(X1))) != meet(X0,X1)
| join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(complement(join(complement(X0),X1)),meet(X0,X1)) ),
inference(resolve,[$cnf( $equal(join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))) )],[refute_0_167,refute_0_168]) ).
cnf(refute_0_170,plain,
join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(complement(join(complement(X0),X1)),meet(X0,X1)),
inference(resolve,[$cnf( $equal(complement(join(complement(X0),complement(X1))),meet(X0,X1)) )],[refute_0_166,refute_0_169]) ).
cnf(refute_0_171,plain,
( join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) != join(complement(join(complement(X0),X1)),meet(X0,X1))
| join(complement(join(complement(X0),X1)),meet(X0,X1)) != join(meet(X0,X1),complement(join(complement(X0),X1)))
| join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(meet(X0,X1),complement(join(complement(X0),X1))) ),
inference(subst,[],[refute_0_100:[bind(X,$fot(join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))))),bind(Y,$fot(join(complement(join(complement(X0),X1)),meet(X0,X1)))),bind(Z,$fot(join(meet(X0,X1),complement(join(complement(X0),X1)))))]]) ).
cnf(refute_0_172,plain,
( join(complement(join(complement(X0),X1)),meet(X0,X1)) != join(meet(X0,X1),complement(join(complement(X0),X1)))
| join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(meet(X0,X1),complement(join(complement(X0),X1))) ),
inference(resolve,[$cnf( $equal(join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),join(complement(join(complement(X0),X1)),meet(X0,X1))) )],[refute_0_170,refute_0_171]) ).
cnf(refute_0_173,plain,
join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(meet(X0,X1),complement(join(complement(X0),X1))),
inference(resolve,[$cnf( $equal(join(complement(join(complement(X0),X1)),meet(X0,X1)),join(meet(X0,X1),complement(join(complement(X0),X1)))) )],[refute_0_164,refute_0_172]) ).
cnf(refute_0_174,plain,
( X0 != join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))
| join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) != join(meet(X0,X1),complement(join(complement(X0),X1)))
| X0 = join(meet(X0,X1),complement(join(complement(X0),X1))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X0,join(meet(X0,X1),complement(join(complement(X0),X1)))) ),[0],$fot(join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))))]]) ).
cnf(refute_0_175,plain,
( X0 != join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))
| X0 = join(meet(X0,X1),complement(join(complement(X0),X1))) ),
inference(resolve,[$cnf( $equal(join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),join(meet(X0,X1),complement(join(complement(X0),X1)))) )],[refute_0_173,refute_0_174]) ).
cnf(refute_0_176,plain,
X0 = join(meet(X0,X1),complement(join(complement(X0),X1))),
inference(resolve,[$cnf( $equal(X0,join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))) )],[refute_0_163,refute_0_175]) ).
cnf(refute_0_177,plain,
X_31 = join(meet(X_31,complement(X_31)),complement(join(complement(X_31),complement(X_31)))),
inference(subst,[],[refute_0_176:[bind(X0,$fot(X_31)),bind(X1,$fot(complement(X_31)))]]) ).
cnf(refute_0_178,plain,
zero = meet(X_31,complement(X_31)),
inference(subst,[],[refute_0_82:[bind(X0,$fot(X_31))]]) ).
cnf(refute_0_179,plain,
( zero != meet(X_31,complement(X_31))
| meet(X_31,complement(X_31)) = zero ),
inference(subst,[],[refute_0_7:[bind(X,$fot(zero)),bind(Y,$fot(meet(X_31,complement(X_31))))]]) ).
cnf(refute_0_180,plain,
meet(X_31,complement(X_31)) = zero,
inference(resolve,[$cnf( $equal(zero,meet(X_31,complement(X_31))) )],[refute_0_178,refute_0_179]) ).
cnf(refute_0_181,plain,
( X_31 != join(meet(X_31,complement(X_31)),complement(join(complement(X_31),complement(X_31))))
| meet(X_31,complement(X_31)) != zero
| X_31 = join(zero,complement(join(complement(X_31),complement(X_31)))) ),
introduced(tautology,[equality,[$cnf( $equal(X_31,join(meet(X_31,complement(X_31)),complement(join(complement(X_31),complement(X_31))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_182,plain,
( X_31 != join(meet(X_31,complement(X_31)),complement(join(complement(X_31),complement(X_31))))
| X_31 = join(zero,complement(join(complement(X_31),complement(X_31)))) ),
inference(resolve,[$cnf( $equal(meet(X_31,complement(X_31)),zero) )],[refute_0_180,refute_0_181]) ).
cnf(refute_0_183,plain,
X_31 = join(zero,complement(join(complement(X_31),complement(X_31)))),
inference(resolve,[$cnf( $equal(X_31,join(meet(X_31,complement(X_31)),complement(join(complement(X_31),complement(X_31))))) )],[refute_0_177,refute_0_182]) ).
cnf(refute_0_184,plain,
complement(join(complement(X_31),complement(X_31))) = meet(X_31,X_31),
inference(subst,[],[refute_0_166:[bind(X0,$fot(X_31)),bind(X1,$fot(X_31))]]) ).
cnf(refute_0_185,plain,
join(zero,complement(join(complement(X_31),complement(X_31)))) = join(zero,complement(join(complement(X_31),complement(X_31)))),
introduced(tautology,[refl,[$fot(join(zero,complement(join(complement(X_31),complement(X_31)))))]]) ).
cnf(refute_0_186,plain,
( complement(join(complement(X_31),complement(X_31))) != meet(X_31,X_31)
| join(zero,complement(join(complement(X_31),complement(X_31)))) != join(zero,complement(join(complement(X_31),complement(X_31))))
| join(zero,complement(join(complement(X_31),complement(X_31)))) = join(zero,meet(X_31,X_31)) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(join(complement(X_31),complement(X_31)))),join(zero,complement(join(complement(X_31),complement(X_31))))) ),[1,1],$fot(meet(X_31,X_31))]]) ).
cnf(refute_0_187,plain,
( complement(join(complement(X_31),complement(X_31))) != meet(X_31,X_31)
| join(zero,complement(join(complement(X_31),complement(X_31)))) = join(zero,meet(X_31,X_31)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(complement(X_31),complement(X_31)))),join(zero,complement(join(complement(X_31),complement(X_31))))) )],[refute_0_185,refute_0_186]) ).
cnf(refute_0_188,plain,
join(zero,complement(join(complement(X_31),complement(X_31)))) = join(zero,meet(X_31,X_31)),
inference(resolve,[$cnf( $equal(complement(join(complement(X_31),complement(X_31))),meet(X_31,X_31)) )],[refute_0_184,refute_0_187]) ).
cnf(refute_0_189,plain,
( X_31 != join(zero,complement(join(complement(X_31),complement(X_31))))
| join(zero,complement(join(complement(X_31),complement(X_31)))) != join(zero,meet(X_31,X_31))
| X_31 = join(zero,meet(X_31,X_31)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_31,join(zero,meet(X_31,X_31))) ),[0],$fot(join(zero,complement(join(complement(X_31),complement(X_31)))))]]) ).
cnf(refute_0_190,plain,
( X_31 != join(zero,complement(join(complement(X_31),complement(X_31))))
| X_31 = join(zero,meet(X_31,X_31)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(complement(X_31),complement(X_31)))),join(zero,meet(X_31,X_31))) )],[refute_0_188,refute_0_189]) ).
cnf(refute_0_191,plain,
X_31 = join(zero,meet(X_31,X_31)),
inference(resolve,[$cnf( $equal(X_31,join(zero,complement(join(complement(X_31),complement(X_31))))) )],[refute_0_183,refute_0_190]) ).
cnf(refute_0_192,plain,
( X_31 != join(zero,meet(X_31,X_31))
| join(zero,meet(X_31,X_31)) = X_31 ),
inference(subst,[],[refute_0_7:[bind(X,$fot(X_31)),bind(Y,$fot(join(zero,meet(X_31,X_31))))]]) ).
cnf(refute_0_193,plain,
join(zero,meet(X_31,X_31)) = X_31,
inference(resolve,[$cnf( $equal(X_31,join(zero,meet(X_31,X_31))) )],[refute_0_191,refute_0_192]) ).
cnf(refute_0_194,plain,
( join(zero,join(zero,meet(X_31,X_31))) != join(zero,meet(X_31,X_31))
| join(zero,meet(X_31,X_31)) != X_31
| join(zero,join(zero,meet(X_31,X_31))) = X_31 ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(zero,join(zero,meet(X_31,X_31))),X_31) ),[0],$fot(join(zero,meet(X_31,X_31)))]]) ).
cnf(refute_0_195,plain,
( join(zero,join(zero,meet(X_31,X_31))) != join(zero,meet(X_31,X_31))
| join(zero,join(zero,meet(X_31,X_31))) = X_31 ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_31,X_31)),X_31) )],[refute_0_193,refute_0_194]) ).
cnf(refute_0_196,plain,
join(zero,join(zero,meet(X_31,X_31))) = X_31,
inference(resolve,[$cnf( $equal(join(zero,join(zero,meet(X_31,X_31))),join(zero,meet(X_31,X_31))) )],[refute_0_158,refute_0_195]) ).
cnf(refute_0_197,plain,
( join(zero,join(zero,meet(X_31,X_31))) != join(zero,meet(X_31,X_31))
| join(zero,meet(X_31,X_31)) != X_31
| join(zero,X_31) = join(zero,meet(X_31,X_31)) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(zero,meet(X_31,X_31))),join(zero,meet(X_31,X_31))) ),[0,1],$fot(X_31)]]) ).
cnf(refute_0_198,plain,
( join(zero,join(zero,meet(X_31,X_31))) != join(zero,meet(X_31,X_31))
| join(zero,X_31) = join(zero,meet(X_31,X_31)) ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_31,X_31)),X_31) )],[refute_0_193,refute_0_197]) ).
cnf(refute_0_199,plain,
join(zero,X_31) = join(zero,meet(X_31,X_31)),
inference(resolve,[$cnf( $equal(join(zero,join(zero,meet(X_31,X_31))),join(zero,meet(X_31,X_31))) )],[refute_0_158,refute_0_198]) ).
cnf(refute_0_200,plain,
( join(zero,X_31) != join(zero,meet(X_31,X_31))
| join(zero,meet(X_31,X_31)) != X_31
| join(zero,X_31) = X_31 ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(zero,X_31),X_31) ),[0],$fot(join(zero,meet(X_31,X_31)))]]) ).
cnf(refute_0_201,plain,
( join(zero,X_31) != join(zero,meet(X_31,X_31))
| join(zero,X_31) = X_31 ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_31,X_31)),X_31) )],[refute_0_193,refute_0_200]) ).
cnf(refute_0_202,plain,
join(zero,X_31) = X_31,
inference(resolve,[$cnf( $equal(join(zero,X_31),join(zero,meet(X_31,X_31))) )],[refute_0_199,refute_0_201]) ).
cnf(refute_0_203,plain,
join(zero,meet(X_31,X_31)) = meet(X_31,X_31),
inference(subst,[],[refute_0_202:[bind(X_31,$fot(meet(X_31,X_31)))]]) ).
cnf(refute_0_204,plain,
( join(zero,join(zero,meet(X_31,X_31))) != join(zero,meet(X_31,X_31))
| join(zero,meet(X_31,X_31)) != meet(X_31,X_31)
| join(zero,join(zero,meet(X_31,X_31))) = meet(X_31,X_31) ),
inference(subst,[],[refute_0_100:[bind(X,$fot(join(zero,join(zero,meet(X_31,X_31))))),bind(Y,$fot(join(zero,meet(X_31,X_31)))),bind(Z,$fot(meet(X_31,X_31)))]]) ).
cnf(refute_0_205,plain,
( join(zero,meet(X_31,X_31)) != meet(X_31,X_31)
| join(zero,join(zero,meet(X_31,X_31))) = meet(X_31,X_31) ),
inference(resolve,[$cnf( $equal(join(zero,join(zero,meet(X_31,X_31))),join(zero,meet(X_31,X_31))) )],[refute_0_158,refute_0_204]) ).
cnf(refute_0_206,plain,
join(zero,join(zero,meet(X_31,X_31))) = meet(X_31,X_31),
inference(resolve,[$cnf( $equal(join(zero,meet(X_31,X_31)),meet(X_31,X_31)) )],[refute_0_203,refute_0_205]) ).
cnf(refute_0_207,plain,
( join(zero,join(zero,meet(X_31,X_31))) != X_31
| join(zero,join(zero,meet(X_31,X_31))) != meet(X_31,X_31)
| meet(X_31,X_31) = X_31 ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(zero,meet(X_31,X_31))),X_31) ),[0],$fot(meet(X_31,X_31))]]) ).
cnf(refute_0_208,plain,
( join(zero,join(zero,meet(X_31,X_31))) != X_31
| meet(X_31,X_31) = X_31 ),
inference(resolve,[$cnf( $equal(join(zero,join(zero,meet(X_31,X_31))),meet(X_31,X_31)) )],[refute_0_206,refute_0_207]) ).
cnf(refute_0_209,plain,
meet(X_31,X_31) = X_31,
inference(resolve,[$cnf( $equal(join(zero,join(zero,meet(X_31,X_31))),X_31) )],[refute_0_196,refute_0_208]) ).
cnf(refute_0_210,plain,
meet(X_96,X_96) = X_96,
inference(subst,[],[refute_0_209:[bind(X_31,$fot(X_96))]]) ).
cnf(refute_0_211,plain,
( meet(X_96,X_96) != X_96
| top != join(complement(X_96),join(complement(X_96),meet(X_96,X_96)))
| top = join(complement(X_96),join(complement(X_96),X_96)) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(X_96),join(complement(X_96),meet(X_96,X_96)))) ),[1,1,1],$fot(X_96)]]) ).
cnf(refute_0_212,plain,
( top != join(complement(X_96),join(complement(X_96),meet(X_96,X_96)))
| top = join(complement(X_96),join(complement(X_96),X_96)) ),
inference(resolve,[$cnf( $equal(meet(X_96,X_96),X_96) )],[refute_0_210,refute_0_211]) ).
cnf(refute_0_213,plain,
top = join(complement(X_96),join(complement(X_96),X_96)),
inference(resolve,[$cnf( $equal(top,join(complement(X_96),join(complement(X_96),meet(X_96,X_96)))) )],[refute_0_75,refute_0_212]) ).
cnf(refute_0_214,plain,
join(X_75,join(complement(X_75),X_77)) = join(join(X_75,complement(X_75)),X_77),
inference(subst,[],[refute_0_68:[bind(X0,$fot(X_75)),bind(X1,$fot(complement(X_75))),bind(X2,$fot(X_77))]]) ).
cnf(refute_0_215,plain,
top = join(X_75,complement(X_75)),
inference(subst,[],[refute_0_59:[bind(X0,$fot(X_75))]]) ).
cnf(refute_0_216,plain,
( top != join(X_75,complement(X_75))
| join(X_75,complement(X_75)) = top ),
inference(subst,[],[refute_0_7:[bind(X,$fot(top)),bind(Y,$fot(join(X_75,complement(X_75))))]]) ).
cnf(refute_0_217,plain,
join(X_75,complement(X_75)) = top,
inference(resolve,[$cnf( $equal(top,join(X_75,complement(X_75))) )],[refute_0_215,refute_0_216]) ).
cnf(refute_0_218,plain,
( join(X_75,complement(X_75)) != top
| join(X_75,join(complement(X_75),X_77)) != join(join(X_75,complement(X_75)),X_77)
| join(X_75,join(complement(X_75),X_77)) = join(top,X_77) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_75,join(complement(X_75),X_77)),join(join(X_75,complement(X_75)),X_77)) ),[1,0],$fot(top)]]) ).
cnf(refute_0_219,plain,
( join(X_75,join(complement(X_75),X_77)) != join(join(X_75,complement(X_75)),X_77)
| join(X_75,join(complement(X_75),X_77)) = join(top,X_77) ),
inference(resolve,[$cnf( $equal(join(X_75,complement(X_75)),top) )],[refute_0_217,refute_0_218]) ).
cnf(refute_0_220,plain,
join(X_75,join(complement(X_75),X_77)) = join(top,X_77),
inference(resolve,[$cnf( $equal(join(X_75,join(complement(X_75),X_77)),join(join(X_75,complement(X_75)),X_77)) )],[refute_0_214,refute_0_219]) ).
cnf(refute_0_221,plain,
join(X_96,join(complement(X_96),complement(X_96))) = join(top,complement(X_96)),
inference(subst,[],[refute_0_220:[bind(X_75,$fot(X_96)),bind(X_77,$fot(complement(X_96)))]]) ).
cnf(refute_0_222,plain,
join(X_75,join(X_76,X_77)) = join(join(X_75,X_76),X_77),
inference(subst,[],[refute_0_68:[bind(X0,$fot(X_75)),bind(X1,$fot(X_76)),bind(X2,$fot(X_77))]]) ).
cnf(refute_0_223,plain,
join(X_76,X_75) = join(X_75,X_76),
inference(subst,[],[refute_0_4:[bind(X0,$fot(X_76)),bind(X1,$fot(X_75))]]) ).
cnf(refute_0_224,plain,
( join(X_76,X_75) != join(X_75,X_76)
| join(X_75,X_76) = join(X_76,X_75) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(X_76,X_75))),bind(Y,$fot(join(X_75,X_76)))]]) ).
cnf(refute_0_225,plain,
join(X_75,X_76) = join(X_76,X_75),
inference(resolve,[$cnf( $equal(join(X_76,X_75),join(X_75,X_76)) )],[refute_0_223,refute_0_224]) ).
cnf(refute_0_226,plain,
( join(X_75,X_76) != join(X_76,X_75)
| join(X_75,join(X_76,X_77)) != join(join(X_75,X_76),X_77)
| join(X_75,join(X_76,X_77)) = join(join(X_76,X_75),X_77) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_75,join(X_76,X_77)),join(join(X_75,X_76),X_77)) ),[1,0],$fot(join(X_76,X_75))]]) ).
cnf(refute_0_227,plain,
( join(X_75,join(X_76,X_77)) != join(join(X_75,X_76),X_77)
| join(X_75,join(X_76,X_77)) = join(join(X_76,X_75),X_77) ),
inference(resolve,[$cnf( $equal(join(X_75,X_76),join(X_76,X_75)) )],[refute_0_225,refute_0_226]) ).
cnf(refute_0_228,plain,
join(X_75,join(X_76,X_77)) = join(join(X_76,X_75),X_77),
inference(resolve,[$cnf( $equal(join(X_75,join(X_76,X_77)),join(join(X_75,X_76),X_77)) )],[refute_0_222,refute_0_227]) ).
cnf(refute_0_229,plain,
join(join(X_76,X_75),X_77) = join(X_76,join(X_75,X_77)),
inference(subst,[],[refute_0_70:[bind(X0,$fot(X_76)),bind(X1,$fot(X_75)),bind(X2,$fot(X_77))]]) ).
cnf(refute_0_230,plain,
( join(X_75,join(X_76,X_77)) != join(join(X_76,X_75),X_77)
| join(join(X_76,X_75),X_77) != join(X_76,join(X_75,X_77))
| join(X_75,join(X_76,X_77)) = join(X_76,join(X_75,X_77)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_75,join(X_76,X_77)),join(X_76,join(X_75,X_77))) ),[0],$fot(join(join(X_76,X_75),X_77))]]) ).
cnf(refute_0_231,plain,
( join(X_75,join(X_76,X_77)) != join(join(X_76,X_75),X_77)
| join(X_75,join(X_76,X_77)) = join(X_76,join(X_75,X_77)) ),
inference(resolve,[$cnf( $equal(join(join(X_76,X_75),X_77),join(X_76,join(X_75,X_77))) )],[refute_0_229,refute_0_230]) ).
cnf(refute_0_232,plain,
join(X_75,join(X_76,X_77)) = join(X_76,join(X_75,X_77)),
inference(resolve,[$cnf( $equal(join(X_75,join(X_76,X_77)),join(join(X_76,X_75),X_77)) )],[refute_0_228,refute_0_231]) ).
cnf(refute_0_233,plain,
( join(X_75,join(X_76,X_77)) != join(X_76,join(X_75,X_77))
| join(X_76,join(X_75,X_77)) = join(X_75,join(X_76,X_77)) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(X_75,join(X_76,X_77)))),bind(Y,$fot(join(X_76,join(X_75,X_77))))]]) ).
cnf(refute_0_234,plain,
join(X_76,join(X_75,X_77)) = join(X_75,join(X_76,X_77)),
inference(resolve,[$cnf( $equal(join(X_75,join(X_76,X_77)),join(X_76,join(X_75,X_77))) )],[refute_0_232,refute_0_233]) ).
cnf(refute_0_235,plain,
join(complement(X_96),join(X_96,complement(X_96))) = join(X_96,join(complement(X_96),complement(X_96))),
inference(subst,[],[refute_0_234:[bind(X_75,$fot(X_96)),bind(X_76,$fot(complement(X_96))),bind(X_77,$fot(complement(X_96)))]]) ).
cnf(refute_0_236,plain,
( join(X_96,join(complement(X_96),complement(X_96))) != join(top,complement(X_96))
| join(complement(X_96),join(X_96,complement(X_96))) != join(X_96,join(complement(X_96),complement(X_96)))
| join(complement(X_96),join(X_96,complement(X_96))) = join(top,complement(X_96)) ),
inference(subst,[],[refute_0_100:[bind(X,$fot(join(complement(X_96),join(X_96,complement(X_96))))),bind(Y,$fot(join(X_96,join(complement(X_96),complement(X_96))))),bind(Z,$fot(join(top,complement(X_96))))]]) ).
cnf(refute_0_237,plain,
( join(X_96,join(complement(X_96),complement(X_96))) != join(top,complement(X_96))
| join(complement(X_96),join(X_96,complement(X_96))) = join(top,complement(X_96)) ),
inference(resolve,[$cnf( $equal(join(complement(X_96),join(X_96,complement(X_96))),join(X_96,join(complement(X_96),complement(X_96)))) )],[refute_0_235,refute_0_236]) ).
cnf(refute_0_238,plain,
join(complement(X_96),join(X_96,complement(X_96))) = join(top,complement(X_96)),
inference(resolve,[$cnf( $equal(join(X_96,join(complement(X_96),complement(X_96))),join(top,complement(X_96))) )],[refute_0_221,refute_0_237]) ).
cnf(refute_0_239,plain,
join(X_77,X_76) = join(X_76,X_77),
inference(subst,[],[refute_0_4:[bind(X0,$fot(X_77)),bind(X1,$fot(X_76))]]) ).
cnf(refute_0_240,plain,
( join(X_77,X_76) != join(X_76,X_77)
| join(X_76,X_77) = join(X_77,X_76) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(X_77,X_76))),bind(Y,$fot(join(X_76,X_77)))]]) ).
cnf(refute_0_241,plain,
join(X_76,X_77) = join(X_77,X_76),
inference(resolve,[$cnf( $equal(join(X_77,X_76),join(X_76,X_77)) )],[refute_0_239,refute_0_240]) ).
cnf(refute_0_242,plain,
( join(X_75,join(X_76,X_77)) != join(join(X_75,X_76),X_77)
| join(X_76,X_77) != join(X_77,X_76)
| join(X_75,join(X_77,X_76)) = join(join(X_75,X_76),X_77) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_75,join(X_76,X_77)),join(join(X_75,X_76),X_77)) ),[0,1],$fot(join(X_77,X_76))]]) ).
cnf(refute_0_243,plain,
( join(X_75,join(X_76,X_77)) != join(join(X_75,X_76),X_77)
| join(X_75,join(X_77,X_76)) = join(join(X_75,X_76),X_77) ),
inference(resolve,[$cnf( $equal(join(X_76,X_77),join(X_77,X_76)) )],[refute_0_241,refute_0_242]) ).
cnf(refute_0_244,plain,
join(X_75,join(X_77,X_76)) = join(join(X_75,X_76),X_77),
inference(resolve,[$cnf( $equal(join(X_75,join(X_76,X_77)),join(join(X_75,X_76),X_77)) )],[refute_0_222,refute_0_243]) ).
cnf(refute_0_245,plain,
join(join(X_75,X_76),X_77) = join(X_75,join(X_76,X_77)),
inference(subst,[],[refute_0_70:[bind(X0,$fot(X_75)),bind(X1,$fot(X_76)),bind(X2,$fot(X_77))]]) ).
cnf(refute_0_246,plain,
( join(X_75,join(X_77,X_76)) != join(join(X_75,X_76),X_77)
| join(join(X_75,X_76),X_77) != join(X_75,join(X_76,X_77))
| join(X_75,join(X_77,X_76)) = join(X_75,join(X_76,X_77)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_75,join(X_77,X_76)),join(X_75,join(X_76,X_77))) ),[0],$fot(join(join(X_75,X_76),X_77))]]) ).
cnf(refute_0_247,plain,
( join(X_75,join(X_77,X_76)) != join(join(X_75,X_76),X_77)
| join(X_75,join(X_77,X_76)) = join(X_75,join(X_76,X_77)) ),
inference(resolve,[$cnf( $equal(join(join(X_75,X_76),X_77),join(X_75,join(X_76,X_77))) )],[refute_0_245,refute_0_246]) ).
cnf(refute_0_248,plain,
join(X_75,join(X_77,X_76)) = join(X_75,join(X_76,X_77)),
inference(resolve,[$cnf( $equal(join(X_75,join(X_77,X_76)),join(join(X_75,X_76),X_77)) )],[refute_0_244,refute_0_247]) ).
cnf(refute_0_249,plain,
( join(X_75,join(X_77,X_76)) != join(X_75,join(X_76,X_77))
| join(X_75,join(X_76,X_77)) = join(X_75,join(X_77,X_76)) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(X_75,join(X_77,X_76)))),bind(Y,$fot(join(X_75,join(X_76,X_77))))]]) ).
cnf(refute_0_250,plain,
join(X_75,join(X_76,X_77)) = join(X_75,join(X_77,X_76)),
inference(resolve,[$cnf( $equal(join(X_75,join(X_77,X_76)),join(X_75,join(X_76,X_77))) )],[refute_0_248,refute_0_249]) ).
cnf(refute_0_251,plain,
join(complement(X_96),join(complement(X_96),X_96)) = join(complement(X_96),join(X_96,complement(X_96))),
inference(subst,[],[refute_0_250:[bind(X_75,$fot(complement(X_96))),bind(X_76,$fot(complement(X_96))),bind(X_77,$fot(X_96))]]) ).
cnf(refute_0_252,plain,
( join(complement(X_96),join(X_96,complement(X_96))) != join(top,complement(X_96))
| join(complement(X_96),join(complement(X_96),X_96)) != join(complement(X_96),join(X_96,complement(X_96)))
| join(complement(X_96),join(complement(X_96),X_96)) = join(top,complement(X_96)) ),
inference(subst,[],[refute_0_100:[bind(X,$fot(join(complement(X_96),join(complement(X_96),X_96)))),bind(Y,$fot(join(complement(X_96),join(X_96,complement(X_96))))),bind(Z,$fot(join(top,complement(X_96))))]]) ).
cnf(refute_0_253,plain,
( join(complement(X_96),join(X_96,complement(X_96))) != join(top,complement(X_96))
| join(complement(X_96),join(complement(X_96),X_96)) = join(top,complement(X_96)) ),
inference(resolve,[$cnf( $equal(join(complement(X_96),join(complement(X_96),X_96)),join(complement(X_96),join(X_96,complement(X_96)))) )],[refute_0_251,refute_0_252]) ).
cnf(refute_0_254,plain,
join(complement(X_96),join(complement(X_96),X_96)) = join(top,complement(X_96)),
inference(resolve,[$cnf( $equal(join(complement(X_96),join(X_96,complement(X_96))),join(top,complement(X_96))) )],[refute_0_238,refute_0_253]) ).
cnf(refute_0_255,plain,
( join(complement(X_96),join(complement(X_96),X_96)) != join(top,complement(X_96))
| top != join(complement(X_96),join(complement(X_96),X_96))
| top = join(top,complement(X_96)) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(X_96),join(complement(X_96),X_96))) ),[1],$fot(join(top,complement(X_96)))]]) ).
cnf(refute_0_256,plain,
( top != join(complement(X_96),join(complement(X_96),X_96))
| top = join(top,complement(X_96)) ),
inference(resolve,[$cnf( $equal(join(complement(X_96),join(complement(X_96),X_96)),join(top,complement(X_96))) )],[refute_0_254,refute_0_255]) ).
cnf(refute_0_257,plain,
top = join(top,complement(X_96)),
inference(resolve,[$cnf( $equal(top,join(complement(X_96),join(complement(X_96),X_96))) )],[refute_0_213,refute_0_256]) ).
cnf(refute_0_258,plain,
top = join(top,complement(complement(X_53))),
inference(subst,[],[refute_0_257:[bind(X_96,$fot(complement(X_53)))]]) ).
cnf(refute_0_259,plain,
X_31 = join(meet(X_31,X_32),complement(join(complement(X_31),X_32))),
inference(subst,[],[refute_0_176:[bind(X0,$fot(X_31)),bind(X1,$fot(X_32))]]) ).
cnf(refute_0_260,plain,
join(X_32,complement(X_31)) = join(complement(X_31),X_32),
inference(subst,[],[refute_0_4:[bind(X0,$fot(X_32)),bind(X1,$fot(complement(X_31)))]]) ).
cnf(refute_0_261,plain,
( join(X_32,complement(X_31)) != join(complement(X_31),X_32)
| join(complement(X_31),X_32) = join(X_32,complement(X_31)) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(X_32,complement(X_31)))),bind(Y,$fot(join(complement(X_31),X_32)))]]) ).
cnf(refute_0_262,plain,
join(complement(X_31),X_32) = join(X_32,complement(X_31)),
inference(resolve,[$cnf( $equal(join(X_32,complement(X_31)),join(complement(X_31),X_32)) )],[refute_0_260,refute_0_261]) ).
cnf(refute_0_263,plain,
( X_31 != join(meet(X_31,X_32),complement(join(complement(X_31),X_32)))
| join(complement(X_31),X_32) != join(X_32,complement(X_31))
| X_31 = join(meet(X_31,X_32),complement(join(X_32,complement(X_31)))) ),
introduced(tautology,[equality,[$cnf( $equal(X_31,join(meet(X_31,X_32),complement(join(complement(X_31),X_32)))) ),[1,1,0],$fot(join(X_32,complement(X_31)))]]) ).
cnf(refute_0_264,plain,
( X_31 != join(meet(X_31,X_32),complement(join(complement(X_31),X_32)))
| X_31 = join(meet(X_31,X_32),complement(join(X_32,complement(X_31)))) ),
inference(resolve,[$cnf( $equal(join(complement(X_31),X_32),join(X_32,complement(X_31))) )],[refute_0_262,refute_0_263]) ).
cnf(refute_0_265,plain,
X_31 = join(meet(X_31,X_32),complement(join(X_32,complement(X_31)))),
inference(resolve,[$cnf( $equal(X_31,join(meet(X_31,X_32),complement(join(complement(X_31),X_32)))) )],[refute_0_259,refute_0_264]) ).
cnf(refute_0_266,plain,
X_53 = join(meet(X_53,complement(X_53)),complement(join(complement(X_53),complement(X_53)))),
inference(subst,[],[refute_0_265:[bind(X_31,$fot(X_53)),bind(X_32,$fot(complement(X_53)))]]) ).
cnf(refute_0_267,plain,
zero = meet(X_53,complement(X_53)),
inference(subst,[],[refute_0_82:[bind(X0,$fot(X_53))]]) ).
cnf(refute_0_268,plain,
( zero != meet(X_53,complement(X_53))
| meet(X_53,complement(X_53)) = zero ),
inference(subst,[],[refute_0_7:[bind(X,$fot(zero)),bind(Y,$fot(meet(X_53,complement(X_53))))]]) ).
cnf(refute_0_269,plain,
meet(X_53,complement(X_53)) = zero,
inference(resolve,[$cnf( $equal(zero,meet(X_53,complement(X_53))) )],[refute_0_267,refute_0_268]) ).
cnf(refute_0_270,plain,
( X_53 != join(meet(X_53,complement(X_53)),complement(join(complement(X_53),complement(X_53))))
| meet(X_53,complement(X_53)) != zero
| X_53 = join(zero,complement(join(complement(X_53),complement(X_53)))) ),
introduced(tautology,[equality,[$cnf( $equal(X_53,join(meet(X_53,complement(X_53)),complement(join(complement(X_53),complement(X_53))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_271,plain,
( X_53 != join(meet(X_53,complement(X_53)),complement(join(complement(X_53),complement(X_53))))
| X_53 = join(zero,complement(join(complement(X_53),complement(X_53)))) ),
inference(resolve,[$cnf( $equal(meet(X_53,complement(X_53)),zero) )],[refute_0_269,refute_0_270]) ).
cnf(refute_0_272,plain,
X_53 = join(zero,complement(join(complement(X_53),complement(X_53)))),
inference(resolve,[$cnf( $equal(X_53,join(meet(X_53,complement(X_53)),complement(join(complement(X_53),complement(X_53))))) )],[refute_0_266,refute_0_271]) ).
cnf(refute_0_273,plain,
join(zero,meet(X_53,X_53)) = X_53,
inference(subst,[],[refute_0_193:[bind(X_31,$fot(X_53))]]) ).
cnf(refute_0_274,plain,
join(complement(top),meet(X_53,X_53)) = join(complement(top),meet(X_53,X_53)),
introduced(tautology,[refl,[$fot(join(complement(top),meet(X_53,X_53)))]]) ).
cnf(refute_0_275,plain,
( complement(top) != zero
| join(complement(top),meet(X_53,X_53)) != join(complement(top),meet(X_53,X_53))
| join(complement(top),meet(X_53,X_53)) = join(zero,meet(X_53,X_53)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(X_53,X_53)),join(complement(top),meet(X_53,X_53))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_276,plain,
( complement(top) != zero
| join(complement(top),meet(X_53,X_53)) = join(zero,meet(X_53,X_53)) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_53,X_53)),join(complement(top),meet(X_53,X_53))) )],[refute_0_274,refute_0_275]) ).
cnf(refute_0_277,plain,
join(complement(top),meet(X_53,X_53)) = join(zero,meet(X_53,X_53)),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_108,refute_0_276]) ).
cnf(refute_0_278,plain,
( join(complement(top),meet(X_53,X_53)) != join(zero,meet(X_53,X_53))
| join(zero,meet(X_53,X_53)) != X_53
| join(complement(top),meet(X_53,X_53)) = X_53 ),
inference(subst,[],[refute_0_100:[bind(X,$fot(join(complement(top),meet(X_53,X_53)))),bind(Y,$fot(join(zero,meet(X_53,X_53)))),bind(Z,$fot(X_53))]]) ).
cnf(refute_0_279,plain,
( join(zero,meet(X_53,X_53)) != X_53
| join(complement(top),meet(X_53,X_53)) = X_53 ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_53,X_53)),join(zero,meet(X_53,X_53))) )],[refute_0_277,refute_0_278]) ).
cnf(refute_0_280,plain,
join(complement(top),meet(X_53,X_53)) = X_53,
inference(resolve,[$cnf( $equal(join(zero,meet(X_53,X_53)),X_53) )],[refute_0_273,refute_0_279]) ).
cnf(refute_0_281,plain,
complement(join(complement(top),meet(X_53,X_53))) = complement(join(complement(top),meet(X_53,X_53))),
introduced(tautology,[refl,[$fot(complement(join(complement(top),meet(X_53,X_53))))]]) ).
cnf(refute_0_282,plain,
( complement(join(complement(top),meet(X_53,X_53))) != complement(join(complement(top),meet(X_53,X_53)))
| join(complement(top),meet(X_53,X_53)) != X_53
| complement(join(complement(top),meet(X_53,X_53))) = complement(X_53) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(top),meet(X_53,X_53))),complement(join(complement(top),meet(X_53,X_53)))) ),[1,0],$fot(X_53)]]) ).
cnf(refute_0_283,plain,
( join(complement(top),meet(X_53,X_53)) != X_53
| complement(join(complement(top),meet(X_53,X_53))) = complement(X_53) ),
inference(resolve,[$cnf( $equal(complement(join(complement(top),meet(X_53,X_53))),complement(join(complement(top),meet(X_53,X_53)))) )],[refute_0_281,refute_0_282]) ).
cnf(refute_0_284,plain,
complement(join(complement(top),meet(X_53,X_53))) = complement(X_53),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_53,X_53)),X_53) )],[refute_0_280,refute_0_283]) ).
cnf(refute_0_285,plain,
meet(X0,join(complement(X_8),complement(X_9))) = complement(join(complement(X0),complement(join(complement(X_8),complement(X_9))))),
inference(subst,[],[refute_0_61:[bind(X1,$fot(join(complement(X_8),complement(X_9))))]]) ).
cnf(refute_0_286,plain,
( complement(join(complement(X_8),complement(X_9))) != meet(X_8,X_9)
| meet(X0,join(complement(X_8),complement(X_9))) != complement(join(complement(X0),complement(join(complement(X_8),complement(X_9)))))
| meet(X0,join(complement(X_8),complement(X_9))) = complement(join(complement(X0),meet(X_8,X_9))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X0,join(complement(X_8),complement(X_9))),complement(join(complement(X0),complement(join(complement(X_8),complement(X_9)))))) ),[1,0,1],$fot(meet(X_8,X_9))]]) ).
cnf(refute_0_287,plain,
( meet(X0,join(complement(X_8),complement(X_9))) != complement(join(complement(X0),complement(join(complement(X_8),complement(X_9)))))
| meet(X0,join(complement(X_8),complement(X_9))) = complement(join(complement(X0),meet(X_8,X_9))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_8),complement(X_9))),meet(X_8,X_9)) )],[refute_0_64,refute_0_286]) ).
cnf(refute_0_288,plain,
meet(X0,join(complement(X_8),complement(X_9))) = complement(join(complement(X0),meet(X_8,X_9))),
inference(resolve,[$cnf( $equal(meet(X0,join(complement(X_8),complement(X_9))),complement(join(complement(X0),complement(join(complement(X_8),complement(X_9)))))) )],[refute_0_285,refute_0_287]) ).
cnf(refute_0_289,plain,
meet(top,join(complement(X_53),complement(X_53))) = complement(join(complement(top),meet(X_53,X_53))),
inference(subst,[],[refute_0_288:[bind(X0,$fot(top)),bind(X_8,$fot(X_53)),bind(X_9,$fot(X_53))]]) ).
cnf(refute_0_290,plain,
( complement(join(complement(top),meet(X_53,X_53))) != complement(X_53)
| meet(top,join(complement(X_53),complement(X_53))) != complement(join(complement(top),meet(X_53,X_53)))
| meet(top,join(complement(X_53),complement(X_53))) = complement(X_53) ),
inference(subst,[],[refute_0_100:[bind(X,$fot(meet(top,join(complement(X_53),complement(X_53))))),bind(Y,$fot(complement(join(complement(top),meet(X_53,X_53))))),bind(Z,$fot(complement(X_53)))]]) ).
cnf(refute_0_291,plain,
( complement(join(complement(top),meet(X_53,X_53))) != complement(X_53)
| meet(top,join(complement(X_53),complement(X_53))) = complement(X_53) ),
inference(resolve,[$cnf( $equal(meet(top,join(complement(X_53),complement(X_53))),complement(join(complement(top),meet(X_53,X_53)))) )],[refute_0_289,refute_0_290]) ).
cnf(refute_0_292,plain,
meet(top,join(complement(X_53),complement(X_53))) = complement(X_53),
inference(resolve,[$cnf( $equal(complement(join(complement(top),meet(X_53,X_53))),complement(X_53)) )],[refute_0_284,refute_0_291]) ).
cnf(refute_0_293,plain,
complement(meet(top,join(complement(X_53),complement(X_53)))) = complement(meet(top,join(complement(X_53),complement(X_53)))),
introduced(tautology,[refl,[$fot(complement(meet(top,join(complement(X_53),complement(X_53)))))]]) ).
cnf(refute_0_294,plain,
( complement(meet(top,join(complement(X_53),complement(X_53)))) != complement(meet(top,join(complement(X_53),complement(X_53))))
| meet(top,join(complement(X_53),complement(X_53))) != complement(X_53)
| complement(meet(top,join(complement(X_53),complement(X_53)))) = complement(complement(X_53)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(meet(top,join(complement(X_53),complement(X_53)))),complement(meet(top,join(complement(X_53),complement(X_53))))) ),[1,0],$fot(complement(X_53))]]) ).
cnf(refute_0_295,plain,
( meet(top,join(complement(X_53),complement(X_53))) != complement(X_53)
| complement(meet(top,join(complement(X_53),complement(X_53)))) = complement(complement(X_53)) ),
inference(resolve,[$cnf( $equal(complement(meet(top,join(complement(X_53),complement(X_53)))),complement(meet(top,join(complement(X_53),complement(X_53))))) )],[refute_0_293,refute_0_294]) ).
cnf(refute_0_296,plain,
complement(meet(top,join(complement(X_53),complement(X_53)))) = complement(complement(X_53)),
inference(resolve,[$cnf( $equal(meet(top,join(complement(X_53),complement(X_53))),complement(X_53)) )],[refute_0_292,refute_0_295]) ).
cnf(refute_0_297,plain,
meet(top,X_19) = join(meet(meet(top,X_19),join(zero,complement(X_19))),complement(join(complement(meet(top,X_19)),join(zero,complement(X_19))))),
inference(subst,[],[refute_0_176:[bind(X0,$fot(meet(top,X_19))),bind(X1,$fot(join(zero,complement(X_19))))]]) ).
cnf(refute_0_298,plain,
zero = meet(join(zero,complement(X_19)),complement(join(zero,complement(X_19)))),
inference(subst,[],[refute_0_82:[bind(X0,$fot(join(zero,complement(X_19))))]]) ).
cnf(refute_0_299,plain,
meet(top,X1) = complement(join(complement(top),complement(X1))),
inference(subst,[],[refute_0_61:[bind(X0,$fot(top))]]) ).
cnf(refute_0_300,plain,
( complement(top) != zero
| meet(top,X1) != complement(join(complement(top),complement(X1)))
| meet(top,X1) = complement(join(zero,complement(X1))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,X1),complement(join(complement(top),complement(X1)))) ),[1,0,0],$fot(zero)]]) ).
cnf(refute_0_301,plain,
( meet(top,X1) != complement(join(complement(top),complement(X1)))
| meet(top,X1) = complement(join(zero,complement(X1))) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_108,refute_0_300]) ).
cnf(refute_0_302,plain,
meet(top,X1) = complement(join(zero,complement(X1))),
inference(resolve,[$cnf( $equal(meet(top,X1),complement(join(complement(top),complement(X1)))) )],[refute_0_299,refute_0_301]) ).
cnf(refute_0_303,plain,
meet(top,X_19) = complement(join(zero,complement(X_19))),
inference(subst,[],[refute_0_302:[bind(X1,$fot(X_19))]]) ).
cnf(refute_0_304,plain,
( meet(top,X_19) != complement(join(zero,complement(X_19)))
| complement(join(zero,complement(X_19))) = meet(top,X_19) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(meet(top,X_19))),bind(Y,$fot(complement(join(zero,complement(X_19)))))]]) ).
cnf(refute_0_305,plain,
complement(join(zero,complement(X_19))) = meet(top,X_19),
inference(resolve,[$cnf( $equal(meet(top,X_19),complement(join(zero,complement(X_19)))) )],[refute_0_303,refute_0_304]) ).
cnf(refute_0_306,plain,
( complement(join(zero,complement(X_19))) != meet(top,X_19)
| zero != meet(join(zero,complement(X_19)),complement(join(zero,complement(X_19))))
| zero = meet(join(zero,complement(X_19)),meet(top,X_19)) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(join(zero,complement(X_19)),complement(join(zero,complement(X_19))))) ),[1,1],$fot(meet(top,X_19))]]) ).
cnf(refute_0_307,plain,
( zero != meet(join(zero,complement(X_19)),complement(join(zero,complement(X_19))))
| zero = meet(join(zero,complement(X_19)),meet(top,X_19)) ),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(X_19))),meet(top,X_19)) )],[refute_0_305,refute_0_306]) ).
cnf(refute_0_308,plain,
zero = meet(join(zero,complement(X_19)),meet(top,X_19)),
inference(resolve,[$cnf( $equal(zero,meet(join(zero,complement(X_19)),complement(join(zero,complement(X_19))))) )],[refute_0_298,refute_0_307]) ).
cnf(refute_0_309,plain,
join(complement(X_9),complement(X_8)) = join(complement(X_8),complement(X_9)),
inference(subst,[],[refute_0_4:[bind(X0,$fot(complement(X_9))),bind(X1,$fot(complement(X_8)))]]) ).
cnf(refute_0_310,plain,
( join(complement(X_9),complement(X_8)) != join(complement(X_8),complement(X_9))
| join(complement(X_8),complement(X_9)) = join(complement(X_9),complement(X_8)) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(complement(X_9),complement(X_8)))),bind(Y,$fot(join(complement(X_8),complement(X_9))))]]) ).
cnf(refute_0_311,plain,
join(complement(X_8),complement(X_9)) = join(complement(X_9),complement(X_8)),
inference(resolve,[$cnf( $equal(join(complement(X_9),complement(X_8)),join(complement(X_8),complement(X_9))) )],[refute_0_309,refute_0_310]) ).
cnf(refute_0_312,plain,
( join(complement(X_8),complement(X_9)) != join(complement(X_9),complement(X_8))
| meet(X_8,X_9) != complement(join(complement(X_8),complement(X_9)))
| meet(X_8,X_9) = complement(join(complement(X_9),complement(X_8))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_8,X_9),complement(join(complement(X_8),complement(X_9)))) ),[1,0],$fot(join(complement(X_9),complement(X_8)))]]) ).
cnf(refute_0_313,plain,
( meet(X_8,X_9) != complement(join(complement(X_8),complement(X_9)))
| meet(X_8,X_9) = complement(join(complement(X_9),complement(X_8))) ),
inference(resolve,[$cnf( $equal(join(complement(X_8),complement(X_9)),join(complement(X_9),complement(X_8))) )],[refute_0_311,refute_0_312]) ).
cnf(refute_0_314,plain,
meet(X_8,X_9) = complement(join(complement(X_9),complement(X_8))),
inference(resolve,[$cnf( $equal(meet(X_8,X_9),complement(join(complement(X_8),complement(X_9)))) )],[refute_0_62,refute_0_313]) ).
cnf(refute_0_315,plain,
complement(join(complement(X_9),complement(X_8))) = meet(X_9,X_8),
inference(subst,[],[refute_0_166:[bind(X0,$fot(X_9)),bind(X1,$fot(X_8))]]) ).
cnf(refute_0_316,plain,
( complement(join(complement(X_9),complement(X_8))) != meet(X_9,X_8)
| meet(X_8,X_9) != complement(join(complement(X_9),complement(X_8)))
| meet(X_8,X_9) = meet(X_9,X_8) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_8,X_9),complement(join(complement(X_9),complement(X_8)))) ),[1],$fot(meet(X_9,X_8))]]) ).
cnf(refute_0_317,plain,
( meet(X_8,X_9) != complement(join(complement(X_9),complement(X_8)))
| meet(X_8,X_9) = meet(X_9,X_8) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_9),complement(X_8))),meet(X_9,X_8)) )],[refute_0_315,refute_0_316]) ).
cnf(refute_0_318,plain,
meet(X_8,X_9) = meet(X_9,X_8),
inference(resolve,[$cnf( $equal(meet(X_8,X_9),complement(join(complement(X_9),complement(X_8)))) )],[refute_0_314,refute_0_317]) ).
cnf(refute_0_319,plain,
( meet(X_8,X_9) != meet(X_9,X_8)
| meet(X_9,X_8) = meet(X_8,X_9) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(meet(X_8,X_9))),bind(Y,$fot(meet(X_9,X_8)))]]) ).
cnf(refute_0_320,plain,
meet(X_9,X_8) = meet(X_8,X_9),
inference(resolve,[$cnf( $equal(meet(X_8,X_9),meet(X_9,X_8)) )],[refute_0_318,refute_0_319]) ).
cnf(refute_0_321,plain,
meet(join(zero,complement(X_19)),meet(top,X_19)) = meet(meet(top,X_19),join(zero,complement(X_19))),
inference(subst,[],[refute_0_320:[bind(X_8,$fot(meet(top,X_19))),bind(X_9,$fot(join(zero,complement(X_19))))]]) ).
cnf(refute_0_322,plain,
( meet(join(zero,complement(X_19)),meet(top,X_19)) != meet(meet(top,X_19),join(zero,complement(X_19)))
| zero != meet(join(zero,complement(X_19)),meet(top,X_19))
| zero = meet(meet(top,X_19),join(zero,complement(X_19))) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(join(zero,complement(X_19)),meet(top,X_19))) ),[1],$fot(meet(meet(top,X_19),join(zero,complement(X_19))))]]) ).
cnf(refute_0_323,plain,
( zero != meet(join(zero,complement(X_19)),meet(top,X_19))
| zero = meet(meet(top,X_19),join(zero,complement(X_19))) ),
inference(resolve,[$cnf( $equal(meet(join(zero,complement(X_19)),meet(top,X_19)),meet(meet(top,X_19),join(zero,complement(X_19)))) )],[refute_0_321,refute_0_322]) ).
cnf(refute_0_324,plain,
zero = meet(meet(top,X_19),join(zero,complement(X_19))),
inference(resolve,[$cnf( $equal(zero,meet(join(zero,complement(X_19)),meet(top,X_19))) )],[refute_0_308,refute_0_323]) ).
cnf(refute_0_325,plain,
( zero != meet(meet(top,X_19),join(zero,complement(X_19)))
| meet(meet(top,X_19),join(zero,complement(X_19))) = zero ),
inference(subst,[],[refute_0_7:[bind(X,$fot(zero)),bind(Y,$fot(meet(meet(top,X_19),join(zero,complement(X_19)))))]]) ).
cnf(refute_0_326,plain,
meet(meet(top,X_19),join(zero,complement(X_19))) = zero,
inference(resolve,[$cnf( $equal(zero,meet(meet(top,X_19),join(zero,complement(X_19)))) )],[refute_0_324,refute_0_325]) ).
cnf(refute_0_327,plain,
( meet(meet(top,X_19),join(zero,complement(X_19))) != zero
| meet(top,X_19) != join(meet(meet(top,X_19),join(zero,complement(X_19))),complement(join(complement(meet(top,X_19)),join(zero,complement(X_19)))))
| meet(top,X_19) = join(zero,complement(join(complement(meet(top,X_19)),join(zero,complement(X_19))))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,X_19),join(meet(meet(top,X_19),join(zero,complement(X_19))),complement(join(complement(meet(top,X_19)),join(zero,complement(X_19)))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_328,plain,
( meet(top,X_19) != join(meet(meet(top,X_19),join(zero,complement(X_19))),complement(join(complement(meet(top,X_19)),join(zero,complement(X_19)))))
| meet(top,X_19) = join(zero,complement(join(complement(meet(top,X_19)),join(zero,complement(X_19))))) ),
inference(resolve,[$cnf( $equal(meet(meet(top,X_19),join(zero,complement(X_19))),zero) )],[refute_0_326,refute_0_327]) ).
cnf(refute_0_329,plain,
meet(top,X_19) = join(zero,complement(join(complement(meet(top,X_19)),join(zero,complement(X_19))))),
inference(resolve,[$cnf( $equal(meet(top,X_19),join(meet(meet(top,X_19),join(zero,complement(X_19))),complement(join(complement(meet(top,X_19)),join(zero,complement(X_19)))))) )],[refute_0_297,refute_0_328]) ).
cnf(refute_0_330,plain,
meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19)))) = join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),join(zero,complement(join(complement(meet(top,X_19)),join(zero,complement(X_19)))))))),
inference(subst,[],[refute_0_329:[bind(X_19,$fot(join(complement(meet(top,X_19)),join(zero,complement(X_19)))))]]) ).
cnf(refute_0_331,plain,
( meet(top,X_19) != join(zero,complement(join(complement(meet(top,X_19)),join(zero,complement(X_19)))))
| join(zero,complement(join(complement(meet(top,X_19)),join(zero,complement(X_19))))) = meet(top,X_19) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(meet(top,X_19))),bind(Y,$fot(join(zero,complement(join(complement(meet(top,X_19)),join(zero,complement(X_19)))))))]]) ).
cnf(refute_0_332,plain,
join(zero,complement(join(complement(meet(top,X_19)),join(zero,complement(X_19))))) = meet(top,X_19),
inference(resolve,[$cnf( $equal(meet(top,X_19),join(zero,complement(join(complement(meet(top,X_19)),join(zero,complement(X_19)))))) )],[refute_0_329,refute_0_331]) ).
cnf(refute_0_333,plain,
( join(zero,complement(join(complement(meet(top,X_19)),join(zero,complement(X_19))))) != meet(top,X_19)
| meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19)))) != join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),join(zero,complement(join(complement(meet(top,X_19)),join(zero,complement(X_19))))))))
| meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19)))) = join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(top,X_19)))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19)))),join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),join(zero,complement(join(complement(meet(top,X_19)),join(zero,complement(X_19))))))))) ),[1,1,0,1],$fot(meet(top,X_19))]]) ).
cnf(refute_0_334,plain,
( meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19)))) != join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),join(zero,complement(join(complement(meet(top,X_19)),join(zero,complement(X_19))))))))
| meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19)))) = join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(top,X_19)))) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(top,X_19)) )],[refute_0_332,refute_0_333]) ).
cnf(refute_0_335,plain,
meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19)))) = join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(top,X_19)))),
inference(resolve,[$cnf( $equal(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19)))),join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),join(zero,complement(join(complement(meet(top,X_19)),join(zero,complement(X_19))))))))) )],[refute_0_330,refute_0_334]) ).
cnf(refute_0_336,plain,
meet(top,join(complement(meet(top,X_46)),join(zero,complement(X_46)))) = complement(join(zero,complement(join(complement(meet(top,X_46)),join(zero,complement(X_46)))))),
inference(subst,[],[refute_0_302:[bind(X1,$fot(join(complement(meet(top,X_46)),join(zero,complement(X_46)))))]]) ).
cnf(refute_0_337,plain,
meet(top,X_46) = join(zero,complement(join(complement(meet(top,X_46)),join(zero,complement(X_46))))),
inference(subst,[],[refute_0_329:[bind(X_19,$fot(X_46))]]) ).
cnf(refute_0_338,plain,
( meet(top,X_46) != join(zero,complement(join(complement(meet(top,X_46)),join(zero,complement(X_46)))))
| join(zero,complement(join(complement(meet(top,X_46)),join(zero,complement(X_46))))) = meet(top,X_46) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(meet(top,X_46))),bind(Y,$fot(join(zero,complement(join(complement(meet(top,X_46)),join(zero,complement(X_46)))))))]]) ).
cnf(refute_0_339,plain,
join(zero,complement(join(complement(meet(top,X_46)),join(zero,complement(X_46))))) = meet(top,X_46),
inference(resolve,[$cnf( $equal(meet(top,X_46),join(zero,complement(join(complement(meet(top,X_46)),join(zero,complement(X_46)))))) )],[refute_0_337,refute_0_338]) ).
cnf(refute_0_340,plain,
( join(zero,complement(join(complement(meet(top,X_46)),join(zero,complement(X_46))))) != meet(top,X_46)
| meet(top,join(complement(meet(top,X_46)),join(zero,complement(X_46)))) != complement(join(zero,complement(join(complement(meet(top,X_46)),join(zero,complement(X_46))))))
| meet(top,join(complement(meet(top,X_46)),join(zero,complement(X_46)))) = complement(meet(top,X_46)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,join(complement(meet(top,X_46)),join(zero,complement(X_46)))),complement(join(zero,complement(join(complement(meet(top,X_46)),join(zero,complement(X_46))))))) ),[1,0],$fot(meet(top,X_46))]]) ).
cnf(refute_0_341,plain,
( meet(top,join(complement(meet(top,X_46)),join(zero,complement(X_46)))) != complement(join(zero,complement(join(complement(meet(top,X_46)),join(zero,complement(X_46))))))
| meet(top,join(complement(meet(top,X_46)),join(zero,complement(X_46)))) = complement(meet(top,X_46)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(complement(meet(top,X_46)),join(zero,complement(X_46))))),meet(top,X_46)) )],[refute_0_339,refute_0_340]) ).
cnf(refute_0_342,plain,
meet(top,join(complement(meet(top,X_46)),join(zero,complement(X_46)))) = complement(meet(top,X_46)),
inference(resolve,[$cnf( $equal(meet(top,join(complement(meet(top,X_46)),join(zero,complement(X_46)))),complement(join(zero,complement(join(complement(meet(top,X_46)),join(zero,complement(X_46))))))) )],[refute_0_336,refute_0_341]) ).
cnf(refute_0_343,plain,
meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19)))) = complement(meet(top,X_19)),
inference(subst,[],[refute_0_342:[bind(X_46,$fot(X_19))]]) ).
cnf(refute_0_344,plain,
( meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19)))) != complement(meet(top,X_19))
| meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19)))) != join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(top,X_19))))
| complement(meet(top,X_19)) = join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(top,X_19)))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19)))),join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(top,X_19))))) ),[0],$fot(complement(meet(top,X_19)))]]) ).
cnf(refute_0_345,plain,
( meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19)))) != join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(top,X_19))))
| complement(meet(top,X_19)) = join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(top,X_19)))) ),
inference(resolve,[$cnf( $equal(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19)))),complement(meet(top,X_19))) )],[refute_0_343,refute_0_344]) ).
cnf(refute_0_346,plain,
X_31 = join(meet(X_31,complement(complement(X_31))),complement(join(complement(X_31),complement(complement(X_31))))),
inference(subst,[],[refute_0_176:[bind(X0,$fot(X_31)),bind(X1,$fot(complement(complement(X_31))))]]) ).
cnf(refute_0_347,plain,
top = join(complement(X_31),complement(complement(X_31))),
inference(subst,[],[refute_0_59:[bind(X0,$fot(complement(X_31)))]]) ).
cnf(refute_0_348,plain,
( top != join(complement(X_31),complement(complement(X_31)))
| join(complement(X_31),complement(complement(X_31))) = top ),
inference(subst,[],[refute_0_7:[bind(X,$fot(top)),bind(Y,$fot(join(complement(X_31),complement(complement(X_31)))))]]) ).
cnf(refute_0_349,plain,
join(complement(X_31),complement(complement(X_31))) = top,
inference(resolve,[$cnf( $equal(top,join(complement(X_31),complement(complement(X_31)))) )],[refute_0_347,refute_0_348]) ).
cnf(refute_0_350,plain,
( X_31 != join(meet(X_31,complement(complement(X_31))),complement(join(complement(X_31),complement(complement(X_31)))))
| join(complement(X_31),complement(complement(X_31))) != top
| X_31 = join(meet(X_31,complement(complement(X_31))),complement(top)) ),
introduced(tautology,[equality,[$cnf( $equal(X_31,join(meet(X_31,complement(complement(X_31))),complement(join(complement(X_31),complement(complement(X_31)))))) ),[1,1,0],$fot(top)]]) ).
cnf(refute_0_351,plain,
( X_31 != join(meet(X_31,complement(complement(X_31))),complement(join(complement(X_31),complement(complement(X_31)))))
| X_31 = join(meet(X_31,complement(complement(X_31))),complement(top)) ),
inference(resolve,[$cnf( $equal(join(complement(X_31),complement(complement(X_31))),top) )],[refute_0_349,refute_0_350]) ).
cnf(refute_0_352,plain,
X_31 = join(meet(X_31,complement(complement(X_31))),complement(top)),
inference(resolve,[$cnf( $equal(X_31,join(meet(X_31,complement(complement(X_31))),complement(join(complement(X_31),complement(complement(X_31)))))) )],[refute_0_346,refute_0_351]) ).
cnf(refute_0_353,plain,
join(complement(top),meet(X_31,complement(complement(X_31)))) = join(complement(top),meet(X_31,complement(complement(X_31)))),
introduced(tautology,[refl,[$fot(join(complement(top),meet(X_31,complement(complement(X_31)))))]]) ).
cnf(refute_0_354,plain,
( complement(top) != zero
| join(complement(top),meet(X_31,complement(complement(X_31)))) != join(complement(top),meet(X_31,complement(complement(X_31))))
| join(complement(top),meet(X_31,complement(complement(X_31)))) = join(zero,meet(X_31,complement(complement(X_31)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(X_31,complement(complement(X_31)))),join(complement(top),meet(X_31,complement(complement(X_31))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_355,plain,
( complement(top) != zero
| join(complement(top),meet(X_31,complement(complement(X_31)))) = join(zero,meet(X_31,complement(complement(X_31)))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_31,complement(complement(X_31)))),join(complement(top),meet(X_31,complement(complement(X_31))))) )],[refute_0_353,refute_0_354]) ).
cnf(refute_0_356,plain,
join(complement(top),meet(X_31,complement(complement(X_31)))) = join(zero,meet(X_31,complement(complement(X_31)))),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_108,refute_0_355]) ).
cnf(refute_0_357,plain,
join(meet(X_31,complement(complement(X_31))),complement(top)) = join(complement(top),meet(X_31,complement(complement(X_31)))),
inference(subst,[],[refute_0_9:[bind(X0,$fot(complement(top))),bind(X1,$fot(meet(X_31,complement(complement(X_31)))))]]) ).
cnf(refute_0_358,plain,
( join(complement(top),meet(X_31,complement(complement(X_31)))) != join(zero,meet(X_31,complement(complement(X_31))))
| join(meet(X_31,complement(complement(X_31))),complement(top)) != join(complement(top),meet(X_31,complement(complement(X_31))))
| join(meet(X_31,complement(complement(X_31))),complement(top)) = join(zero,meet(X_31,complement(complement(X_31)))) ),
inference(subst,[],[refute_0_100:[bind(X,$fot(join(meet(X_31,complement(complement(X_31))),complement(top)))),bind(Y,$fot(join(complement(top),meet(X_31,complement(complement(X_31)))))),bind(Z,$fot(join(zero,meet(X_31,complement(complement(X_31))))))]]) ).
cnf(refute_0_359,plain,
( join(complement(top),meet(X_31,complement(complement(X_31)))) != join(zero,meet(X_31,complement(complement(X_31))))
| join(meet(X_31,complement(complement(X_31))),complement(top)) = join(zero,meet(X_31,complement(complement(X_31)))) ),
inference(resolve,[$cnf( $equal(join(meet(X_31,complement(complement(X_31))),complement(top)),join(complement(top),meet(X_31,complement(complement(X_31))))) )],[refute_0_357,refute_0_358]) ).
cnf(refute_0_360,plain,
join(meet(X_31,complement(complement(X_31))),complement(top)) = join(zero,meet(X_31,complement(complement(X_31)))),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_31,complement(complement(X_31)))),join(zero,meet(X_31,complement(complement(X_31))))) )],[refute_0_356,refute_0_359]) ).
cnf(refute_0_361,plain,
( X_31 != join(meet(X_31,complement(complement(X_31))),complement(top))
| join(meet(X_31,complement(complement(X_31))),complement(top)) != join(zero,meet(X_31,complement(complement(X_31))))
| X_31 = join(zero,meet(X_31,complement(complement(X_31)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_31,join(zero,meet(X_31,complement(complement(X_31))))) ),[0],$fot(join(meet(X_31,complement(complement(X_31))),complement(top)))]]) ).
cnf(refute_0_362,plain,
( X_31 != join(meet(X_31,complement(complement(X_31))),complement(top))
| X_31 = join(zero,meet(X_31,complement(complement(X_31)))) ),
inference(resolve,[$cnf( $equal(join(meet(X_31,complement(complement(X_31))),complement(top)),join(zero,meet(X_31,complement(complement(X_31))))) )],[refute_0_360,refute_0_361]) ).
cnf(refute_0_363,plain,
X_31 = join(zero,meet(X_31,complement(complement(X_31)))),
inference(resolve,[$cnf( $equal(X_31,join(meet(X_31,complement(complement(X_31))),complement(top))) )],[refute_0_352,refute_0_362]) ).
cnf(refute_0_364,plain,
join(zero,complement(X1)) = join(zero,meet(join(zero,complement(X1)),complement(complement(join(zero,complement(X1)))))),
inference(subst,[],[refute_0_363:[bind(X_31,$fot(join(zero,complement(X1))))]]) ).
cnf(refute_0_365,plain,
( meet(top,X1) != complement(join(zero,complement(X1)))
| complement(join(zero,complement(X1))) = meet(top,X1) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(meet(top,X1))),bind(Y,$fot(complement(join(zero,complement(X1)))))]]) ).
cnf(refute_0_366,plain,
complement(join(zero,complement(X1))) = meet(top,X1),
inference(resolve,[$cnf( $equal(meet(top,X1),complement(join(zero,complement(X1)))) )],[refute_0_302,refute_0_365]) ).
cnf(refute_0_367,plain,
( complement(join(zero,complement(X1))) != meet(top,X1)
| join(zero,complement(X1)) != join(zero,meet(join(zero,complement(X1)),complement(complement(join(zero,complement(X1))))))
| join(zero,complement(X1)) = join(zero,meet(join(zero,complement(X1)),complement(meet(top,X1)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(X1)),join(zero,meet(join(zero,complement(X1)),complement(complement(join(zero,complement(X1))))))) ),[1,1,1,0],$fot(meet(top,X1))]]) ).
cnf(refute_0_368,plain,
( join(zero,complement(X1)) != join(zero,meet(join(zero,complement(X1)),complement(complement(join(zero,complement(X1))))))
| join(zero,complement(X1)) = join(zero,meet(join(zero,complement(X1)),complement(meet(top,X1)))) ),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(X1))),meet(top,X1)) )],[refute_0_366,refute_0_367]) ).
cnf(refute_0_369,plain,
join(zero,complement(X1)) = join(zero,meet(join(zero,complement(X1)),complement(meet(top,X1)))),
inference(resolve,[$cnf( $equal(join(zero,complement(X1)),join(zero,meet(join(zero,complement(X1)),complement(complement(join(zero,complement(X1))))))) )],[refute_0_364,refute_0_368]) ).
cnf(refute_0_370,plain,
meet(join(zero,complement(X1)),complement(meet(top,X1))) = meet(complement(meet(top,X1)),join(zero,complement(X1))),
inference(subst,[],[refute_0_320:[bind(X_8,$fot(complement(meet(top,X1)))),bind(X_9,$fot(join(zero,complement(X1))))]]) ).
cnf(refute_0_371,plain,
join(zero,meet(join(zero,complement(X1)),complement(meet(top,X1)))) = join(zero,meet(join(zero,complement(X1)),complement(meet(top,X1)))),
introduced(tautology,[refl,[$fot(join(zero,meet(join(zero,complement(X1)),complement(meet(top,X1)))))]]) ).
cnf(refute_0_372,plain,
( join(zero,meet(join(zero,complement(X1)),complement(meet(top,X1)))) != join(zero,meet(join(zero,complement(X1)),complement(meet(top,X1))))
| meet(join(zero,complement(X1)),complement(meet(top,X1))) != meet(complement(meet(top,X1)),join(zero,complement(X1)))
| join(zero,meet(join(zero,complement(X1)),complement(meet(top,X1)))) = join(zero,meet(complement(meet(top,X1)),join(zero,complement(X1)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,meet(join(zero,complement(X1)),complement(meet(top,X1)))),join(zero,meet(join(zero,complement(X1)),complement(meet(top,X1))))) ),[1,1],$fot(meet(complement(meet(top,X1)),join(zero,complement(X1))))]]) ).
cnf(refute_0_373,plain,
( meet(join(zero,complement(X1)),complement(meet(top,X1))) != meet(complement(meet(top,X1)),join(zero,complement(X1)))
| join(zero,meet(join(zero,complement(X1)),complement(meet(top,X1)))) = join(zero,meet(complement(meet(top,X1)),join(zero,complement(X1)))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(join(zero,complement(X1)),complement(meet(top,X1)))),join(zero,meet(join(zero,complement(X1)),complement(meet(top,X1))))) )],[refute_0_371,refute_0_372]) ).
cnf(refute_0_374,plain,
join(zero,meet(join(zero,complement(X1)),complement(meet(top,X1)))) = join(zero,meet(complement(meet(top,X1)),join(zero,complement(X1)))),
inference(resolve,[$cnf( $equal(meet(join(zero,complement(X1)),complement(meet(top,X1))),meet(complement(meet(top,X1)),join(zero,complement(X1)))) )],[refute_0_370,refute_0_373]) ).
cnf(refute_0_375,plain,
( join(zero,complement(X1)) != join(zero,meet(join(zero,complement(X1)),complement(meet(top,X1))))
| join(zero,meet(join(zero,complement(X1)),complement(meet(top,X1)))) != join(zero,meet(complement(meet(top,X1)),join(zero,complement(X1))))
| join(zero,complement(X1)) = join(zero,meet(complement(meet(top,X1)),join(zero,complement(X1)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(zero,complement(X1)),join(zero,meet(complement(meet(top,X1)),join(zero,complement(X1))))) ),[0],$fot(join(zero,meet(join(zero,complement(X1)),complement(meet(top,X1)))))]]) ).
cnf(refute_0_376,plain,
( join(zero,complement(X1)) != join(zero,meet(join(zero,complement(X1)),complement(meet(top,X1))))
| join(zero,complement(X1)) = join(zero,meet(complement(meet(top,X1)),join(zero,complement(X1)))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(join(zero,complement(X1)),complement(meet(top,X1)))),join(zero,meet(complement(meet(top,X1)),join(zero,complement(X1))))) )],[refute_0_374,refute_0_375]) ).
cnf(refute_0_377,plain,
join(zero,complement(X1)) = join(zero,meet(complement(meet(top,X1)),join(zero,complement(X1)))),
inference(resolve,[$cnf( $equal(join(zero,complement(X1)),join(zero,meet(join(zero,complement(X1)),complement(meet(top,X1))))) )],[refute_0_369,refute_0_376]) ).
cnf(refute_0_378,plain,
( join(zero,complement(X1)) != join(zero,meet(complement(meet(top,X1)),join(zero,complement(X1))))
| join(zero,meet(complement(meet(top,X1)),join(zero,complement(X1)))) = join(zero,complement(X1)) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(zero,complement(X1)))),bind(Y,$fot(join(zero,meet(complement(meet(top,X1)),join(zero,complement(X1))))))]]) ).
cnf(refute_0_379,plain,
join(zero,meet(complement(meet(top,X1)),join(zero,complement(X1)))) = join(zero,complement(X1)),
inference(resolve,[$cnf( $equal(join(zero,complement(X1)),join(zero,meet(complement(meet(top,X1)),join(zero,complement(X1))))) )],[refute_0_377,refute_0_378]) ).
cnf(refute_0_380,plain,
join(zero,meet(complement(meet(top,X_19)),join(zero,complement(X_19)))) = join(zero,complement(X_19)),
inference(subst,[],[refute_0_379:[bind(X1,$fot(X_19))]]) ).
cnf(refute_0_381,plain,
meet(join(zero,complement(X_19)),complement(meet(top,X_19))) = meet(complement(meet(top,X_19)),join(zero,complement(X_19))),
inference(subst,[],[refute_0_320:[bind(X_8,$fot(complement(meet(top,X_19)))),bind(X_9,$fot(join(zero,complement(X_19))))]]) ).
cnf(refute_0_382,plain,
meet(join(zero,complement(X_19)),meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))) = meet(join(zero,complement(X_19)),meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),
introduced(tautology,[refl,[$fot(meet(join(zero,complement(X_19)),meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))))]]) ).
cnf(refute_0_383,plain,
( meet(join(zero,complement(X_19)),meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))) != meet(join(zero,complement(X_19)),meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19)))))
| meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19)))) != complement(meet(top,X_19))
| meet(join(zero,complement(X_19)),meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))) = meet(join(zero,complement(X_19)),complement(meet(top,X_19))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(zero,complement(X_19)),meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(join(zero,complement(X_19)),meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19)))))) ),[1,1],$fot(complement(meet(top,X_19)))]]) ).
cnf(refute_0_384,plain,
( meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19)))) != complement(meet(top,X_19))
| meet(join(zero,complement(X_19)),meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))) = meet(join(zero,complement(X_19)),complement(meet(top,X_19))) ),
inference(resolve,[$cnf( $equal(meet(join(zero,complement(X_19)),meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(join(zero,complement(X_19)),meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19)))))) )],[refute_0_382,refute_0_383]) ).
cnf(refute_0_385,plain,
meet(join(zero,complement(X_19)),meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))) = meet(join(zero,complement(X_19)),complement(meet(top,X_19))),
inference(resolve,[$cnf( $equal(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19)))),complement(meet(top,X_19))) )],[refute_0_343,refute_0_384]) ).
cnf(refute_0_386,plain,
( meet(join(zero,complement(X_19)),complement(meet(top,X_19))) != meet(complement(meet(top,X_19)),join(zero,complement(X_19)))
| meet(join(zero,complement(X_19)),meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))) != meet(join(zero,complement(X_19)),complement(meet(top,X_19)))
| meet(join(zero,complement(X_19)),meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))) = meet(complement(meet(top,X_19)),join(zero,complement(X_19))) ),
inference(subst,[],[refute_0_100:[bind(X,$fot(meet(join(zero,complement(X_19)),meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))))),bind(Y,$fot(meet(join(zero,complement(X_19)),complement(meet(top,X_19))))),bind(Z,$fot(meet(complement(meet(top,X_19)),join(zero,complement(X_19)))))]]) ).
cnf(refute_0_387,plain,
( meet(join(zero,complement(X_19)),complement(meet(top,X_19))) != meet(complement(meet(top,X_19)),join(zero,complement(X_19)))
| meet(join(zero,complement(X_19)),meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))) = meet(complement(meet(top,X_19)),join(zero,complement(X_19))) ),
inference(resolve,[$cnf( $equal(meet(join(zero,complement(X_19)),meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(join(zero,complement(X_19)),complement(meet(top,X_19)))) )],[refute_0_385,refute_0_386]) ).
cnf(refute_0_388,plain,
meet(join(zero,complement(X_19)),meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))) = meet(complement(meet(top,X_19)),join(zero,complement(X_19))),
inference(resolve,[$cnf( $equal(meet(join(zero,complement(X_19)),complement(meet(top,X_19))),meet(complement(meet(top,X_19)),join(zero,complement(X_19)))) )],[refute_0_381,refute_0_387]) ).
cnf(refute_0_389,plain,
meet(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19)))),join(zero,complement(X_19))) = meet(join(zero,complement(X_19)),meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),
inference(subst,[],[refute_0_320:[bind(X_8,$fot(join(zero,complement(X_19)))),bind(X_9,$fot(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))))]]) ).
cnf(refute_0_390,plain,
meet(X0,join(zero,complement(X_19))) = complement(join(complement(X0),complement(join(zero,complement(X_19))))),
inference(subst,[],[refute_0_61:[bind(X1,$fot(join(zero,complement(X_19))))]]) ).
cnf(refute_0_391,plain,
( complement(join(zero,complement(X_19))) != meet(top,X_19)
| meet(X0,join(zero,complement(X_19))) != complement(join(complement(X0),complement(join(zero,complement(X_19)))))
| meet(X0,join(zero,complement(X_19))) = complement(join(complement(X0),meet(top,X_19))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X0,join(zero,complement(X_19))),complement(join(complement(X0),complement(join(zero,complement(X_19)))))) ),[1,0,1],$fot(meet(top,X_19))]]) ).
cnf(refute_0_392,plain,
( meet(X0,join(zero,complement(X_19))) != complement(join(complement(X0),complement(join(zero,complement(X_19)))))
| meet(X0,join(zero,complement(X_19))) = complement(join(complement(X0),meet(top,X_19))) ),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(X_19))),meet(top,X_19)) )],[refute_0_305,refute_0_391]) ).
cnf(refute_0_393,plain,
meet(X0,join(zero,complement(X_19))) = complement(join(complement(X0),meet(top,X_19))),
inference(resolve,[$cnf( $equal(meet(X0,join(zero,complement(X_19))),complement(join(complement(X0),complement(join(zero,complement(X_19)))))) )],[refute_0_390,refute_0_392]) ).
cnf(refute_0_394,plain,
( meet(X0,join(zero,complement(X_19))) != complement(join(complement(X0),meet(top,X_19)))
| complement(join(complement(X0),meet(top,X_19))) = meet(X0,join(zero,complement(X_19))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(meet(X0,join(zero,complement(X_19))))),bind(Y,$fot(complement(join(complement(X0),meet(top,X_19)))))]]) ).
cnf(refute_0_395,plain,
complement(join(complement(X0),meet(top,X_19))) = meet(X0,join(zero,complement(X_19))),
inference(resolve,[$cnf( $equal(meet(X0,join(zero,complement(X_19))),complement(join(complement(X0),meet(top,X_19)))) )],[refute_0_393,refute_0_394]) ).
cnf(refute_0_396,plain,
complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(top,X_19))) = meet(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19)))),join(zero,complement(X_19))),
inference(subst,[],[refute_0_395:[bind(X0,$fot(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))))]]) ).
cnf(refute_0_397,plain,
( complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(top,X_19))) != meet(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19)))),join(zero,complement(X_19)))
| meet(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19)))),join(zero,complement(X_19))) != meet(join(zero,complement(X_19)),meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19)))))
| complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(top,X_19))) = meet(join(zero,complement(X_19)),meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))) ),
inference(subst,[],[refute_0_100:[bind(X,$fot(complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(top,X_19))))),bind(Y,$fot(meet(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19)))),join(zero,complement(X_19))))),bind(Z,$fot(meet(join(zero,complement(X_19)),meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19)))))))]]) ).
cnf(refute_0_398,plain,
( meet(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19)))),join(zero,complement(X_19))) != meet(join(zero,complement(X_19)),meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19)))))
| complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(top,X_19))) = meet(join(zero,complement(X_19)),meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(top,X_19))),meet(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19)))),join(zero,complement(X_19)))) )],[refute_0_396,refute_0_397]) ).
cnf(refute_0_399,plain,
complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(top,X_19))) = meet(join(zero,complement(X_19)),meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),
inference(resolve,[$cnf( $equal(meet(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19)))),join(zero,complement(X_19))),meet(join(zero,complement(X_19)),meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19)))))) )],[refute_0_389,refute_0_398]) ).
cnf(refute_0_400,plain,
( complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(top,X_19))) != meet(join(zero,complement(X_19)),meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19)))))
| meet(join(zero,complement(X_19)),meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))) != meet(complement(meet(top,X_19)),join(zero,complement(X_19)))
| complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(top,X_19))) = meet(complement(meet(top,X_19)),join(zero,complement(X_19))) ),
inference(subst,[],[refute_0_100:[bind(X,$fot(complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(top,X_19))))),bind(Y,$fot(meet(join(zero,complement(X_19)),meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))))),bind(Z,$fot(meet(complement(meet(top,X_19)),join(zero,complement(X_19)))))]]) ).
cnf(refute_0_401,plain,
( meet(join(zero,complement(X_19)),meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))) != meet(complement(meet(top,X_19)),join(zero,complement(X_19)))
| complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(top,X_19))) = meet(complement(meet(top,X_19)),join(zero,complement(X_19))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(top,X_19))),meet(join(zero,complement(X_19)),meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19)))))) )],[refute_0_399,refute_0_400]) ).
cnf(refute_0_402,plain,
complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(top,X_19))) = meet(complement(meet(top,X_19)),join(zero,complement(X_19))),
inference(resolve,[$cnf( $equal(meet(join(zero,complement(X_19)),meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(complement(meet(top,X_19)),join(zero,complement(X_19)))) )],[refute_0_388,refute_0_401]) ).
cnf(refute_0_403,plain,
join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(top,X_19)))) = join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(top,X_19)))),
introduced(tautology,[refl,[$fot(join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(top,X_19)))))]]) ).
cnf(refute_0_404,plain,
( complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(top,X_19))) != meet(complement(meet(top,X_19)),join(zero,complement(X_19)))
| join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(top,X_19)))) != join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(top,X_19))))
| join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(top,X_19)))) = join(zero,meet(complement(meet(top,X_19)),join(zero,complement(X_19)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(top,X_19)))),join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(top,X_19))))) ),[1,1],$fot(meet(complement(meet(top,X_19)),join(zero,complement(X_19))))]]) ).
cnf(refute_0_405,plain,
( complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(top,X_19))) != meet(complement(meet(top,X_19)),join(zero,complement(X_19)))
| join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(top,X_19)))) = join(zero,meet(complement(meet(top,X_19)),join(zero,complement(X_19)))) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(top,X_19)))),join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(top,X_19))))) )],[refute_0_403,refute_0_404]) ).
cnf(refute_0_406,plain,
join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(top,X_19)))) = join(zero,meet(complement(meet(top,X_19)),join(zero,complement(X_19)))),
inference(resolve,[$cnf( $equal(complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(top,X_19))),meet(complement(meet(top,X_19)),join(zero,complement(X_19)))) )],[refute_0_402,refute_0_405]) ).
cnf(refute_0_407,plain,
( join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(top,X_19)))) != join(zero,meet(complement(meet(top,X_19)),join(zero,complement(X_19))))
| join(zero,meet(complement(meet(top,X_19)),join(zero,complement(X_19)))) != join(zero,complement(X_19))
| join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(top,X_19)))) = join(zero,complement(X_19)) ),
inference(subst,[],[refute_0_100:[bind(X,$fot(join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(top,X_19)))))),bind(Y,$fot(join(zero,meet(complement(meet(top,X_19)),join(zero,complement(X_19)))))),bind(Z,$fot(join(zero,complement(X_19))))]]) ).
cnf(refute_0_408,plain,
( join(zero,meet(complement(meet(top,X_19)),join(zero,complement(X_19)))) != join(zero,complement(X_19))
| join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(top,X_19)))) = join(zero,complement(X_19)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(top,X_19)))),join(zero,meet(complement(meet(top,X_19)),join(zero,complement(X_19))))) )],[refute_0_406,refute_0_407]) ).
cnf(refute_0_409,plain,
join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(top,X_19)))) = join(zero,complement(X_19)),
inference(resolve,[$cnf( $equal(join(zero,meet(complement(meet(top,X_19)),join(zero,complement(X_19)))),join(zero,complement(X_19))) )],[refute_0_380,refute_0_408]) ).
cnf(refute_0_410,plain,
( complement(meet(top,X_19)) != join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(top,X_19))))
| join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(top,X_19)))) != join(zero,complement(X_19))
| complement(meet(top,X_19)) = join(zero,complement(X_19)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(meet(top,X_19)),join(zero,complement(X_19))) ),[0],$fot(join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(top,X_19)))))]]) ).
cnf(refute_0_411,plain,
( complement(meet(top,X_19)) != join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(top,X_19))))
| complement(meet(top,X_19)) = join(zero,complement(X_19)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(top,X_19)))),join(zero,complement(X_19))) )],[refute_0_409,refute_0_410]) ).
cnf(refute_0_412,plain,
( meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19)))) != join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(top,X_19))))
| complement(meet(top,X_19)) = join(zero,complement(X_19)) ),
inference(resolve,[$cnf( $equal(complement(meet(top,X_19)),join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(top,X_19))))) )],[refute_0_345,refute_0_411]) ).
cnf(refute_0_413,plain,
complement(meet(top,X_19)) = join(zero,complement(X_19)),
inference(resolve,[$cnf( $equal(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19)))),join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_19)),join(zero,complement(X_19))))),meet(top,X_19))))) )],[refute_0_335,refute_0_412]) ).
cnf(refute_0_414,plain,
( complement(meet(top,X_19)) != join(zero,complement(X_19))
| join(zero,complement(X_19)) = complement(meet(top,X_19)) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(complement(meet(top,X_19)))),bind(Y,$fot(join(zero,complement(X_19))))]]) ).
cnf(refute_0_415,plain,
join(zero,complement(X_19)) = complement(meet(top,X_19)),
inference(resolve,[$cnf( $equal(complement(meet(top,X_19)),join(zero,complement(X_19))) )],[refute_0_413,refute_0_414]) ).
cnf(refute_0_416,plain,
join(zero,complement(join(complement(X_53),complement(X_53)))) = complement(meet(top,join(complement(X_53),complement(X_53)))),
inference(subst,[],[refute_0_415:[bind(X_19,$fot(join(complement(X_53),complement(X_53))))]]) ).
cnf(refute_0_417,plain,
( complement(meet(top,join(complement(X_53),complement(X_53)))) != complement(complement(X_53))
| join(zero,complement(join(complement(X_53),complement(X_53)))) != complement(meet(top,join(complement(X_53),complement(X_53))))
| join(zero,complement(join(complement(X_53),complement(X_53)))) = complement(complement(X_53)) ),
inference(subst,[],[refute_0_100:[bind(X,$fot(join(zero,complement(join(complement(X_53),complement(X_53)))))),bind(Y,$fot(complement(meet(top,join(complement(X_53),complement(X_53)))))),bind(Z,$fot(complement(complement(X_53))))]]) ).
cnf(refute_0_418,plain,
( complement(meet(top,join(complement(X_53),complement(X_53)))) != complement(complement(X_53))
| join(zero,complement(join(complement(X_53),complement(X_53)))) = complement(complement(X_53)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(complement(X_53),complement(X_53)))),complement(meet(top,join(complement(X_53),complement(X_53))))) )],[refute_0_416,refute_0_417]) ).
cnf(refute_0_419,plain,
join(zero,complement(join(complement(X_53),complement(X_53)))) = complement(complement(X_53)),
inference(resolve,[$cnf( $equal(complement(meet(top,join(complement(X_53),complement(X_53)))),complement(complement(X_53))) )],[refute_0_296,refute_0_418]) ).
cnf(refute_0_420,plain,
( X_53 != join(zero,complement(join(complement(X_53),complement(X_53))))
| join(zero,complement(join(complement(X_53),complement(X_53)))) != complement(complement(X_53))
| X_53 = complement(complement(X_53)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_53,complement(complement(X_53))) ),[0],$fot(join(zero,complement(join(complement(X_53),complement(X_53)))))]]) ).
cnf(refute_0_421,plain,
( X_53 != join(zero,complement(join(complement(X_53),complement(X_53))))
| X_53 = complement(complement(X_53)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(complement(X_53),complement(X_53)))),complement(complement(X_53))) )],[refute_0_419,refute_0_420]) ).
cnf(refute_0_422,plain,
X_53 = complement(complement(X_53)),
inference(resolve,[$cnf( $equal(X_53,join(zero,complement(join(complement(X_53),complement(X_53))))) )],[refute_0_272,refute_0_421]) ).
cnf(refute_0_423,plain,
( X_53 != complement(complement(X_53))
| complement(complement(X_53)) = X_53 ),
inference(subst,[],[refute_0_7:[bind(X,$fot(X_53)),bind(Y,$fot(complement(complement(X_53))))]]) ).
cnf(refute_0_424,plain,
complement(complement(X_53)) = X_53,
inference(resolve,[$cnf( $equal(X_53,complement(complement(X_53))) )],[refute_0_422,refute_0_423]) ).
cnf(refute_0_425,plain,
( complement(complement(X_53)) != X_53
| top != join(top,complement(complement(X_53)))
| top = join(top,X_53) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(top,complement(complement(X_53)))) ),[1,1],$fot(X_53)]]) ).
cnf(refute_0_426,plain,
( top != join(top,complement(complement(X_53)))
| top = join(top,X_53) ),
inference(resolve,[$cnf( $equal(complement(complement(X_53)),X_53) )],[refute_0_424,refute_0_425]) ).
cnf(refute_0_427,plain,
top = join(top,X_53),
inference(resolve,[$cnf( $equal(top,join(top,complement(complement(X_53)))) )],[refute_0_258,refute_0_426]) ).
cnf(refute_0_428,plain,
top = join(top,composition(X_87,top)),
inference(subst,[],[refute_0_427:[bind(X_53,$fot(composition(X_87,top)))]]) ).
cnf(refute_0_429,plain,
( top != join(top,composition(X_87,top))
| join(top,composition(X_87,top)) = top ),
inference(subst,[],[refute_0_7:[bind(X,$fot(top)),bind(Y,$fot(join(top,composition(X_87,top))))]]) ).
cnf(refute_0_430,plain,
join(top,composition(X_87,top)) = top,
inference(resolve,[$cnf( $equal(top,join(top,composition(X_87,top))) )],[refute_0_428,refute_0_429]) ).
cnf(refute_0_431,plain,
( composition(join(X_87,one),top) != join(top,composition(X_87,top))
| join(top,composition(X_87,top)) != top
| composition(join(X_87,one),top) = top ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(join(X_87,one),top),top) ),[0],$fot(join(top,composition(X_87,top)))]]) ).
cnf(refute_0_432,plain,
( composition(join(X_87,one),top) != join(top,composition(X_87,top))
| composition(join(X_87,one),top) = top ),
inference(resolve,[$cnf( $equal(join(top,composition(X_87,top)),top) )],[refute_0_430,refute_0_431]) ).
cnf(refute_0_433,plain,
composition(join(X_87,one),top) = top,
inference(resolve,[$cnf( $equal(composition(join(X_87,one),top),join(top,composition(X_87,top))) )],[refute_0_58,refute_0_432]) ).
cnf(refute_0_434,plain,
composition(join(top,one),top) = top,
inference(subst,[],[refute_0_433:[bind(X_87,$fot(top))]]) ).
cnf(refute_0_435,plain,
top = join(top,one),
inference(subst,[],[refute_0_427:[bind(X_53,$fot(one))]]) ).
cnf(refute_0_436,plain,
( top != join(top,one)
| join(top,one) = top ),
inference(subst,[],[refute_0_7:[bind(X,$fot(top)),bind(Y,$fot(join(top,one)))]]) ).
cnf(refute_0_437,plain,
join(top,one) = top,
inference(resolve,[$cnf( $equal(top,join(top,one)) )],[refute_0_435,refute_0_436]) ).
cnf(refute_0_438,plain,
( composition(join(top,one),top) != top
| join(top,one) != top
| composition(top,top) = top ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(top,one),top),top) ),[0,0],$fot(top)]]) ).
cnf(refute_0_439,plain,
( composition(join(top,one),top) != top
| composition(top,top) = top ),
inference(resolve,[$cnf( $equal(join(top,one),top) )],[refute_0_437,refute_0_438]) ).
cnf(refute_0_440,plain,
composition(top,top) = top,
inference(resolve,[$cnf( $equal(composition(join(top,one),top),top) )],[refute_0_434,refute_0_439]) ).
cnf(refute_0_441,plain,
( composition(top,top) != top
| join(complement(top),composition(converse(top),complement(composition(top,top)))) != complement(top)
| join(complement(top),composition(converse(top),complement(top))) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),composition(converse(top),complement(composition(top,top)))),complement(top)) ),[0,1,1,0],$fot(top)]]) ).
cnf(refute_0_442,plain,
( join(complement(top),composition(converse(top),complement(composition(top,top)))) != complement(top)
| join(complement(top),composition(converse(top),complement(top))) = complement(top) ),
inference(resolve,[$cnf( $equal(composition(top,top),top) )],[refute_0_440,refute_0_441]) ).
cnf(refute_0_443,plain,
join(complement(top),composition(converse(top),complement(top))) = complement(top),
inference(resolve,[$cnf( $equal(join(complement(top),composition(converse(top),complement(composition(top,top)))),complement(top)) )],[refute_0_14,refute_0_442]) ).
cnf(refute_0_444,plain,
composition(top,complement(top)) = composition(top,complement(top)),
introduced(tautology,[refl,[$fot(composition(top,complement(top)))]]) ).
cnf(refute_0_445,plain,
( complement(top) != zero
| composition(top,complement(top)) != composition(top,complement(top))
| composition(top,complement(top)) = composition(top,zero) ),
introduced(tautology,[equality,[$cnf( $equal(composition(top,complement(top)),composition(top,complement(top))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_446,plain,
( complement(top) != zero
| composition(top,complement(top)) = composition(top,zero) ),
inference(resolve,[$cnf( $equal(composition(top,complement(top)),composition(top,complement(top))) )],[refute_0_444,refute_0_445]) ).
cnf(refute_0_447,plain,
composition(top,complement(top)) = composition(top,zero),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_108,refute_0_446]) ).
cnf(refute_0_448,plain,
converse(top) = join(meet(converse(top),meet(zero,converse(complement(converse(top))))),complement(join(complement(converse(top)),meet(zero,converse(complement(converse(top))))))),
inference(subst,[],[refute_0_176:[bind(X0,$fot(converse(top))),bind(X1,$fot(meet(zero,converse(complement(converse(top))))))]]) ).
cnf(refute_0_449,plain,
X_31 = join(meet(X_31,converse(complement(converse(complement(X_31))))),complement(join(complement(X_31),converse(complement(converse(complement(X_31))))))),
inference(subst,[],[refute_0_176:[bind(X0,$fot(X_31)),bind(X1,$fot(converse(complement(converse(complement(X_31))))))]]) ).
cnf(refute_0_450,plain,
converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_451,plain,
converse(join(converse(X0),X_13)) = join(converse(converse(X0)),converse(X_13)),
inference(subst,[],[refute_0_450:[bind(X0,$fot(converse(X0))),bind(X1,$fot(X_13))]]) ).
cnf(refute_0_452,plain,
( converse(converse(X0)) != X0
| converse(join(converse(X0),X_13)) != join(converse(converse(X0)),converse(X_13))
| converse(join(converse(X0),X_13)) = join(X0,converse(X_13)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(X0),X_13)),join(converse(converse(X0)),converse(X_13))) ),[1,0],$fot(X0)]]) ).
cnf(refute_0_453,plain,
( converse(join(converse(X0),X_13)) != join(converse(converse(X0)),converse(X_13))
| converse(join(converse(X0),X_13)) = join(X0,converse(X_13)) ),
inference(resolve,[$cnf( $equal(converse(converse(X0)),X0) )],[refute_0_18,refute_0_452]) ).
cnf(refute_0_454,plain,
converse(join(converse(X0),X_13)) = join(X0,converse(X_13)),
inference(resolve,[$cnf( $equal(converse(join(converse(X0),X_13)),join(converse(converse(X0)),converse(X_13))) )],[refute_0_451,refute_0_453]) ).
cnf(refute_0_455,plain,
converse(join(converse(X_16),complement(converse(X_16)))) = join(X_16,converse(complement(converse(X_16)))),
inference(subst,[],[refute_0_454:[bind(X0,$fot(X_16)),bind(X_13,$fot(complement(converse(X_16))))]]) ).
cnf(refute_0_456,plain,
top = join(converse(X_16),complement(converse(X_16))),
inference(subst,[],[refute_0_59:[bind(X0,$fot(converse(X_16)))]]) ).
cnf(refute_0_457,plain,
( top != join(converse(X_16),complement(converse(X_16)))
| join(converse(X_16),complement(converse(X_16))) = top ),
inference(subst,[],[refute_0_7:[bind(X,$fot(top)),bind(Y,$fot(join(converse(X_16),complement(converse(X_16)))))]]) ).
cnf(refute_0_458,plain,
join(converse(X_16),complement(converse(X_16))) = top,
inference(resolve,[$cnf( $equal(top,join(converse(X_16),complement(converse(X_16)))) )],[refute_0_456,refute_0_457]) ).
cnf(refute_0_459,plain,
( converse(join(converse(X_16),complement(converse(X_16)))) != join(X_16,converse(complement(converse(X_16))))
| join(converse(X_16),complement(converse(X_16))) != top
| converse(top) = join(X_16,converse(complement(converse(X_16)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(X_16),complement(converse(X_16)))),join(X_16,converse(complement(converse(X_16))))) ),[0,0],$fot(top)]]) ).
cnf(refute_0_460,plain,
( converse(join(converse(X_16),complement(converse(X_16)))) != join(X_16,converse(complement(converse(X_16))))
| converse(top) = join(X_16,converse(complement(converse(X_16)))) ),
inference(resolve,[$cnf( $equal(join(converse(X_16),complement(converse(X_16))),top) )],[refute_0_458,refute_0_459]) ).
cnf(refute_0_461,plain,
converse(top) = join(X_16,converse(complement(converse(X_16)))),
inference(resolve,[$cnf( $equal(converse(join(converse(X_16),complement(converse(X_16)))),join(X_16,converse(complement(converse(X_16))))) )],[refute_0_455,refute_0_460]) ).
cnf(refute_0_462,plain,
converse(top) = join(complement(X_31),converse(complement(converse(complement(X_31))))),
inference(subst,[],[refute_0_461:[bind(X_16,$fot(complement(X_31)))]]) ).
cnf(refute_0_463,plain,
( converse(top) != join(complement(X_31),converse(complement(converse(complement(X_31)))))
| join(complement(X_31),converse(complement(converse(complement(X_31))))) = converse(top) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(converse(top))),bind(Y,$fot(join(complement(X_31),converse(complement(converse(complement(X_31)))))))]]) ).
cnf(refute_0_464,plain,
join(complement(X_31),converse(complement(converse(complement(X_31))))) = converse(top),
inference(resolve,[$cnf( $equal(converse(top),join(complement(X_31),converse(complement(converse(complement(X_31)))))) )],[refute_0_462,refute_0_463]) ).
cnf(refute_0_465,plain,
( X_31 != join(meet(X_31,converse(complement(converse(complement(X_31))))),complement(join(complement(X_31),converse(complement(converse(complement(X_31)))))))
| join(complement(X_31),converse(complement(converse(complement(X_31))))) != converse(top)
| X_31 = join(meet(X_31,converse(complement(converse(complement(X_31))))),complement(converse(top))) ),
introduced(tautology,[equality,[$cnf( $equal(X_31,join(meet(X_31,converse(complement(converse(complement(X_31))))),complement(join(complement(X_31),converse(complement(converse(complement(X_31)))))))) ),[1,1,0],$fot(converse(top))]]) ).
cnf(refute_0_466,plain,
( X_31 != join(meet(X_31,converse(complement(converse(complement(X_31))))),complement(join(complement(X_31),converse(complement(converse(complement(X_31)))))))
| X_31 = join(meet(X_31,converse(complement(converse(complement(X_31))))),complement(converse(top))) ),
inference(resolve,[$cnf( $equal(join(complement(X_31),converse(complement(converse(complement(X_31))))),converse(top)) )],[refute_0_464,refute_0_465]) ).
cnf(refute_0_467,plain,
X_31 = join(meet(X_31,converse(complement(converse(complement(X_31))))),complement(converse(top))),
inference(resolve,[$cnf( $equal(X_31,join(meet(X_31,converse(complement(converse(complement(X_31))))),complement(join(complement(X_31),converse(complement(converse(complement(X_31)))))))) )],[refute_0_449,refute_0_466]) ).
cnf(refute_0_468,plain,
join(meet(X_31,converse(complement(converse(complement(X_31))))),complement(converse(top))) = join(complement(converse(top)),meet(X_31,converse(complement(converse(complement(X_31)))))),
inference(subst,[],[refute_0_9:[bind(X0,$fot(complement(converse(top)))),bind(X1,$fot(meet(X_31,converse(complement(converse(complement(X_31)))))))]]) ).
cnf(refute_0_469,plain,
( X_31 != join(meet(X_31,converse(complement(converse(complement(X_31))))),complement(converse(top)))
| join(meet(X_31,converse(complement(converse(complement(X_31))))),complement(converse(top))) != join(complement(converse(top)),meet(X_31,converse(complement(converse(complement(X_31))))))
| X_31 = join(complement(converse(top)),meet(X_31,converse(complement(converse(complement(X_31)))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_31,join(complement(converse(top)),meet(X_31,converse(complement(converse(complement(X_31))))))) ),[0],$fot(join(meet(X_31,converse(complement(converse(complement(X_31))))),complement(converse(top))))]]) ).
cnf(refute_0_470,plain,
( X_31 != join(meet(X_31,converse(complement(converse(complement(X_31))))),complement(converse(top)))
| X_31 = join(complement(converse(top)),meet(X_31,converse(complement(converse(complement(X_31)))))) ),
inference(resolve,[$cnf( $equal(join(meet(X_31,converse(complement(converse(complement(X_31))))),complement(converse(top))),join(complement(converse(top)),meet(X_31,converse(complement(converse(complement(X_31))))))) )],[refute_0_468,refute_0_469]) ).
cnf(refute_0_471,plain,
X_31 = join(complement(converse(top)),meet(X_31,converse(complement(converse(complement(X_31)))))),
inference(resolve,[$cnf( $equal(X_31,join(meet(X_31,converse(complement(converse(complement(X_31))))),complement(converse(top)))) )],[refute_0_467,refute_0_470]) ).
cnf(refute_0_472,plain,
zero = join(complement(converse(top)),meet(zero,converse(complement(converse(complement(zero)))))),
inference(subst,[],[refute_0_471:[bind(X_31,$fot(zero))]]) ).
cnf(refute_0_473,plain,
X_31 = join(meet(X_31,complement(X1)),complement(join(complement(X_31),complement(X1)))),
inference(subst,[],[refute_0_176:[bind(X0,$fot(X_31)),bind(X1,$fot(complement(X1)))]]) ).
cnf(refute_0_474,plain,
meet(X_31,X1) = complement(join(complement(X_31),complement(X1))),
inference(subst,[],[refute_0_61:[bind(X0,$fot(X_31))]]) ).
cnf(refute_0_475,plain,
( meet(X_31,X1) != complement(join(complement(X_31),complement(X1)))
| complement(join(complement(X_31),complement(X1))) = meet(X_31,X1) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(meet(X_31,X1))),bind(Y,$fot(complement(join(complement(X_31),complement(X1)))))]]) ).
cnf(refute_0_476,plain,
complement(join(complement(X_31),complement(X1))) = meet(X_31,X1),
inference(resolve,[$cnf( $equal(meet(X_31,X1),complement(join(complement(X_31),complement(X1)))) )],[refute_0_474,refute_0_475]) ).
cnf(refute_0_477,plain,
( X_31 != join(meet(X_31,complement(X1)),complement(join(complement(X_31),complement(X1))))
| complement(join(complement(X_31),complement(X1))) != meet(X_31,X1)
| X_31 = join(meet(X_31,complement(X1)),meet(X_31,X1)) ),
introduced(tautology,[equality,[$cnf( $equal(X_31,join(meet(X_31,complement(X1)),complement(join(complement(X_31),complement(X1))))) ),[1,1],$fot(meet(X_31,X1))]]) ).
cnf(refute_0_478,plain,
( X_31 != join(meet(X_31,complement(X1)),complement(join(complement(X_31),complement(X1))))
| X_31 = join(meet(X_31,complement(X1)),meet(X_31,X1)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_31),complement(X1))),meet(X_31,X1)) )],[refute_0_476,refute_0_477]) ).
cnf(refute_0_479,plain,
X_31 = join(meet(X_31,complement(X1)),meet(X_31,X1)),
inference(resolve,[$cnf( $equal(X_31,join(meet(X_31,complement(X1)),complement(join(complement(X_31),complement(X1))))) )],[refute_0_473,refute_0_478]) ).
cnf(refute_0_480,plain,
join(meet(X_31,complement(X1)),meet(X_31,X1)) = join(meet(X_31,X1),meet(X_31,complement(X1))),
inference(subst,[],[refute_0_9:[bind(X0,$fot(meet(X_31,X1))),bind(X1,$fot(meet(X_31,complement(X1))))]]) ).
cnf(refute_0_481,plain,
( X_31 != join(meet(X_31,complement(X1)),meet(X_31,X1))
| join(meet(X_31,complement(X1)),meet(X_31,X1)) != join(meet(X_31,X1),meet(X_31,complement(X1)))
| X_31 = join(meet(X_31,X1),meet(X_31,complement(X1))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_31,join(meet(X_31,X1),meet(X_31,complement(X1)))) ),[0],$fot(join(meet(X_31,complement(X1)),meet(X_31,X1)))]]) ).
cnf(refute_0_482,plain,
( X_31 != join(meet(X_31,complement(X1)),meet(X_31,X1))
| X_31 = join(meet(X_31,X1),meet(X_31,complement(X1))) ),
inference(resolve,[$cnf( $equal(join(meet(X_31,complement(X1)),meet(X_31,X1)),join(meet(X_31,X1),meet(X_31,complement(X1)))) )],[refute_0_480,refute_0_481]) ).
cnf(refute_0_483,plain,
X_31 = join(meet(X_31,X1),meet(X_31,complement(X1))),
inference(resolve,[$cnf( $equal(X_31,join(meet(X_31,complement(X1)),meet(X_31,X1))) )],[refute_0_479,refute_0_482]) ).
cnf(refute_0_484,plain,
X_39 = join(meet(X_39,top),meet(X_39,complement(top))),
inference(subst,[],[refute_0_483:[bind(X1,$fot(top)),bind(X_31,$fot(X_39))]]) ).
cnf(refute_0_485,plain,
( X_39 != join(meet(X_39,top),meet(X_39,complement(top)))
| complement(top) != zero
| X_39 = join(meet(X_39,top),meet(X_39,zero)) ),
introduced(tautology,[equality,[$cnf( $equal(X_39,join(meet(X_39,top),meet(X_39,complement(top)))) ),[1,1,1],$fot(zero)]]) ).
cnf(refute_0_486,plain,
( X_39 != join(meet(X_39,top),meet(X_39,complement(top)))
| X_39 = join(meet(X_39,top),meet(X_39,zero)) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_108,refute_0_485]) ).
cnf(refute_0_487,plain,
X_39 = join(meet(X_39,top),meet(X_39,zero)),
inference(resolve,[$cnf( $equal(X_39,join(meet(X_39,top),meet(X_39,complement(top)))) )],[refute_0_484,refute_0_486]) ).
cnf(refute_0_488,plain,
X_42 = join(meet(X_42,top),meet(X_42,zero)),
inference(subst,[],[refute_0_487:[bind(X_39,$fot(X_42))]]) ).
cnf(refute_0_489,plain,
meet(zero,X_42) = meet(X_42,zero),
inference(subst,[],[refute_0_318:[bind(X_8,$fot(zero)),bind(X_9,$fot(X_42))]]) ).
cnf(refute_0_490,plain,
( meet(zero,X_42) != meet(X_42,zero)
| meet(X_42,zero) = meet(zero,X_42) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(meet(zero,X_42))),bind(Y,$fot(meet(X_42,zero)))]]) ).
cnf(refute_0_491,plain,
meet(X_42,zero) = meet(zero,X_42),
inference(resolve,[$cnf( $equal(meet(zero,X_42),meet(X_42,zero)) )],[refute_0_489,refute_0_490]) ).
cnf(refute_0_492,plain,
( X_42 != join(meet(X_42,top),meet(X_42,zero))
| meet(X_42,zero) != meet(zero,X_42)
| X_42 = join(meet(X_42,top),meet(zero,X_42)) ),
introduced(tautology,[equality,[$cnf( $equal(X_42,join(meet(X_42,top),meet(X_42,zero))) ),[1,1],$fot(meet(zero,X_42))]]) ).
cnf(refute_0_493,plain,
( X_42 != join(meet(X_42,top),meet(X_42,zero))
| X_42 = join(meet(X_42,top),meet(zero,X_42)) ),
inference(resolve,[$cnf( $equal(meet(X_42,zero),meet(zero,X_42)) )],[refute_0_491,refute_0_492]) ).
cnf(refute_0_494,plain,
X_42 = join(meet(X_42,top),meet(zero,X_42)),
inference(resolve,[$cnf( $equal(X_42,join(meet(X_42,top),meet(X_42,zero))) )],[refute_0_488,refute_0_493]) ).
cnf(refute_0_495,plain,
complement(zero) = join(meet(complement(zero),top),meet(zero,complement(zero))),
inference(subst,[],[refute_0_494:[bind(X_42,$fot(complement(zero)))]]) ).
cnf(refute_0_496,plain,
zero = meet(zero,complement(zero)),
inference(subst,[],[refute_0_82:[bind(X0,$fot(zero))]]) ).
cnf(refute_0_497,plain,
( zero != meet(zero,complement(zero))
| meet(zero,complement(zero)) = zero ),
inference(subst,[],[refute_0_7:[bind(X,$fot(zero)),bind(Y,$fot(meet(zero,complement(zero))))]]) ).
cnf(refute_0_498,plain,
meet(zero,complement(zero)) = zero,
inference(resolve,[$cnf( $equal(zero,meet(zero,complement(zero))) )],[refute_0_496,refute_0_497]) ).
cnf(refute_0_499,plain,
( complement(zero) != join(meet(complement(zero),top),meet(zero,complement(zero)))
| meet(zero,complement(zero)) != zero
| complement(zero) = join(meet(complement(zero),top),zero) ),
introduced(tautology,[equality,[$cnf( $equal(complement(zero),join(meet(complement(zero),top),meet(zero,complement(zero)))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_500,plain,
( complement(zero) != join(meet(complement(zero),top),meet(zero,complement(zero)))
| complement(zero) = join(meet(complement(zero),top),zero) ),
inference(resolve,[$cnf( $equal(meet(zero,complement(zero)),zero) )],[refute_0_498,refute_0_499]) ).
cnf(refute_0_501,plain,
complement(zero) = join(meet(complement(zero),top),zero),
inference(resolve,[$cnf( $equal(complement(zero),join(meet(complement(zero),top),meet(zero,complement(zero)))) )],[refute_0_495,refute_0_500]) ).
cnf(refute_0_502,plain,
top = join(meet(top,X_32),complement(join(complement(top),X_32))),
inference(subst,[],[refute_0_176:[bind(X0,$fot(top)),bind(X1,$fot(X_32))]]) ).
cnf(refute_0_503,plain,
( complement(top) != zero
| top != join(meet(top,X_32),complement(join(complement(top),X_32)))
| top = join(meet(top,X_32),complement(join(zero,X_32))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(meet(top,X_32),complement(join(complement(top),X_32)))) ),[1,1,0,0],$fot(zero)]]) ).
cnf(refute_0_504,plain,
( top != join(meet(top,X_32),complement(join(complement(top),X_32)))
| top = join(meet(top,X_32),complement(join(zero,X_32))) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_108,refute_0_503]) ).
cnf(refute_0_505,plain,
top = join(meet(top,X_32),complement(join(zero,X_32))),
inference(resolve,[$cnf( $equal(top,join(meet(top,X_32),complement(join(complement(top),X_32)))) )],[refute_0_502,refute_0_504]) ).
cnf(refute_0_506,plain,
top = join(meet(top,complement(zero)),complement(join(zero,complement(zero)))),
inference(subst,[],[refute_0_505:[bind(X_32,$fot(complement(zero)))]]) ).
cnf(refute_0_507,plain,
top = join(zero,complement(zero)),
inference(subst,[],[refute_0_59:[bind(X0,$fot(zero))]]) ).
cnf(refute_0_508,plain,
( top != join(zero,complement(zero))
| join(zero,complement(zero)) = top ),
inference(subst,[],[refute_0_7:[bind(X,$fot(top)),bind(Y,$fot(join(zero,complement(zero))))]]) ).
cnf(refute_0_509,plain,
join(zero,complement(zero)) = top,
inference(resolve,[$cnf( $equal(top,join(zero,complement(zero))) )],[refute_0_507,refute_0_508]) ).
cnf(refute_0_510,plain,
( join(zero,complement(zero)) != top
| top != join(meet(top,complement(zero)),complement(join(zero,complement(zero))))
| top = join(meet(top,complement(zero)),complement(top)) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(meet(top,complement(zero)),complement(join(zero,complement(zero))))) ),[1,1,0],$fot(top)]]) ).
cnf(refute_0_511,plain,
( top != join(meet(top,complement(zero)),complement(join(zero,complement(zero))))
| top = join(meet(top,complement(zero)),complement(top)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(zero)),top) )],[refute_0_509,refute_0_510]) ).
cnf(refute_0_512,plain,
top = join(meet(top,complement(zero)),complement(top)),
inference(resolve,[$cnf( $equal(top,join(meet(top,complement(zero)),complement(join(zero,complement(zero))))) )],[refute_0_506,refute_0_511]) ).
cnf(refute_0_513,plain,
join(complement(top),meet(top,complement(zero))) = join(complement(top),meet(top,complement(zero))),
introduced(tautology,[refl,[$fot(join(complement(top),meet(top,complement(zero))))]]) ).
cnf(refute_0_514,plain,
( complement(top) != zero
| join(complement(top),meet(top,complement(zero))) != join(complement(top),meet(top,complement(zero)))
| join(complement(top),meet(top,complement(zero))) = join(zero,meet(top,complement(zero))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(top,complement(zero))),join(complement(top),meet(top,complement(zero)))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_515,plain,
( complement(top) != zero
| join(complement(top),meet(top,complement(zero))) = join(zero,meet(top,complement(zero))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(top,complement(zero))),join(complement(top),meet(top,complement(zero)))) )],[refute_0_513,refute_0_514]) ).
cnf(refute_0_516,plain,
join(complement(top),meet(top,complement(zero))) = join(zero,meet(top,complement(zero))),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_108,refute_0_515]) ).
cnf(refute_0_517,plain,
join(meet(top,complement(zero)),complement(top)) = join(complement(top),meet(top,complement(zero))),
inference(subst,[],[refute_0_9:[bind(X0,$fot(complement(top))),bind(X1,$fot(meet(top,complement(zero))))]]) ).
cnf(refute_0_518,plain,
( join(complement(top),meet(top,complement(zero))) != join(zero,meet(top,complement(zero)))
| join(meet(top,complement(zero)),complement(top)) != join(complement(top),meet(top,complement(zero)))
| join(meet(top,complement(zero)),complement(top)) = join(zero,meet(top,complement(zero))) ),
inference(subst,[],[refute_0_100:[bind(X,$fot(join(meet(top,complement(zero)),complement(top)))),bind(Y,$fot(join(complement(top),meet(top,complement(zero))))),bind(Z,$fot(join(zero,meet(top,complement(zero)))))]]) ).
cnf(refute_0_519,plain,
( join(complement(top),meet(top,complement(zero))) != join(zero,meet(top,complement(zero)))
| join(meet(top,complement(zero)),complement(top)) = join(zero,meet(top,complement(zero))) ),
inference(resolve,[$cnf( $equal(join(meet(top,complement(zero)),complement(top)),join(complement(top),meet(top,complement(zero)))) )],[refute_0_517,refute_0_518]) ).
cnf(refute_0_520,plain,
join(meet(top,complement(zero)),complement(top)) = join(zero,meet(top,complement(zero))),
inference(resolve,[$cnf( $equal(join(complement(top),meet(top,complement(zero))),join(zero,meet(top,complement(zero)))) )],[refute_0_516,refute_0_519]) ).
cnf(refute_0_521,plain,
( join(meet(top,complement(zero)),complement(top)) != join(zero,meet(top,complement(zero)))
| top != join(meet(top,complement(zero)),complement(top))
| top = join(zero,meet(top,complement(zero))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(meet(top,complement(zero)),complement(top))) ),[1],$fot(join(zero,meet(top,complement(zero))))]]) ).
cnf(refute_0_522,plain,
( top != join(meet(top,complement(zero)),complement(top))
| top = join(zero,meet(top,complement(zero))) ),
inference(resolve,[$cnf( $equal(join(meet(top,complement(zero)),complement(top)),join(zero,meet(top,complement(zero)))) )],[refute_0_520,refute_0_521]) ).
cnf(refute_0_523,plain,
top = join(zero,meet(top,complement(zero))),
inference(resolve,[$cnf( $equal(top,join(meet(top,complement(zero)),complement(top))) )],[refute_0_512,refute_0_522]) ).
cnf(refute_0_524,plain,
( top != join(zero,meet(top,complement(zero)))
| join(zero,meet(top,complement(zero))) = top ),
inference(subst,[],[refute_0_7:[bind(X,$fot(top)),bind(Y,$fot(join(zero,meet(top,complement(zero)))))]]) ).
cnf(refute_0_525,plain,
join(zero,meet(top,complement(zero))) = top,
inference(resolve,[$cnf( $equal(top,join(zero,meet(top,complement(zero)))) )],[refute_0_523,refute_0_524]) ).
cnf(refute_0_526,plain,
meet(X0,top) = complement(join(complement(X0),complement(top))),
inference(subst,[],[refute_0_61:[bind(X1,$fot(top))]]) ).
cnf(refute_0_527,plain,
( complement(top) != zero
| meet(X0,top) != complement(join(complement(X0),complement(top)))
| meet(X0,top) = complement(join(complement(X0),zero)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X0,top),complement(join(complement(X0),complement(top)))) ),[1,0,1],$fot(zero)]]) ).
cnf(refute_0_528,plain,
( meet(X0,top) != complement(join(complement(X0),complement(top)))
| meet(X0,top) = complement(join(complement(X0),zero)) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_108,refute_0_527]) ).
cnf(refute_0_529,plain,
meet(X0,top) = complement(join(complement(X0),zero)),
inference(resolve,[$cnf( $equal(meet(X0,top),complement(join(complement(X0),complement(top)))) )],[refute_0_526,refute_0_528]) ).
cnf(refute_0_530,plain,
complement(join(zero,complement(X0))) = meet(top,X0),
inference(subst,[],[refute_0_366:[bind(X1,$fot(X0))]]) ).
cnf(refute_0_531,plain,
join(complement(X0),zero) = join(zero,complement(X0)),
inference(subst,[],[refute_0_9:[bind(X0,$fot(zero)),bind(X1,$fot(complement(X0)))]]) ).
cnf(refute_0_532,plain,
complement(join(complement(X0),zero)) = complement(join(complement(X0),zero)),
introduced(tautology,[refl,[$fot(complement(join(complement(X0),zero)))]]) ).
cnf(refute_0_533,plain,
( complement(join(complement(X0),zero)) != complement(join(complement(X0),zero))
| join(complement(X0),zero) != join(zero,complement(X0))
| complement(join(complement(X0),zero)) = complement(join(zero,complement(X0))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(X0),zero)),complement(join(complement(X0),zero))) ),[1,0],$fot(join(zero,complement(X0)))]]) ).
cnf(refute_0_534,plain,
( join(complement(X0),zero) != join(zero,complement(X0))
| complement(join(complement(X0),zero)) = complement(join(zero,complement(X0))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X0),zero)),complement(join(complement(X0),zero))) )],[refute_0_532,refute_0_533]) ).
cnf(refute_0_535,plain,
complement(join(complement(X0),zero)) = complement(join(zero,complement(X0))),
inference(resolve,[$cnf( $equal(join(complement(X0),zero),join(zero,complement(X0))) )],[refute_0_531,refute_0_534]) ).
cnf(refute_0_536,plain,
( complement(join(complement(X0),zero)) != complement(join(zero,complement(X0)))
| complement(join(zero,complement(X0))) != meet(top,X0)
| complement(join(complement(X0),zero)) = meet(top,X0) ),
inference(subst,[],[refute_0_100:[bind(X,$fot(complement(join(complement(X0),zero)))),bind(Y,$fot(complement(join(zero,complement(X0))))),bind(Z,$fot(meet(top,X0)))]]) ).
cnf(refute_0_537,plain,
( complement(join(zero,complement(X0))) != meet(top,X0)
| complement(join(complement(X0),zero)) = meet(top,X0) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X0),zero)),complement(join(zero,complement(X0)))) )],[refute_0_535,refute_0_536]) ).
cnf(refute_0_538,plain,
complement(join(complement(X0),zero)) = meet(top,X0),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(X0))),meet(top,X0)) )],[refute_0_530,refute_0_537]) ).
cnf(refute_0_539,plain,
( complement(join(complement(X0),zero)) != meet(top,X0)
| meet(X0,top) != complement(join(complement(X0),zero))
| meet(X0,top) = meet(top,X0) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X0,top),complement(join(complement(X0),zero))) ),[1],$fot(meet(top,X0))]]) ).
cnf(refute_0_540,plain,
( meet(X0,top) != complement(join(complement(X0),zero))
| meet(X0,top) = meet(top,X0) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X0),zero)),meet(top,X0)) )],[refute_0_538,refute_0_539]) ).
cnf(refute_0_541,plain,
meet(X0,top) = meet(top,X0),
inference(resolve,[$cnf( $equal(meet(X0,top),complement(join(complement(X0),zero))) )],[refute_0_529,refute_0_540]) ).
cnf(refute_0_542,plain,
meet(complement(zero),top) = meet(top,complement(zero)),
inference(subst,[],[refute_0_541:[bind(X0,$fot(complement(zero)))]]) ).
cnf(refute_0_543,plain,
join(zero,meet(complement(zero),top)) = join(zero,meet(complement(zero),top)),
introduced(tautology,[refl,[$fot(join(zero,meet(complement(zero),top)))]]) ).
cnf(refute_0_544,plain,
( join(zero,meet(complement(zero),top)) != join(zero,meet(complement(zero),top))
| meet(complement(zero),top) != meet(top,complement(zero))
| join(zero,meet(complement(zero),top)) = join(zero,meet(top,complement(zero))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,meet(complement(zero),top)),join(zero,meet(complement(zero),top))) ),[1,1],$fot(meet(top,complement(zero)))]]) ).
cnf(refute_0_545,plain,
( meet(complement(zero),top) != meet(top,complement(zero))
| join(zero,meet(complement(zero),top)) = join(zero,meet(top,complement(zero))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(complement(zero),top)),join(zero,meet(complement(zero),top))) )],[refute_0_543,refute_0_544]) ).
cnf(refute_0_546,plain,
join(zero,meet(complement(zero),top)) = join(zero,meet(top,complement(zero))),
inference(resolve,[$cnf( $equal(meet(complement(zero),top),meet(top,complement(zero))) )],[refute_0_542,refute_0_545]) ).
cnf(refute_0_547,plain,
( join(zero,meet(complement(zero),top)) != join(zero,meet(top,complement(zero)))
| join(zero,meet(top,complement(zero))) != top
| join(zero,meet(complement(zero),top)) = top ),
inference(subst,[],[refute_0_100:[bind(X,$fot(join(zero,meet(complement(zero),top)))),bind(Y,$fot(join(zero,meet(top,complement(zero))))),bind(Z,$fot(top))]]) ).
cnf(refute_0_548,plain,
( join(zero,meet(top,complement(zero))) != top
| join(zero,meet(complement(zero),top)) = top ),
inference(resolve,[$cnf( $equal(join(zero,meet(complement(zero),top)),join(zero,meet(top,complement(zero)))) )],[refute_0_546,refute_0_547]) ).
cnf(refute_0_549,plain,
join(zero,meet(complement(zero),top)) = top,
inference(resolve,[$cnf( $equal(join(zero,meet(top,complement(zero))),top) )],[refute_0_525,refute_0_548]) ).
cnf(refute_0_550,plain,
join(meet(complement(zero),top),zero) = join(zero,meet(complement(zero),top)),
inference(subst,[],[refute_0_9:[bind(X0,$fot(zero)),bind(X1,$fot(meet(complement(zero),top)))]]) ).
cnf(refute_0_551,plain,
( join(meet(complement(zero),top),zero) != join(zero,meet(complement(zero),top))
| join(zero,meet(complement(zero),top)) != top
| join(meet(complement(zero),top),zero) = top ),
inference(subst,[],[refute_0_100:[bind(X,$fot(join(meet(complement(zero),top),zero))),bind(Y,$fot(join(zero,meet(complement(zero),top)))),bind(Z,$fot(top))]]) ).
cnf(refute_0_552,plain,
( join(zero,meet(complement(zero),top)) != top
| join(meet(complement(zero),top),zero) = top ),
inference(resolve,[$cnf( $equal(join(meet(complement(zero),top),zero),join(zero,meet(complement(zero),top))) )],[refute_0_550,refute_0_551]) ).
cnf(refute_0_553,plain,
join(meet(complement(zero),top),zero) = top,
inference(resolve,[$cnf( $equal(join(zero,meet(complement(zero),top)),top) )],[refute_0_549,refute_0_552]) ).
cnf(refute_0_554,plain,
( complement(zero) != join(meet(complement(zero),top),zero)
| join(meet(complement(zero),top),zero) != top
| complement(zero) = top ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(zero),top) ),[0],$fot(join(meet(complement(zero),top),zero))]]) ).
cnf(refute_0_555,plain,
( complement(zero) != join(meet(complement(zero),top),zero)
| complement(zero) = top ),
inference(resolve,[$cnf( $equal(join(meet(complement(zero),top),zero),top) )],[refute_0_553,refute_0_554]) ).
cnf(refute_0_556,plain,
complement(zero) = top,
inference(resolve,[$cnf( $equal(complement(zero),join(meet(complement(zero),top),zero)) )],[refute_0_501,refute_0_555]) ).
cnf(refute_0_557,plain,
( complement(zero) != top
| zero != join(complement(converse(top)),meet(zero,converse(complement(converse(complement(zero))))))
| zero = join(complement(converse(top)),meet(zero,converse(complement(converse(top))))) ),
introduced(tautology,[equality,[$cnf( $equal(zero,join(complement(converse(top)),meet(zero,converse(complement(converse(complement(zero))))))) ),[1,1,1,0,0,0],$fot(top)]]) ).
cnf(refute_0_558,plain,
( zero != join(complement(converse(top)),meet(zero,converse(complement(converse(complement(zero))))))
| zero = join(complement(converse(top)),meet(zero,converse(complement(converse(top))))) ),
inference(resolve,[$cnf( $equal(complement(zero),top) )],[refute_0_556,refute_0_557]) ).
cnf(refute_0_559,plain,
zero = join(complement(converse(top)),meet(zero,converse(complement(converse(top))))),
inference(resolve,[$cnf( $equal(zero,join(complement(converse(top)),meet(zero,converse(complement(converse(complement(zero))))))) )],[refute_0_472,refute_0_558]) ).
cnf(refute_0_560,plain,
( zero != join(complement(converse(top)),meet(zero,converse(complement(converse(top)))))
| join(complement(converse(top)),meet(zero,converse(complement(converse(top))))) = zero ),
inference(subst,[],[refute_0_7:[bind(X,$fot(zero)),bind(Y,$fot(join(complement(converse(top)),meet(zero,converse(complement(converse(top)))))))]]) ).
cnf(refute_0_561,plain,
join(complement(converse(top)),meet(zero,converse(complement(converse(top))))) = zero,
inference(resolve,[$cnf( $equal(zero,join(complement(converse(top)),meet(zero,converse(complement(converse(top)))))) )],[refute_0_559,refute_0_560]) ).
cnf(refute_0_562,plain,
( converse(top) != join(meet(converse(top),meet(zero,converse(complement(converse(top))))),complement(join(complement(converse(top)),meet(zero,converse(complement(converse(top)))))))
| join(complement(converse(top)),meet(zero,converse(complement(converse(top))))) != zero
| converse(top) = join(meet(converse(top),meet(zero,converse(complement(converse(top))))),complement(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(top),join(meet(converse(top),meet(zero,converse(complement(converse(top))))),complement(join(complement(converse(top)),meet(zero,converse(complement(converse(top)))))))) ),[1,1,0],$fot(zero)]]) ).
cnf(refute_0_563,plain,
( converse(top) != join(meet(converse(top),meet(zero,converse(complement(converse(top))))),complement(join(complement(converse(top)),meet(zero,converse(complement(converse(top)))))))
| converse(top) = join(meet(converse(top),meet(zero,converse(complement(converse(top))))),complement(zero)) ),
inference(resolve,[$cnf( $equal(join(complement(converse(top)),meet(zero,converse(complement(converse(top))))),zero) )],[refute_0_561,refute_0_562]) ).
cnf(refute_0_564,plain,
converse(top) = join(meet(converse(top),meet(zero,converse(complement(converse(top))))),complement(zero)),
inference(resolve,[$cnf( $equal(converse(top),join(meet(converse(top),meet(zero,converse(complement(converse(top))))),complement(join(complement(converse(top)),meet(zero,converse(complement(converse(top)))))))) )],[refute_0_448,refute_0_563]) ).
cnf(refute_0_565,plain,
join(complement(zero),meet(converse(top),meet(zero,converse(complement(converse(top)))))) = join(complement(zero),meet(converse(top),meet(zero,converse(complement(converse(top)))))),
introduced(tautology,[refl,[$fot(join(complement(zero),meet(converse(top),meet(zero,converse(complement(converse(top)))))))]]) ).
cnf(refute_0_566,plain,
( complement(zero) != top
| join(complement(zero),meet(converse(top),meet(zero,converse(complement(converse(top)))))) != join(complement(zero),meet(converse(top),meet(zero,converse(complement(converse(top))))))
| join(complement(zero),meet(converse(top),meet(zero,converse(complement(converse(top)))))) = join(top,meet(converse(top),meet(zero,converse(complement(converse(top)))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(zero),meet(converse(top),meet(zero,converse(complement(converse(top)))))),join(complement(zero),meet(converse(top),meet(zero,converse(complement(converse(top))))))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_567,plain,
( complement(zero) != top
| join(complement(zero),meet(converse(top),meet(zero,converse(complement(converse(top)))))) = join(top,meet(converse(top),meet(zero,converse(complement(converse(top)))))) ),
inference(resolve,[$cnf( $equal(join(complement(zero),meet(converse(top),meet(zero,converse(complement(converse(top)))))),join(complement(zero),meet(converse(top),meet(zero,converse(complement(converse(top))))))) )],[refute_0_565,refute_0_566]) ).
cnf(refute_0_568,plain,
join(complement(zero),meet(converse(top),meet(zero,converse(complement(converse(top)))))) = join(top,meet(converse(top),meet(zero,converse(complement(converse(top)))))),
inference(resolve,[$cnf( $equal(complement(zero),top) )],[refute_0_556,refute_0_567]) ).
cnf(refute_0_569,plain,
join(meet(converse(top),meet(zero,converse(complement(converse(top))))),complement(zero)) = join(complement(zero),meet(converse(top),meet(zero,converse(complement(converse(top)))))),
inference(subst,[],[refute_0_9:[bind(X0,$fot(complement(zero))),bind(X1,$fot(meet(converse(top),meet(zero,converse(complement(converse(top)))))))]]) ).
cnf(refute_0_570,plain,
( join(complement(zero),meet(converse(top),meet(zero,converse(complement(converse(top)))))) != join(top,meet(converse(top),meet(zero,converse(complement(converse(top))))))
| join(meet(converse(top),meet(zero,converse(complement(converse(top))))),complement(zero)) != join(complement(zero),meet(converse(top),meet(zero,converse(complement(converse(top))))))
| join(meet(converse(top),meet(zero,converse(complement(converse(top))))),complement(zero)) = join(top,meet(converse(top),meet(zero,converse(complement(converse(top)))))) ),
inference(subst,[],[refute_0_100:[bind(X,$fot(join(meet(converse(top),meet(zero,converse(complement(converse(top))))),complement(zero)))),bind(Y,$fot(join(complement(zero),meet(converse(top),meet(zero,converse(complement(converse(top)))))))),bind(Z,$fot(join(top,meet(converse(top),meet(zero,converse(complement(converse(top))))))))]]) ).
cnf(refute_0_571,plain,
( join(complement(zero),meet(converse(top),meet(zero,converse(complement(converse(top)))))) != join(top,meet(converse(top),meet(zero,converse(complement(converse(top))))))
| join(meet(converse(top),meet(zero,converse(complement(converse(top))))),complement(zero)) = join(top,meet(converse(top),meet(zero,converse(complement(converse(top)))))) ),
inference(resolve,[$cnf( $equal(join(meet(converse(top),meet(zero,converse(complement(converse(top))))),complement(zero)),join(complement(zero),meet(converse(top),meet(zero,converse(complement(converse(top))))))) )],[refute_0_569,refute_0_570]) ).
cnf(refute_0_572,plain,
join(meet(converse(top),meet(zero,converse(complement(converse(top))))),complement(zero)) = join(top,meet(converse(top),meet(zero,converse(complement(converse(top)))))),
inference(resolve,[$cnf( $equal(join(complement(zero),meet(converse(top),meet(zero,converse(complement(converse(top)))))),join(top,meet(converse(top),meet(zero,converse(complement(converse(top))))))) )],[refute_0_568,refute_0_571]) ).
cnf(refute_0_573,plain,
( converse(top) != join(meet(converse(top),meet(zero,converse(complement(converse(top))))),complement(zero))
| join(meet(converse(top),meet(zero,converse(complement(converse(top))))),complement(zero)) != join(top,meet(converse(top),meet(zero,converse(complement(converse(top))))))
| converse(top) = join(top,meet(converse(top),meet(zero,converse(complement(converse(top)))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(top),join(top,meet(converse(top),meet(zero,converse(complement(converse(top))))))) ),[0],$fot(join(meet(converse(top),meet(zero,converse(complement(converse(top))))),complement(zero)))]]) ).
cnf(refute_0_574,plain,
( converse(top) != join(meet(converse(top),meet(zero,converse(complement(converse(top))))),complement(zero))
| converse(top) = join(top,meet(converse(top),meet(zero,converse(complement(converse(top)))))) ),
inference(resolve,[$cnf( $equal(join(meet(converse(top),meet(zero,converse(complement(converse(top))))),complement(zero)),join(top,meet(converse(top),meet(zero,converse(complement(converse(top))))))) )],[refute_0_572,refute_0_573]) ).
cnf(refute_0_575,plain,
converse(top) = join(top,meet(converse(top),meet(zero,converse(complement(converse(top)))))),
inference(resolve,[$cnf( $equal(converse(top),join(meet(converse(top),meet(zero,converse(complement(converse(top))))),complement(zero))) )],[refute_0_564,refute_0_574]) ).
cnf(refute_0_576,plain,
( top != join(top,X_53)
| join(top,X_53) = top ),
inference(subst,[],[refute_0_7:[bind(X,$fot(top)),bind(Y,$fot(join(top,X_53)))]]) ).
cnf(refute_0_577,plain,
join(top,X_53) = top,
inference(resolve,[$cnf( $equal(top,join(top,X_53)) )],[refute_0_427,refute_0_576]) ).
cnf(refute_0_578,plain,
join(top,meet(converse(top),meet(zero,converse(complement(converse(top)))))) = top,
inference(subst,[],[refute_0_577:[bind(X_53,$fot(meet(converse(top),meet(zero,converse(complement(converse(top)))))))]]) ).
cnf(refute_0_579,plain,
( converse(top) != join(top,meet(converse(top),meet(zero,converse(complement(converse(top))))))
| join(top,meet(converse(top),meet(zero,converse(complement(converse(top)))))) != top
| converse(top) = top ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(top),top) ),[0],$fot(join(top,meet(converse(top),meet(zero,converse(complement(converse(top)))))))]]) ).
cnf(refute_0_580,plain,
( converse(top) != join(top,meet(converse(top),meet(zero,converse(complement(converse(top))))))
| converse(top) = top ),
inference(resolve,[$cnf( $equal(join(top,meet(converse(top),meet(zero,converse(complement(converse(top)))))),top) )],[refute_0_578,refute_0_579]) ).
cnf(refute_0_581,plain,
converse(top) = top,
inference(resolve,[$cnf( $equal(converse(top),join(top,meet(converse(top),meet(zero,converse(complement(converse(top))))))) )],[refute_0_575,refute_0_580]) ).
cnf(refute_0_582,plain,
top = join(join(X_75,X_76),complement(join(X_75,X_76))),
inference(subst,[],[refute_0_59:[bind(X0,$fot(join(X_75,X_76)))]]) ).
cnf(refute_0_583,plain,
join(X_75,join(X_76,complement(join(X_75,X_76)))) = join(join(X_75,X_76),complement(join(X_75,X_76))),
inference(subst,[],[refute_0_68:[bind(X0,$fot(X_75)),bind(X1,$fot(X_76)),bind(X2,$fot(complement(join(X_75,X_76))))]]) ).
cnf(refute_0_584,plain,
( join(X_75,join(X_76,complement(join(X_75,X_76)))) != join(join(X_75,X_76),complement(join(X_75,X_76)))
| join(join(X_75,X_76),complement(join(X_75,X_76))) = join(X_75,join(X_76,complement(join(X_75,X_76)))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(X_75,join(X_76,complement(join(X_75,X_76)))))),bind(Y,$fot(join(join(X_75,X_76),complement(join(X_75,X_76)))))]]) ).
cnf(refute_0_585,plain,
join(join(X_75,X_76),complement(join(X_75,X_76))) = join(X_75,join(X_76,complement(join(X_75,X_76)))),
inference(resolve,[$cnf( $equal(join(X_75,join(X_76,complement(join(X_75,X_76)))),join(join(X_75,X_76),complement(join(X_75,X_76)))) )],[refute_0_583,refute_0_584]) ).
cnf(refute_0_586,plain,
( join(join(X_75,X_76),complement(join(X_75,X_76))) != join(X_75,join(X_76,complement(join(X_75,X_76))))
| top != join(join(X_75,X_76),complement(join(X_75,X_76)))
| top = join(X_75,join(X_76,complement(join(X_75,X_76)))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(join(X_75,X_76),complement(join(X_75,X_76)))) ),[1],$fot(join(X_75,join(X_76,complement(join(X_75,X_76)))))]]) ).
cnf(refute_0_587,plain,
( top != join(join(X_75,X_76),complement(join(X_75,X_76)))
| top = join(X_75,join(X_76,complement(join(X_75,X_76)))) ),
inference(resolve,[$cnf( $equal(join(join(X_75,X_76),complement(join(X_75,X_76))),join(X_75,join(X_76,complement(join(X_75,X_76))))) )],[refute_0_585,refute_0_586]) ).
cnf(refute_0_588,plain,
top = join(X_75,join(X_76,complement(join(X_75,X_76)))),
inference(resolve,[$cnf( $equal(top,join(join(X_75,X_76),complement(join(X_75,X_76)))) )],[refute_0_582,refute_0_587]) ).
cnf(refute_0_589,plain,
top = join(X_75,join(top,complement(join(X_75,top)))),
inference(subst,[],[refute_0_588:[bind(X_76,$fot(top))]]) ).
cnf(refute_0_590,plain,
top = join(top,complement(join(X_75,top))),
inference(subst,[],[refute_0_257:[bind(X_96,$fot(join(X_75,top)))]]) ).
cnf(refute_0_591,plain,
( top != join(top,complement(join(X_75,top)))
| join(top,complement(join(X_75,top))) = top ),
inference(subst,[],[refute_0_7:[bind(X,$fot(top)),bind(Y,$fot(join(top,complement(join(X_75,top)))))]]) ).
cnf(refute_0_592,plain,
join(top,complement(join(X_75,top))) = top,
inference(resolve,[$cnf( $equal(top,join(top,complement(join(X_75,top)))) )],[refute_0_590,refute_0_591]) ).
cnf(refute_0_593,plain,
( join(top,complement(join(X_75,top))) != top
| top != join(X_75,join(top,complement(join(X_75,top))))
| top = join(X_75,top) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(X_75,join(top,complement(join(X_75,top))))) ),[1,1],$fot(top)]]) ).
cnf(refute_0_594,plain,
( top != join(X_75,join(top,complement(join(X_75,top))))
| top = join(X_75,top) ),
inference(resolve,[$cnf( $equal(join(top,complement(join(X_75,top))),top) )],[refute_0_592,refute_0_593]) ).
cnf(refute_0_595,plain,
top = join(X_75,top),
inference(resolve,[$cnf( $equal(top,join(X_75,join(top,complement(join(X_75,top))))) )],[refute_0_589,refute_0_594]) ).
cnf(refute_0_596,plain,
( top != join(X_75,top)
| join(X_75,top) = top ),
inference(subst,[],[refute_0_7:[bind(X,$fot(top)),bind(Y,$fot(join(X_75,top)))]]) ).
cnf(refute_0_597,plain,
join(X_75,top) = top,
inference(resolve,[$cnf( $equal(top,join(X_75,top)) )],[refute_0_595,refute_0_596]) ).
cnf(refute_0_598,plain,
join(one,top) = top,
inference(subst,[],[refute_0_597:[bind(X_75,$fot(one))]]) ).
cnf(refute_0_599,plain,
converse(join(one,top)) = converse(join(one,top)),
introduced(tautology,[refl,[$fot(converse(join(one,top)))]]) ).
cnf(refute_0_600,plain,
( converse(join(one,top)) != converse(join(one,top))
| join(one,top) != top
| converse(join(one,top)) = converse(top) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(one,top)),converse(join(one,top))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_601,plain,
( join(one,top) != top
| converse(join(one,top)) = converse(top) ),
inference(resolve,[$cnf( $equal(converse(join(one,top)),converse(join(one,top))) )],[refute_0_599,refute_0_600]) ).
cnf(refute_0_602,plain,
converse(join(one,top)) = converse(top),
inference(resolve,[$cnf( $equal(join(one,top),top) )],[refute_0_598,refute_0_601]) ).
cnf(refute_0_603,plain,
( converse(join(one,top)) != converse(top)
| converse(top) != top
| converse(join(one,top)) = top ),
inference(subst,[],[refute_0_100:[bind(X,$fot(converse(join(one,top)))),bind(Y,$fot(converse(top))),bind(Z,$fot(top))]]) ).
cnf(refute_0_604,plain,
( converse(top) != top
| converse(join(one,top)) = top ),
inference(resolve,[$cnf( $equal(converse(join(one,top)),converse(top)) )],[refute_0_602,refute_0_603]) ).
cnf(refute_0_605,plain,
converse(join(one,top)) = top,
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_0_581,refute_0_604]) ).
cnf(refute_0_606,plain,
converse(join(converse(one),X_13)) = join(one,converse(X_13)),
inference(subst,[],[refute_0_454:[bind(X0,$fot(one))]]) ).
cnf(refute_0_607,plain,
( converse(join(converse(one),X_13)) != join(one,converse(X_13))
| converse(one) != one
| converse(join(one,X_13)) = join(one,converse(X_13)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(one),X_13)),join(one,converse(X_13))) ),[0,0,0],$fot(one)]]) ).
cnf(refute_0_608,plain,
( converse(join(converse(one),X_13)) != join(one,converse(X_13))
| converse(join(one,X_13)) = join(one,converse(X_13)) ),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_40,refute_0_607]) ).
cnf(refute_0_609,plain,
converse(join(one,X_13)) = join(one,converse(X_13)),
inference(resolve,[$cnf( $equal(converse(join(converse(one),X_13)),join(one,converse(X_13))) )],[refute_0_606,refute_0_608]) ).
cnf(refute_0_610,plain,
( converse(join(one,X_13)) != join(one,converse(X_13))
| join(one,converse(X_13)) = converse(join(one,X_13)) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(converse(join(one,X_13)))),bind(Y,$fot(join(one,converse(X_13))))]]) ).
cnf(refute_0_611,plain,
join(one,converse(X_13)) = converse(join(one,X_13)),
inference(resolve,[$cnf( $equal(converse(join(one,X_13)),join(one,converse(X_13))) )],[refute_0_609,refute_0_610]) ).
cnf(refute_0_612,plain,
join(one,converse(top)) = converse(join(one,top)),
inference(subst,[],[refute_0_611:[bind(X_13,$fot(top))]]) ).
cnf(refute_0_613,plain,
( converse(join(one,top)) != top
| join(one,converse(top)) != converse(join(one,top))
| join(one,converse(top)) = top ),
inference(subst,[],[refute_0_100:[bind(X,$fot(join(one,converse(top)))),bind(Y,$fot(converse(join(one,top)))),bind(Z,$fot(top))]]) ).
cnf(refute_0_614,plain,
( converse(join(one,top)) != top
| join(one,converse(top)) = top ),
inference(resolve,[$cnf( $equal(join(one,converse(top)),converse(join(one,top))) )],[refute_0_612,refute_0_613]) ).
cnf(refute_0_615,plain,
join(one,converse(top)) = top,
inference(resolve,[$cnf( $equal(converse(join(one,top)),top) )],[refute_0_605,refute_0_614]) ).
cnf(refute_0_616,plain,
composition(join(one,converse(top)),complement(top)) = composition(join(one,converse(top)),complement(top)),
introduced(tautology,[refl,[$fot(composition(join(one,converse(top)),complement(top)))]]) ).
cnf(refute_0_617,plain,
( composition(join(one,converse(top)),complement(top)) != composition(join(one,converse(top)),complement(top))
| join(one,converse(top)) != top
| composition(join(one,converse(top)),complement(top)) = composition(top,complement(top)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,converse(top)),complement(top)),composition(join(one,converse(top)),complement(top))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_618,plain,
( join(one,converse(top)) != top
| composition(join(one,converse(top)),complement(top)) = composition(top,complement(top)) ),
inference(resolve,[$cnf( $equal(composition(join(one,converse(top)),complement(top)),composition(join(one,converse(top)),complement(top))) )],[refute_0_616,refute_0_617]) ).
cnf(refute_0_619,plain,
composition(join(one,converse(top)),complement(top)) = composition(top,complement(top)),
inference(resolve,[$cnf( $equal(join(one,converse(top)),top) )],[refute_0_615,refute_0_618]) ).
cnf(refute_0_620,plain,
( composition(join(one,converse(top)),complement(top)) != composition(top,complement(top))
| composition(top,complement(top)) != composition(top,zero)
| composition(join(one,converse(top)),complement(top)) = composition(top,zero) ),
inference(subst,[],[refute_0_100:[bind(X,$fot(composition(join(one,converse(top)),complement(top)))),bind(Y,$fot(composition(top,complement(top)))),bind(Z,$fot(composition(top,zero)))]]) ).
cnf(refute_0_621,plain,
( composition(top,complement(top)) != composition(top,zero)
| composition(join(one,converse(top)),complement(top)) = composition(top,zero) ),
inference(resolve,[$cnf( $equal(composition(join(one,converse(top)),complement(top)),composition(top,complement(top))) )],[refute_0_619,refute_0_620]) ).
cnf(refute_0_622,plain,
composition(join(one,converse(top)),complement(top)) = composition(top,zero),
inference(resolve,[$cnf( $equal(composition(top,complement(top)),composition(top,zero)) )],[refute_0_447,refute_0_621]) ).
cnf(refute_0_623,plain,
composition(join(X_90,one),X_91) = join(X_91,composition(X_90,X_91)),
inference(subst,[],[refute_0_57:[bind(X_87,$fot(X_90)),bind(X_89,$fot(X_91))]]) ).
cnf(refute_0_624,plain,
join(one,X_90) = join(X_90,one),
inference(subst,[],[refute_0_4:[bind(X0,$fot(one)),bind(X1,$fot(X_90))]]) ).
cnf(refute_0_625,plain,
( join(one,X_90) != join(X_90,one)
| join(X_90,one) = join(one,X_90) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(one,X_90))),bind(Y,$fot(join(X_90,one)))]]) ).
cnf(refute_0_626,plain,
join(X_90,one) = join(one,X_90),
inference(resolve,[$cnf( $equal(join(one,X_90),join(X_90,one)) )],[refute_0_624,refute_0_625]) ).
cnf(refute_0_627,plain,
( composition(join(X_90,one),X_91) != join(X_91,composition(X_90,X_91))
| join(X_90,one) != join(one,X_90)
| composition(join(one,X_90),X_91) = join(X_91,composition(X_90,X_91)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(X_90,one),X_91),join(X_91,composition(X_90,X_91))) ),[0,0],$fot(join(one,X_90))]]) ).
cnf(refute_0_628,plain,
( composition(join(X_90,one),X_91) != join(X_91,composition(X_90,X_91))
| composition(join(one,X_90),X_91) = join(X_91,composition(X_90,X_91)) ),
inference(resolve,[$cnf( $equal(join(X_90,one),join(one,X_90)) )],[refute_0_626,refute_0_627]) ).
cnf(refute_0_629,plain,
composition(join(one,X_90),X_91) = join(X_91,composition(X_90,X_91)),
inference(resolve,[$cnf( $equal(composition(join(X_90,one),X_91),join(X_91,composition(X_90,X_91))) )],[refute_0_623,refute_0_628]) ).
cnf(refute_0_630,plain,
( composition(join(X_87,one),X_89) != join(X_89,composition(X_87,X_89))
| join(X_89,composition(X_87,X_89)) = composition(join(X_87,one),X_89) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(composition(join(X_87,one),X_89))),bind(Y,$fot(join(X_89,composition(X_87,X_89))))]]) ).
cnf(refute_0_631,plain,
join(X_89,composition(X_87,X_89)) = composition(join(X_87,one),X_89),
inference(resolve,[$cnf( $equal(composition(join(X_87,one),X_89),join(X_89,composition(X_87,X_89))) )],[refute_0_57,refute_0_630]) ).
cnf(refute_0_632,plain,
join(X_91,composition(X_90,X_91)) = composition(join(X_90,one),X_91),
inference(subst,[],[refute_0_631:[bind(X_87,$fot(X_90)),bind(X_89,$fot(X_91))]]) ).
cnf(refute_0_633,plain,
( composition(join(one,X_90),X_91) != join(X_91,composition(X_90,X_91))
| join(X_91,composition(X_90,X_91)) != composition(join(X_90,one),X_91)
| composition(join(one,X_90),X_91) = composition(join(X_90,one),X_91) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(join(one,X_90),X_91),composition(join(X_90,one),X_91)) ),[0],$fot(join(X_91,composition(X_90,X_91)))]]) ).
cnf(refute_0_634,plain,
( composition(join(one,X_90),X_91) != join(X_91,composition(X_90,X_91))
| composition(join(one,X_90),X_91) = composition(join(X_90,one),X_91) ),
inference(resolve,[$cnf( $equal(join(X_91,composition(X_90,X_91)),composition(join(X_90,one),X_91)) )],[refute_0_632,refute_0_633]) ).
cnf(refute_0_635,plain,
composition(join(one,X_90),X_91) = composition(join(X_90,one),X_91),
inference(resolve,[$cnf( $equal(composition(join(one,X_90),X_91),join(X_91,composition(X_90,X_91))) )],[refute_0_629,refute_0_634]) ).
cnf(refute_0_636,plain,
( composition(join(one,X_90),X_91) != composition(join(X_90,one),X_91)
| composition(join(X_90,one),X_91) = composition(join(one,X_90),X_91) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(composition(join(one,X_90),X_91))),bind(Y,$fot(composition(join(X_90,one),X_91)))]]) ).
cnf(refute_0_637,plain,
composition(join(X_90,one),X_91) = composition(join(one,X_90),X_91),
inference(resolve,[$cnf( $equal(composition(join(one,X_90),X_91),composition(join(X_90,one),X_91)) )],[refute_0_635,refute_0_636]) ).
cnf(refute_0_638,plain,
composition(join(converse(top),one),complement(top)) = composition(join(one,converse(top)),complement(top)),
inference(subst,[],[refute_0_637:[bind(X_90,$fot(converse(top))),bind(X_91,$fot(complement(top)))]]) ).
cnf(refute_0_639,plain,
join(complement(top),composition(converse(top),complement(top))) = composition(join(converse(top),one),complement(top)),
inference(subst,[],[refute_0_631:[bind(X_87,$fot(converse(top))),bind(X_89,$fot(complement(top)))]]) ).
cnf(refute_0_640,plain,
( composition(join(converse(top),one),complement(top)) != composition(join(one,converse(top)),complement(top))
| join(complement(top),composition(converse(top),complement(top))) != composition(join(converse(top),one),complement(top))
| join(complement(top),composition(converse(top),complement(top))) = composition(join(one,converse(top)),complement(top)) ),
inference(subst,[],[refute_0_100:[bind(X,$fot(join(complement(top),composition(converse(top),complement(top))))),bind(Y,$fot(composition(join(converse(top),one),complement(top)))),bind(Z,$fot(composition(join(one,converse(top)),complement(top))))]]) ).
cnf(refute_0_641,plain,
( composition(join(converse(top),one),complement(top)) != composition(join(one,converse(top)),complement(top))
| join(complement(top),composition(converse(top),complement(top))) = composition(join(one,converse(top)),complement(top)) ),
inference(resolve,[$cnf( $equal(join(complement(top),composition(converse(top),complement(top))),composition(join(converse(top),one),complement(top))) )],[refute_0_639,refute_0_640]) ).
cnf(refute_0_642,plain,
join(complement(top),composition(converse(top),complement(top))) = composition(join(one,converse(top)),complement(top)),
inference(resolve,[$cnf( $equal(composition(join(converse(top),one),complement(top)),composition(join(one,converse(top)),complement(top))) )],[refute_0_638,refute_0_641]) ).
cnf(refute_0_643,plain,
( composition(join(one,converse(top)),complement(top)) != composition(top,zero)
| join(complement(top),composition(converse(top),complement(top))) != composition(join(one,converse(top)),complement(top))
| join(complement(top),composition(converse(top),complement(top))) = composition(top,zero) ),
inference(subst,[],[refute_0_100:[bind(X,$fot(join(complement(top),composition(converse(top),complement(top))))),bind(Y,$fot(composition(join(one,converse(top)),complement(top)))),bind(Z,$fot(composition(top,zero)))]]) ).
cnf(refute_0_644,plain,
( composition(join(one,converse(top)),complement(top)) != composition(top,zero)
| join(complement(top),composition(converse(top),complement(top))) = composition(top,zero) ),
inference(resolve,[$cnf( $equal(join(complement(top),composition(converse(top),complement(top))),composition(join(one,converse(top)),complement(top))) )],[refute_0_642,refute_0_643]) ).
cnf(refute_0_645,plain,
join(complement(top),composition(converse(top),complement(top))) = composition(top,zero),
inference(resolve,[$cnf( $equal(composition(join(one,converse(top)),complement(top)),composition(top,zero)) )],[refute_0_622,refute_0_644]) ).
cnf(refute_0_646,plain,
( join(complement(top),composition(converse(top),complement(top))) != complement(top)
| join(complement(top),composition(converse(top),complement(top))) != composition(top,zero)
| composition(top,zero) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),composition(converse(top),complement(top))),complement(top)) ),[0],$fot(composition(top,zero))]]) ).
cnf(refute_0_647,plain,
( join(complement(top),composition(converse(top),complement(top))) != complement(top)
| composition(top,zero) = complement(top) ),
inference(resolve,[$cnf( $equal(join(complement(top),composition(converse(top),complement(top))),composition(top,zero)) )],[refute_0_645,refute_0_646]) ).
cnf(refute_0_648,plain,
( complement(top) != zero
| composition(top,zero) != complement(top)
| composition(top,zero) = zero ),
introduced(tautology,[equality,[$cnf( $equal(composition(top,zero),complement(top)) ),[1],$fot(zero)]]) ).
cnf(refute_0_649,plain,
( composition(top,zero) != complement(top)
| composition(top,zero) = zero ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_108,refute_0_648]) ).
cnf(refute_0_650,plain,
( join(complement(top),composition(converse(top),complement(top))) != complement(top)
| composition(top,zero) = zero ),
inference(resolve,[$cnf( $equal(composition(top,zero),complement(top)) )],[refute_0_647,refute_0_649]) ).
cnf(refute_0_651,plain,
composition(top,zero) = zero,
inference(resolve,[$cnf( $equal(join(complement(top),composition(converse(top),complement(top))),complement(top)) )],[refute_0_443,refute_0_650]) ).
cnf(refute_0_652,plain,
( composition(join(top,X1),zero) != join(composition(top,zero),composition(X1,zero))
| composition(top,zero) != zero
| composition(join(top,X1),zero) = join(zero,composition(X1,zero)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(top,X1),zero),join(composition(top,zero),composition(X1,zero))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_653,plain,
( composition(join(top,X1),zero) != join(composition(top,zero),composition(X1,zero))
| composition(join(top,X1),zero) = join(zero,composition(X1,zero)) ),
inference(resolve,[$cnf( $equal(composition(top,zero),zero) )],[refute_0_651,refute_0_652]) ).
cnf(refute_0_654,plain,
composition(join(top,X1),zero) = join(zero,composition(X1,zero)),
inference(resolve,[$cnf( $equal(composition(join(top,X1),zero),join(composition(top,zero),composition(X1,zero))) )],[refute_0_2,refute_0_653]) ).
cnf(refute_0_655,plain,
join(top,X1) = top,
inference(subst,[],[refute_0_577:[bind(X_53,$fot(X1))]]) ).
cnf(refute_0_656,plain,
composition(join(top,X1),zero) = composition(join(top,X1),zero),
introduced(tautology,[refl,[$fot(composition(join(top,X1),zero))]]) ).
cnf(refute_0_657,plain,
( composition(join(top,X1),zero) != composition(join(top,X1),zero)
| join(top,X1) != top
| composition(join(top,X1),zero) = composition(top,zero) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(top,X1),zero),composition(join(top,X1),zero)) ),[1,0],$fot(top)]]) ).
cnf(refute_0_658,plain,
( join(top,X1) != top
| composition(join(top,X1),zero) = composition(top,zero) ),
inference(resolve,[$cnf( $equal(composition(join(top,X1),zero),composition(join(top,X1),zero)) )],[refute_0_656,refute_0_657]) ).
cnf(refute_0_659,plain,
composition(join(top,X1),zero) = composition(top,zero),
inference(resolve,[$cnf( $equal(join(top,X1),top) )],[refute_0_655,refute_0_658]) ).
cnf(refute_0_660,plain,
( composition(join(top,X1),zero) != composition(top,zero)
| composition(top,zero) != zero
| composition(join(top,X1),zero) = zero ),
inference(subst,[],[refute_0_100:[bind(X,$fot(composition(join(top,X1),zero))),bind(Y,$fot(composition(top,zero))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_661,plain,
( composition(top,zero) != zero
| composition(join(top,X1),zero) = zero ),
inference(resolve,[$cnf( $equal(composition(join(top,X1),zero),composition(top,zero)) )],[refute_0_659,refute_0_660]) ).
cnf(refute_0_662,plain,
composition(join(top,X1),zero) = zero,
inference(resolve,[$cnf( $equal(composition(top,zero),zero) )],[refute_0_651,refute_0_661]) ).
cnf(refute_0_663,plain,
( composition(join(top,X1),zero) != join(zero,composition(X1,zero))
| composition(join(top,X1),zero) != zero
| zero = join(zero,composition(X1,zero)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(top,X1),zero),join(zero,composition(X1,zero))) ),[0],$fot(zero)]]) ).
cnf(refute_0_664,plain,
( composition(join(top,X1),zero) != join(zero,composition(X1,zero))
| zero = join(zero,composition(X1,zero)) ),
inference(resolve,[$cnf( $equal(composition(join(top,X1),zero),zero) )],[refute_0_662,refute_0_663]) ).
cnf(refute_0_665,plain,
join(zero,composition(X_90,zero)) = composition(X_90,zero),
inference(subst,[],[refute_0_202:[bind(X_31,$fot(composition(X_90,zero)))]]) ).
cnf(refute_0_666,plain,
composition(join(X_90,one),zero) = join(zero,composition(X_90,zero)),
inference(subst,[],[refute_0_57:[bind(X_87,$fot(X_90)),bind(X_89,$fot(zero))]]) ).
cnf(refute_0_667,plain,
( composition(join(X_90,one),zero) != join(zero,composition(X_90,zero))
| join(zero,composition(X_90,zero)) = composition(join(X_90,one),zero) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(composition(join(X_90,one),zero))),bind(Y,$fot(join(zero,composition(X_90,zero))))]]) ).
cnf(refute_0_668,plain,
join(zero,composition(X_90,zero)) = composition(join(X_90,one),zero),
inference(resolve,[$cnf( $equal(composition(join(X_90,one),zero),join(zero,composition(X_90,zero))) )],[refute_0_666,refute_0_667]) ).
cnf(refute_0_669,plain,
( join(zero,composition(X_90,zero)) != composition(X_90,zero)
| join(zero,composition(X_90,zero)) != composition(join(X_90,one),zero)
| composition(join(X_90,one),zero) = composition(X_90,zero) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,composition(X_90,zero)),composition(X_90,zero)) ),[0],$fot(composition(join(X_90,one),zero))]]) ).
cnf(refute_0_670,plain,
( join(zero,composition(X_90,zero)) != composition(X_90,zero)
| composition(join(X_90,one),zero) = composition(X_90,zero) ),
inference(resolve,[$cnf( $equal(join(zero,composition(X_90,zero)),composition(join(X_90,one),zero)) )],[refute_0_668,refute_0_669]) ).
cnf(refute_0_671,plain,
composition(join(X_90,one),zero) = composition(X_90,zero),
inference(resolve,[$cnf( $equal(join(zero,composition(X_90,zero)),composition(X_90,zero)) )],[refute_0_665,refute_0_670]) ).
cnf(refute_0_672,plain,
composition(join(X1,one),zero) = composition(X1,zero),
inference(subst,[],[refute_0_671:[bind(X_90,$fot(X1))]]) ).
cnf(refute_0_673,plain,
join(zero,composition(X1,zero)) = composition(join(X1,one),zero),
inference(subst,[],[refute_0_631:[bind(X_87,$fot(X1)),bind(X_89,$fot(zero))]]) ).
cnf(refute_0_674,plain,
( composition(join(X1,one),zero) != composition(X1,zero)
| join(zero,composition(X1,zero)) != composition(join(X1,one),zero)
| join(zero,composition(X1,zero)) = composition(X1,zero) ),
inference(subst,[],[refute_0_100:[bind(X,$fot(join(zero,composition(X1,zero)))),bind(Y,$fot(composition(join(X1,one),zero))),bind(Z,$fot(composition(X1,zero)))]]) ).
cnf(refute_0_675,plain,
( composition(join(X1,one),zero) != composition(X1,zero)
| join(zero,composition(X1,zero)) = composition(X1,zero) ),
inference(resolve,[$cnf( $equal(join(zero,composition(X1,zero)),composition(join(X1,one),zero)) )],[refute_0_673,refute_0_674]) ).
cnf(refute_0_676,plain,
join(zero,composition(X1,zero)) = composition(X1,zero),
inference(resolve,[$cnf( $equal(composition(join(X1,one),zero),composition(X1,zero)) )],[refute_0_672,refute_0_675]) ).
cnf(refute_0_677,plain,
( join(zero,composition(X1,zero)) != composition(X1,zero)
| zero != join(zero,composition(X1,zero))
| zero = composition(X1,zero) ),
introduced(tautology,[equality,[$cnf( $equal(zero,join(zero,composition(X1,zero))) ),[1],$fot(composition(X1,zero))]]) ).
cnf(refute_0_678,plain,
( zero != join(zero,composition(X1,zero))
| zero = composition(X1,zero) ),
inference(resolve,[$cnf( $equal(join(zero,composition(X1,zero)),composition(X1,zero)) )],[refute_0_676,refute_0_677]) ).
cnf(refute_0_679,plain,
( composition(join(top,X1),zero) != join(zero,composition(X1,zero))
| zero = composition(X1,zero) ),
inference(resolve,[$cnf( $equal(zero,join(zero,composition(X1,zero))) )],[refute_0_664,refute_0_678]) ).
cnf(refute_0_680,plain,
zero = composition(X1,zero),
inference(resolve,[$cnf( $equal(composition(join(top,X1),zero),join(zero,composition(X1,zero))) )],[refute_0_654,refute_0_679]) ).
cnf(refute_0_681,plain,
( zero != composition(X1,zero)
| composition(X1,zero) = zero ),
inference(subst,[],[refute_0_7:[bind(X,$fot(zero)),bind(Y,$fot(composition(X1,zero)))]]) ).
cnf(refute_0_682,plain,
composition(X1,zero) = zero,
inference(resolve,[$cnf( $equal(zero,composition(X1,zero)) )],[refute_0_680,refute_0_681]) ).
cnf(refute_0_683,plain,
composition(skolemFOFtoCNF_X0,zero) = zero,
inference(subst,[],[refute_0_682:[bind(X1,$fot(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_684,plain,
( composition(skolemFOFtoCNF_X0,zero) != zero
| zero != zero
| composition(skolemFOFtoCNF_X0,zero) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(skolemFOFtoCNF_X0,zero),zero) ),[0],$fot(zero)]]) ).
cnf(refute_0_685,plain,
( zero != zero
| composition(skolemFOFtoCNF_X0,zero) = zero ),
inference(resolve,[$cnf( $equal(composition(skolemFOFtoCNF_X0,zero),zero) )],[refute_0_683,refute_0_684]) ).
cnf(refute_0_686,plain,
zero != zero,
inference(resolve,[$cnf( $equal(composition(skolemFOFtoCNF_X0,zero),zero) )],[refute_0_685,refute_0_0]) ).
cnf(refute_0_687,plain,
zero = zero,
introduced(tautology,[refl,[$fot(zero)]]) ).
cnf(refute_0_688,plain,
$false,
inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_687,refute_0_686]) ).
fof(negate_1_0,plain,
~ ! [X0] :
( composition(X0,zero) = zero
=> composition(zero,X0) = zero ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [X0] :
( composition(zero,X0) != zero
& composition(X0,zero) = zero ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
( composition(zero,skolemFOFtoCNF_X0_1) != zero
& composition(skolemFOFtoCNF_X0_1,zero) = zero ),
inference(skolemize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
composition(zero,skolemFOFtoCNF_X0_1) != zero,
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(canonicalize,[],[converse_multiplicativity]) ).
fof(normalize_1_4,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(specialize,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
! [X0] : converse(converse(X0)) = X0,
inference(canonicalize,[],[converse_idempotence]) ).
fof(normalize_1_6,plain,
! [X0] : converse(converse(X0)) = X0,
inference(specialize,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(canonicalize,[],[def_zero]) ).
fof(normalize_1_8,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(specialize,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(canonicalize,[],[maddux4_definiton_of_meet]) ).
fof(normalize_1_10,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(specialize,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
! [X0] : top = join(X0,complement(X0)),
inference(canonicalize,[],[def_top]) ).
fof(normalize_1_12,plain,
! [X0] : top = join(X0,complement(X0)),
inference(specialize,[],[normalize_1_11]) ).
fof(normalize_1_13,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(canonicalize,[],[maddux3_a_kind_of_de_Morgan]) ).
fof(normalize_1_14,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(specialize,[],[normalize_1_13]) ).
fof(normalize_1_15,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(canonicalize,[],[maddux1_join_commutativity]) ).
fof(normalize_1_16,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(specialize,[],[normalize_1_15]) ).
fof(normalize_1_17,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(canonicalize,[],[converse_additivity]) ).
fof(normalize_1_18,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(specialize,[],[normalize_1_17]) ).
fof(normalize_1_19,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(canonicalize,[],[maddux2_join_associativity]) ).
fof(normalize_1_20,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(specialize,[],[normalize_1_19]) ).
fof(normalize_1_21,plain,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(canonicalize,[],[converse_cancellativity]) ).
fof(normalize_1_22,plain,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(specialize,[],[normalize_1_21]) ).
fof(normalize_1_23,plain,
! [X0] : composition(X0,one) = X0,
inference(canonicalize,[],[composition_identity]) ).
fof(normalize_1_24,plain,
! [X0] : composition(X0,one) = X0,
inference(specialize,[],[normalize_1_23]) ).
fof(normalize_1_25,plain,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(canonicalize,[],[composition_distributivity]) ).
fof(normalize_1_26,plain,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(specialize,[],[normalize_1_25]) ).
fof(normalize_1_27,plain,
! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
inference(canonicalize,[],[composition_associativity]) ).
fof(normalize_1_28,plain,
! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
inference(specialize,[],[normalize_1_27]) ).
fof(normalize_1_29,plain,
composition(skolemFOFtoCNF_X0_1,zero) = zero,
inference(conjunct,[],[normalize_1_1]) ).
cnf(refute_1_0,plain,
composition(zero,skolemFOFtoCNF_X0_1) != zero,
inference(canonicalize,[],[normalize_1_2]) ).
cnf(refute_1_1,plain,
converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(canonicalize,[],[normalize_1_4]) ).
cnf(refute_1_2,plain,
converse(composition(X_111,converse(X0))) = composition(converse(converse(X0)),converse(X_111)),
inference(subst,[],[refute_1_1:[bind(X0,$fot(X_111)),bind(X1,$fot(converse(X0)))]]) ).
cnf(refute_1_3,plain,
converse(converse(X0)) = X0,
inference(canonicalize,[],[normalize_1_6]) ).
cnf(refute_1_4,plain,
( converse(composition(X_111,converse(X0))) != composition(converse(converse(X0)),converse(X_111))
| converse(converse(X0)) != X0
| converse(composition(X_111,converse(X0))) = composition(X0,converse(X_111)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(X_111,converse(X0))),composition(converse(converse(X0)),converse(X_111))) ),[1,0],$fot(X0)]]) ).
cnf(refute_1_5,plain,
( converse(composition(X_111,converse(X0))) != composition(converse(converse(X0)),converse(X_111))
| converse(composition(X_111,converse(X0))) = composition(X0,converse(X_111)) ),
inference(resolve,[$cnf( $equal(converse(converse(X0)),X0) )],[refute_1_3,refute_1_4]) ).
cnf(refute_1_6,plain,
converse(composition(X_111,converse(X0))) = composition(X0,converse(X_111)),
inference(resolve,[$cnf( $equal(converse(composition(X_111,converse(X0))),composition(converse(converse(X0)),converse(X_111))) )],[refute_1_2,refute_1_5]) ).
cnf(refute_1_7,plain,
converse(composition(X_111,converse(zero))) = composition(zero,converse(X_111)),
inference(subst,[],[refute_1_6:[bind(X0,$fot(zero))]]) ).
cnf(refute_1_8,plain,
zero = meet(X0,complement(X0)),
inference(canonicalize,[],[normalize_1_8]) ).
cnf(refute_1_9,plain,
zero = meet(converse(zero),complement(converse(zero))),
inference(subst,[],[refute_1_8:[bind(X0,$fot(converse(zero)))]]) ).
cnf(refute_1_10,plain,
converse(converse(complement(converse(zero)))) = complement(converse(zero)),
inference(subst,[],[refute_1_3:[bind(X0,$fot(complement(converse(zero))))]]) ).
cnf(refute_1_11,plain,
meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(canonicalize,[],[normalize_1_10]) ).
cnf(refute_1_12,plain,
meet(top,X1) = complement(join(complement(top),complement(X1))),
inference(subst,[],[refute_1_11:[bind(X0,$fot(top))]]) ).
cnf(refute_1_13,plain,
zero = meet(join(complement(X_137),complement(X_138)),complement(join(complement(X_137),complement(X_138)))),
inference(subst,[],[refute_1_8:[bind(X0,$fot(join(complement(X_137),complement(X_138))))]]) ).
cnf(refute_1_14,plain,
meet(X_137,X_138) = complement(join(complement(X_137),complement(X_138))),
inference(subst,[],[refute_1_11:[bind(X0,$fot(X_137)),bind(X1,$fot(X_138))]]) ).
cnf(refute_1_15,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_1_16,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_1_17,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_1_15,refute_1_16]) ).
cnf(refute_1_18,plain,
( meet(X_137,X_138) != complement(join(complement(X_137),complement(X_138)))
| complement(join(complement(X_137),complement(X_138))) = meet(X_137,X_138) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(meet(X_137,X_138))),bind(Y,$fot(complement(join(complement(X_137),complement(X_138)))))]]) ).
cnf(refute_1_19,plain,
complement(join(complement(X_137),complement(X_138))) = meet(X_137,X_138),
inference(resolve,[$cnf( $equal(meet(X_137,X_138),complement(join(complement(X_137),complement(X_138)))) )],[refute_1_14,refute_1_18]) ).
cnf(refute_1_20,plain,
( complement(join(complement(X_137),complement(X_138))) != meet(X_137,X_138)
| zero != meet(join(complement(X_137),complement(X_138)),complement(join(complement(X_137),complement(X_138))))
| zero = meet(join(complement(X_137),complement(X_138)),meet(X_137,X_138)) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(join(complement(X_137),complement(X_138)),complement(join(complement(X_137),complement(X_138))))) ),[1,1],$fot(meet(X_137,X_138))]]) ).
cnf(refute_1_21,plain,
( zero != meet(join(complement(X_137),complement(X_138)),complement(join(complement(X_137),complement(X_138))))
| zero = meet(join(complement(X_137),complement(X_138)),meet(X_137,X_138)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_137),complement(X_138))),meet(X_137,X_138)) )],[refute_1_19,refute_1_20]) ).
cnf(refute_1_22,plain,
zero = meet(join(complement(X_137),complement(X_138)),meet(X_137,X_138)),
inference(resolve,[$cnf( $equal(zero,meet(join(complement(X_137),complement(X_138)),complement(join(complement(X_137),complement(X_138))))) )],[refute_1_13,refute_1_21]) ).
cnf(refute_1_23,plain,
top = join(X0,complement(X0)),
inference(canonicalize,[],[normalize_1_12]) ).
cnf(refute_1_24,plain,
( top != join(X0,complement(X0))
| join(X0,complement(X0)) = top ),
inference(subst,[],[refute_1_17:[bind(X,$fot(top)),bind(Y,$fot(join(X0,complement(X0))))]]) ).
cnf(refute_1_25,plain,
join(X0,complement(X0)) = top,
inference(resolve,[$cnf( $equal(top,join(X0,complement(X0))) )],[refute_1_23,refute_1_24]) ).
cnf(refute_1_26,plain,
join(meet(X_137,X_138),complement(meet(X_137,X_138))) = top,
inference(subst,[],[refute_1_25:[bind(X0,$fot(meet(X_137,X_138)))]]) ).
cnf(refute_1_27,plain,
complement(join(meet(X_137,X_138),complement(meet(X_137,X_138)))) = complement(join(meet(X_137,X_138),complement(meet(X_137,X_138)))),
introduced(tautology,[refl,[$fot(complement(join(meet(X_137,X_138),complement(meet(X_137,X_138)))))]]) ).
cnf(refute_1_28,plain,
( complement(join(meet(X_137,X_138),complement(meet(X_137,X_138)))) != complement(join(meet(X_137,X_138),complement(meet(X_137,X_138))))
| join(meet(X_137,X_138),complement(meet(X_137,X_138))) != top
| complement(join(meet(X_137,X_138),complement(meet(X_137,X_138)))) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(meet(X_137,X_138),complement(meet(X_137,X_138)))),complement(join(meet(X_137,X_138),complement(meet(X_137,X_138))))) ),[1,0],$fot(top)]]) ).
cnf(refute_1_29,plain,
( join(meet(X_137,X_138),complement(meet(X_137,X_138))) != top
| complement(join(meet(X_137,X_138),complement(meet(X_137,X_138)))) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(join(meet(X_137,X_138),complement(meet(X_137,X_138)))),complement(join(meet(X_137,X_138),complement(meet(X_137,X_138))))) )],[refute_1_27,refute_1_28]) ).
cnf(refute_1_30,plain,
complement(join(meet(X_137,X_138),complement(meet(X_137,X_138)))) = complement(top),
inference(resolve,[$cnf( $equal(join(meet(X_137,X_138),complement(meet(X_137,X_138))),top) )],[refute_1_26,refute_1_29]) ).
cnf(refute_1_31,plain,
meet(join(complement(X_137),complement(X_138)),X1) = complement(join(complement(join(complement(X_137),complement(X_138))),complement(X1))),
inference(subst,[],[refute_1_11:[bind(X0,$fot(join(complement(X_137),complement(X_138))))]]) ).
cnf(refute_1_32,plain,
( complement(join(complement(X_137),complement(X_138))) != meet(X_137,X_138)
| meet(join(complement(X_137),complement(X_138)),X1) != complement(join(complement(join(complement(X_137),complement(X_138))),complement(X1)))
| meet(join(complement(X_137),complement(X_138)),X1) = complement(join(meet(X_137,X_138),complement(X1))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(complement(X_137),complement(X_138)),X1),complement(join(complement(join(complement(X_137),complement(X_138))),complement(X1)))) ),[1,0,0],$fot(meet(X_137,X_138))]]) ).
cnf(refute_1_33,plain,
( meet(join(complement(X_137),complement(X_138)),X1) != complement(join(complement(join(complement(X_137),complement(X_138))),complement(X1)))
| meet(join(complement(X_137),complement(X_138)),X1) = complement(join(meet(X_137,X_138),complement(X1))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_137),complement(X_138))),meet(X_137,X_138)) )],[refute_1_19,refute_1_32]) ).
cnf(refute_1_34,plain,
meet(join(complement(X_137),complement(X_138)),X1) = complement(join(meet(X_137,X_138),complement(X1))),
inference(resolve,[$cnf( $equal(meet(join(complement(X_137),complement(X_138)),X1),complement(join(complement(join(complement(X_137),complement(X_138))),complement(X1)))) )],[refute_1_31,refute_1_33]) ).
cnf(refute_1_35,plain,
meet(join(complement(X_137),complement(X_138)),meet(X_137,X_138)) = complement(join(meet(X_137,X_138),complement(meet(X_137,X_138)))),
inference(subst,[],[refute_1_34:[bind(X1,$fot(meet(X_137,X_138)))]]) ).
cnf(refute_1_36,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_1_37,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_1_17,refute_1_36]) ).
cnf(refute_1_38,plain,
( complement(join(meet(X_137,X_138),complement(meet(X_137,X_138)))) != complement(top)
| meet(join(complement(X_137),complement(X_138)),meet(X_137,X_138)) != complement(join(meet(X_137,X_138),complement(meet(X_137,X_138))))
| meet(join(complement(X_137),complement(X_138)),meet(X_137,X_138)) = complement(top) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(meet(join(complement(X_137),complement(X_138)),meet(X_137,X_138)))),bind(Y,$fot(complement(join(meet(X_137,X_138),complement(meet(X_137,X_138)))))),bind(Z,$fot(complement(top)))]]) ).
cnf(refute_1_39,plain,
( complement(join(meet(X_137,X_138),complement(meet(X_137,X_138)))) != complement(top)
| meet(join(complement(X_137),complement(X_138)),meet(X_137,X_138)) = complement(top) ),
inference(resolve,[$cnf( $equal(meet(join(complement(X_137),complement(X_138)),meet(X_137,X_138)),complement(join(meet(X_137,X_138),complement(meet(X_137,X_138))))) )],[refute_1_35,refute_1_38]) ).
cnf(refute_1_40,plain,
meet(join(complement(X_137),complement(X_138)),meet(X_137,X_138)) = complement(top),
inference(resolve,[$cnf( $equal(complement(join(meet(X_137,X_138),complement(meet(X_137,X_138)))),complement(top)) )],[refute_1_30,refute_1_39]) ).
cnf(refute_1_41,plain,
( meet(join(complement(X_137),complement(X_138)),meet(X_137,X_138)) != complement(top)
| zero != meet(join(complement(X_137),complement(X_138)),meet(X_137,X_138))
| zero = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(join(complement(X_137),complement(X_138)),meet(X_137,X_138))) ),[1],$fot(complement(top))]]) ).
cnf(refute_1_42,plain,
( zero != meet(join(complement(X_137),complement(X_138)),meet(X_137,X_138))
| zero = complement(top) ),
inference(resolve,[$cnf( $equal(meet(join(complement(X_137),complement(X_138)),meet(X_137,X_138)),complement(top)) )],[refute_1_40,refute_1_41]) ).
cnf(refute_1_43,plain,
zero = complement(top),
inference(resolve,[$cnf( $equal(zero,meet(join(complement(X_137),complement(X_138)),meet(X_137,X_138))) )],[refute_1_22,refute_1_42]) ).
cnf(refute_1_44,plain,
( zero != complement(top)
| complement(top) = zero ),
inference(subst,[],[refute_1_17:[bind(X,$fot(zero)),bind(Y,$fot(complement(top)))]]) ).
cnf(refute_1_45,plain,
complement(top) = zero,
inference(resolve,[$cnf( $equal(zero,complement(top)) )],[refute_1_43,refute_1_44]) ).
cnf(refute_1_46,plain,
( complement(top) != zero
| meet(top,X1) != complement(join(complement(top),complement(X1)))
| meet(top,X1) = complement(join(zero,complement(X1))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,X1),complement(join(complement(top),complement(X1)))) ),[1,0,0],$fot(zero)]]) ).
cnf(refute_1_47,plain,
( meet(top,X1) != complement(join(complement(top),complement(X1)))
| meet(top,X1) = complement(join(zero,complement(X1))) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_1_45,refute_1_46]) ).
cnf(refute_1_48,plain,
meet(top,X1) = complement(join(zero,complement(X1))),
inference(resolve,[$cnf( $equal(meet(top,X1),complement(join(complement(top),complement(X1)))) )],[refute_1_12,refute_1_47]) ).
cnf(refute_1_49,plain,
X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(canonicalize,[],[normalize_1_14]) ).
cnf(refute_1_50,plain,
join(X0,X1) = join(X1,X0),
inference(canonicalize,[],[normalize_1_16]) ).
cnf(refute_1_51,plain,
( join(X0,X1) != join(X1,X0)
| join(X1,X0) = join(X0,X1) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(join(X0,X1))),bind(Y,$fot(join(X1,X0)))]]) ).
cnf(refute_1_52,plain,
join(X1,X0) = join(X0,X1),
inference(resolve,[$cnf( $equal(join(X0,X1),join(X1,X0)) )],[refute_1_50,refute_1_51]) ).
cnf(refute_1_53,plain,
join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),
inference(subst,[],[refute_1_52:[bind(X0,$fot(complement(join(complement(X0),X1)))),bind(X1,$fot(complement(join(complement(X0),complement(X1)))))]]) ).
cnf(refute_1_54,plain,
( X0 != join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1)))
| join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) != join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))
| X0 = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X0,join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))) ),[0],$fot(join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))))]]) ).
cnf(refute_1_55,plain,
( X0 != join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1)))
| X0 = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) ),
inference(resolve,[$cnf( $equal(join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))) )],[refute_1_53,refute_1_54]) ).
cnf(refute_1_56,plain,
X0 = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),
inference(resolve,[$cnf( $equal(X0,join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1)))) )],[refute_1_49,refute_1_55]) ).
cnf(refute_1_57,plain,
join(complement(join(complement(X0),X1)),meet(X0,X1)) = join(meet(X0,X1),complement(join(complement(X0),X1))),
inference(subst,[],[refute_1_52:[bind(X0,$fot(meet(X0,X1))),bind(X1,$fot(complement(join(complement(X0),X1))))]]) ).
cnf(refute_1_58,plain,
( meet(X0,X1) != complement(join(complement(X0),complement(X1)))
| complement(join(complement(X0),complement(X1))) = meet(X0,X1) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(meet(X0,X1))),bind(Y,$fot(complement(join(complement(X0),complement(X1)))))]]) ).
cnf(refute_1_59,plain,
complement(join(complement(X0),complement(X1))) = meet(X0,X1),
inference(resolve,[$cnf( $equal(meet(X0,X1),complement(join(complement(X0),complement(X1)))) )],[refute_1_11,refute_1_58]) ).
cnf(refute_1_60,plain,
join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),
introduced(tautology,[refl,[$fot(join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))))]]) ).
cnf(refute_1_61,plain,
( complement(join(complement(X0),complement(X1))) != meet(X0,X1)
| join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) != join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))
| join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(complement(join(complement(X0),X1)),meet(X0,X1)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))) ),[1,1],$fot(meet(X0,X1))]]) ).
cnf(refute_1_62,plain,
( complement(join(complement(X0),complement(X1))) != meet(X0,X1)
| join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(complement(join(complement(X0),X1)),meet(X0,X1)) ),
inference(resolve,[$cnf( $equal(join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))) )],[refute_1_60,refute_1_61]) ).
cnf(refute_1_63,plain,
join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(complement(join(complement(X0),X1)),meet(X0,X1)),
inference(resolve,[$cnf( $equal(complement(join(complement(X0),complement(X1))),meet(X0,X1)) )],[refute_1_59,refute_1_62]) ).
cnf(refute_1_64,plain,
( join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) != join(complement(join(complement(X0),X1)),meet(X0,X1))
| join(complement(join(complement(X0),X1)),meet(X0,X1)) != join(meet(X0,X1),complement(join(complement(X0),X1)))
| join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(meet(X0,X1),complement(join(complement(X0),X1))) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))))),bind(Y,$fot(join(complement(join(complement(X0),X1)),meet(X0,X1)))),bind(Z,$fot(join(meet(X0,X1),complement(join(complement(X0),X1)))))]]) ).
cnf(refute_1_65,plain,
( join(complement(join(complement(X0),X1)),meet(X0,X1)) != join(meet(X0,X1),complement(join(complement(X0),X1)))
| join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(meet(X0,X1),complement(join(complement(X0),X1))) ),
inference(resolve,[$cnf( $equal(join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),join(complement(join(complement(X0),X1)),meet(X0,X1))) )],[refute_1_63,refute_1_64]) ).
cnf(refute_1_66,plain,
join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(meet(X0,X1),complement(join(complement(X0),X1))),
inference(resolve,[$cnf( $equal(join(complement(join(complement(X0),X1)),meet(X0,X1)),join(meet(X0,X1),complement(join(complement(X0),X1)))) )],[refute_1_57,refute_1_65]) ).
cnf(refute_1_67,plain,
( X0 != join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))
| join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) != join(meet(X0,X1),complement(join(complement(X0),X1)))
| X0 = join(meet(X0,X1),complement(join(complement(X0),X1))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X0,join(meet(X0,X1),complement(join(complement(X0),X1)))) ),[0],$fot(join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))))]]) ).
cnf(refute_1_68,plain,
( X0 != join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))
| X0 = join(meet(X0,X1),complement(join(complement(X0),X1))) ),
inference(resolve,[$cnf( $equal(join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),join(meet(X0,X1),complement(join(complement(X0),X1)))) )],[refute_1_66,refute_1_67]) ).
cnf(refute_1_69,plain,
X0 = join(meet(X0,X1),complement(join(complement(X0),X1))),
inference(resolve,[$cnf( $equal(X0,join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))) )],[refute_1_56,refute_1_68]) ).
cnf(refute_1_70,plain,
X_176 = join(meet(X_176,top),complement(join(complement(X_176),top))),
inference(subst,[],[refute_1_69:[bind(X0,$fot(X_176)),bind(X1,$fot(top))]]) ).
cnf(refute_1_71,plain,
converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(canonicalize,[],[normalize_1_18]) ).
cnf(refute_1_72,plain,
converse(join(converse(X0),X_110)) = join(converse(converse(X0)),converse(X_110)),
inference(subst,[],[refute_1_71:[bind(X0,$fot(converse(X0))),bind(X1,$fot(X_110))]]) ).
cnf(refute_1_73,plain,
( converse(converse(X0)) != X0
| converse(join(converse(X0),X_110)) != join(converse(converse(X0)),converse(X_110))
| converse(join(converse(X0),X_110)) = join(X0,converse(X_110)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(X0),X_110)),join(converse(converse(X0)),converse(X_110))) ),[1,0],$fot(X0)]]) ).
cnf(refute_1_74,plain,
( converse(join(converse(X0),X_110)) != join(converse(converse(X0)),converse(X_110))
| converse(join(converse(X0),X_110)) = join(X0,converse(X_110)) ),
inference(resolve,[$cnf( $equal(converse(converse(X0)),X0) )],[refute_1_3,refute_1_73]) ).
cnf(refute_1_75,plain,
converse(join(converse(X0),X_110)) = join(X0,converse(X_110)),
inference(resolve,[$cnf( $equal(converse(join(converse(X0),X_110)),join(converse(converse(X0)),converse(X_110))) )],[refute_1_72,refute_1_74]) ).
cnf(refute_1_76,plain,
converse(join(converse(X_115),complement(converse(X_115)))) = join(X_115,converse(complement(converse(X_115)))),
inference(subst,[],[refute_1_75:[bind(X0,$fot(X_115)),bind(X_110,$fot(complement(converse(X_115))))]]) ).
cnf(refute_1_77,plain,
top = join(converse(X_115),complement(converse(X_115))),
inference(subst,[],[refute_1_23:[bind(X0,$fot(converse(X_115)))]]) ).
cnf(refute_1_78,plain,
( top != join(converse(X_115),complement(converse(X_115)))
| join(converse(X_115),complement(converse(X_115))) = top ),
inference(subst,[],[refute_1_17:[bind(X,$fot(top)),bind(Y,$fot(join(converse(X_115),complement(converse(X_115)))))]]) ).
cnf(refute_1_79,plain,
join(converse(X_115),complement(converse(X_115))) = top,
inference(resolve,[$cnf( $equal(top,join(converse(X_115),complement(converse(X_115)))) )],[refute_1_77,refute_1_78]) ).
cnf(refute_1_80,plain,
( converse(join(converse(X_115),complement(converse(X_115)))) != join(X_115,converse(complement(converse(X_115))))
| join(converse(X_115),complement(converse(X_115))) != top
| converse(top) = join(X_115,converse(complement(converse(X_115)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(X_115),complement(converse(X_115)))),join(X_115,converse(complement(converse(X_115))))) ),[0,0],$fot(top)]]) ).
cnf(refute_1_81,plain,
( converse(join(converse(X_115),complement(converse(X_115)))) != join(X_115,converse(complement(converse(X_115))))
| converse(top) = join(X_115,converse(complement(converse(X_115)))) ),
inference(resolve,[$cnf( $equal(join(converse(X_115),complement(converse(X_115))),top) )],[refute_1_79,refute_1_80]) ).
cnf(refute_1_82,plain,
converse(top) = join(X_115,converse(complement(converse(X_115)))),
inference(resolve,[$cnf( $equal(converse(join(converse(X_115),complement(converse(X_115)))),join(X_115,converse(complement(converse(X_115))))) )],[refute_1_76,refute_1_81]) ).
cnf(refute_1_83,plain,
top = join(converse(top),complement(converse(top))),
inference(subst,[],[refute_1_23:[bind(X0,$fot(converse(top)))]]) ).
cnf(refute_1_84,plain,
join(converse(top),complement(X_156)) = join(complement(X_156),converse(top)),
inference(subst,[],[refute_1_50:[bind(X0,$fot(converse(top))),bind(X1,$fot(complement(X_156)))]]) ).
cnf(refute_1_85,plain,
converse(top) = join(join(X_120,X_121),converse(complement(converse(join(X_120,X_121))))),
inference(subst,[],[refute_1_82:[bind(X_115,$fot(join(X_120,X_121)))]]) ).
cnf(refute_1_86,plain,
join(converse(X0),converse(X1)) = join(converse(X1),converse(X0)),
inference(subst,[],[refute_1_50:[bind(X0,$fot(converse(X0))),bind(X1,$fot(converse(X1)))]]) ).
cnf(refute_1_87,plain,
( converse(join(X0,X1)) != join(converse(X0),converse(X1))
| join(converse(X0),converse(X1)) != join(converse(X1),converse(X0))
| converse(join(X0,X1)) = join(converse(X1),converse(X0)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(join(X0,X1)),join(converse(X1),converse(X0))) ),[0],$fot(join(converse(X0),converse(X1)))]]) ).
cnf(refute_1_88,plain,
( converse(join(X0,X1)) != join(converse(X0),converse(X1))
| converse(join(X0,X1)) = join(converse(X1),converse(X0)) ),
inference(resolve,[$cnf( $equal(join(converse(X0),converse(X1)),join(converse(X1),converse(X0))) )],[refute_1_86,refute_1_87]) ).
cnf(refute_1_89,plain,
converse(join(X0,X1)) = join(converse(X1),converse(X0)),
inference(resolve,[$cnf( $equal(converse(join(X0,X1)),join(converse(X0),converse(X1))) )],[refute_1_71,refute_1_88]) ).
cnf(refute_1_90,plain,
( converse(join(X0,X1)) != join(converse(X0),converse(X1))
| join(converse(X0),converse(X1)) = converse(join(X0,X1)) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(converse(join(X0,X1)))),bind(Y,$fot(join(converse(X0),converse(X1))))]]) ).
cnf(refute_1_91,plain,
join(converse(X0),converse(X1)) = converse(join(X0,X1)),
inference(resolve,[$cnf( $equal(converse(join(X0,X1)),join(converse(X0),converse(X1))) )],[refute_1_71,refute_1_90]) ).
cnf(refute_1_92,plain,
join(converse(X1),converse(X0)) = converse(join(X1,X0)),
inference(subst,[],[refute_1_91:[bind(X0,$fot(X1)),bind(X1,$fot(X0))]]) ).
cnf(refute_1_93,plain,
( converse(join(X0,X1)) != join(converse(X1),converse(X0))
| join(converse(X1),converse(X0)) != converse(join(X1,X0))
| converse(join(X0,X1)) = converse(join(X1,X0)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(join(X0,X1)),converse(join(X1,X0))) ),[0],$fot(join(converse(X1),converse(X0)))]]) ).
cnf(refute_1_94,plain,
( converse(join(X0,X1)) != join(converse(X1),converse(X0))
| converse(join(X0,X1)) = converse(join(X1,X0)) ),
inference(resolve,[$cnf( $equal(join(converse(X1),converse(X0)),converse(join(X1,X0))) )],[refute_1_92,refute_1_93]) ).
cnf(refute_1_95,plain,
converse(join(X0,X1)) = converse(join(X1,X0)),
inference(resolve,[$cnf( $equal(converse(join(X0,X1)),join(converse(X1),converse(X0))) )],[refute_1_89,refute_1_94]) ).
cnf(refute_1_96,plain,
converse(join(X_120,X_121)) = converse(join(X_121,X_120)),
inference(subst,[],[refute_1_95:[bind(X0,$fot(X_120)),bind(X1,$fot(X_121))]]) ).
cnf(refute_1_97,plain,
( converse(join(X_120,X_121)) != converse(join(X_121,X_120))
| converse(top) != join(join(X_120,X_121),converse(complement(converse(join(X_120,X_121)))))
| converse(top) = join(join(X_120,X_121),converse(complement(converse(join(X_121,X_120))))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(top),join(join(X_120,X_121),converse(complement(converse(join(X_120,X_121)))))) ),[1,1,0,0],$fot(converse(join(X_121,X_120)))]]) ).
cnf(refute_1_98,plain,
( converse(top) != join(join(X_120,X_121),converse(complement(converse(join(X_120,X_121)))))
| converse(top) = join(join(X_120,X_121),converse(complement(converse(join(X_121,X_120))))) ),
inference(resolve,[$cnf( $equal(converse(join(X_120,X_121)),converse(join(X_121,X_120))) )],[refute_1_96,refute_1_97]) ).
cnf(refute_1_99,plain,
converse(top) = join(join(X_120,X_121),converse(complement(converse(join(X_121,X_120))))),
inference(resolve,[$cnf( $equal(converse(top),join(join(X_120,X_121),converse(complement(converse(join(X_120,X_121)))))) )],[refute_1_85,refute_1_98]) ).
cnf(refute_1_100,plain,
join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(canonicalize,[],[normalize_1_20]) ).
cnf(refute_1_101,plain,
( join(X0,join(X1,X2)) != join(join(X0,X1),X2)
| join(join(X0,X1),X2) = join(X0,join(X1,X2)) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(join(X0,join(X1,X2)))),bind(Y,$fot(join(join(X0,X1),X2)))]]) ).
cnf(refute_1_102,plain,
join(join(X0,X1),X2) = join(X0,join(X1,X2)),
inference(resolve,[$cnf( $equal(join(X0,join(X1,X2)),join(join(X0,X1),X2)) )],[refute_1_100,refute_1_101]) ).
cnf(refute_1_103,plain,
join(join(X_120,X_121),converse(complement(converse(join(X_121,X_120))))) = join(X_120,join(X_121,converse(complement(converse(join(X_121,X_120)))))),
inference(subst,[],[refute_1_102:[bind(X0,$fot(X_120)),bind(X1,$fot(X_121)),bind(X2,$fot(converse(complement(converse(join(X_121,X_120))))))]]) ).
cnf(refute_1_104,plain,
( converse(top) != join(join(X_120,X_121),converse(complement(converse(join(X_121,X_120)))))
| join(join(X_120,X_121),converse(complement(converse(join(X_121,X_120))))) != join(X_120,join(X_121,converse(complement(converse(join(X_121,X_120))))))
| converse(top) = join(X_120,join(X_121,converse(complement(converse(join(X_121,X_120)))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(top),join(X_120,join(X_121,converse(complement(converse(join(X_121,X_120))))))) ),[0],$fot(join(join(X_120,X_121),converse(complement(converse(join(X_121,X_120))))))]]) ).
cnf(refute_1_105,plain,
( converse(top) != join(join(X_120,X_121),converse(complement(converse(join(X_121,X_120)))))
| converse(top) = join(X_120,join(X_121,converse(complement(converse(join(X_121,X_120)))))) ),
inference(resolve,[$cnf( $equal(join(join(X_120,X_121),converse(complement(converse(join(X_121,X_120))))),join(X_120,join(X_121,converse(complement(converse(join(X_121,X_120))))))) )],[refute_1_103,refute_1_104]) ).
cnf(refute_1_106,plain,
converse(top) = join(X_120,join(X_121,converse(complement(converse(join(X_121,X_120)))))),
inference(resolve,[$cnf( $equal(converse(top),join(join(X_120,X_121),converse(complement(converse(join(X_121,X_120)))))) )],[refute_1_99,refute_1_105]) ).
cnf(refute_1_107,plain,
converse(top) = join(complement(X_134),join(complement(X_134),converse(complement(converse(join(complement(X_134),complement(X_134))))))),
inference(subst,[],[refute_1_106:[bind(X_120,$fot(complement(X_134))),bind(X_121,$fot(complement(X_134)))]]) ).
cnf(refute_1_108,plain,
join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(canonicalize,[],[normalize_1_22]) ).
cnf(refute_1_109,plain,
join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))),
inference(subst,[],[refute_1_52:[bind(X0,$fot(complement(X1))),bind(X1,$fot(composition(converse(X0),complement(composition(X0,X1)))))]]) ).
cnf(refute_1_110,plain,
( join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) != complement(X1)
| join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) != join(complement(X1),composition(converse(X0),complement(composition(X0,X1))))
| join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))) = complement(X1) ),
introduced(tautology,[equality,[$cnf( $equal(join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),complement(X1)) ),[0],$fot(join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))))]]) ).
cnf(refute_1_111,plain,
( join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) != complement(X1)
| join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))) = complement(X1) ),
inference(resolve,[$cnf( $equal(join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),join(complement(X1),composition(converse(X0),complement(composition(X0,X1))))) )],[refute_1_109,refute_1_110]) ).
cnf(refute_1_112,plain,
join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))) = complement(X1),
inference(resolve,[$cnf( $equal(join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),complement(X1)) )],[refute_1_108,refute_1_111]) ).
cnf(refute_1_113,plain,
join(complement(X_134),composition(converse(one),complement(composition(one,X_134)))) = complement(X_134),
inference(subst,[],[refute_1_112:[bind(X0,$fot(one)),bind(X1,$fot(X_134))]]) ).
cnf(refute_1_114,plain,
converse(composition(converse(X0),X_112)) = composition(converse(X_112),converse(converse(X0))),
inference(subst,[],[refute_1_1:[bind(X0,$fot(converse(X0))),bind(X1,$fot(X_112))]]) ).
cnf(refute_1_115,plain,
( converse(composition(converse(X0),X_112)) != composition(converse(X_112),converse(converse(X0)))
| converse(converse(X0)) != X0
| converse(composition(converse(X0),X_112)) = composition(converse(X_112),X0) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(X0),X_112)),composition(converse(X_112),converse(converse(X0)))) ),[1,1],$fot(X0)]]) ).
cnf(refute_1_116,plain,
( converse(composition(converse(X0),X_112)) != composition(converse(X_112),converse(converse(X0)))
| converse(composition(converse(X0),X_112)) = composition(converse(X_112),X0) ),
inference(resolve,[$cnf( $equal(converse(converse(X0)),X0) )],[refute_1_3,refute_1_115]) ).
cnf(refute_1_117,plain,
converse(composition(converse(X0),X_112)) = composition(converse(X_112),X0),
inference(resolve,[$cnf( $equal(converse(composition(converse(X0),X_112)),composition(converse(X_112),converse(converse(X0)))) )],[refute_1_114,refute_1_116]) ).
cnf(refute_1_118,plain,
converse(composition(converse(X_126),one)) = composition(converse(one),X_126),
inference(subst,[],[refute_1_117:[bind(X0,$fot(X_126)),bind(X_112,$fot(one))]]) ).
cnf(refute_1_119,plain,
composition(X0,one) = X0,
inference(canonicalize,[],[normalize_1_24]) ).
cnf(refute_1_120,plain,
composition(converse(X_126),one) = converse(X_126),
inference(subst,[],[refute_1_119:[bind(X0,$fot(converse(X_126)))]]) ).
cnf(refute_1_121,plain,
( composition(converse(X_126),one) != converse(X_126)
| converse(composition(converse(X_126),one)) != composition(converse(one),X_126)
| converse(converse(X_126)) = composition(converse(one),X_126) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(X_126),one)),composition(converse(one),X_126)) ),[0,0],$fot(converse(X_126))]]) ).
cnf(refute_1_122,plain,
( converse(composition(converse(X_126),one)) != composition(converse(one),X_126)
| converse(converse(X_126)) = composition(converse(one),X_126) ),
inference(resolve,[$cnf( $equal(composition(converse(X_126),one),converse(X_126)) )],[refute_1_120,refute_1_121]) ).
cnf(refute_1_123,plain,
converse(converse(X_126)) = composition(converse(one),X_126),
inference(resolve,[$cnf( $equal(converse(composition(converse(X_126),one)),composition(converse(one),X_126)) )],[refute_1_118,refute_1_122]) ).
cnf(refute_1_124,plain,
converse(converse(X_126)) = X_126,
inference(subst,[],[refute_1_3:[bind(X0,$fot(X_126))]]) ).
cnf(refute_1_125,plain,
( converse(converse(X_126)) != X_126
| converse(converse(X_126)) != composition(converse(one),X_126)
| X_126 = composition(converse(one),X_126) ),
introduced(tautology,[equality,[$cnf( $equal(converse(converse(X_126)),composition(converse(one),X_126)) ),[0],$fot(X_126)]]) ).
cnf(refute_1_126,plain,
( converse(converse(X_126)) != composition(converse(one),X_126)
| X_126 = composition(converse(one),X_126) ),
inference(resolve,[$cnf( $equal(converse(converse(X_126)),X_126) )],[refute_1_124,refute_1_125]) ).
cnf(refute_1_127,plain,
X_126 = composition(converse(one),X_126),
inference(resolve,[$cnf( $equal(converse(converse(X_126)),composition(converse(one),X_126)) )],[refute_1_123,refute_1_126]) ).
cnf(refute_1_128,plain,
composition(converse(one),one) = converse(one),
inference(subst,[],[refute_1_119:[bind(X0,$fot(converse(one)))]]) ).
cnf(refute_1_129,plain,
one = composition(converse(one),one),
inference(subst,[],[refute_1_127:[bind(X_126,$fot(one))]]) ).
cnf(refute_1_130,plain,
( one != composition(converse(one),one)
| composition(converse(one),one) = one ),
inference(subst,[],[refute_1_17:[bind(X,$fot(one)),bind(Y,$fot(composition(converse(one),one)))]]) ).
cnf(refute_1_131,plain,
composition(converse(one),one) = one,
inference(resolve,[$cnf( $equal(one,composition(converse(one),one)) )],[refute_1_129,refute_1_130]) ).
cnf(refute_1_132,plain,
( composition(converse(one),one) != converse(one)
| composition(converse(one),one) != one
| one = converse(one) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(one),one),converse(one)) ),[0],$fot(one)]]) ).
cnf(refute_1_133,plain,
( composition(converse(one),one) != converse(one)
| one = converse(one) ),
inference(resolve,[$cnf( $equal(composition(converse(one),one),one) )],[refute_1_131,refute_1_132]) ).
cnf(refute_1_134,plain,
one = converse(one),
inference(resolve,[$cnf( $equal(composition(converse(one),one),converse(one)) )],[refute_1_128,refute_1_133]) ).
cnf(refute_1_135,plain,
( one != converse(one)
| converse(one) = one ),
inference(subst,[],[refute_1_17:[bind(X,$fot(one)),bind(Y,$fot(converse(one)))]]) ).
cnf(refute_1_136,plain,
converse(one) = one,
inference(resolve,[$cnf( $equal(one,converse(one)) )],[refute_1_134,refute_1_135]) ).
cnf(refute_1_137,plain,
composition(converse(one),X_126) = composition(converse(one),X_126),
introduced(tautology,[refl,[$fot(composition(converse(one),X_126))]]) ).
cnf(refute_1_138,plain,
( composition(converse(one),X_126) != composition(converse(one),X_126)
| converse(one) != one
| composition(converse(one),X_126) = composition(one,X_126) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(one),X_126),composition(converse(one),X_126)) ),[1,0],$fot(one)]]) ).
cnf(refute_1_139,plain,
( converse(one) != one
| composition(converse(one),X_126) = composition(one,X_126) ),
inference(resolve,[$cnf( $equal(composition(converse(one),X_126),composition(converse(one),X_126)) )],[refute_1_137,refute_1_138]) ).
cnf(refute_1_140,plain,
composition(converse(one),X_126) = composition(one,X_126),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_1_136,refute_1_139]) ).
cnf(refute_1_141,plain,
( X_126 != composition(converse(one),X_126)
| composition(converse(one),X_126) != composition(one,X_126)
| X_126 = composition(one,X_126) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_126,composition(one,X_126)) ),[0],$fot(composition(converse(one),X_126))]]) ).
cnf(refute_1_142,plain,
( X_126 != composition(converse(one),X_126)
| X_126 = composition(one,X_126) ),
inference(resolve,[$cnf( $equal(composition(converse(one),X_126),composition(one,X_126)) )],[refute_1_140,refute_1_141]) ).
cnf(refute_1_143,plain,
X_126 = composition(one,X_126),
inference(resolve,[$cnf( $equal(X_126,composition(converse(one),X_126)) )],[refute_1_127,refute_1_142]) ).
cnf(refute_1_144,plain,
X_134 = composition(one,X_134),
inference(subst,[],[refute_1_143:[bind(X_126,$fot(X_134))]]) ).
cnf(refute_1_145,plain,
( X_134 != composition(one,X_134)
| composition(one,X_134) = X_134 ),
inference(subst,[],[refute_1_17:[bind(X,$fot(X_134)),bind(Y,$fot(composition(one,X_134)))]]) ).
cnf(refute_1_146,plain,
composition(one,X_134) = X_134,
inference(resolve,[$cnf( $equal(X_134,composition(one,X_134)) )],[refute_1_144,refute_1_145]) ).
cnf(refute_1_147,plain,
( composition(one,X_134) != X_134
| join(complement(X_134),composition(converse(one),complement(composition(one,X_134)))) != complement(X_134)
| join(complement(X_134),composition(converse(one),complement(X_134))) = complement(X_134) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_134),composition(converse(one),complement(composition(one,X_134)))),complement(X_134)) ),[0,1,1,0],$fot(X_134)]]) ).
cnf(refute_1_148,plain,
( join(complement(X_134),composition(converse(one),complement(composition(one,X_134)))) != complement(X_134)
| join(complement(X_134),composition(converse(one),complement(X_134))) = complement(X_134) ),
inference(resolve,[$cnf( $equal(composition(one,X_134),X_134) )],[refute_1_146,refute_1_147]) ).
cnf(refute_1_149,plain,
join(complement(X_134),composition(converse(one),complement(X_134))) = complement(X_134),
inference(resolve,[$cnf( $equal(join(complement(X_134),composition(converse(one),complement(composition(one,X_134)))),complement(X_134)) )],[refute_1_113,refute_1_148]) ).
cnf(refute_1_150,plain,
( X_126 != composition(one,X_126)
| composition(one,X_126) = X_126 ),
inference(subst,[],[refute_1_17:[bind(X,$fot(X_126)),bind(Y,$fot(composition(one,X_126)))]]) ).
cnf(refute_1_151,plain,
composition(one,X_126) = X_126,
inference(resolve,[$cnf( $equal(X_126,composition(one,X_126)) )],[refute_1_143,refute_1_150]) ).
cnf(refute_1_152,plain,
composition(one,complement(X_134)) = complement(X_134),
inference(subst,[],[refute_1_151:[bind(X_126,$fot(complement(X_134)))]]) ).
cnf(refute_1_153,plain,
composition(converse(one),complement(X_134)) = composition(converse(one),complement(X_134)),
introduced(tautology,[refl,[$fot(composition(converse(one),complement(X_134)))]]) ).
cnf(refute_1_154,plain,
( composition(converse(one),complement(X_134)) != composition(converse(one),complement(X_134))
| converse(one) != one
| composition(converse(one),complement(X_134)) = composition(one,complement(X_134)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(one),complement(X_134)),composition(converse(one),complement(X_134))) ),[1,0],$fot(one)]]) ).
cnf(refute_1_155,plain,
( converse(one) != one
| composition(converse(one),complement(X_134)) = composition(one,complement(X_134)) ),
inference(resolve,[$cnf( $equal(composition(converse(one),complement(X_134)),composition(converse(one),complement(X_134))) )],[refute_1_153,refute_1_154]) ).
cnf(refute_1_156,plain,
composition(converse(one),complement(X_134)) = composition(one,complement(X_134)),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_1_136,refute_1_155]) ).
cnf(refute_1_157,plain,
( composition(converse(one),complement(X_134)) != composition(one,complement(X_134))
| composition(one,complement(X_134)) != complement(X_134)
| composition(converse(one),complement(X_134)) = complement(X_134) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(composition(converse(one),complement(X_134)))),bind(Y,$fot(composition(one,complement(X_134)))),bind(Z,$fot(complement(X_134)))]]) ).
cnf(refute_1_158,plain,
( composition(one,complement(X_134)) != complement(X_134)
| composition(converse(one),complement(X_134)) = complement(X_134) ),
inference(resolve,[$cnf( $equal(composition(converse(one),complement(X_134)),composition(one,complement(X_134))) )],[refute_1_156,refute_1_157]) ).
cnf(refute_1_159,plain,
composition(converse(one),complement(X_134)) = complement(X_134),
inference(resolve,[$cnf( $equal(composition(one,complement(X_134)),complement(X_134)) )],[refute_1_152,refute_1_158]) ).
cnf(refute_1_160,plain,
join(complement(X_134),composition(converse(one),complement(X_134))) = join(complement(X_134),composition(converse(one),complement(X_134))),
introduced(tautology,[refl,[$fot(join(complement(X_134),composition(converse(one),complement(X_134))))]]) ).
cnf(refute_1_161,plain,
( composition(converse(one),complement(X_134)) != complement(X_134)
| join(complement(X_134),composition(converse(one),complement(X_134))) != join(complement(X_134),composition(converse(one),complement(X_134)))
| join(complement(X_134),composition(converse(one),complement(X_134))) = join(complement(X_134),complement(X_134)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_134),composition(converse(one),complement(X_134))),join(complement(X_134),composition(converse(one),complement(X_134)))) ),[1,1],$fot(complement(X_134))]]) ).
cnf(refute_1_162,plain,
( composition(converse(one),complement(X_134)) != complement(X_134)
| join(complement(X_134),composition(converse(one),complement(X_134))) = join(complement(X_134),complement(X_134)) ),
inference(resolve,[$cnf( $equal(join(complement(X_134),composition(converse(one),complement(X_134))),join(complement(X_134),composition(converse(one),complement(X_134)))) )],[refute_1_160,refute_1_161]) ).
cnf(refute_1_163,plain,
join(complement(X_134),composition(converse(one),complement(X_134))) = join(complement(X_134),complement(X_134)),
inference(resolve,[$cnf( $equal(composition(converse(one),complement(X_134)),complement(X_134)) )],[refute_1_159,refute_1_162]) ).
cnf(refute_1_164,plain,
( join(complement(X_134),composition(converse(one),complement(X_134))) != complement(X_134)
| join(complement(X_134),composition(converse(one),complement(X_134))) != join(complement(X_134),complement(X_134))
| join(complement(X_134),complement(X_134)) = complement(X_134) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_134),composition(converse(one),complement(X_134))),complement(X_134)) ),[0],$fot(join(complement(X_134),complement(X_134)))]]) ).
cnf(refute_1_165,plain,
( join(complement(X_134),composition(converse(one),complement(X_134))) != complement(X_134)
| join(complement(X_134),complement(X_134)) = complement(X_134) ),
inference(resolve,[$cnf( $equal(join(complement(X_134),composition(converse(one),complement(X_134))),join(complement(X_134),complement(X_134))) )],[refute_1_163,refute_1_164]) ).
cnf(refute_1_166,plain,
join(complement(X_134),complement(X_134)) = complement(X_134),
inference(resolve,[$cnf( $equal(join(complement(X_134),composition(converse(one),complement(X_134))),complement(X_134)) )],[refute_1_149,refute_1_165]) ).
cnf(refute_1_167,plain,
( converse(top) != join(complement(X_134),join(complement(X_134),converse(complement(converse(join(complement(X_134),complement(X_134)))))))
| join(complement(X_134),complement(X_134)) != complement(X_134)
| converse(top) = join(complement(X_134),join(complement(X_134),converse(complement(converse(complement(X_134)))))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(top),join(complement(X_134),join(complement(X_134),converse(complement(converse(join(complement(X_134),complement(X_134)))))))) ),[1,1,1,0,0,0],$fot(complement(X_134))]]) ).
cnf(refute_1_168,plain,
( converse(top) != join(complement(X_134),join(complement(X_134),converse(complement(converse(join(complement(X_134),complement(X_134)))))))
| converse(top) = join(complement(X_134),join(complement(X_134),converse(complement(converse(complement(X_134)))))) ),
inference(resolve,[$cnf( $equal(join(complement(X_134),complement(X_134)),complement(X_134)) )],[refute_1_166,refute_1_167]) ).
cnf(refute_1_169,plain,
converse(top) = join(complement(X_134),join(complement(X_134),converse(complement(converse(complement(X_134)))))),
inference(resolve,[$cnf( $equal(converse(top),join(complement(X_134),join(complement(X_134),converse(complement(converse(join(complement(X_134),complement(X_134)))))))) )],[refute_1_107,refute_1_168]) ).
cnf(refute_1_170,plain,
( converse(top) != join(X_115,converse(complement(converse(X_115))))
| join(X_115,converse(complement(converse(X_115)))) = converse(top) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(converse(top))),bind(Y,$fot(join(X_115,converse(complement(converse(X_115))))))]]) ).
cnf(refute_1_171,plain,
join(X_115,converse(complement(converse(X_115)))) = converse(top),
inference(resolve,[$cnf( $equal(converse(top),join(X_115,converse(complement(converse(X_115))))) )],[refute_1_82,refute_1_170]) ).
cnf(refute_1_172,plain,
join(complement(X_134),converse(complement(converse(complement(X_134))))) = converse(top),
inference(subst,[],[refute_1_171:[bind(X_115,$fot(complement(X_134)))]]) ).
cnf(refute_1_173,plain,
join(complement(X_134),join(complement(X_134),converse(complement(converse(complement(X_134)))))) = join(complement(X_134),join(complement(X_134),converse(complement(converse(complement(X_134)))))),
introduced(tautology,[refl,[$fot(join(complement(X_134),join(complement(X_134),converse(complement(converse(complement(X_134)))))))]]) ).
cnf(refute_1_174,plain,
( join(complement(X_134),converse(complement(converse(complement(X_134))))) != converse(top)
| join(complement(X_134),join(complement(X_134),converse(complement(converse(complement(X_134)))))) != join(complement(X_134),join(complement(X_134),converse(complement(converse(complement(X_134))))))
| join(complement(X_134),join(complement(X_134),converse(complement(converse(complement(X_134)))))) = join(complement(X_134),converse(top)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_134),join(complement(X_134),converse(complement(converse(complement(X_134)))))),join(complement(X_134),join(complement(X_134),converse(complement(converse(complement(X_134))))))) ),[1,1],$fot(converse(top))]]) ).
cnf(refute_1_175,plain,
( join(complement(X_134),converse(complement(converse(complement(X_134))))) != converse(top)
| join(complement(X_134),join(complement(X_134),converse(complement(converse(complement(X_134)))))) = join(complement(X_134),converse(top)) ),
inference(resolve,[$cnf( $equal(join(complement(X_134),join(complement(X_134),converse(complement(converse(complement(X_134)))))),join(complement(X_134),join(complement(X_134),converse(complement(converse(complement(X_134))))))) )],[refute_1_173,refute_1_174]) ).
cnf(refute_1_176,plain,
join(complement(X_134),join(complement(X_134),converse(complement(converse(complement(X_134)))))) = join(complement(X_134),converse(top)),
inference(resolve,[$cnf( $equal(join(complement(X_134),converse(complement(converse(complement(X_134))))),converse(top)) )],[refute_1_172,refute_1_175]) ).
cnf(refute_1_177,plain,
( converse(top) != join(complement(X_134),join(complement(X_134),converse(complement(converse(complement(X_134))))))
| join(complement(X_134),join(complement(X_134),converse(complement(converse(complement(X_134)))))) != join(complement(X_134),converse(top))
| converse(top) = join(complement(X_134),converse(top)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(top),join(complement(X_134),converse(top))) ),[0],$fot(join(complement(X_134),join(complement(X_134),converse(complement(converse(complement(X_134)))))))]]) ).
cnf(refute_1_178,plain,
( converse(top) != join(complement(X_134),join(complement(X_134),converse(complement(converse(complement(X_134))))))
| converse(top) = join(complement(X_134),converse(top)) ),
inference(resolve,[$cnf( $equal(join(complement(X_134),join(complement(X_134),converse(complement(converse(complement(X_134)))))),join(complement(X_134),converse(top))) )],[refute_1_176,refute_1_177]) ).
cnf(refute_1_179,plain,
converse(top) = join(complement(X_134),converse(top)),
inference(resolve,[$cnf( $equal(converse(top),join(complement(X_134),join(complement(X_134),converse(complement(converse(complement(X_134))))))) )],[refute_1_169,refute_1_178]) ).
cnf(refute_1_180,plain,
converse(top) = join(complement(X_156),converse(top)),
inference(subst,[],[refute_1_179:[bind(X_134,$fot(X_156))]]) ).
cnf(refute_1_181,plain,
( converse(top) != join(complement(X_156),converse(top))
| join(complement(X_156),converse(top)) = converse(top) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(converse(top))),bind(Y,$fot(join(complement(X_156),converse(top))))]]) ).
cnf(refute_1_182,plain,
join(complement(X_156),converse(top)) = converse(top),
inference(resolve,[$cnf( $equal(converse(top),join(complement(X_156),converse(top))) )],[refute_1_180,refute_1_181]) ).
cnf(refute_1_183,plain,
( join(complement(X_156),converse(top)) != converse(top)
| join(converse(top),complement(X_156)) != join(complement(X_156),converse(top))
| join(converse(top),complement(X_156)) = converse(top) ),
introduced(tautology,[equality,[$cnf( $equal(join(converse(top),complement(X_156)),join(complement(X_156),converse(top))) ),[1],$fot(converse(top))]]) ).
cnf(refute_1_184,plain,
( join(converse(top),complement(X_156)) != join(complement(X_156),converse(top))
| join(converse(top),complement(X_156)) = converse(top) ),
inference(resolve,[$cnf( $equal(join(complement(X_156),converse(top)),converse(top)) )],[refute_1_182,refute_1_183]) ).
cnf(refute_1_185,plain,
join(converse(top),complement(X_156)) = converse(top),
inference(resolve,[$cnf( $equal(join(converse(top),complement(X_156)),join(complement(X_156),converse(top))) )],[refute_1_84,refute_1_184]) ).
cnf(refute_1_186,plain,
join(converse(top),complement(converse(top))) = converse(top),
inference(subst,[],[refute_1_185:[bind(X_156,$fot(converse(top)))]]) ).
cnf(refute_1_187,plain,
( join(converse(top),complement(converse(top))) != converse(top)
| top != join(converse(top),complement(converse(top)))
| top = converse(top) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(converse(top),complement(converse(top)))) ),[1],$fot(converse(top))]]) ).
cnf(refute_1_188,plain,
( top != join(converse(top),complement(converse(top)))
| top = converse(top) ),
inference(resolve,[$cnf( $equal(join(converse(top),complement(converse(top))),converse(top)) )],[refute_1_186,refute_1_187]) ).
cnf(refute_1_189,plain,
top = converse(top),
inference(resolve,[$cnf( $equal(top,join(converse(top),complement(converse(top)))) )],[refute_1_83,refute_1_188]) ).
cnf(refute_1_190,plain,
( top != converse(top)
| converse(top) = top ),
inference(subst,[],[refute_1_17:[bind(X,$fot(top)),bind(Y,$fot(converse(top)))]]) ).
cnf(refute_1_191,plain,
converse(top) = top,
inference(resolve,[$cnf( $equal(top,converse(top)) )],[refute_1_189,refute_1_190]) ).
cnf(refute_1_192,plain,
( converse(top) != join(X_115,converse(complement(converse(X_115))))
| converse(top) != top
| top = join(X_115,converse(complement(converse(X_115)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(top),join(X_115,converse(complement(converse(X_115))))) ),[0],$fot(top)]]) ).
cnf(refute_1_193,plain,
( converse(top) != join(X_115,converse(complement(converse(X_115))))
| top = join(X_115,converse(complement(converse(X_115)))) ),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_1_191,refute_1_192]) ).
cnf(refute_1_194,plain,
top = join(X_115,converse(complement(converse(X_115)))),
inference(resolve,[$cnf( $equal(converse(top),join(X_115,converse(complement(converse(X_115))))) )],[refute_1_82,refute_1_193]) ).
cnf(refute_1_195,plain,
top = join(join(X_169,top),converse(complement(converse(join(X_169,top))))),
inference(subst,[],[refute_1_194:[bind(X_115,$fot(join(X_169,top)))]]) ).
cnf(refute_1_196,plain,
converse(top) = join(join(converse(X0),X_110),converse(complement(converse(join(converse(X0),X_110))))),
inference(subst,[],[refute_1_82:[bind(X_115,$fot(join(converse(X0),X_110)))]]) ).
cnf(refute_1_197,plain,
( converse(join(converse(X0),X_110)) != join(X0,converse(X_110))
| converse(top) != join(join(converse(X0),X_110),converse(complement(converse(join(converse(X0),X_110)))))
| converse(top) = join(join(converse(X0),X_110),converse(complement(join(X0,converse(X_110))))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(top),join(join(converse(X0),X_110),converse(complement(converse(join(converse(X0),X_110)))))) ),[1,1,0,0],$fot(join(X0,converse(X_110)))]]) ).
cnf(refute_1_198,plain,
( converse(top) != join(join(converse(X0),X_110),converse(complement(converse(join(converse(X0),X_110)))))
| converse(top) = join(join(converse(X0),X_110),converse(complement(join(X0,converse(X_110))))) ),
inference(resolve,[$cnf( $equal(converse(join(converse(X0),X_110)),join(X0,converse(X_110))) )],[refute_1_75,refute_1_197]) ).
cnf(refute_1_199,plain,
converse(top) = join(join(converse(X0),X_110),converse(complement(join(X0,converse(X_110))))),
inference(resolve,[$cnf( $equal(converse(top),join(join(converse(X0),X_110),converse(complement(converse(join(converse(X0),X_110)))))) )],[refute_1_196,refute_1_198]) ).
cnf(refute_1_200,plain,
converse(join(X_109,converse(X0))) = join(converse(X_109),converse(converse(X0))),
inference(subst,[],[refute_1_71:[bind(X0,$fot(X_109)),bind(X1,$fot(converse(X0)))]]) ).
cnf(refute_1_201,plain,
( converse(converse(X0)) != X0
| converse(join(X_109,converse(X0))) != join(converse(X_109),converse(converse(X0)))
| converse(join(X_109,converse(X0))) = join(converse(X_109),X0) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(X_109,converse(X0))),join(converse(X_109),converse(converse(X0)))) ),[1,1],$fot(X0)]]) ).
cnf(refute_1_202,plain,
( converse(join(X_109,converse(X0))) != join(converse(X_109),converse(converse(X0)))
| converse(join(X_109,converse(X0))) = join(converse(X_109),X0) ),
inference(resolve,[$cnf( $equal(converse(converse(X0)),X0) )],[refute_1_3,refute_1_201]) ).
cnf(refute_1_203,plain,
converse(join(X_109,converse(X0))) = join(converse(X_109),X0),
inference(resolve,[$cnf( $equal(converse(join(X_109,converse(X0))),join(converse(X_109),converse(converse(X0)))) )],[refute_1_200,refute_1_202]) ).
cnf(refute_1_204,plain,
converse(join(X_109,converse(join(X_114,converse(X_113))))) = join(converse(X_109),join(X_114,converse(X_113))),
inference(subst,[],[refute_1_203:[bind(X0,$fot(join(X_114,converse(X_113))))]]) ).
cnf(refute_1_205,plain,
converse(join(X_114,converse(X_113))) = join(converse(X_114),X_113),
inference(subst,[],[refute_1_203:[bind(X0,$fot(X_113)),bind(X_109,$fot(X_114))]]) ).
cnf(refute_1_206,plain,
( converse(join(X_109,converse(join(X_114,converse(X_113))))) != join(converse(X_109),join(X_114,converse(X_113)))
| converse(join(X_114,converse(X_113))) != join(converse(X_114),X_113)
| converse(join(X_109,join(converse(X_114),X_113))) = join(converse(X_109),join(X_114,converse(X_113))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(X_109,converse(join(X_114,converse(X_113))))),join(converse(X_109),join(X_114,converse(X_113)))) ),[0,0,1],$fot(join(converse(X_114),X_113))]]) ).
cnf(refute_1_207,plain,
( converse(join(X_109,converse(join(X_114,converse(X_113))))) != join(converse(X_109),join(X_114,converse(X_113)))
| converse(join(X_109,join(converse(X_114),X_113))) = join(converse(X_109),join(X_114,converse(X_113))) ),
inference(resolve,[$cnf( $equal(converse(join(X_114,converse(X_113))),join(converse(X_114),X_113)) )],[refute_1_205,refute_1_206]) ).
cnf(refute_1_208,plain,
converse(join(X_109,join(converse(X_114),X_113))) = join(converse(X_109),join(X_114,converse(X_113))),
inference(resolve,[$cnf( $equal(converse(join(X_109,converse(join(X_114,converse(X_113))))),join(converse(X_109),join(X_114,converse(X_113)))) )],[refute_1_204,refute_1_207]) ).
cnf(refute_1_209,plain,
( converse(join(X_109,join(converse(X_114),X_113))) != join(converse(X_109),join(X_114,converse(X_113)))
| join(converse(X_109),join(X_114,converse(X_113))) = converse(join(X_109,join(converse(X_114),X_113))) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(converse(join(X_109,join(converse(X_114),X_113))))),bind(Y,$fot(join(converse(X_109),join(X_114,converse(X_113)))))]]) ).
cnf(refute_1_210,plain,
join(converse(X_109),join(X_114,converse(X_113))) = converse(join(X_109,join(converse(X_114),X_113))),
inference(resolve,[$cnf( $equal(converse(join(X_109,join(converse(X_114),X_113))),join(converse(X_109),join(X_114,converse(X_113)))) )],[refute_1_208,refute_1_209]) ).
cnf(refute_1_211,plain,
join(converse(X0),join(X_110,converse(complement(join(X0,converse(X_110)))))) = converse(join(X0,join(converse(X_110),complement(join(X0,converse(X_110)))))),
inference(subst,[],[refute_1_210:[bind(X_109,$fot(X0)),bind(X_113,$fot(complement(join(X0,converse(X_110))))),bind(X_114,$fot(X_110))]]) ).
cnf(refute_1_212,plain,
join(join(converse(X0),X_110),converse(complement(join(X0,converse(X_110))))) = join(converse(X0),join(X_110,converse(complement(join(X0,converse(X_110)))))),
inference(subst,[],[refute_1_102:[bind(X0,$fot(converse(X0))),bind(X1,$fot(X_110)),bind(X2,$fot(converse(complement(join(X0,converse(X_110))))))]]) ).
cnf(refute_1_213,plain,
( join(converse(X0),join(X_110,converse(complement(join(X0,converse(X_110)))))) != converse(join(X0,join(converse(X_110),complement(join(X0,converse(X_110))))))
| join(join(converse(X0),X_110),converse(complement(join(X0,converse(X_110))))) != join(converse(X0),join(X_110,converse(complement(join(X0,converse(X_110))))))
| join(join(converse(X0),X_110),converse(complement(join(X0,converse(X_110))))) = converse(join(X0,join(converse(X_110),complement(join(X0,converse(X_110)))))) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(join(converse(X0),X_110),converse(complement(join(X0,converse(X_110))))))),bind(Y,$fot(join(converse(X0),join(X_110,converse(complement(join(X0,converse(X_110)))))))),bind(Z,$fot(converse(join(X0,join(converse(X_110),complement(join(X0,converse(X_110))))))))]]) ).
cnf(refute_1_214,plain,
( join(converse(X0),join(X_110,converse(complement(join(X0,converse(X_110)))))) != converse(join(X0,join(converse(X_110),complement(join(X0,converse(X_110))))))
| join(join(converse(X0),X_110),converse(complement(join(X0,converse(X_110))))) = converse(join(X0,join(converse(X_110),complement(join(X0,converse(X_110)))))) ),
inference(resolve,[$cnf( $equal(join(join(converse(X0),X_110),converse(complement(join(X0,converse(X_110))))),join(converse(X0),join(X_110,converse(complement(join(X0,converse(X_110))))))) )],[refute_1_212,refute_1_213]) ).
cnf(refute_1_215,plain,
join(join(converse(X0),X_110),converse(complement(join(X0,converse(X_110))))) = converse(join(X0,join(converse(X_110),complement(join(X0,converse(X_110)))))),
inference(resolve,[$cnf( $equal(join(converse(X0),join(X_110,converse(complement(join(X0,converse(X_110)))))),converse(join(X0,join(converse(X_110),complement(join(X0,converse(X_110))))))) )],[refute_1_211,refute_1_214]) ).
cnf(refute_1_216,plain,
( converse(top) != join(join(converse(X0),X_110),converse(complement(join(X0,converse(X_110)))))
| join(join(converse(X0),X_110),converse(complement(join(X0,converse(X_110))))) != converse(join(X0,join(converse(X_110),complement(join(X0,converse(X_110))))))
| converse(top) = converse(join(X0,join(converse(X_110),complement(join(X0,converse(X_110)))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(top),converse(join(X0,join(converse(X_110),complement(join(X0,converse(X_110))))))) ),[0],$fot(join(join(converse(X0),X_110),converse(complement(join(X0,converse(X_110))))))]]) ).
cnf(refute_1_217,plain,
( converse(top) != join(join(converse(X0),X_110),converse(complement(join(X0,converse(X_110)))))
| converse(top) = converse(join(X0,join(converse(X_110),complement(join(X0,converse(X_110)))))) ),
inference(resolve,[$cnf( $equal(join(join(converse(X0),X_110),converse(complement(join(X0,converse(X_110))))),converse(join(X0,join(converse(X_110),complement(join(X0,converse(X_110))))))) )],[refute_1_215,refute_1_216]) ).
cnf(refute_1_218,plain,
converse(top) = converse(join(X0,join(converse(X_110),complement(join(X0,converse(X_110)))))),
inference(resolve,[$cnf( $equal(converse(top),join(join(converse(X0),X_110),converse(complement(join(X0,converse(X_110)))))) )],[refute_1_199,refute_1_217]) ).
cnf(refute_1_219,plain,
( converse(top) != converse(join(X0,join(converse(X_110),complement(join(X0,converse(X_110))))))
| converse(top) != top
| top = converse(join(X0,join(converse(X_110),complement(join(X0,converse(X_110)))))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(top),converse(join(X0,join(converse(X_110),complement(join(X0,converse(X_110))))))) ),[0],$fot(top)]]) ).
cnf(refute_1_220,plain,
( converse(top) != converse(join(X0,join(converse(X_110),complement(join(X0,converse(X_110))))))
| top = converse(join(X0,join(converse(X_110),complement(join(X0,converse(X_110)))))) ),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_1_191,refute_1_219]) ).
cnf(refute_1_221,plain,
top = converse(join(X0,join(converse(X_110),complement(join(X0,converse(X_110)))))),
inference(resolve,[$cnf( $equal(converse(top),converse(join(X0,join(converse(X_110),complement(join(X0,converse(X_110))))))) )],[refute_1_218,refute_1_220]) ).
cnf(refute_1_222,plain,
top = converse(join(X0,join(converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168)))))),complement(join(X0,converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168))))))))))),
inference(subst,[],[refute_1_221:[bind(X_110,$fot(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168)))))))]]) ).
cnf(refute_1_223,plain,
top = converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168)))))),
inference(subst,[],[refute_1_221:[bind(X0,$fot(X_167)),bind(X_110,$fot(X_168))]]) ).
cnf(refute_1_224,plain,
( top != converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168))))))
| converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168)))))) = top ),
inference(subst,[],[refute_1_17:[bind(X,$fot(top)),bind(Y,$fot(converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168))))))))]]) ).
cnf(refute_1_225,plain,
converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168)))))) = top,
inference(resolve,[$cnf( $equal(top,converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168))))))) )],[refute_1_223,refute_1_224]) ).
cnf(refute_1_226,plain,
( converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168)))))) != top
| top != converse(join(X0,join(converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168)))))),complement(join(X0,converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168)))))))))))
| top = converse(join(X0,join(top,complement(join(X0,converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168))))))))))) ),
introduced(tautology,[equality,[$cnf( $equal(top,converse(join(X0,join(converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168)))))),complement(join(X0,converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168)))))))))))) ),[1,0,1,0],$fot(top)]]) ).
cnf(refute_1_227,plain,
( top != converse(join(X0,join(converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168)))))),complement(join(X0,converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168)))))))))))
| top = converse(join(X0,join(top,complement(join(X0,converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168))))))))))) ),
inference(resolve,[$cnf( $equal(converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168)))))),top) )],[refute_1_225,refute_1_226]) ).
cnf(refute_1_228,plain,
top = converse(join(X0,join(top,complement(join(X0,converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168))))))))))),
inference(resolve,[$cnf( $equal(top,converse(join(X0,join(converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168)))))),complement(join(X0,converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168)))))))))))) )],[refute_1_222,refute_1_227]) ).
cnf(refute_1_229,plain,
top = join(join(complement(X_137),complement(X_138)),complement(join(complement(X_137),complement(X_138)))),
inference(subst,[],[refute_1_23:[bind(X0,$fot(join(complement(X_137),complement(X_138))))]]) ).
cnf(refute_1_230,plain,
( complement(join(complement(X_137),complement(X_138))) != meet(X_137,X_138)
| top != join(join(complement(X_137),complement(X_138)),complement(join(complement(X_137),complement(X_138))))
| top = join(join(complement(X_137),complement(X_138)),meet(X_137,X_138)) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(join(complement(X_137),complement(X_138)),complement(join(complement(X_137),complement(X_138))))) ),[1,1],$fot(meet(X_137,X_138))]]) ).
cnf(refute_1_231,plain,
( top != join(join(complement(X_137),complement(X_138)),complement(join(complement(X_137),complement(X_138))))
| top = join(join(complement(X_137),complement(X_138)),meet(X_137,X_138)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_137),complement(X_138))),meet(X_137,X_138)) )],[refute_1_19,refute_1_230]) ).
cnf(refute_1_232,plain,
top = join(join(complement(X_137),complement(X_138)),meet(X_137,X_138)),
inference(resolve,[$cnf( $equal(top,join(join(complement(X_137),complement(X_138)),complement(join(complement(X_137),complement(X_138))))) )],[refute_1_229,refute_1_231]) ).
cnf(refute_1_233,plain,
join(join(complement(X_137),complement(X_138)),meet(X_137,X_138)) = join(complement(X_137),join(complement(X_138),meet(X_137,X_138))),
inference(subst,[],[refute_1_102:[bind(X0,$fot(complement(X_137))),bind(X1,$fot(complement(X_138))),bind(X2,$fot(meet(X_137,X_138)))]]) ).
cnf(refute_1_234,plain,
( join(join(complement(X_137),complement(X_138)),meet(X_137,X_138)) != join(complement(X_137),join(complement(X_138),meet(X_137,X_138)))
| top != join(join(complement(X_137),complement(X_138)),meet(X_137,X_138))
| top = join(complement(X_137),join(complement(X_138),meet(X_137,X_138))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(join(complement(X_137),complement(X_138)),meet(X_137,X_138))) ),[1],$fot(join(complement(X_137),join(complement(X_138),meet(X_137,X_138))))]]) ).
cnf(refute_1_235,plain,
( top != join(join(complement(X_137),complement(X_138)),meet(X_137,X_138))
| top = join(complement(X_137),join(complement(X_138),meet(X_137,X_138))) ),
inference(resolve,[$cnf( $equal(join(join(complement(X_137),complement(X_138)),meet(X_137,X_138)),join(complement(X_137),join(complement(X_138),meet(X_137,X_138)))) )],[refute_1_233,refute_1_234]) ).
cnf(refute_1_236,plain,
top = join(complement(X_137),join(complement(X_138),meet(X_137,X_138))),
inference(resolve,[$cnf( $equal(top,join(join(complement(X_137),complement(X_138)),meet(X_137,X_138))) )],[refute_1_232,refute_1_235]) ).
cnf(refute_1_237,plain,
top = join(complement(X_146),join(complement(X_146),meet(X_146,X_146))),
inference(subst,[],[refute_1_236:[bind(X_137,$fot(X_146)),bind(X_138,$fot(X_146))]]) ).
cnf(refute_1_238,plain,
meet(X_138,X_138) = complement(join(complement(X_138),complement(X_138))),
inference(subst,[],[refute_1_11:[bind(X0,$fot(X_138)),bind(X1,$fot(X_138))]]) ).
cnf(refute_1_239,plain,
join(complement(X_138),complement(X_138)) = complement(X_138),
inference(subst,[],[refute_1_166:[bind(X_134,$fot(X_138))]]) ).
cnf(refute_1_240,plain,
( join(complement(X_138),complement(X_138)) != complement(X_138)
| meet(X_138,X_138) != complement(join(complement(X_138),complement(X_138)))
| meet(X_138,X_138) = complement(complement(X_138)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_138,X_138),complement(join(complement(X_138),complement(X_138)))) ),[1,0],$fot(complement(X_138))]]) ).
cnf(refute_1_241,plain,
( meet(X_138,X_138) != complement(join(complement(X_138),complement(X_138)))
| meet(X_138,X_138) = complement(complement(X_138)) ),
inference(resolve,[$cnf( $equal(join(complement(X_138),complement(X_138)),complement(X_138)) )],[refute_1_239,refute_1_240]) ).
cnf(refute_1_242,plain,
meet(X_138,X_138) = complement(complement(X_138)),
inference(resolve,[$cnf( $equal(meet(X_138,X_138),complement(join(complement(X_138),complement(X_138)))) )],[refute_1_238,refute_1_241]) ).
cnf(refute_1_243,plain,
meet(X_146,X_146) = complement(complement(X_146)),
inference(subst,[],[refute_1_242:[bind(X_138,$fot(X_146))]]) ).
cnf(refute_1_244,plain,
( meet(X_146,X_146) != complement(complement(X_146))
| top != join(complement(X_146),join(complement(X_146),meet(X_146,X_146)))
| top = join(complement(X_146),join(complement(X_146),complement(complement(X_146)))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(X_146),join(complement(X_146),meet(X_146,X_146)))) ),[1,1,1],$fot(complement(complement(X_146)))]]) ).
cnf(refute_1_245,plain,
( top != join(complement(X_146),join(complement(X_146),meet(X_146,X_146)))
| top = join(complement(X_146),join(complement(X_146),complement(complement(X_146)))) ),
inference(resolve,[$cnf( $equal(meet(X_146,X_146),complement(complement(X_146))) )],[refute_1_243,refute_1_244]) ).
cnf(refute_1_246,plain,
top = join(complement(X_146),join(complement(X_146),complement(complement(X_146)))),
inference(resolve,[$cnf( $equal(top,join(complement(X_146),join(complement(X_146),meet(X_146,X_146)))) )],[refute_1_237,refute_1_245]) ).
cnf(refute_1_247,plain,
join(complement(X_146),top) = join(top,complement(X_146)),
inference(subst,[],[refute_1_52:[bind(X0,$fot(top)),bind(X1,$fot(complement(X_146)))]]) ).
cnf(refute_1_248,plain,
join(complement(X_146),complement(complement(X_146))) = top,
inference(subst,[],[refute_1_25:[bind(X0,$fot(complement(X_146)))]]) ).
cnf(refute_1_249,plain,
join(complement(X_146),join(complement(X_146),complement(complement(X_146)))) = join(complement(X_146),join(complement(X_146),complement(complement(X_146)))),
introduced(tautology,[refl,[$fot(join(complement(X_146),join(complement(X_146),complement(complement(X_146)))))]]) ).
cnf(refute_1_250,plain,
( join(complement(X_146),complement(complement(X_146))) != top
| join(complement(X_146),join(complement(X_146),complement(complement(X_146)))) != join(complement(X_146),join(complement(X_146),complement(complement(X_146))))
| join(complement(X_146),join(complement(X_146),complement(complement(X_146)))) = join(complement(X_146),top) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_146),join(complement(X_146),complement(complement(X_146)))),join(complement(X_146),join(complement(X_146),complement(complement(X_146))))) ),[1,1],$fot(top)]]) ).
cnf(refute_1_251,plain,
( join(complement(X_146),complement(complement(X_146))) != top
| join(complement(X_146),join(complement(X_146),complement(complement(X_146)))) = join(complement(X_146),top) ),
inference(resolve,[$cnf( $equal(join(complement(X_146),join(complement(X_146),complement(complement(X_146)))),join(complement(X_146),join(complement(X_146),complement(complement(X_146))))) )],[refute_1_249,refute_1_250]) ).
cnf(refute_1_252,plain,
join(complement(X_146),join(complement(X_146),complement(complement(X_146)))) = join(complement(X_146),top),
inference(resolve,[$cnf( $equal(join(complement(X_146),complement(complement(X_146))),top) )],[refute_1_248,refute_1_251]) ).
cnf(refute_1_253,plain,
( join(complement(X_146),join(complement(X_146),complement(complement(X_146)))) != join(complement(X_146),top)
| join(complement(X_146),top) != join(top,complement(X_146))
| join(complement(X_146),join(complement(X_146),complement(complement(X_146)))) = join(top,complement(X_146)) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(complement(X_146),join(complement(X_146),complement(complement(X_146)))))),bind(Y,$fot(join(complement(X_146),top))),bind(Z,$fot(join(top,complement(X_146))))]]) ).
cnf(refute_1_254,plain,
( join(complement(X_146),top) != join(top,complement(X_146))
| join(complement(X_146),join(complement(X_146),complement(complement(X_146)))) = join(top,complement(X_146)) ),
inference(resolve,[$cnf( $equal(join(complement(X_146),join(complement(X_146),complement(complement(X_146)))),join(complement(X_146),top)) )],[refute_1_252,refute_1_253]) ).
cnf(refute_1_255,plain,
join(complement(X_146),join(complement(X_146),complement(complement(X_146)))) = join(top,complement(X_146)),
inference(resolve,[$cnf( $equal(join(complement(X_146),top),join(top,complement(X_146))) )],[refute_1_247,refute_1_254]) ).
cnf(refute_1_256,plain,
( join(complement(X_146),join(complement(X_146),complement(complement(X_146)))) != join(top,complement(X_146))
| top != join(complement(X_146),join(complement(X_146),complement(complement(X_146))))
| top = join(top,complement(X_146)) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(X_146),join(complement(X_146),complement(complement(X_146))))) ),[1],$fot(join(top,complement(X_146)))]]) ).
cnf(refute_1_257,plain,
( top != join(complement(X_146),join(complement(X_146),complement(complement(X_146))))
| top = join(top,complement(X_146)) ),
inference(resolve,[$cnf( $equal(join(complement(X_146),join(complement(X_146),complement(complement(X_146)))),join(top,complement(X_146))) )],[refute_1_255,refute_1_256]) ).
cnf(refute_1_258,plain,
top = join(top,complement(X_146)),
inference(resolve,[$cnf( $equal(top,join(complement(X_146),join(complement(X_146),complement(complement(X_146))))) )],[refute_1_246,refute_1_257]) ).
cnf(refute_1_259,plain,
( top != join(top,complement(X_146))
| join(top,complement(X_146)) = top ),
inference(subst,[],[refute_1_17:[bind(X,$fot(top)),bind(Y,$fot(join(top,complement(X_146))))]]) ).
cnf(refute_1_260,plain,
join(top,complement(X_146)) = top,
inference(resolve,[$cnf( $equal(top,join(top,complement(X_146))) )],[refute_1_258,refute_1_259]) ).
cnf(refute_1_261,plain,
join(top,complement(join(X0,converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168))))))))) = top,
inference(subst,[],[refute_1_260:[bind(X_146,$fot(join(X0,converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168)))))))))]]) ).
cnf(refute_1_262,plain,
join(X0,join(top,complement(join(X0,converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168)))))))))) = join(X0,join(top,complement(join(X0,converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168)))))))))),
introduced(tautology,[refl,[$fot(join(X0,join(top,complement(join(X0,converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168)))))))))))]]) ).
cnf(refute_1_263,plain,
( join(X0,join(top,complement(join(X0,converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168)))))))))) != join(X0,join(top,complement(join(X0,converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168))))))))))
| join(top,complement(join(X0,converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168))))))))) != top
| join(X0,join(top,complement(join(X0,converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168)))))))))) = join(X0,top) ),
introduced(tautology,[equality,[$cnf( $equal(join(X0,join(top,complement(join(X0,converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168)))))))))),join(X0,join(top,complement(join(X0,converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168))))))))))) ),[1,1],$fot(top)]]) ).
cnf(refute_1_264,plain,
( join(top,complement(join(X0,converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168))))))))) != top
| join(X0,join(top,complement(join(X0,converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168)))))))))) = join(X0,top) ),
inference(resolve,[$cnf( $equal(join(X0,join(top,complement(join(X0,converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168)))))))))),join(X0,join(top,complement(join(X0,converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168))))))))))) )],[refute_1_262,refute_1_263]) ).
cnf(refute_1_265,plain,
join(X0,join(top,complement(join(X0,converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168)))))))))) = join(X0,top),
inference(resolve,[$cnf( $equal(join(top,complement(join(X0,converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168))))))))),top) )],[refute_1_261,refute_1_264]) ).
cnf(refute_1_266,plain,
converse(join(X0,join(top,complement(join(X0,converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168))))))))))) = converse(join(X0,join(top,complement(join(X0,converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168))))))))))),
introduced(tautology,[refl,[$fot(converse(join(X0,join(top,complement(join(X0,converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168))))))))))))]]) ).
cnf(refute_1_267,plain,
( converse(join(X0,join(top,complement(join(X0,converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168))))))))))) != converse(join(X0,join(top,complement(join(X0,converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168)))))))))))
| join(X0,join(top,complement(join(X0,converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168)))))))))) != join(X0,top)
| converse(join(X0,join(top,complement(join(X0,converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168))))))))))) = converse(join(X0,top)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(X0,join(top,complement(join(X0,converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168))))))))))),converse(join(X0,join(top,complement(join(X0,converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168)))))))))))) ),[1,0],$fot(join(X0,top))]]) ).
cnf(refute_1_268,plain,
( join(X0,join(top,complement(join(X0,converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168)))))))))) != join(X0,top)
| converse(join(X0,join(top,complement(join(X0,converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168))))))))))) = converse(join(X0,top)) ),
inference(resolve,[$cnf( $equal(converse(join(X0,join(top,complement(join(X0,converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168))))))))))),converse(join(X0,join(top,complement(join(X0,converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168)))))))))))) )],[refute_1_266,refute_1_267]) ).
cnf(refute_1_269,plain,
converse(join(X0,join(top,complement(join(X0,converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168))))))))))) = converse(join(X0,top)),
inference(resolve,[$cnf( $equal(join(X0,join(top,complement(join(X0,converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168)))))))))),join(X0,top)) )],[refute_1_265,refute_1_268]) ).
cnf(refute_1_270,plain,
( converse(join(X0,join(top,complement(join(X0,converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168))))))))))) != converse(join(X0,top))
| top != converse(join(X0,join(top,complement(join(X0,converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168)))))))))))
| top = converse(join(X0,top)) ),
introduced(tautology,[equality,[$cnf( $equal(top,converse(join(X0,join(top,complement(join(X0,converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168)))))))))))) ),[1],$fot(converse(join(X0,top)))]]) ).
cnf(refute_1_271,plain,
( top != converse(join(X0,join(top,complement(join(X0,converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168)))))))))))
| top = converse(join(X0,top)) ),
inference(resolve,[$cnf( $equal(converse(join(X0,join(top,complement(join(X0,converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168))))))))))),converse(join(X0,top))) )],[refute_1_269,refute_1_270]) ).
cnf(refute_1_272,plain,
top = converse(join(X0,top)),
inference(resolve,[$cnf( $equal(top,converse(join(X0,join(top,complement(join(X0,converse(join(X_167,join(converse(X_168),complement(join(X_167,converse(X_168)))))))))))) )],[refute_1_228,refute_1_271]) ).
cnf(refute_1_273,plain,
top = converse(join(X_169,top)),
inference(subst,[],[refute_1_272:[bind(X0,$fot(X_169))]]) ).
cnf(refute_1_274,plain,
( top != converse(join(X_169,top))
| converse(join(X_169,top)) = top ),
inference(subst,[],[refute_1_17:[bind(X,$fot(top)),bind(Y,$fot(converse(join(X_169,top))))]]) ).
cnf(refute_1_275,plain,
converse(join(X_169,top)) = top,
inference(resolve,[$cnf( $equal(top,converse(join(X_169,top))) )],[refute_1_273,refute_1_274]) ).
cnf(refute_1_276,plain,
( converse(join(X_169,top)) != top
| top != join(join(X_169,top),converse(complement(converse(join(X_169,top)))))
| top = join(join(X_169,top),converse(complement(top))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(join(X_169,top),converse(complement(converse(join(X_169,top)))))) ),[1,1,0,0],$fot(top)]]) ).
cnf(refute_1_277,plain,
( top != join(join(X_169,top),converse(complement(converse(join(X_169,top)))))
| top = join(join(X_169,top),converse(complement(top))) ),
inference(resolve,[$cnf( $equal(converse(join(X_169,top)),top) )],[refute_1_275,refute_1_276]) ).
cnf(refute_1_278,plain,
top = join(join(X_169,top),converse(complement(top))),
inference(resolve,[$cnf( $equal(top,join(join(X_169,top),converse(complement(converse(join(X_169,top)))))) )],[refute_1_195,refute_1_277]) ).
cnf(refute_1_279,plain,
converse(join(converse(top),X_110)) = join(top,converse(X_110)),
inference(subst,[],[refute_1_75:[bind(X0,$fot(top))]]) ).
cnf(refute_1_280,plain,
( converse(join(converse(top),X_110)) != join(top,converse(X_110))
| converse(top) != top
| converse(join(top,X_110)) = join(top,converse(X_110)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(top),X_110)),join(top,converse(X_110))) ),[0,0,0],$fot(top)]]) ).
cnf(refute_1_281,plain,
( converse(join(converse(top),X_110)) != join(top,converse(X_110))
| converse(join(top,X_110)) = join(top,converse(X_110)) ),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_1_191,refute_1_280]) ).
cnf(refute_1_282,plain,
converse(join(top,X_110)) = join(top,converse(X_110)),
inference(resolve,[$cnf( $equal(converse(join(converse(top),X_110)),join(top,converse(X_110))) )],[refute_1_279,refute_1_281]) ).
cnf(refute_1_283,plain,
converse(join(X_109,converse(join(one,join(one,join(zero,complement(join(one,one)))))))) = join(converse(X_109),join(one,join(one,join(zero,complement(join(one,one)))))),
inference(subst,[],[refute_1_203:[bind(X0,$fot(join(one,join(one,join(zero,complement(join(one,one)))))))]]) ).
cnf(refute_1_284,plain,
converse(top) = join(converse(complement(converse(X_155))),join(X_155,converse(complement(converse(join(X_155,converse(complement(converse(X_155))))))))),
inference(subst,[],[refute_1_106:[bind(X_120,$fot(converse(complement(converse(X_155))))),bind(X_121,$fot(X_155))]]) ).
cnf(refute_1_285,plain,
converse(top) = join(X_155,converse(complement(converse(X_155)))),
inference(subst,[],[refute_1_82:[bind(X_115,$fot(X_155))]]) ).
cnf(refute_1_286,plain,
( converse(top) != join(X_155,converse(complement(converse(X_155))))
| join(X_155,converse(complement(converse(X_155)))) = converse(top) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(converse(top))),bind(Y,$fot(join(X_155,converse(complement(converse(X_155))))))]]) ).
cnf(refute_1_287,plain,
join(X_155,converse(complement(converse(X_155)))) = converse(top),
inference(resolve,[$cnf( $equal(converse(top),join(X_155,converse(complement(converse(X_155))))) )],[refute_1_285,refute_1_286]) ).
cnf(refute_1_288,plain,
( converse(top) != join(converse(complement(converse(X_155))),join(X_155,converse(complement(converse(join(X_155,converse(complement(converse(X_155)))))))))
| join(X_155,converse(complement(converse(X_155)))) != converse(top)
| converse(top) = join(converse(complement(converse(X_155))),join(X_155,converse(complement(converse(converse(top)))))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(top),join(converse(complement(converse(X_155))),join(X_155,converse(complement(converse(join(X_155,converse(complement(converse(X_155)))))))))) ),[1,1,1,0,0,0],$fot(converse(top))]]) ).
cnf(refute_1_289,plain,
( converse(top) != join(converse(complement(converse(X_155))),join(X_155,converse(complement(converse(join(X_155,converse(complement(converse(X_155)))))))))
| converse(top) = join(converse(complement(converse(X_155))),join(X_155,converse(complement(converse(converse(top)))))) ),
inference(resolve,[$cnf( $equal(join(X_155,converse(complement(converse(X_155)))),converse(top)) )],[refute_1_287,refute_1_288]) ).
cnf(refute_1_290,plain,
converse(top) = join(converse(complement(converse(X_155))),join(X_155,converse(complement(converse(converse(top)))))),
inference(resolve,[$cnf( $equal(converse(top),join(converse(complement(converse(X_155))),join(X_155,converse(complement(converse(join(X_155,converse(complement(converse(X_155)))))))))) )],[refute_1_284,refute_1_289]) ).
cnf(refute_1_291,plain,
join(complement(converse(X_155)),zero) = join(zero,complement(converse(X_155))),
inference(subst,[],[refute_1_52:[bind(X0,$fot(zero)),bind(X1,$fot(complement(converse(X_155))))]]) ).
cnf(refute_1_292,plain,
converse(converse(top)) = top,
inference(subst,[],[refute_1_3:[bind(X0,$fot(top))]]) ).
cnf(refute_1_293,plain,
complement(converse(converse(top))) = complement(converse(converse(top))),
introduced(tautology,[refl,[$fot(complement(converse(converse(top))))]]) ).
cnf(refute_1_294,plain,
( complement(converse(converse(top))) != complement(converse(converse(top)))
| converse(converse(top)) != top
| complement(converse(converse(top))) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(complement(converse(converse(top))),complement(converse(converse(top)))) ),[1,0],$fot(top)]]) ).
cnf(refute_1_295,plain,
( converse(converse(top)) != top
| complement(converse(converse(top))) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(converse(converse(top))),complement(converse(converse(top)))) )],[refute_1_293,refute_1_294]) ).
cnf(refute_1_296,plain,
complement(converse(converse(top))) = complement(top),
inference(resolve,[$cnf( $equal(converse(converse(top)),top) )],[refute_1_292,refute_1_295]) ).
cnf(refute_1_297,plain,
( complement(converse(converse(top))) != complement(top)
| complement(top) != zero
| complement(converse(converse(top))) = zero ),
inference(subst,[],[refute_1_37:[bind(X,$fot(complement(converse(converse(top))))),bind(Y,$fot(complement(top))),bind(Z,$fot(zero))]]) ).
cnf(refute_1_298,plain,
( complement(top) != zero
| complement(converse(converse(top))) = zero ),
inference(resolve,[$cnf( $equal(complement(converse(converse(top))),complement(top)) )],[refute_1_296,refute_1_297]) ).
cnf(refute_1_299,plain,
complement(converse(converse(top))) = zero,
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_1_45,refute_1_298]) ).
cnf(refute_1_300,plain,
join(complement(converse(X_155)),complement(converse(converse(top)))) = join(complement(converse(X_155)),complement(converse(converse(top)))),
introduced(tautology,[refl,[$fot(join(complement(converse(X_155)),complement(converse(converse(top)))))]]) ).
cnf(refute_1_301,plain,
( complement(converse(converse(top))) != zero
| join(complement(converse(X_155)),complement(converse(converse(top)))) != join(complement(converse(X_155)),complement(converse(converse(top))))
| join(complement(converse(X_155)),complement(converse(converse(top)))) = join(complement(converse(X_155)),zero) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(converse(X_155)),complement(converse(converse(top)))),join(complement(converse(X_155)),complement(converse(converse(top))))) ),[1,1],$fot(zero)]]) ).
cnf(refute_1_302,plain,
( complement(converse(converse(top))) != zero
| join(complement(converse(X_155)),complement(converse(converse(top)))) = join(complement(converse(X_155)),zero) ),
inference(resolve,[$cnf( $equal(join(complement(converse(X_155)),complement(converse(converse(top)))),join(complement(converse(X_155)),complement(converse(converse(top))))) )],[refute_1_300,refute_1_301]) ).
cnf(refute_1_303,plain,
join(complement(converse(X_155)),complement(converse(converse(top)))) = join(complement(converse(X_155)),zero),
inference(resolve,[$cnf( $equal(complement(converse(converse(top))),zero) )],[refute_1_299,refute_1_302]) ).
cnf(refute_1_304,plain,
( join(complement(converse(X_155)),complement(converse(converse(top)))) != join(complement(converse(X_155)),zero)
| join(complement(converse(X_155)),zero) != join(zero,complement(converse(X_155)))
| join(complement(converse(X_155)),complement(converse(converse(top)))) = join(zero,complement(converse(X_155))) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(complement(converse(X_155)),complement(converse(converse(top)))))),bind(Y,$fot(join(complement(converse(X_155)),zero))),bind(Z,$fot(join(zero,complement(converse(X_155)))))]]) ).
cnf(refute_1_305,plain,
( join(complement(converse(X_155)),zero) != join(zero,complement(converse(X_155)))
| join(complement(converse(X_155)),complement(converse(converse(top)))) = join(zero,complement(converse(X_155))) ),
inference(resolve,[$cnf( $equal(join(complement(converse(X_155)),complement(converse(converse(top)))),join(complement(converse(X_155)),zero)) )],[refute_1_303,refute_1_304]) ).
cnf(refute_1_306,plain,
join(complement(converse(X_155)),complement(converse(converse(top)))) = join(zero,complement(converse(X_155))),
inference(resolve,[$cnf( $equal(join(complement(converse(X_155)),zero),join(zero,complement(converse(X_155)))) )],[refute_1_291,refute_1_305]) ).
cnf(refute_1_307,plain,
converse(join(complement(converse(X_155)),complement(converse(converse(top))))) = converse(join(complement(converse(X_155)),complement(converse(converse(top))))),
introduced(tautology,[refl,[$fot(converse(join(complement(converse(X_155)),complement(converse(converse(top))))))]]) ).
cnf(refute_1_308,plain,
( converse(join(complement(converse(X_155)),complement(converse(converse(top))))) != converse(join(complement(converse(X_155)),complement(converse(converse(top)))))
| join(complement(converse(X_155)),complement(converse(converse(top)))) != join(zero,complement(converse(X_155)))
| converse(join(complement(converse(X_155)),complement(converse(converse(top))))) = converse(join(zero,complement(converse(X_155)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(complement(converse(X_155)),complement(converse(converse(top))))),converse(join(complement(converse(X_155)),complement(converse(converse(top)))))) ),[1,0],$fot(join(zero,complement(converse(X_155))))]]) ).
cnf(refute_1_309,plain,
( join(complement(converse(X_155)),complement(converse(converse(top)))) != join(zero,complement(converse(X_155)))
| converse(join(complement(converse(X_155)),complement(converse(converse(top))))) = converse(join(zero,complement(converse(X_155)))) ),
inference(resolve,[$cnf( $equal(converse(join(complement(converse(X_155)),complement(converse(converse(top))))),converse(join(complement(converse(X_155)),complement(converse(converse(top)))))) )],[refute_1_307,refute_1_308]) ).
cnf(refute_1_310,plain,
converse(join(complement(converse(X_155)),complement(converse(converse(top))))) = converse(join(zero,complement(converse(X_155)))),
inference(resolve,[$cnf( $equal(join(complement(converse(X_155)),complement(converse(converse(top)))),join(zero,complement(converse(X_155)))) )],[refute_1_306,refute_1_309]) ).
cnf(refute_1_311,plain,
join(converse(complement(converse(X_155))),converse(complement(converse(converse(top))))) = converse(join(complement(converse(X_155)),complement(converse(converse(top))))),
inference(subst,[],[refute_1_91:[bind(X0,$fot(complement(converse(X_155)))),bind(X1,$fot(complement(converse(converse(top)))))]]) ).
cnf(refute_1_312,plain,
( converse(join(complement(converse(X_155)),complement(converse(converse(top))))) != converse(join(zero,complement(converse(X_155))))
| join(converse(complement(converse(X_155))),converse(complement(converse(converse(top))))) != converse(join(complement(converse(X_155)),complement(converse(converse(top)))))
| join(converse(complement(converse(X_155))),converse(complement(converse(converse(top))))) = converse(join(zero,complement(converse(X_155)))) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(converse(complement(converse(X_155))),converse(complement(converse(converse(top))))))),bind(Y,$fot(converse(join(complement(converse(X_155)),complement(converse(converse(top))))))),bind(Z,$fot(converse(join(zero,complement(converse(X_155))))))]]) ).
cnf(refute_1_313,plain,
( converse(join(complement(converse(X_155)),complement(converse(converse(top))))) != converse(join(zero,complement(converse(X_155))))
| join(converse(complement(converse(X_155))),converse(complement(converse(converse(top))))) = converse(join(zero,complement(converse(X_155)))) ),
inference(resolve,[$cnf( $equal(join(converse(complement(converse(X_155))),converse(complement(converse(converse(top))))),converse(join(complement(converse(X_155)),complement(converse(converse(top)))))) )],[refute_1_311,refute_1_312]) ).
cnf(refute_1_314,plain,
join(converse(complement(converse(X_155))),converse(complement(converse(converse(top))))) = converse(join(zero,complement(converse(X_155)))),
inference(resolve,[$cnf( $equal(converse(join(complement(converse(X_155)),complement(converse(converse(top))))),converse(join(zero,complement(converse(X_155))))) )],[refute_1_310,refute_1_313]) ).
cnf(refute_1_315,plain,
join(X_155,join(converse(complement(converse(X_155))),converse(complement(converse(converse(top)))))) = join(X_155,join(converse(complement(converse(X_155))),converse(complement(converse(converse(top)))))),
introduced(tautology,[refl,[$fot(join(X_155,join(converse(complement(converse(X_155))),converse(complement(converse(converse(top)))))))]]) ).
cnf(refute_1_316,plain,
( join(X_155,join(converse(complement(converse(X_155))),converse(complement(converse(converse(top)))))) != join(X_155,join(converse(complement(converse(X_155))),converse(complement(converse(converse(top))))))
| join(converse(complement(converse(X_155))),converse(complement(converse(converse(top))))) != converse(join(zero,complement(converse(X_155))))
| join(X_155,join(converse(complement(converse(X_155))),converse(complement(converse(converse(top)))))) = join(X_155,converse(join(zero,complement(converse(X_155))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_155,join(converse(complement(converse(X_155))),converse(complement(converse(converse(top)))))),join(X_155,join(converse(complement(converse(X_155))),converse(complement(converse(converse(top))))))) ),[1,1],$fot(converse(join(zero,complement(converse(X_155)))))]]) ).
cnf(refute_1_317,plain,
( join(converse(complement(converse(X_155))),converse(complement(converse(converse(top))))) != converse(join(zero,complement(converse(X_155))))
| join(X_155,join(converse(complement(converse(X_155))),converse(complement(converse(converse(top)))))) = join(X_155,converse(join(zero,complement(converse(X_155))))) ),
inference(resolve,[$cnf( $equal(join(X_155,join(converse(complement(converse(X_155))),converse(complement(converse(converse(top)))))),join(X_155,join(converse(complement(converse(X_155))),converse(complement(converse(converse(top))))))) )],[refute_1_315,refute_1_316]) ).
cnf(refute_1_318,plain,
join(X_155,join(converse(complement(converse(X_155))),converse(complement(converse(converse(top)))))) = join(X_155,converse(join(zero,complement(converse(X_155))))),
inference(resolve,[$cnf( $equal(join(converse(complement(converse(X_155))),converse(complement(converse(converse(top))))),converse(join(zero,complement(converse(X_155))))) )],[refute_1_314,refute_1_317]) ).
cnf(refute_1_319,plain,
converse(join(converse(join(X_120,X_121)),X_110)) = join(join(X_120,X_121),converse(X_110)),
inference(subst,[],[refute_1_75:[bind(X0,$fot(join(X_120,X_121)))]]) ).
cnf(refute_1_320,plain,
( converse(join(X_120,X_121)) != converse(join(X_121,X_120))
| converse(join(converse(join(X_120,X_121)),X_110)) != join(join(X_120,X_121),converse(X_110))
| converse(join(converse(join(X_121,X_120)),X_110)) = join(join(X_120,X_121),converse(X_110)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(join(X_120,X_121)),X_110)),join(join(X_120,X_121),converse(X_110))) ),[0,0,0],$fot(converse(join(X_121,X_120)))]]) ).
cnf(refute_1_321,plain,
( converse(join(converse(join(X_120,X_121)),X_110)) != join(join(X_120,X_121),converse(X_110))
| converse(join(converse(join(X_121,X_120)),X_110)) = join(join(X_120,X_121),converse(X_110)) ),
inference(resolve,[$cnf( $equal(converse(join(X_120,X_121)),converse(join(X_121,X_120))) )],[refute_1_96,refute_1_320]) ).
cnf(refute_1_322,plain,
converse(join(converse(join(X_121,X_120)),X_110)) = join(join(X_120,X_121),converse(X_110)),
inference(resolve,[$cnf( $equal(converse(join(converse(join(X_120,X_121)),X_110)),join(join(X_120,X_121),converse(X_110))) )],[refute_1_319,refute_1_321]) ).
cnf(refute_1_323,plain,
join(join(X_121,X_120),converse(X_110)) = join(X_121,join(X_120,converse(X_110))),
inference(subst,[],[refute_1_102:[bind(X0,$fot(X_121)),bind(X1,$fot(X_120)),bind(X2,$fot(converse(X_110)))]]) ).
cnf(refute_1_324,plain,
converse(join(converse(join(X_121,X_120)),X_110)) = join(join(X_121,X_120),converse(X_110)),
inference(subst,[],[refute_1_75:[bind(X0,$fot(join(X_121,X_120)))]]) ).
cnf(refute_1_325,plain,
( converse(join(converse(join(X_121,X_120)),X_110)) != join(join(X_121,X_120),converse(X_110))
| join(join(X_121,X_120),converse(X_110)) != join(X_121,join(X_120,converse(X_110)))
| converse(join(converse(join(X_121,X_120)),X_110)) = join(X_121,join(X_120,converse(X_110))) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(converse(join(converse(join(X_121,X_120)),X_110)))),bind(Y,$fot(join(join(X_121,X_120),converse(X_110)))),bind(Z,$fot(join(X_121,join(X_120,converse(X_110)))))]]) ).
cnf(refute_1_326,plain,
( join(join(X_121,X_120),converse(X_110)) != join(X_121,join(X_120,converse(X_110)))
| converse(join(converse(join(X_121,X_120)),X_110)) = join(X_121,join(X_120,converse(X_110))) ),
inference(resolve,[$cnf( $equal(converse(join(converse(join(X_121,X_120)),X_110)),join(join(X_121,X_120),converse(X_110))) )],[refute_1_324,refute_1_325]) ).
cnf(refute_1_327,plain,
converse(join(converse(join(X_121,X_120)),X_110)) = join(X_121,join(X_120,converse(X_110))),
inference(resolve,[$cnf( $equal(join(join(X_121,X_120),converse(X_110)),join(X_121,join(X_120,converse(X_110)))) )],[refute_1_323,refute_1_326]) ).
cnf(refute_1_328,plain,
( converse(join(converse(join(X_121,X_120)),X_110)) != join(X_121,join(X_120,converse(X_110)))
| converse(join(converse(join(X_121,X_120)),X_110)) != join(join(X_120,X_121),converse(X_110))
| join(X_121,join(X_120,converse(X_110))) = join(join(X_120,X_121),converse(X_110)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(join(X_121,X_120)),X_110)),join(join(X_120,X_121),converse(X_110))) ),[0],$fot(join(X_121,join(X_120,converse(X_110))))]]) ).
cnf(refute_1_329,plain,
( converse(join(converse(join(X_121,X_120)),X_110)) != join(join(X_120,X_121),converse(X_110))
| join(X_121,join(X_120,converse(X_110))) = join(join(X_120,X_121),converse(X_110)) ),
inference(resolve,[$cnf( $equal(converse(join(converse(join(X_121,X_120)),X_110)),join(X_121,join(X_120,converse(X_110)))) )],[refute_1_327,refute_1_328]) ).
cnf(refute_1_330,plain,
join(join(X_120,X_121),converse(X_110)) = join(X_120,join(X_121,converse(X_110))),
inference(subst,[],[refute_1_102:[bind(X0,$fot(X_120)),bind(X1,$fot(X_121)),bind(X2,$fot(converse(X_110)))]]) ).
cnf(refute_1_331,plain,
( join(X_121,join(X_120,converse(X_110))) != join(join(X_120,X_121),converse(X_110))
| join(join(X_120,X_121),converse(X_110)) != join(X_120,join(X_121,converse(X_110)))
| join(X_121,join(X_120,converse(X_110))) = join(X_120,join(X_121,converse(X_110))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_121,join(X_120,converse(X_110))),join(X_120,join(X_121,converse(X_110)))) ),[0],$fot(join(join(X_120,X_121),converse(X_110)))]]) ).
cnf(refute_1_332,plain,
( join(X_121,join(X_120,converse(X_110))) != join(join(X_120,X_121),converse(X_110))
| join(X_121,join(X_120,converse(X_110))) = join(X_120,join(X_121,converse(X_110))) ),
inference(resolve,[$cnf( $equal(join(join(X_120,X_121),converse(X_110)),join(X_120,join(X_121,converse(X_110)))) )],[refute_1_330,refute_1_331]) ).
cnf(refute_1_333,plain,
( converse(join(converse(join(X_121,X_120)),X_110)) != join(join(X_120,X_121),converse(X_110))
| join(X_121,join(X_120,converse(X_110))) = join(X_120,join(X_121,converse(X_110))) ),
inference(resolve,[$cnf( $equal(join(X_121,join(X_120,converse(X_110))),join(join(X_120,X_121),converse(X_110))) )],[refute_1_329,refute_1_332]) ).
cnf(refute_1_334,plain,
join(X_121,join(X_120,converse(X_110))) = join(X_120,join(X_121,converse(X_110))),
inference(resolve,[$cnf( $equal(converse(join(converse(join(X_121,X_120)),X_110)),join(join(X_120,X_121),converse(X_110))) )],[refute_1_322,refute_1_333]) ).
cnf(refute_1_335,plain,
( join(X_121,join(X_120,converse(X_110))) != join(X_120,join(X_121,converse(X_110)))
| join(X_120,join(X_121,converse(X_110))) = join(X_121,join(X_120,converse(X_110))) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(join(X_121,join(X_120,converse(X_110))))),bind(Y,$fot(join(X_120,join(X_121,converse(X_110)))))]]) ).
cnf(refute_1_336,plain,
join(X_120,join(X_121,converse(X_110))) = join(X_121,join(X_120,converse(X_110))),
inference(resolve,[$cnf( $equal(join(X_121,join(X_120,converse(X_110))),join(X_120,join(X_121,converse(X_110)))) )],[refute_1_334,refute_1_335]) ).
cnf(refute_1_337,plain,
join(converse(complement(converse(X_155))),join(X_155,converse(complement(converse(converse(top)))))) = join(X_155,join(converse(complement(converse(X_155))),converse(complement(converse(converse(top)))))),
inference(subst,[],[refute_1_336:[bind(X_110,$fot(complement(converse(converse(top))))),bind(X_120,$fot(converse(complement(converse(X_155))))),bind(X_121,$fot(X_155))]]) ).
cnf(refute_1_338,plain,
( join(X_155,join(converse(complement(converse(X_155))),converse(complement(converse(converse(top)))))) != join(X_155,converse(join(zero,complement(converse(X_155)))))
| join(converse(complement(converse(X_155))),join(X_155,converse(complement(converse(converse(top)))))) != join(X_155,join(converse(complement(converse(X_155))),converse(complement(converse(converse(top))))))
| join(converse(complement(converse(X_155))),join(X_155,converse(complement(converse(converse(top)))))) = join(X_155,converse(join(zero,complement(converse(X_155))))) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(converse(complement(converse(X_155))),join(X_155,converse(complement(converse(converse(top)))))))),bind(Y,$fot(join(X_155,join(converse(complement(converse(X_155))),converse(complement(converse(converse(top)))))))),bind(Z,$fot(join(X_155,converse(join(zero,complement(converse(X_155)))))))]]) ).
cnf(refute_1_339,plain,
( join(X_155,join(converse(complement(converse(X_155))),converse(complement(converse(converse(top)))))) != join(X_155,converse(join(zero,complement(converse(X_155)))))
| join(converse(complement(converse(X_155))),join(X_155,converse(complement(converse(converse(top)))))) = join(X_155,converse(join(zero,complement(converse(X_155))))) ),
inference(resolve,[$cnf( $equal(join(converse(complement(converse(X_155))),join(X_155,converse(complement(converse(converse(top)))))),join(X_155,join(converse(complement(converse(X_155))),converse(complement(converse(converse(top))))))) )],[refute_1_337,refute_1_338]) ).
cnf(refute_1_340,plain,
join(converse(complement(converse(X_155))),join(X_155,converse(complement(converse(converse(top)))))) = join(X_155,converse(join(zero,complement(converse(X_155))))),
inference(resolve,[$cnf( $equal(join(X_155,join(converse(complement(converse(X_155))),converse(complement(converse(converse(top)))))),join(X_155,converse(join(zero,complement(converse(X_155)))))) )],[refute_1_318,refute_1_339]) ).
cnf(refute_1_341,plain,
( converse(top) != join(converse(complement(converse(X_155))),join(X_155,converse(complement(converse(converse(top))))))
| join(converse(complement(converse(X_155))),join(X_155,converse(complement(converse(converse(top)))))) != join(X_155,converse(join(zero,complement(converse(X_155)))))
| converse(top) = join(X_155,converse(join(zero,complement(converse(X_155))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(top),join(X_155,converse(join(zero,complement(converse(X_155)))))) ),[0],$fot(join(converse(complement(converse(X_155))),join(X_155,converse(complement(converse(converse(top)))))))]]) ).
cnf(refute_1_342,plain,
( converse(top) != join(converse(complement(converse(X_155))),join(X_155,converse(complement(converse(converse(top))))))
| converse(top) = join(X_155,converse(join(zero,complement(converse(X_155))))) ),
inference(resolve,[$cnf( $equal(join(converse(complement(converse(X_155))),join(X_155,converse(complement(converse(converse(top)))))),join(X_155,converse(join(zero,complement(converse(X_155)))))) )],[refute_1_340,refute_1_341]) ).
cnf(refute_1_343,plain,
converse(top) = join(X_155,converse(join(zero,complement(converse(X_155))))),
inference(resolve,[$cnf( $equal(converse(top),join(converse(complement(converse(X_155))),join(X_155,converse(complement(converse(converse(top))))))) )],[refute_1_290,refute_1_342]) ).
cnf(refute_1_344,plain,
( converse(top) != join(X_155,converse(join(zero,complement(converse(X_155)))))
| converse(top) != top
| top = join(X_155,converse(join(zero,complement(converse(X_155))))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(top),join(X_155,converse(join(zero,complement(converse(X_155)))))) ),[0],$fot(top)]]) ).
cnf(refute_1_345,plain,
( converse(top) != join(X_155,converse(join(zero,complement(converse(X_155)))))
| top = join(X_155,converse(join(zero,complement(converse(X_155))))) ),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_1_191,refute_1_344]) ).
cnf(refute_1_346,plain,
top = join(X_155,converse(join(zero,complement(converse(X_155))))),
inference(resolve,[$cnf( $equal(converse(top),join(X_155,converse(join(zero,complement(converse(X_155)))))) )],[refute_1_343,refute_1_345]) ).
cnf(refute_1_347,plain,
top = join(join(one,one),converse(join(zero,complement(converse(join(one,one)))))),
inference(subst,[],[refute_1_346:[bind(X_155,$fot(join(one,one)))]]) ).
cnf(refute_1_348,plain,
converse(join(converse(one),X_110)) = join(one,converse(X_110)),
inference(subst,[],[refute_1_75:[bind(X0,$fot(one))]]) ).
cnf(refute_1_349,plain,
( converse(join(converse(one),X_110)) != join(one,converse(X_110))
| converse(one) != one
| converse(join(one,X_110)) = join(one,converse(X_110)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(one),X_110)),join(one,converse(X_110))) ),[0,0,0],$fot(one)]]) ).
cnf(refute_1_350,plain,
( converse(join(converse(one),X_110)) != join(one,converse(X_110))
| converse(join(one,X_110)) = join(one,converse(X_110)) ),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_1_136,refute_1_349]) ).
cnf(refute_1_351,plain,
converse(join(one,X_110)) = join(one,converse(X_110)),
inference(resolve,[$cnf( $equal(converse(join(converse(one),X_110)),join(one,converse(X_110))) )],[refute_1_348,refute_1_350]) ).
cnf(refute_1_352,plain,
converse(join(one,one)) = join(one,converse(one)),
inference(subst,[],[refute_1_351:[bind(X_110,$fot(one))]]) ).
cnf(refute_1_353,plain,
( converse(join(one,one)) != join(one,converse(one))
| converse(one) != one
| converse(join(one,one)) = join(one,one) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(one,one)),join(one,converse(one))) ),[1,1],$fot(one)]]) ).
cnf(refute_1_354,plain,
( converse(join(one,one)) != join(one,converse(one))
| converse(join(one,one)) = join(one,one) ),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_1_136,refute_1_353]) ).
cnf(refute_1_355,plain,
converse(join(one,one)) = join(one,one),
inference(resolve,[$cnf( $equal(converse(join(one,one)),join(one,converse(one))) )],[refute_1_352,refute_1_354]) ).
cnf(refute_1_356,plain,
( converse(join(one,one)) != join(one,one)
| top != join(join(one,one),converse(join(zero,complement(converse(join(one,one))))))
| top = join(join(one,one),converse(join(zero,complement(join(one,one))))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(join(one,one),converse(join(zero,complement(converse(join(one,one))))))) ),[1,1,0,1,0],$fot(join(one,one))]]) ).
cnf(refute_1_357,plain,
( top != join(join(one,one),converse(join(zero,complement(converse(join(one,one))))))
| top = join(join(one,one),converse(join(zero,complement(join(one,one))))) ),
inference(resolve,[$cnf( $equal(converse(join(one,one)),join(one,one)) )],[refute_1_355,refute_1_356]) ).
cnf(refute_1_358,plain,
top = join(join(one,one),converse(join(zero,complement(join(one,one))))),
inference(resolve,[$cnf( $equal(top,join(join(one,one),converse(join(zero,complement(converse(join(one,one))))))) )],[refute_1_347,refute_1_357]) ).
cnf(refute_1_359,plain,
( converse(join(one,X_110)) != join(one,converse(X_110))
| join(one,converse(X_110)) = converse(join(one,X_110)) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(converse(join(one,X_110)))),bind(Y,$fot(join(one,converse(X_110))))]]) ).
cnf(refute_1_360,plain,
join(one,converse(X_110)) = converse(join(one,X_110)),
inference(resolve,[$cnf( $equal(converse(join(one,X_110)),join(one,converse(X_110))) )],[refute_1_351,refute_1_359]) ).
cnf(refute_1_361,plain,
join(one,converse(join(one,join(zero,complement(join(one,one)))))) = converse(join(one,join(one,join(zero,complement(join(one,one)))))),
inference(subst,[],[refute_1_360:[bind(X_110,$fot(join(one,join(zero,complement(join(one,one))))))]]) ).
cnf(refute_1_362,plain,
join(one,converse(join(zero,complement(join(one,one))))) = converse(join(one,join(zero,complement(join(one,one))))),
inference(subst,[],[refute_1_360:[bind(X_110,$fot(join(zero,complement(join(one,one)))))]]) ).
cnf(refute_1_363,plain,
join(one,join(one,converse(join(zero,complement(join(one,one)))))) = join(one,join(one,converse(join(zero,complement(join(one,one)))))),
introduced(tautology,[refl,[$fot(join(one,join(one,converse(join(zero,complement(join(one,one)))))))]]) ).
cnf(refute_1_364,plain,
( join(one,converse(join(zero,complement(join(one,one))))) != converse(join(one,join(zero,complement(join(one,one)))))
| join(one,join(one,converse(join(zero,complement(join(one,one)))))) != join(one,join(one,converse(join(zero,complement(join(one,one))))))
| join(one,join(one,converse(join(zero,complement(join(one,one)))))) = join(one,converse(join(one,join(zero,complement(join(one,one)))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(one,converse(join(zero,complement(join(one,one)))))),join(one,join(one,converse(join(zero,complement(join(one,one))))))) ),[1,1],$fot(converse(join(one,join(zero,complement(join(one,one))))))]]) ).
cnf(refute_1_365,plain,
( join(one,converse(join(zero,complement(join(one,one))))) != converse(join(one,join(zero,complement(join(one,one)))))
| join(one,join(one,converse(join(zero,complement(join(one,one)))))) = join(one,converse(join(one,join(zero,complement(join(one,one)))))) ),
inference(resolve,[$cnf( $equal(join(one,join(one,converse(join(zero,complement(join(one,one)))))),join(one,join(one,converse(join(zero,complement(join(one,one))))))) )],[refute_1_363,refute_1_364]) ).
cnf(refute_1_366,plain,
join(one,join(one,converse(join(zero,complement(join(one,one)))))) = join(one,converse(join(one,join(zero,complement(join(one,one)))))),
inference(resolve,[$cnf( $equal(join(one,converse(join(zero,complement(join(one,one))))),converse(join(one,join(zero,complement(join(one,one)))))) )],[refute_1_362,refute_1_365]) ).
cnf(refute_1_367,plain,
( join(one,converse(join(one,join(zero,complement(join(one,one)))))) != converse(join(one,join(one,join(zero,complement(join(one,one))))))
| join(one,join(one,converse(join(zero,complement(join(one,one)))))) != join(one,converse(join(one,join(zero,complement(join(one,one))))))
| join(one,join(one,converse(join(zero,complement(join(one,one)))))) = converse(join(one,join(one,join(zero,complement(join(one,one)))))) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(one,join(one,converse(join(zero,complement(join(one,one)))))))),bind(Y,$fot(join(one,converse(join(one,join(zero,complement(join(one,one)))))))),bind(Z,$fot(converse(join(one,join(one,join(zero,complement(join(one,one))))))))]]) ).
cnf(refute_1_368,plain,
( join(one,converse(join(one,join(zero,complement(join(one,one)))))) != converse(join(one,join(one,join(zero,complement(join(one,one))))))
| join(one,join(one,converse(join(zero,complement(join(one,one)))))) = converse(join(one,join(one,join(zero,complement(join(one,one)))))) ),
inference(resolve,[$cnf( $equal(join(one,join(one,converse(join(zero,complement(join(one,one)))))),join(one,converse(join(one,join(zero,complement(join(one,one))))))) )],[refute_1_366,refute_1_367]) ).
cnf(refute_1_369,plain,
join(one,join(one,converse(join(zero,complement(join(one,one)))))) = converse(join(one,join(one,join(zero,complement(join(one,one)))))),
inference(resolve,[$cnf( $equal(join(one,converse(join(one,join(zero,complement(join(one,one)))))),converse(join(one,join(one,join(zero,complement(join(one,one))))))) )],[refute_1_361,refute_1_368]) ).
cnf(refute_1_370,plain,
join(join(one,one),converse(join(zero,complement(join(one,one))))) = join(one,join(one,converse(join(zero,complement(join(one,one)))))),
inference(subst,[],[refute_1_102:[bind(X0,$fot(one)),bind(X1,$fot(one)),bind(X2,$fot(converse(join(zero,complement(join(one,one))))))]]) ).
cnf(refute_1_371,plain,
( join(join(one,one),converse(join(zero,complement(join(one,one))))) != join(one,join(one,converse(join(zero,complement(join(one,one))))))
| join(one,join(one,converse(join(zero,complement(join(one,one)))))) != converse(join(one,join(one,join(zero,complement(join(one,one))))))
| join(join(one,one),converse(join(zero,complement(join(one,one))))) = converse(join(one,join(one,join(zero,complement(join(one,one)))))) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(join(one,one),converse(join(zero,complement(join(one,one))))))),bind(Y,$fot(join(one,join(one,converse(join(zero,complement(join(one,one)))))))),bind(Z,$fot(converse(join(one,join(one,join(zero,complement(join(one,one))))))))]]) ).
cnf(refute_1_372,plain,
( join(one,join(one,converse(join(zero,complement(join(one,one)))))) != converse(join(one,join(one,join(zero,complement(join(one,one))))))
| join(join(one,one),converse(join(zero,complement(join(one,one))))) = converse(join(one,join(one,join(zero,complement(join(one,one)))))) ),
inference(resolve,[$cnf( $equal(join(join(one,one),converse(join(zero,complement(join(one,one))))),join(one,join(one,converse(join(zero,complement(join(one,one))))))) )],[refute_1_370,refute_1_371]) ).
cnf(refute_1_373,plain,
join(join(one,one),converse(join(zero,complement(join(one,one))))) = converse(join(one,join(one,join(zero,complement(join(one,one)))))),
inference(resolve,[$cnf( $equal(join(one,join(one,converse(join(zero,complement(join(one,one)))))),converse(join(one,join(one,join(zero,complement(join(one,one))))))) )],[refute_1_369,refute_1_372]) ).
cnf(refute_1_374,plain,
( join(join(one,one),converse(join(zero,complement(join(one,one))))) != converse(join(one,join(one,join(zero,complement(join(one,one))))))
| top != join(join(one,one),converse(join(zero,complement(join(one,one)))))
| top = converse(join(one,join(one,join(zero,complement(join(one,one)))))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(join(one,one),converse(join(zero,complement(join(one,one)))))) ),[1],$fot(converse(join(one,join(one,join(zero,complement(join(one,one)))))))]]) ).
cnf(refute_1_375,plain,
( top != join(join(one,one),converse(join(zero,complement(join(one,one)))))
| top = converse(join(one,join(one,join(zero,complement(join(one,one)))))) ),
inference(resolve,[$cnf( $equal(join(join(one,one),converse(join(zero,complement(join(one,one))))),converse(join(one,join(one,join(zero,complement(join(one,one))))))) )],[refute_1_373,refute_1_374]) ).
cnf(refute_1_376,plain,
top = converse(join(one,join(one,join(zero,complement(join(one,one)))))),
inference(resolve,[$cnf( $equal(top,join(join(one,one),converse(join(zero,complement(join(one,one)))))) )],[refute_1_358,refute_1_375]) ).
cnf(refute_1_377,plain,
( top != converse(join(one,join(one,join(zero,complement(join(one,one))))))
| converse(join(one,join(one,join(zero,complement(join(one,one)))))) = top ),
inference(subst,[],[refute_1_17:[bind(X,$fot(top)),bind(Y,$fot(converse(join(one,join(one,join(zero,complement(join(one,one))))))))]]) ).
cnf(refute_1_378,plain,
converse(join(one,join(one,join(zero,complement(join(one,one)))))) = top,
inference(resolve,[$cnf( $equal(top,converse(join(one,join(one,join(zero,complement(join(one,one))))))) )],[refute_1_376,refute_1_377]) ).
cnf(refute_1_379,plain,
( converse(join(X_109,converse(join(one,join(one,join(zero,complement(join(one,one)))))))) != join(converse(X_109),join(one,join(one,join(zero,complement(join(one,one))))))
| converse(join(one,join(one,join(zero,complement(join(one,one)))))) != top
| converse(join(X_109,top)) = join(converse(X_109),join(one,join(one,join(zero,complement(join(one,one)))))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(X_109,converse(join(one,join(one,join(zero,complement(join(one,one)))))))),join(converse(X_109),join(one,join(one,join(zero,complement(join(one,one))))))) ),[0,0,1],$fot(top)]]) ).
cnf(refute_1_380,plain,
( converse(join(X_109,converse(join(one,join(one,join(zero,complement(join(one,one)))))))) != join(converse(X_109),join(one,join(one,join(zero,complement(join(one,one))))))
| converse(join(X_109,top)) = join(converse(X_109),join(one,join(one,join(zero,complement(join(one,one)))))) ),
inference(resolve,[$cnf( $equal(converse(join(one,join(one,join(zero,complement(join(one,one)))))),top) )],[refute_1_378,refute_1_379]) ).
cnf(refute_1_381,plain,
converse(join(X_109,top)) = join(converse(X_109),join(one,join(one,join(zero,complement(join(one,one)))))),
inference(resolve,[$cnf( $equal(converse(join(X_109,converse(join(one,join(one,join(zero,complement(join(one,one)))))))),join(converse(X_109),join(one,join(one,join(zero,complement(join(one,one))))))) )],[refute_1_283,refute_1_380]) ).
cnf(refute_1_382,plain,
( converse(join(top,X_110)) != join(top,converse(X_110))
| join(top,converse(X_110)) = converse(join(top,X_110)) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(converse(join(top,X_110)))),bind(Y,$fot(join(top,converse(X_110))))]]) ).
cnf(refute_1_383,plain,
join(top,converse(X_110)) = converse(join(top,X_110)),
inference(resolve,[$cnf( $equal(converse(join(top,X_110)),join(top,converse(X_110))) )],[refute_1_282,refute_1_382]) ).
cnf(refute_1_384,plain,
join(top,converse(X_109)) = converse(join(top,X_109)),
inference(subst,[],[refute_1_383:[bind(X_110,$fot(X_109))]]) ).
cnf(refute_1_385,plain,
join(converse(X_109),top) = join(top,converse(X_109)),
inference(subst,[],[refute_1_52:[bind(X0,$fot(top)),bind(X1,$fot(converse(X_109)))]]) ).
cnf(refute_1_386,plain,
( join(converse(X_109),top) != join(top,converse(X_109))
| join(top,converse(X_109)) != converse(join(top,X_109))
| join(converse(X_109),top) = converse(join(top,X_109)) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(converse(X_109),top))),bind(Y,$fot(join(top,converse(X_109)))),bind(Z,$fot(converse(join(top,X_109))))]]) ).
cnf(refute_1_387,plain,
( join(top,converse(X_109)) != converse(join(top,X_109))
| join(converse(X_109),top) = converse(join(top,X_109)) ),
inference(resolve,[$cnf( $equal(join(converse(X_109),top),join(top,converse(X_109))) )],[refute_1_385,refute_1_386]) ).
cnf(refute_1_388,plain,
join(converse(X_109),top) = converse(join(top,X_109)),
inference(resolve,[$cnf( $equal(join(top,converse(X_109)),converse(join(top,X_109))) )],[refute_1_384,refute_1_387]) ).
cnf(refute_1_389,plain,
converse(converse(join(one,join(one,join(zero,complement(join(one,one))))))) = join(one,join(one,join(zero,complement(join(one,one))))),
inference(subst,[],[refute_1_3:[bind(X0,$fot(join(one,join(one,join(zero,complement(join(one,one)))))))]]) ).
cnf(refute_1_390,plain,
( converse(converse(join(one,join(one,join(zero,complement(join(one,one))))))) != join(one,join(one,join(zero,complement(join(one,one)))))
| converse(join(one,join(one,join(zero,complement(join(one,one)))))) != top
| converse(top) = join(one,join(one,join(zero,complement(join(one,one))))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(converse(join(one,join(one,join(zero,complement(join(one,one))))))),join(one,join(one,join(zero,complement(join(one,one)))))) ),[0,0],$fot(top)]]) ).
cnf(refute_1_391,plain,
( converse(converse(join(one,join(one,join(zero,complement(join(one,one))))))) != join(one,join(one,join(zero,complement(join(one,one)))))
| converse(top) = join(one,join(one,join(zero,complement(join(one,one))))) ),
inference(resolve,[$cnf( $equal(converse(join(one,join(one,join(zero,complement(join(one,one)))))),top) )],[refute_1_378,refute_1_390]) ).
cnf(refute_1_392,plain,
converse(top) = join(one,join(one,join(zero,complement(join(one,one))))),
inference(resolve,[$cnf( $equal(converse(converse(join(one,join(one,join(zero,complement(join(one,one))))))),join(one,join(one,join(zero,complement(join(one,one)))))) )],[refute_1_389,refute_1_391]) ).
cnf(refute_1_393,plain,
( converse(top) != join(one,join(one,join(zero,complement(join(one,one)))))
| converse(top) != top
| top = join(one,join(one,join(zero,complement(join(one,one))))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(top),join(one,join(one,join(zero,complement(join(one,one)))))) ),[0],$fot(top)]]) ).
cnf(refute_1_394,plain,
( converse(top) != join(one,join(one,join(zero,complement(join(one,one)))))
| top = join(one,join(one,join(zero,complement(join(one,one))))) ),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_1_191,refute_1_393]) ).
cnf(refute_1_395,plain,
top = join(one,join(one,join(zero,complement(join(one,one))))),
inference(resolve,[$cnf( $equal(converse(top),join(one,join(one,join(zero,complement(join(one,one)))))) )],[refute_1_392,refute_1_394]) ).
cnf(refute_1_396,plain,
( top != join(one,join(one,join(zero,complement(join(one,one)))))
| join(one,join(one,join(zero,complement(join(one,one))))) = top ),
inference(subst,[],[refute_1_17:[bind(X,$fot(top)),bind(Y,$fot(join(one,join(one,join(zero,complement(join(one,one)))))))]]) ).
cnf(refute_1_397,plain,
join(one,join(one,join(zero,complement(join(one,one))))) = top,
inference(resolve,[$cnf( $equal(top,join(one,join(one,join(zero,complement(join(one,one)))))) )],[refute_1_395,refute_1_396]) ).
cnf(refute_1_398,plain,
join(converse(X_109),join(one,join(one,join(zero,complement(join(one,one)))))) = join(converse(X_109),join(one,join(one,join(zero,complement(join(one,one)))))),
introduced(tautology,[refl,[$fot(join(converse(X_109),join(one,join(one,join(zero,complement(join(one,one)))))))]]) ).
cnf(refute_1_399,plain,
( join(converse(X_109),join(one,join(one,join(zero,complement(join(one,one)))))) != join(converse(X_109),join(one,join(one,join(zero,complement(join(one,one))))))
| join(one,join(one,join(zero,complement(join(one,one))))) != top
| join(converse(X_109),join(one,join(one,join(zero,complement(join(one,one)))))) = join(converse(X_109),top) ),
introduced(tautology,[equality,[$cnf( $equal(join(converse(X_109),join(one,join(one,join(zero,complement(join(one,one)))))),join(converse(X_109),join(one,join(one,join(zero,complement(join(one,one))))))) ),[1,1],$fot(top)]]) ).
cnf(refute_1_400,plain,
( join(one,join(one,join(zero,complement(join(one,one))))) != top
| join(converse(X_109),join(one,join(one,join(zero,complement(join(one,one)))))) = join(converse(X_109),top) ),
inference(resolve,[$cnf( $equal(join(converse(X_109),join(one,join(one,join(zero,complement(join(one,one)))))),join(converse(X_109),join(one,join(one,join(zero,complement(join(one,one))))))) )],[refute_1_398,refute_1_399]) ).
cnf(refute_1_401,plain,
join(converse(X_109),join(one,join(one,join(zero,complement(join(one,one)))))) = join(converse(X_109),top),
inference(resolve,[$cnf( $equal(join(one,join(one,join(zero,complement(join(one,one))))),top) )],[refute_1_397,refute_1_400]) ).
cnf(refute_1_402,plain,
( join(converse(X_109),join(one,join(one,join(zero,complement(join(one,one)))))) != join(converse(X_109),top)
| join(converse(X_109),top) != converse(join(top,X_109))
| join(converse(X_109),join(one,join(one,join(zero,complement(join(one,one)))))) = converse(join(top,X_109)) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(converse(X_109),join(one,join(one,join(zero,complement(join(one,one)))))))),bind(Y,$fot(join(converse(X_109),top))),bind(Z,$fot(converse(join(top,X_109))))]]) ).
cnf(refute_1_403,plain,
( join(converse(X_109),top) != converse(join(top,X_109))
| join(converse(X_109),join(one,join(one,join(zero,complement(join(one,one)))))) = converse(join(top,X_109)) ),
inference(resolve,[$cnf( $equal(join(converse(X_109),join(one,join(one,join(zero,complement(join(one,one)))))),join(converse(X_109),top)) )],[refute_1_401,refute_1_402]) ).
cnf(refute_1_404,plain,
join(converse(X_109),join(one,join(one,join(zero,complement(join(one,one)))))) = converse(join(top,X_109)),
inference(resolve,[$cnf( $equal(join(converse(X_109),top),converse(join(top,X_109))) )],[refute_1_388,refute_1_403]) ).
cnf(refute_1_405,plain,
( converse(join(X_109,top)) != join(converse(X_109),join(one,join(one,join(zero,complement(join(one,one))))))
| join(converse(X_109),join(one,join(one,join(zero,complement(join(one,one)))))) != converse(join(top,X_109))
| converse(join(X_109,top)) = converse(join(top,X_109)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(join(X_109,top)),converse(join(top,X_109))) ),[0],$fot(join(converse(X_109),join(one,join(one,join(zero,complement(join(one,one)))))))]]) ).
cnf(refute_1_406,plain,
( converse(join(X_109,top)) != join(converse(X_109),join(one,join(one,join(zero,complement(join(one,one))))))
| converse(join(X_109,top)) = converse(join(top,X_109)) ),
inference(resolve,[$cnf( $equal(join(converse(X_109),join(one,join(one,join(zero,complement(join(one,one)))))),converse(join(top,X_109))) )],[refute_1_404,refute_1_405]) ).
cnf(refute_1_407,plain,
converse(join(X_109,top)) = converse(join(top,X_109)),
inference(resolve,[$cnf( $equal(converse(join(X_109,top)),join(converse(X_109),join(one,join(one,join(zero,complement(join(one,one))))))) )],[refute_1_381,refute_1_406]) ).
cnf(refute_1_408,plain,
( top != converse(join(X0,top))
| converse(join(X0,top)) = top ),
inference(subst,[],[refute_1_17:[bind(X,$fot(top)),bind(Y,$fot(converse(join(X0,top))))]]) ).
cnf(refute_1_409,plain,
converse(join(X0,top)) = top,
inference(resolve,[$cnf( $equal(top,converse(join(X0,top))) )],[refute_1_272,refute_1_408]) ).
cnf(refute_1_410,plain,
converse(join(X_109,top)) = top,
inference(subst,[],[refute_1_409:[bind(X0,$fot(X_109))]]) ).
cnf(refute_1_411,plain,
( converse(join(X_109,top)) != converse(join(top,X_109))
| converse(join(X_109,top)) != top
| top = converse(join(top,X_109)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(X_109,top)),converse(join(top,X_109))) ),[0],$fot(top)]]) ).
cnf(refute_1_412,plain,
( converse(join(X_109,top)) != converse(join(top,X_109))
| top = converse(join(top,X_109)) ),
inference(resolve,[$cnf( $equal(converse(join(X_109,top)),top) )],[refute_1_410,refute_1_411]) ).
cnf(refute_1_413,plain,
top = converse(join(top,X_109)),
inference(resolve,[$cnf( $equal(converse(join(X_109,top)),converse(join(top,X_109))) )],[refute_1_407,refute_1_412]) ).
cnf(refute_1_414,plain,
( top != converse(join(top,X_109))
| converse(join(top,X_109)) = top ),
inference(subst,[],[refute_1_17:[bind(X,$fot(top)),bind(Y,$fot(converse(join(top,X_109))))]]) ).
cnf(refute_1_415,plain,
converse(join(top,X_109)) = top,
inference(resolve,[$cnf( $equal(top,converse(join(top,X_109))) )],[refute_1_413,refute_1_414]) ).
cnf(refute_1_416,plain,
converse(join(top,X_110)) = top,
inference(subst,[],[refute_1_415:[bind(X_109,$fot(X_110))]]) ).
cnf(refute_1_417,plain,
( converse(join(top,X_110)) != join(top,converse(X_110))
| converse(join(top,X_110)) != top
| top = join(top,converse(X_110)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(top,X_110)),join(top,converse(X_110))) ),[0],$fot(top)]]) ).
cnf(refute_1_418,plain,
( converse(join(top,X_110)) != join(top,converse(X_110))
| top = join(top,converse(X_110)) ),
inference(resolve,[$cnf( $equal(converse(join(top,X_110)),top) )],[refute_1_416,refute_1_417]) ).
cnf(refute_1_419,plain,
top = join(top,converse(X_110)),
inference(resolve,[$cnf( $equal(converse(join(top,X_110)),join(top,converse(X_110))) )],[refute_1_282,refute_1_418]) ).
cnf(refute_1_420,plain,
( top != join(top,converse(X_110))
| join(top,converse(X_110)) = top ),
inference(subst,[],[refute_1_17:[bind(X,$fot(top)),bind(Y,$fot(join(top,converse(X_110))))]]) ).
cnf(refute_1_421,plain,
join(top,converse(X_110)) = top,
inference(resolve,[$cnf( $equal(top,join(top,converse(X_110))) )],[refute_1_419,refute_1_420]) ).
cnf(refute_1_422,plain,
join(top,converse(complement(top))) = top,
inference(subst,[],[refute_1_421:[bind(X_110,$fot(complement(top)))]]) ).
cnf(refute_1_423,plain,
join(X_169,join(top,converse(complement(top)))) = join(X_169,join(top,converse(complement(top)))),
introduced(tautology,[refl,[$fot(join(X_169,join(top,converse(complement(top)))))]]) ).
cnf(refute_1_424,plain,
( join(X_169,join(top,converse(complement(top)))) != join(X_169,join(top,converse(complement(top))))
| join(top,converse(complement(top))) != top
| join(X_169,join(top,converse(complement(top)))) = join(X_169,top) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_169,join(top,converse(complement(top)))),join(X_169,join(top,converse(complement(top))))) ),[1,1],$fot(top)]]) ).
cnf(refute_1_425,plain,
( join(top,converse(complement(top))) != top
| join(X_169,join(top,converse(complement(top)))) = join(X_169,top) ),
inference(resolve,[$cnf( $equal(join(X_169,join(top,converse(complement(top)))),join(X_169,join(top,converse(complement(top))))) )],[refute_1_423,refute_1_424]) ).
cnf(refute_1_426,plain,
join(X_169,join(top,converse(complement(top)))) = join(X_169,top),
inference(resolve,[$cnf( $equal(join(top,converse(complement(top))),top) )],[refute_1_422,refute_1_425]) ).
cnf(refute_1_427,plain,
join(join(X_169,top),converse(complement(top))) = join(X_169,join(top,converse(complement(top)))),
inference(subst,[],[refute_1_102:[bind(X0,$fot(X_169)),bind(X1,$fot(top)),bind(X2,$fot(converse(complement(top))))]]) ).
cnf(refute_1_428,plain,
( join(X_169,join(top,converse(complement(top)))) != join(X_169,top)
| join(join(X_169,top),converse(complement(top))) != join(X_169,join(top,converse(complement(top))))
| join(join(X_169,top),converse(complement(top))) = join(X_169,top) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(join(X_169,top),converse(complement(top))))),bind(Y,$fot(join(X_169,join(top,converse(complement(top)))))),bind(Z,$fot(join(X_169,top)))]]) ).
cnf(refute_1_429,plain,
( join(X_169,join(top,converse(complement(top)))) != join(X_169,top)
| join(join(X_169,top),converse(complement(top))) = join(X_169,top) ),
inference(resolve,[$cnf( $equal(join(join(X_169,top),converse(complement(top))),join(X_169,join(top,converse(complement(top))))) )],[refute_1_427,refute_1_428]) ).
cnf(refute_1_430,plain,
join(join(X_169,top),converse(complement(top))) = join(X_169,top),
inference(resolve,[$cnf( $equal(join(X_169,join(top,converse(complement(top)))),join(X_169,top)) )],[refute_1_426,refute_1_429]) ).
cnf(refute_1_431,plain,
( join(join(X_169,top),converse(complement(top))) != join(X_169,top)
| top != join(join(X_169,top),converse(complement(top)))
| top = join(X_169,top) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(join(X_169,top),converse(complement(top)))) ),[1],$fot(join(X_169,top))]]) ).
cnf(refute_1_432,plain,
( top != join(join(X_169,top),converse(complement(top)))
| top = join(X_169,top) ),
inference(resolve,[$cnf( $equal(join(join(X_169,top),converse(complement(top))),join(X_169,top)) )],[refute_1_430,refute_1_431]) ).
cnf(refute_1_433,plain,
top = join(X_169,top),
inference(resolve,[$cnf( $equal(top,join(join(X_169,top),converse(complement(top)))) )],[refute_1_278,refute_1_432]) ).
cnf(refute_1_434,plain,
top = join(complement(X_176),top),
inference(subst,[],[refute_1_433:[bind(X_169,$fot(complement(X_176)))]]) ).
cnf(refute_1_435,plain,
( top != join(complement(X_176),top)
| join(complement(X_176),top) = top ),
inference(subst,[],[refute_1_17:[bind(X,$fot(top)),bind(Y,$fot(join(complement(X_176),top)))]]) ).
cnf(refute_1_436,plain,
join(complement(X_176),top) = top,
inference(resolve,[$cnf( $equal(top,join(complement(X_176),top)) )],[refute_1_434,refute_1_435]) ).
cnf(refute_1_437,plain,
( X_176 != join(meet(X_176,top),complement(join(complement(X_176),top)))
| join(complement(X_176),top) != top
| X_176 = join(meet(X_176,top),complement(top)) ),
introduced(tautology,[equality,[$cnf( $equal(X_176,join(meet(X_176,top),complement(join(complement(X_176),top)))) ),[1,1,0],$fot(top)]]) ).
cnf(refute_1_438,plain,
( X_176 != join(meet(X_176,top),complement(join(complement(X_176),top)))
| X_176 = join(meet(X_176,top),complement(top)) ),
inference(resolve,[$cnf( $equal(join(complement(X_176),top),top) )],[refute_1_436,refute_1_437]) ).
cnf(refute_1_439,plain,
X_176 = join(meet(X_176,top),complement(top)),
inference(resolve,[$cnf( $equal(X_176,join(meet(X_176,top),complement(join(complement(X_176),top)))) )],[refute_1_70,refute_1_438]) ).
cnf(refute_1_440,plain,
join(complement(top),meet(X_176,top)) = join(complement(top),meet(X_176,top)),
introduced(tautology,[refl,[$fot(join(complement(top),meet(X_176,top)))]]) ).
cnf(refute_1_441,plain,
( complement(top) != zero
| join(complement(top),meet(X_176,top)) != join(complement(top),meet(X_176,top))
| join(complement(top),meet(X_176,top)) = join(zero,meet(X_176,top)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(X_176,top)),join(complement(top),meet(X_176,top))) ),[1,0],$fot(zero)]]) ).
cnf(refute_1_442,plain,
( complement(top) != zero
| join(complement(top),meet(X_176,top)) = join(zero,meet(X_176,top)) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_176,top)),join(complement(top),meet(X_176,top))) )],[refute_1_440,refute_1_441]) ).
cnf(refute_1_443,plain,
join(complement(top),meet(X_176,top)) = join(zero,meet(X_176,top)),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_1_45,refute_1_442]) ).
cnf(refute_1_444,plain,
join(meet(X_176,top),complement(top)) = join(complement(top),meet(X_176,top)),
inference(subst,[],[refute_1_52:[bind(X0,$fot(complement(top))),bind(X1,$fot(meet(X_176,top)))]]) ).
cnf(refute_1_445,plain,
( join(complement(top),meet(X_176,top)) != join(zero,meet(X_176,top))
| join(meet(X_176,top),complement(top)) != join(complement(top),meet(X_176,top))
| join(meet(X_176,top),complement(top)) = join(zero,meet(X_176,top)) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(meet(X_176,top),complement(top)))),bind(Y,$fot(join(complement(top),meet(X_176,top)))),bind(Z,$fot(join(zero,meet(X_176,top))))]]) ).
cnf(refute_1_446,plain,
( join(complement(top),meet(X_176,top)) != join(zero,meet(X_176,top))
| join(meet(X_176,top),complement(top)) = join(zero,meet(X_176,top)) ),
inference(resolve,[$cnf( $equal(join(meet(X_176,top),complement(top)),join(complement(top),meet(X_176,top))) )],[refute_1_444,refute_1_445]) ).
cnf(refute_1_447,plain,
join(meet(X_176,top),complement(top)) = join(zero,meet(X_176,top)),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_176,top)),join(zero,meet(X_176,top))) )],[refute_1_443,refute_1_446]) ).
cnf(refute_1_448,plain,
( X_176 != join(meet(X_176,top),complement(top))
| join(meet(X_176,top),complement(top)) != join(zero,meet(X_176,top))
| X_176 = join(zero,meet(X_176,top)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_176,join(zero,meet(X_176,top))) ),[0],$fot(join(meet(X_176,top),complement(top)))]]) ).
cnf(refute_1_449,plain,
( X_176 != join(meet(X_176,top),complement(top))
| X_176 = join(zero,meet(X_176,top)) ),
inference(resolve,[$cnf( $equal(join(meet(X_176,top),complement(top)),join(zero,meet(X_176,top))) )],[refute_1_447,refute_1_448]) ).
cnf(refute_1_450,plain,
X_176 = join(zero,meet(X_176,top)),
inference(resolve,[$cnf( $equal(X_176,join(meet(X_176,top),complement(top))) )],[refute_1_439,refute_1_449]) ).
cnf(refute_1_451,plain,
X_178 = join(zero,meet(X_178,top)),
inference(subst,[],[refute_1_450:[bind(X_176,$fot(X_178))]]) ).
cnf(refute_1_452,plain,
join(complement(X_138),complement(X_137)) = join(complement(X_137),complement(X_138)),
inference(subst,[],[refute_1_50:[bind(X0,$fot(complement(X_138))),bind(X1,$fot(complement(X_137)))]]) ).
cnf(refute_1_453,plain,
( join(complement(X_138),complement(X_137)) != join(complement(X_137),complement(X_138))
| join(complement(X_137),complement(X_138)) = join(complement(X_138),complement(X_137)) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(join(complement(X_138),complement(X_137)))),bind(Y,$fot(join(complement(X_137),complement(X_138))))]]) ).
cnf(refute_1_454,plain,
join(complement(X_137),complement(X_138)) = join(complement(X_138),complement(X_137)),
inference(resolve,[$cnf( $equal(join(complement(X_138),complement(X_137)),join(complement(X_137),complement(X_138))) )],[refute_1_452,refute_1_453]) ).
cnf(refute_1_455,plain,
( join(complement(X_137),complement(X_138)) != join(complement(X_138),complement(X_137))
| meet(X_137,X_138) != complement(join(complement(X_137),complement(X_138)))
| meet(X_137,X_138) = complement(join(complement(X_138),complement(X_137))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_137,X_138),complement(join(complement(X_137),complement(X_138)))) ),[1,0],$fot(join(complement(X_138),complement(X_137)))]]) ).
cnf(refute_1_456,plain,
( meet(X_137,X_138) != complement(join(complement(X_137),complement(X_138)))
| meet(X_137,X_138) = complement(join(complement(X_138),complement(X_137))) ),
inference(resolve,[$cnf( $equal(join(complement(X_137),complement(X_138)),join(complement(X_138),complement(X_137))) )],[refute_1_454,refute_1_455]) ).
cnf(refute_1_457,plain,
meet(X_137,X_138) = complement(join(complement(X_138),complement(X_137))),
inference(resolve,[$cnf( $equal(meet(X_137,X_138),complement(join(complement(X_137),complement(X_138)))) )],[refute_1_14,refute_1_456]) ).
cnf(refute_1_458,plain,
complement(join(complement(X_138),complement(X_137))) = meet(X_138,X_137),
inference(subst,[],[refute_1_59:[bind(X0,$fot(X_138)),bind(X1,$fot(X_137))]]) ).
cnf(refute_1_459,plain,
( complement(join(complement(X_138),complement(X_137))) != meet(X_138,X_137)
| meet(X_137,X_138) != complement(join(complement(X_138),complement(X_137)))
| meet(X_137,X_138) = meet(X_138,X_137) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_137,X_138),complement(join(complement(X_138),complement(X_137)))) ),[1],$fot(meet(X_138,X_137))]]) ).
cnf(refute_1_460,plain,
( meet(X_137,X_138) != complement(join(complement(X_138),complement(X_137)))
| meet(X_137,X_138) = meet(X_138,X_137) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_138),complement(X_137))),meet(X_138,X_137)) )],[refute_1_458,refute_1_459]) ).
cnf(refute_1_461,plain,
meet(X_137,X_138) = meet(X_138,X_137),
inference(resolve,[$cnf( $equal(meet(X_137,X_138),complement(join(complement(X_138),complement(X_137)))) )],[refute_1_457,refute_1_460]) ).
cnf(refute_1_462,plain,
meet(top,X_178) = meet(X_178,top),
inference(subst,[],[refute_1_461:[bind(X_137,$fot(top)),bind(X_138,$fot(X_178))]]) ).
cnf(refute_1_463,plain,
( meet(top,X_178) != meet(X_178,top)
| meet(X_178,top) = meet(top,X_178) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(meet(top,X_178))),bind(Y,$fot(meet(X_178,top)))]]) ).
cnf(refute_1_464,plain,
meet(X_178,top) = meet(top,X_178),
inference(resolve,[$cnf( $equal(meet(top,X_178),meet(X_178,top)) )],[refute_1_462,refute_1_463]) ).
cnf(refute_1_465,plain,
( X_178 != join(zero,meet(X_178,top))
| meet(X_178,top) != meet(top,X_178)
| X_178 = join(zero,meet(top,X_178)) ),
introduced(tautology,[equality,[$cnf( $equal(X_178,join(zero,meet(X_178,top))) ),[1,1],$fot(meet(top,X_178))]]) ).
cnf(refute_1_466,plain,
( X_178 != join(zero,meet(X_178,top))
| X_178 = join(zero,meet(top,X_178)) ),
inference(resolve,[$cnf( $equal(meet(X_178,top),meet(top,X_178)) )],[refute_1_464,refute_1_465]) ).
cnf(refute_1_467,plain,
X_178 = join(zero,meet(top,X_178)),
inference(resolve,[$cnf( $equal(X_178,join(zero,meet(X_178,top))) )],[refute_1_451,refute_1_466]) ).
cnf(refute_1_468,plain,
complement(X_181) = join(zero,meet(top,complement(X_181))),
inference(subst,[],[refute_1_467:[bind(X_178,$fot(complement(X_181)))]]) ).
cnf(refute_1_469,plain,
meet(top,complement(X_180)) = complement(join(zero,complement(complement(X_180)))),
inference(subst,[],[refute_1_48:[bind(X1,$fot(complement(X_180)))]]) ).
cnf(refute_1_470,plain,
X_176 = join(meet(X_176,complement(X_176)),complement(join(complement(X_176),complement(X_176)))),
inference(subst,[],[refute_1_69:[bind(X0,$fot(X_176)),bind(X1,$fot(complement(X_176)))]]) ).
cnf(refute_1_471,plain,
join(complement(X_176),complement(X_176)) = complement(X_176),
inference(subst,[],[refute_1_166:[bind(X_134,$fot(X_176))]]) ).
cnf(refute_1_472,plain,
( X_176 != join(meet(X_176,complement(X_176)),complement(join(complement(X_176),complement(X_176))))
| join(complement(X_176),complement(X_176)) != complement(X_176)
| X_176 = join(meet(X_176,complement(X_176)),complement(complement(X_176))) ),
introduced(tautology,[equality,[$cnf( $equal(X_176,join(meet(X_176,complement(X_176)),complement(join(complement(X_176),complement(X_176))))) ),[1,1,0],$fot(complement(X_176))]]) ).
cnf(refute_1_473,plain,
( X_176 != join(meet(X_176,complement(X_176)),complement(join(complement(X_176),complement(X_176))))
| X_176 = join(meet(X_176,complement(X_176)),complement(complement(X_176))) ),
inference(resolve,[$cnf( $equal(join(complement(X_176),complement(X_176)),complement(X_176)) )],[refute_1_471,refute_1_472]) ).
cnf(refute_1_474,plain,
X_176 = join(meet(X_176,complement(X_176)),complement(complement(X_176))),
inference(resolve,[$cnf( $equal(X_176,join(meet(X_176,complement(X_176)),complement(join(complement(X_176),complement(X_176))))) )],[refute_1_470,refute_1_473]) ).
cnf(refute_1_475,plain,
join(complement(complement(X_176)),zero) = join(zero,complement(complement(X_176))),
inference(subst,[],[refute_1_52:[bind(X0,$fot(zero)),bind(X1,$fot(complement(complement(X_176))))]]) ).
cnf(refute_1_476,plain,
( zero != meet(X0,complement(X0))
| meet(X0,complement(X0)) = zero ),
inference(subst,[],[refute_1_17:[bind(X,$fot(zero)),bind(Y,$fot(meet(X0,complement(X0))))]]) ).
cnf(refute_1_477,plain,
meet(X0,complement(X0)) = zero,
inference(resolve,[$cnf( $equal(zero,meet(X0,complement(X0))) )],[refute_1_8,refute_1_476]) ).
cnf(refute_1_478,plain,
meet(X_176,complement(X_176)) = zero,
inference(subst,[],[refute_1_477:[bind(X0,$fot(X_176))]]) ).
cnf(refute_1_479,plain,
join(complement(complement(X_176)),meet(X_176,complement(X_176))) = join(complement(complement(X_176)),meet(X_176,complement(X_176))),
introduced(tautology,[refl,[$fot(join(complement(complement(X_176)),meet(X_176,complement(X_176))))]]) ).
cnf(refute_1_480,plain,
( join(complement(complement(X_176)),meet(X_176,complement(X_176))) != join(complement(complement(X_176)),meet(X_176,complement(X_176)))
| meet(X_176,complement(X_176)) != zero
| join(complement(complement(X_176)),meet(X_176,complement(X_176))) = join(complement(complement(X_176)),zero) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(complement(X_176)),meet(X_176,complement(X_176))),join(complement(complement(X_176)),meet(X_176,complement(X_176)))) ),[1,1],$fot(zero)]]) ).
cnf(refute_1_481,plain,
( meet(X_176,complement(X_176)) != zero
| join(complement(complement(X_176)),meet(X_176,complement(X_176))) = join(complement(complement(X_176)),zero) ),
inference(resolve,[$cnf( $equal(join(complement(complement(X_176)),meet(X_176,complement(X_176))),join(complement(complement(X_176)),meet(X_176,complement(X_176)))) )],[refute_1_479,refute_1_480]) ).
cnf(refute_1_482,plain,
join(complement(complement(X_176)),meet(X_176,complement(X_176))) = join(complement(complement(X_176)),zero),
inference(resolve,[$cnf( $equal(meet(X_176,complement(X_176)),zero) )],[refute_1_478,refute_1_481]) ).
cnf(refute_1_483,plain,
( join(complement(complement(X_176)),meet(X_176,complement(X_176))) != join(complement(complement(X_176)),zero)
| join(complement(complement(X_176)),zero) != join(zero,complement(complement(X_176)))
| join(complement(complement(X_176)),meet(X_176,complement(X_176))) = join(zero,complement(complement(X_176))) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(complement(complement(X_176)),meet(X_176,complement(X_176))))),bind(Y,$fot(join(complement(complement(X_176)),zero))),bind(Z,$fot(join(zero,complement(complement(X_176)))))]]) ).
cnf(refute_1_484,plain,
( join(complement(complement(X_176)),zero) != join(zero,complement(complement(X_176)))
| join(complement(complement(X_176)),meet(X_176,complement(X_176))) = join(zero,complement(complement(X_176))) ),
inference(resolve,[$cnf( $equal(join(complement(complement(X_176)),meet(X_176,complement(X_176))),join(complement(complement(X_176)),zero)) )],[refute_1_482,refute_1_483]) ).
cnf(refute_1_485,plain,
join(complement(complement(X_176)),meet(X_176,complement(X_176))) = join(zero,complement(complement(X_176))),
inference(resolve,[$cnf( $equal(join(complement(complement(X_176)),zero),join(zero,complement(complement(X_176)))) )],[refute_1_475,refute_1_484]) ).
cnf(refute_1_486,plain,
join(meet(X_176,complement(X_176)),complement(complement(X_176))) = join(complement(complement(X_176)),meet(X_176,complement(X_176))),
inference(subst,[],[refute_1_52:[bind(X0,$fot(complement(complement(X_176)))),bind(X1,$fot(meet(X_176,complement(X_176))))]]) ).
cnf(refute_1_487,plain,
( join(complement(complement(X_176)),meet(X_176,complement(X_176))) != join(zero,complement(complement(X_176)))
| join(meet(X_176,complement(X_176)),complement(complement(X_176))) != join(complement(complement(X_176)),meet(X_176,complement(X_176)))
| join(meet(X_176,complement(X_176)),complement(complement(X_176))) = join(zero,complement(complement(X_176))) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(meet(X_176,complement(X_176)),complement(complement(X_176))))),bind(Y,$fot(join(complement(complement(X_176)),meet(X_176,complement(X_176))))),bind(Z,$fot(join(zero,complement(complement(X_176)))))]]) ).
cnf(refute_1_488,plain,
( join(complement(complement(X_176)),meet(X_176,complement(X_176))) != join(zero,complement(complement(X_176)))
| join(meet(X_176,complement(X_176)),complement(complement(X_176))) = join(zero,complement(complement(X_176))) ),
inference(resolve,[$cnf( $equal(join(meet(X_176,complement(X_176)),complement(complement(X_176))),join(complement(complement(X_176)),meet(X_176,complement(X_176)))) )],[refute_1_486,refute_1_487]) ).
cnf(refute_1_489,plain,
join(meet(X_176,complement(X_176)),complement(complement(X_176))) = join(zero,complement(complement(X_176))),
inference(resolve,[$cnf( $equal(join(complement(complement(X_176)),meet(X_176,complement(X_176))),join(zero,complement(complement(X_176)))) )],[refute_1_485,refute_1_488]) ).
cnf(refute_1_490,plain,
( X_176 != join(meet(X_176,complement(X_176)),complement(complement(X_176)))
| join(meet(X_176,complement(X_176)),complement(complement(X_176))) != join(zero,complement(complement(X_176)))
| X_176 = join(zero,complement(complement(X_176))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_176,join(zero,complement(complement(X_176)))) ),[0],$fot(join(meet(X_176,complement(X_176)),complement(complement(X_176))))]]) ).
cnf(refute_1_491,plain,
( X_176 != join(meet(X_176,complement(X_176)),complement(complement(X_176)))
| X_176 = join(zero,complement(complement(X_176))) ),
inference(resolve,[$cnf( $equal(join(meet(X_176,complement(X_176)),complement(complement(X_176))),join(zero,complement(complement(X_176)))) )],[refute_1_489,refute_1_490]) ).
cnf(refute_1_492,plain,
X_176 = join(zero,complement(complement(X_176))),
inference(resolve,[$cnf( $equal(X_176,join(meet(X_176,complement(X_176)),complement(complement(X_176)))) )],[refute_1_474,refute_1_491]) ).
cnf(refute_1_493,plain,
X_180 = join(zero,complement(complement(X_180))),
inference(subst,[],[refute_1_492:[bind(X_176,$fot(X_180))]]) ).
cnf(refute_1_494,plain,
( X_180 != join(zero,complement(complement(X_180)))
| join(zero,complement(complement(X_180))) = X_180 ),
inference(subst,[],[refute_1_17:[bind(X,$fot(X_180)),bind(Y,$fot(join(zero,complement(complement(X_180)))))]]) ).
cnf(refute_1_495,plain,
join(zero,complement(complement(X_180))) = X_180,
inference(resolve,[$cnf( $equal(X_180,join(zero,complement(complement(X_180)))) )],[refute_1_493,refute_1_494]) ).
cnf(refute_1_496,plain,
( join(zero,complement(complement(X_180))) != X_180
| meet(top,complement(X_180)) != complement(join(zero,complement(complement(X_180))))
| meet(top,complement(X_180)) = complement(X_180) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,complement(X_180)),complement(join(zero,complement(complement(X_180))))) ),[1,0],$fot(X_180)]]) ).
cnf(refute_1_497,plain,
( meet(top,complement(X_180)) != complement(join(zero,complement(complement(X_180))))
| meet(top,complement(X_180)) = complement(X_180) ),
inference(resolve,[$cnf( $equal(join(zero,complement(complement(X_180))),X_180) )],[refute_1_495,refute_1_496]) ).
cnf(refute_1_498,plain,
meet(top,complement(X_180)) = complement(X_180),
inference(resolve,[$cnf( $equal(meet(top,complement(X_180)),complement(join(zero,complement(complement(X_180))))) )],[refute_1_469,refute_1_497]) ).
cnf(refute_1_499,plain,
meet(top,complement(X_181)) = complement(X_181),
inference(subst,[],[refute_1_498:[bind(X_180,$fot(X_181))]]) ).
cnf(refute_1_500,plain,
( complement(X_181) != join(zero,meet(top,complement(X_181)))
| meet(top,complement(X_181)) != complement(X_181)
| complement(X_181) = join(zero,complement(X_181)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(X_181),join(zero,meet(top,complement(X_181)))) ),[1,1],$fot(complement(X_181))]]) ).
cnf(refute_1_501,plain,
( complement(X_181) != join(zero,meet(top,complement(X_181)))
| complement(X_181) = join(zero,complement(X_181)) ),
inference(resolve,[$cnf( $equal(meet(top,complement(X_181)),complement(X_181)) )],[refute_1_499,refute_1_500]) ).
cnf(refute_1_502,plain,
complement(X_181) = join(zero,complement(X_181)),
inference(resolve,[$cnf( $equal(complement(X_181),join(zero,meet(top,complement(X_181)))) )],[refute_1_468,refute_1_501]) ).
cnf(refute_1_503,plain,
( complement(X_181) != join(zero,complement(X_181))
| join(zero,complement(X_181)) = complement(X_181) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(complement(X_181))),bind(Y,$fot(join(zero,complement(X_181))))]]) ).
cnf(refute_1_504,plain,
join(zero,complement(X_181)) = complement(X_181),
inference(resolve,[$cnf( $equal(complement(X_181),join(zero,complement(X_181))) )],[refute_1_502,refute_1_503]) ).
cnf(refute_1_505,plain,
join(zero,complement(X1)) = complement(X1),
inference(subst,[],[refute_1_504:[bind(X_181,$fot(X1))]]) ).
cnf(refute_1_506,plain,
complement(join(zero,complement(X1))) = complement(join(zero,complement(X1))),
introduced(tautology,[refl,[$fot(complement(join(zero,complement(X1))))]]) ).
cnf(refute_1_507,plain,
( complement(join(zero,complement(X1))) != complement(join(zero,complement(X1)))
| join(zero,complement(X1)) != complement(X1)
| complement(join(zero,complement(X1))) = complement(complement(X1)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(zero,complement(X1))),complement(join(zero,complement(X1)))) ),[1,0],$fot(complement(X1))]]) ).
cnf(refute_1_508,plain,
( join(zero,complement(X1)) != complement(X1)
| complement(join(zero,complement(X1))) = complement(complement(X1)) ),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(X1))),complement(join(zero,complement(X1)))) )],[refute_1_506,refute_1_507]) ).
cnf(refute_1_509,plain,
complement(join(zero,complement(X1))) = complement(complement(X1)),
inference(resolve,[$cnf( $equal(join(zero,complement(X1)),complement(X1)) )],[refute_1_505,refute_1_508]) ).
cnf(refute_1_510,plain,
( complement(join(zero,complement(X1))) != complement(complement(X1))
| meet(top,X1) != complement(join(zero,complement(X1)))
| meet(top,X1) = complement(complement(X1)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,X1),complement(join(zero,complement(X1)))) ),[1],$fot(complement(complement(X1)))]]) ).
cnf(refute_1_511,plain,
( meet(top,X1) != complement(join(zero,complement(X1)))
| meet(top,X1) = complement(complement(X1)) ),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(X1))),complement(complement(X1))) )],[refute_1_509,refute_1_510]) ).
cnf(refute_1_512,plain,
meet(top,X1) = complement(complement(X1)),
inference(resolve,[$cnf( $equal(meet(top,X1),complement(join(zero,complement(X1)))) )],[refute_1_48,refute_1_511]) ).
cnf(refute_1_513,plain,
join(zero,complement(complement(X_176))) = complement(complement(X_176)),
inference(subst,[],[refute_1_504:[bind(X_181,$fot(complement(X_176)))]]) ).
cnf(refute_1_514,plain,
( X_176 != join(zero,complement(complement(X_176)))
| join(zero,complement(complement(X_176))) != complement(complement(X_176))
| X_176 = complement(complement(X_176)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_176,complement(complement(X_176))) ),[0],$fot(join(zero,complement(complement(X_176))))]]) ).
cnf(refute_1_515,plain,
( X_176 != join(zero,complement(complement(X_176)))
| X_176 = complement(complement(X_176)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(complement(X_176))),complement(complement(X_176))) )],[refute_1_513,refute_1_514]) ).
cnf(refute_1_516,plain,
X_176 = complement(complement(X_176)),
inference(resolve,[$cnf( $equal(X_176,join(zero,complement(complement(X_176)))) )],[refute_1_492,refute_1_515]) ).
cnf(refute_1_517,plain,
( X_176 != complement(complement(X_176))
| complement(complement(X_176)) = X_176 ),
inference(subst,[],[refute_1_17:[bind(X,$fot(X_176)),bind(Y,$fot(complement(complement(X_176))))]]) ).
cnf(refute_1_518,plain,
complement(complement(X_176)) = X_176,
inference(resolve,[$cnf( $equal(X_176,complement(complement(X_176))) )],[refute_1_516,refute_1_517]) ).
cnf(refute_1_519,plain,
complement(complement(X1)) = X1,
inference(subst,[],[refute_1_518:[bind(X_176,$fot(X1))]]) ).
cnf(refute_1_520,plain,
( complement(complement(X1)) != X1
| meet(top,X1) != complement(complement(X1))
| meet(top,X1) = X1 ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,X1),complement(complement(X1))) ),[1],$fot(X1)]]) ).
cnf(refute_1_521,plain,
( meet(top,X1) != complement(complement(X1))
| meet(top,X1) = X1 ),
inference(resolve,[$cnf( $equal(complement(complement(X1)),X1) )],[refute_1_519,refute_1_520]) ).
cnf(refute_1_522,plain,
meet(top,X1) = X1,
inference(resolve,[$cnf( $equal(meet(top,X1),complement(complement(X1))) )],[refute_1_512,refute_1_521]) ).
cnf(refute_1_523,plain,
meet(top,converse(complement(converse(complement(top))))) = converse(complement(converse(complement(top)))),
inference(subst,[],[refute_1_522:[bind(X1,$fot(converse(complement(converse(complement(top))))))]]) ).
cnf(refute_1_524,plain,
X_176 = join(meet(X_176,converse(complement(converse(complement(X_176))))),complement(join(complement(X_176),converse(complement(converse(complement(X_176))))))),
inference(subst,[],[refute_1_69:[bind(X0,$fot(X_176)),bind(X1,$fot(converse(complement(converse(complement(X_176))))))]]) ).
cnf(refute_1_525,plain,
top = join(complement(X_176),converse(complement(converse(complement(X_176))))),
inference(subst,[],[refute_1_194:[bind(X_115,$fot(complement(X_176)))]]) ).
cnf(refute_1_526,plain,
( top != join(complement(X_176),converse(complement(converse(complement(X_176)))))
| join(complement(X_176),converse(complement(converse(complement(X_176))))) = top ),
inference(subst,[],[refute_1_17:[bind(X,$fot(top)),bind(Y,$fot(join(complement(X_176),converse(complement(converse(complement(X_176)))))))]]) ).
cnf(refute_1_527,plain,
join(complement(X_176),converse(complement(converse(complement(X_176))))) = top,
inference(resolve,[$cnf( $equal(top,join(complement(X_176),converse(complement(converse(complement(X_176)))))) )],[refute_1_525,refute_1_526]) ).
cnf(refute_1_528,plain,
( X_176 != join(meet(X_176,converse(complement(converse(complement(X_176))))),complement(join(complement(X_176),converse(complement(converse(complement(X_176)))))))
| join(complement(X_176),converse(complement(converse(complement(X_176))))) != top
| X_176 = join(meet(X_176,converse(complement(converse(complement(X_176))))),complement(top)) ),
introduced(tautology,[equality,[$cnf( $equal(X_176,join(meet(X_176,converse(complement(converse(complement(X_176))))),complement(join(complement(X_176),converse(complement(converse(complement(X_176)))))))) ),[1,1,0],$fot(top)]]) ).
cnf(refute_1_529,plain,
( X_176 != join(meet(X_176,converse(complement(converse(complement(X_176))))),complement(join(complement(X_176),converse(complement(converse(complement(X_176)))))))
| X_176 = join(meet(X_176,converse(complement(converse(complement(X_176))))),complement(top)) ),
inference(resolve,[$cnf( $equal(join(complement(X_176),converse(complement(converse(complement(X_176))))),top) )],[refute_1_527,refute_1_528]) ).
cnf(refute_1_530,plain,
X_176 = join(meet(X_176,converse(complement(converse(complement(X_176))))),complement(top)),
inference(resolve,[$cnf( $equal(X_176,join(meet(X_176,converse(complement(converse(complement(X_176))))),complement(join(complement(X_176),converse(complement(converse(complement(X_176)))))))) )],[refute_1_524,refute_1_529]) ).
cnf(refute_1_531,plain,
join(complement(top),meet(X_176,converse(complement(converse(complement(X_176)))))) = join(complement(top),meet(X_176,converse(complement(converse(complement(X_176)))))),
introduced(tautology,[refl,[$fot(join(complement(top),meet(X_176,converse(complement(converse(complement(X_176)))))))]]) ).
cnf(refute_1_532,plain,
( complement(top) != zero
| join(complement(top),meet(X_176,converse(complement(converse(complement(X_176)))))) != join(complement(top),meet(X_176,converse(complement(converse(complement(X_176))))))
| join(complement(top),meet(X_176,converse(complement(converse(complement(X_176)))))) = join(zero,meet(X_176,converse(complement(converse(complement(X_176)))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(X_176,converse(complement(converse(complement(X_176)))))),join(complement(top),meet(X_176,converse(complement(converse(complement(X_176))))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_1_533,plain,
( complement(top) != zero
| join(complement(top),meet(X_176,converse(complement(converse(complement(X_176)))))) = join(zero,meet(X_176,converse(complement(converse(complement(X_176)))))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_176,converse(complement(converse(complement(X_176)))))),join(complement(top),meet(X_176,converse(complement(converse(complement(X_176))))))) )],[refute_1_531,refute_1_532]) ).
cnf(refute_1_534,plain,
join(complement(top),meet(X_176,converse(complement(converse(complement(X_176)))))) = join(zero,meet(X_176,converse(complement(converse(complement(X_176)))))),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_1_45,refute_1_533]) ).
cnf(refute_1_535,plain,
join(meet(X_176,converse(complement(converse(complement(X_176))))),complement(top)) = join(complement(top),meet(X_176,converse(complement(converse(complement(X_176)))))),
inference(subst,[],[refute_1_52:[bind(X0,$fot(complement(top))),bind(X1,$fot(meet(X_176,converse(complement(converse(complement(X_176)))))))]]) ).
cnf(refute_1_536,plain,
( join(complement(top),meet(X_176,converse(complement(converse(complement(X_176)))))) != join(zero,meet(X_176,converse(complement(converse(complement(X_176))))))
| join(meet(X_176,converse(complement(converse(complement(X_176))))),complement(top)) != join(complement(top),meet(X_176,converse(complement(converse(complement(X_176))))))
| join(meet(X_176,converse(complement(converse(complement(X_176))))),complement(top)) = join(zero,meet(X_176,converse(complement(converse(complement(X_176)))))) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(meet(X_176,converse(complement(converse(complement(X_176))))),complement(top)))),bind(Y,$fot(join(complement(top),meet(X_176,converse(complement(converse(complement(X_176)))))))),bind(Z,$fot(join(zero,meet(X_176,converse(complement(converse(complement(X_176))))))))]]) ).
cnf(refute_1_537,plain,
( join(complement(top),meet(X_176,converse(complement(converse(complement(X_176)))))) != join(zero,meet(X_176,converse(complement(converse(complement(X_176))))))
| join(meet(X_176,converse(complement(converse(complement(X_176))))),complement(top)) = join(zero,meet(X_176,converse(complement(converse(complement(X_176)))))) ),
inference(resolve,[$cnf( $equal(join(meet(X_176,converse(complement(converse(complement(X_176))))),complement(top)),join(complement(top),meet(X_176,converse(complement(converse(complement(X_176))))))) )],[refute_1_535,refute_1_536]) ).
cnf(refute_1_538,plain,
join(meet(X_176,converse(complement(converse(complement(X_176))))),complement(top)) = join(zero,meet(X_176,converse(complement(converse(complement(X_176)))))),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_176,converse(complement(converse(complement(X_176)))))),join(zero,meet(X_176,converse(complement(converse(complement(X_176))))))) )],[refute_1_534,refute_1_537]) ).
cnf(refute_1_539,plain,
( X_176 != join(meet(X_176,converse(complement(converse(complement(X_176))))),complement(top))
| join(meet(X_176,converse(complement(converse(complement(X_176))))),complement(top)) != join(zero,meet(X_176,converse(complement(converse(complement(X_176))))))
| X_176 = join(zero,meet(X_176,converse(complement(converse(complement(X_176)))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_176,join(zero,meet(X_176,converse(complement(converse(complement(X_176))))))) ),[0],$fot(join(meet(X_176,converse(complement(converse(complement(X_176))))),complement(top)))]]) ).
cnf(refute_1_540,plain,
( X_176 != join(meet(X_176,converse(complement(converse(complement(X_176))))),complement(top))
| X_176 = join(zero,meet(X_176,converse(complement(converse(complement(X_176)))))) ),
inference(resolve,[$cnf( $equal(join(meet(X_176,converse(complement(converse(complement(X_176))))),complement(top)),join(zero,meet(X_176,converse(complement(converse(complement(X_176))))))) )],[refute_1_538,refute_1_539]) ).
cnf(refute_1_541,plain,
X_176 = join(zero,meet(X_176,converse(complement(converse(complement(X_176)))))),
inference(resolve,[$cnf( $equal(X_176,join(meet(X_176,converse(complement(converse(complement(X_176))))),complement(top))) )],[refute_1_530,refute_1_540]) ).
cnf(refute_1_542,plain,
X_176 = join(meet(X_176,complement(complement(X_176))),complement(join(complement(X_176),complement(complement(X_176))))),
inference(subst,[],[refute_1_69:[bind(X0,$fot(X_176)),bind(X1,$fot(complement(complement(X_176))))]]) ).
cnf(refute_1_543,plain,
top = join(complement(X_176),complement(complement(X_176))),
inference(subst,[],[refute_1_23:[bind(X0,$fot(complement(X_176)))]]) ).
cnf(refute_1_544,plain,
( top != join(complement(X_176),complement(complement(X_176)))
| join(complement(X_176),complement(complement(X_176))) = top ),
inference(subst,[],[refute_1_17:[bind(X,$fot(top)),bind(Y,$fot(join(complement(X_176),complement(complement(X_176)))))]]) ).
cnf(refute_1_545,plain,
join(complement(X_176),complement(complement(X_176))) = top,
inference(resolve,[$cnf( $equal(top,join(complement(X_176),complement(complement(X_176)))) )],[refute_1_543,refute_1_544]) ).
cnf(refute_1_546,plain,
( X_176 != join(meet(X_176,complement(complement(X_176))),complement(join(complement(X_176),complement(complement(X_176)))))
| join(complement(X_176),complement(complement(X_176))) != top
| X_176 = join(meet(X_176,complement(complement(X_176))),complement(top)) ),
introduced(tautology,[equality,[$cnf( $equal(X_176,join(meet(X_176,complement(complement(X_176))),complement(join(complement(X_176),complement(complement(X_176)))))) ),[1,1,0],$fot(top)]]) ).
cnf(refute_1_547,plain,
( X_176 != join(meet(X_176,complement(complement(X_176))),complement(join(complement(X_176),complement(complement(X_176)))))
| X_176 = join(meet(X_176,complement(complement(X_176))),complement(top)) ),
inference(resolve,[$cnf( $equal(join(complement(X_176),complement(complement(X_176))),top) )],[refute_1_545,refute_1_546]) ).
cnf(refute_1_548,plain,
X_176 = join(meet(X_176,complement(complement(X_176))),complement(top)),
inference(resolve,[$cnf( $equal(X_176,join(meet(X_176,complement(complement(X_176))),complement(join(complement(X_176),complement(complement(X_176)))))) )],[refute_1_542,refute_1_547]) ).
cnf(refute_1_549,plain,
join(complement(top),meet(X_176,complement(complement(X_176)))) = join(complement(top),meet(X_176,complement(complement(X_176)))),
introduced(tautology,[refl,[$fot(join(complement(top),meet(X_176,complement(complement(X_176)))))]]) ).
cnf(refute_1_550,plain,
( complement(top) != zero
| join(complement(top),meet(X_176,complement(complement(X_176)))) != join(complement(top),meet(X_176,complement(complement(X_176))))
| join(complement(top),meet(X_176,complement(complement(X_176)))) = join(zero,meet(X_176,complement(complement(X_176)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(X_176,complement(complement(X_176)))),join(complement(top),meet(X_176,complement(complement(X_176))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_1_551,plain,
( complement(top) != zero
| join(complement(top),meet(X_176,complement(complement(X_176)))) = join(zero,meet(X_176,complement(complement(X_176)))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_176,complement(complement(X_176)))),join(complement(top),meet(X_176,complement(complement(X_176))))) )],[refute_1_549,refute_1_550]) ).
cnf(refute_1_552,plain,
join(complement(top),meet(X_176,complement(complement(X_176)))) = join(zero,meet(X_176,complement(complement(X_176)))),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_1_45,refute_1_551]) ).
cnf(refute_1_553,plain,
join(meet(X_176,complement(complement(X_176))),complement(top)) = join(complement(top),meet(X_176,complement(complement(X_176)))),
inference(subst,[],[refute_1_52:[bind(X0,$fot(complement(top))),bind(X1,$fot(meet(X_176,complement(complement(X_176)))))]]) ).
cnf(refute_1_554,plain,
( join(complement(top),meet(X_176,complement(complement(X_176)))) != join(zero,meet(X_176,complement(complement(X_176))))
| join(meet(X_176,complement(complement(X_176))),complement(top)) != join(complement(top),meet(X_176,complement(complement(X_176))))
| join(meet(X_176,complement(complement(X_176))),complement(top)) = join(zero,meet(X_176,complement(complement(X_176)))) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(meet(X_176,complement(complement(X_176))),complement(top)))),bind(Y,$fot(join(complement(top),meet(X_176,complement(complement(X_176)))))),bind(Z,$fot(join(zero,meet(X_176,complement(complement(X_176))))))]]) ).
cnf(refute_1_555,plain,
( join(complement(top),meet(X_176,complement(complement(X_176)))) != join(zero,meet(X_176,complement(complement(X_176))))
| join(meet(X_176,complement(complement(X_176))),complement(top)) = join(zero,meet(X_176,complement(complement(X_176)))) ),
inference(resolve,[$cnf( $equal(join(meet(X_176,complement(complement(X_176))),complement(top)),join(complement(top),meet(X_176,complement(complement(X_176))))) )],[refute_1_553,refute_1_554]) ).
cnf(refute_1_556,plain,
join(meet(X_176,complement(complement(X_176))),complement(top)) = join(zero,meet(X_176,complement(complement(X_176)))),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_176,complement(complement(X_176)))),join(zero,meet(X_176,complement(complement(X_176))))) )],[refute_1_552,refute_1_555]) ).
cnf(refute_1_557,plain,
( X_176 != join(meet(X_176,complement(complement(X_176))),complement(top))
| join(meet(X_176,complement(complement(X_176))),complement(top)) != join(zero,meet(X_176,complement(complement(X_176))))
| X_176 = join(zero,meet(X_176,complement(complement(X_176)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_176,join(zero,meet(X_176,complement(complement(X_176))))) ),[0],$fot(join(meet(X_176,complement(complement(X_176))),complement(top)))]]) ).
cnf(refute_1_558,plain,
( X_176 != join(meet(X_176,complement(complement(X_176))),complement(top))
| X_176 = join(zero,meet(X_176,complement(complement(X_176)))) ),
inference(resolve,[$cnf( $equal(join(meet(X_176,complement(complement(X_176))),complement(top)),join(zero,meet(X_176,complement(complement(X_176))))) )],[refute_1_556,refute_1_557]) ).
cnf(refute_1_559,plain,
X_176 = join(zero,meet(X_176,complement(complement(X_176)))),
inference(resolve,[$cnf( $equal(X_176,join(meet(X_176,complement(complement(X_176))),complement(top))) )],[refute_1_548,refute_1_558]) ).
cnf(refute_1_560,plain,
complement(complement(X_138)) = X_138,
inference(subst,[],[refute_1_518:[bind(X_176,$fot(X_138))]]) ).
cnf(refute_1_561,plain,
( complement(complement(X_138)) != X_138
| meet(X_138,X_138) != complement(complement(X_138))
| meet(X_138,X_138) = X_138 ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_138,X_138),complement(complement(X_138))) ),[1],$fot(X_138)]]) ).
cnf(refute_1_562,plain,
( meet(X_138,X_138) != complement(complement(X_138))
| meet(X_138,X_138) = X_138 ),
inference(resolve,[$cnf( $equal(complement(complement(X_138)),X_138) )],[refute_1_560,refute_1_561]) ).
cnf(refute_1_563,plain,
meet(X_138,X_138) = X_138,
inference(resolve,[$cnf( $equal(meet(X_138,X_138),complement(complement(X_138))) )],[refute_1_242,refute_1_562]) ).
cnf(refute_1_564,plain,
meet(X_176,X_176) = X_176,
inference(subst,[],[refute_1_563:[bind(X_138,$fot(X_176))]]) ).
cnf(refute_1_565,plain,
meet(X_176,complement(complement(X_176))) = meet(X_176,complement(complement(X_176))),
introduced(tautology,[refl,[$fot(meet(X_176,complement(complement(X_176))))]]) ).
cnf(refute_1_566,plain,
( complement(complement(X_176)) != X_176
| meet(X_176,complement(complement(X_176))) != meet(X_176,complement(complement(X_176)))
| meet(X_176,complement(complement(X_176))) = meet(X_176,X_176) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_176,complement(complement(X_176))),meet(X_176,complement(complement(X_176)))) ),[1,1],$fot(X_176)]]) ).
cnf(refute_1_567,plain,
( complement(complement(X_176)) != X_176
| meet(X_176,complement(complement(X_176))) = meet(X_176,X_176) ),
inference(resolve,[$cnf( $equal(meet(X_176,complement(complement(X_176))),meet(X_176,complement(complement(X_176)))) )],[refute_1_565,refute_1_566]) ).
cnf(refute_1_568,plain,
meet(X_176,complement(complement(X_176))) = meet(X_176,X_176),
inference(resolve,[$cnf( $equal(complement(complement(X_176)),X_176) )],[refute_1_518,refute_1_567]) ).
cnf(refute_1_569,plain,
( meet(X_176,X_176) != X_176
| meet(X_176,complement(complement(X_176))) != meet(X_176,X_176)
| meet(X_176,complement(complement(X_176))) = X_176 ),
inference(subst,[],[refute_1_37:[bind(X,$fot(meet(X_176,complement(complement(X_176))))),bind(Y,$fot(meet(X_176,X_176))),bind(Z,$fot(X_176))]]) ).
cnf(refute_1_570,plain,
( meet(X_176,X_176) != X_176
| meet(X_176,complement(complement(X_176))) = X_176 ),
inference(resolve,[$cnf( $equal(meet(X_176,complement(complement(X_176))),meet(X_176,X_176)) )],[refute_1_568,refute_1_569]) ).
cnf(refute_1_571,plain,
meet(X_176,complement(complement(X_176))) = X_176,
inference(resolve,[$cnf( $equal(meet(X_176,X_176),X_176) )],[refute_1_564,refute_1_570]) ).
cnf(refute_1_572,plain,
join(zero,meet(X_176,complement(complement(X_176)))) = join(zero,meet(X_176,complement(complement(X_176)))),
introduced(tautology,[refl,[$fot(join(zero,meet(X_176,complement(complement(X_176)))))]]) ).
cnf(refute_1_573,plain,
( join(zero,meet(X_176,complement(complement(X_176)))) != join(zero,meet(X_176,complement(complement(X_176))))
| meet(X_176,complement(complement(X_176))) != X_176
| join(zero,meet(X_176,complement(complement(X_176)))) = join(zero,X_176) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,meet(X_176,complement(complement(X_176)))),join(zero,meet(X_176,complement(complement(X_176))))) ),[1,1],$fot(X_176)]]) ).
cnf(refute_1_574,plain,
( meet(X_176,complement(complement(X_176))) != X_176
| join(zero,meet(X_176,complement(complement(X_176)))) = join(zero,X_176) ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_176,complement(complement(X_176)))),join(zero,meet(X_176,complement(complement(X_176))))) )],[refute_1_572,refute_1_573]) ).
cnf(refute_1_575,plain,
join(zero,meet(X_176,complement(complement(X_176)))) = join(zero,X_176),
inference(resolve,[$cnf( $equal(meet(X_176,complement(complement(X_176))),X_176) )],[refute_1_571,refute_1_574]) ).
cnf(refute_1_576,plain,
( X_176 != join(zero,meet(X_176,complement(complement(X_176))))
| join(zero,meet(X_176,complement(complement(X_176)))) != join(zero,X_176)
| X_176 = join(zero,X_176) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_176,join(zero,X_176)) ),[0],$fot(join(zero,meet(X_176,complement(complement(X_176)))))]]) ).
cnf(refute_1_577,plain,
( X_176 != join(zero,meet(X_176,complement(complement(X_176))))
| X_176 = join(zero,X_176) ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_176,complement(complement(X_176)))),join(zero,X_176)) )],[refute_1_575,refute_1_576]) ).
cnf(refute_1_578,plain,
X_176 = join(zero,X_176),
inference(resolve,[$cnf( $equal(X_176,join(zero,meet(X_176,complement(complement(X_176))))) )],[refute_1_559,refute_1_577]) ).
cnf(refute_1_579,plain,
( X_176 != join(zero,X_176)
| join(zero,X_176) = X_176 ),
inference(subst,[],[refute_1_17:[bind(X,$fot(X_176)),bind(Y,$fot(join(zero,X_176)))]]) ).
cnf(refute_1_580,plain,
join(zero,X_176) = X_176,
inference(resolve,[$cnf( $equal(X_176,join(zero,X_176)) )],[refute_1_578,refute_1_579]) ).
cnf(refute_1_581,plain,
join(zero,meet(X_176,converse(complement(converse(complement(X_176)))))) = meet(X_176,converse(complement(converse(complement(X_176))))),
inference(subst,[],[refute_1_580:[bind(X_176,$fot(meet(X_176,converse(complement(converse(complement(X_176)))))))]]) ).
cnf(refute_1_582,plain,
( X_176 != join(zero,meet(X_176,converse(complement(converse(complement(X_176))))))
| join(zero,meet(X_176,converse(complement(converse(complement(X_176)))))) != meet(X_176,converse(complement(converse(complement(X_176)))))
| X_176 = meet(X_176,converse(complement(converse(complement(X_176))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_176,meet(X_176,converse(complement(converse(complement(X_176)))))) ),[0],$fot(join(zero,meet(X_176,converse(complement(converse(complement(X_176)))))))]]) ).
cnf(refute_1_583,plain,
( X_176 != join(zero,meet(X_176,converse(complement(converse(complement(X_176))))))
| X_176 = meet(X_176,converse(complement(converse(complement(X_176))))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_176,converse(complement(converse(complement(X_176)))))),meet(X_176,converse(complement(converse(complement(X_176)))))) )],[refute_1_581,refute_1_582]) ).
cnf(refute_1_584,plain,
X_176 = meet(X_176,converse(complement(converse(complement(X_176))))),
inference(resolve,[$cnf( $equal(X_176,join(zero,meet(X_176,converse(complement(converse(complement(X_176))))))) )],[refute_1_541,refute_1_583]) ).
cnf(refute_1_585,plain,
top = meet(top,converse(complement(converse(complement(top))))),
inference(subst,[],[refute_1_584:[bind(X_176,$fot(top))]]) ).
cnf(refute_1_586,plain,
( top != meet(top,converse(complement(converse(complement(top)))))
| meet(top,converse(complement(converse(complement(top))))) = top ),
inference(subst,[],[refute_1_17:[bind(X,$fot(top)),bind(Y,$fot(meet(top,converse(complement(converse(complement(top)))))))]]) ).
cnf(refute_1_587,plain,
meet(top,converse(complement(converse(complement(top))))) = top,
inference(resolve,[$cnf( $equal(top,meet(top,converse(complement(converse(complement(top)))))) )],[refute_1_585,refute_1_586]) ).
cnf(refute_1_588,plain,
( meet(top,converse(complement(converse(complement(top))))) != converse(complement(converse(complement(top))))
| meet(top,converse(complement(converse(complement(top))))) != top
| top = converse(complement(converse(complement(top)))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,converse(complement(converse(complement(top))))),converse(complement(converse(complement(top))))) ),[0],$fot(top)]]) ).
cnf(refute_1_589,plain,
( meet(top,converse(complement(converse(complement(top))))) != converse(complement(converse(complement(top))))
| top = converse(complement(converse(complement(top)))) ),
inference(resolve,[$cnf( $equal(meet(top,converse(complement(converse(complement(top))))),top) )],[refute_1_587,refute_1_588]) ).
cnf(refute_1_590,plain,
top = converse(complement(converse(complement(top)))),
inference(resolve,[$cnf( $equal(meet(top,converse(complement(converse(complement(top))))),converse(complement(converse(complement(top))))) )],[refute_1_523,refute_1_589]) ).
cnf(refute_1_591,plain,
converse(complement(top)) = converse(complement(top)),
introduced(tautology,[refl,[$fot(converse(complement(top)))]]) ).
cnf(refute_1_592,plain,
( complement(top) != zero
| converse(complement(top)) != converse(complement(top))
| converse(complement(top)) = converse(zero) ),
introduced(tautology,[equality,[$cnf( $equal(converse(complement(top)),converse(complement(top))) ),[1,0],$fot(zero)]]) ).
cnf(refute_1_593,plain,
( complement(top) != zero
| converse(complement(top)) = converse(zero) ),
inference(resolve,[$cnf( $equal(converse(complement(top)),converse(complement(top))) )],[refute_1_591,refute_1_592]) ).
cnf(refute_1_594,plain,
converse(complement(top)) = converse(zero),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_1_45,refute_1_593]) ).
cnf(refute_1_595,plain,
complement(converse(complement(top))) = complement(converse(complement(top))),
introduced(tautology,[refl,[$fot(complement(converse(complement(top))))]]) ).
cnf(refute_1_596,plain,
( complement(converse(complement(top))) != complement(converse(complement(top)))
| converse(complement(top)) != converse(zero)
| complement(converse(complement(top))) = complement(converse(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(converse(complement(top))),complement(converse(complement(top)))) ),[1,0],$fot(converse(zero))]]) ).
cnf(refute_1_597,plain,
( converse(complement(top)) != converse(zero)
| complement(converse(complement(top))) = complement(converse(zero)) ),
inference(resolve,[$cnf( $equal(complement(converse(complement(top))),complement(converse(complement(top)))) )],[refute_1_595,refute_1_596]) ).
cnf(refute_1_598,plain,
complement(converse(complement(top))) = complement(converse(zero)),
inference(resolve,[$cnf( $equal(converse(complement(top)),converse(zero)) )],[refute_1_594,refute_1_597]) ).
cnf(refute_1_599,plain,
converse(complement(converse(complement(top)))) = converse(complement(converse(complement(top)))),
introduced(tautology,[refl,[$fot(converse(complement(converse(complement(top)))))]]) ).
cnf(refute_1_600,plain,
( complement(converse(complement(top))) != complement(converse(zero))
| converse(complement(converse(complement(top)))) != converse(complement(converse(complement(top))))
| converse(complement(converse(complement(top)))) = converse(complement(converse(zero))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(complement(converse(complement(top)))),converse(complement(converse(complement(top))))) ),[1,0],$fot(complement(converse(zero)))]]) ).
cnf(refute_1_601,plain,
( complement(converse(complement(top))) != complement(converse(zero))
| converse(complement(converse(complement(top)))) = converse(complement(converse(zero))) ),
inference(resolve,[$cnf( $equal(converse(complement(converse(complement(top)))),converse(complement(converse(complement(top))))) )],[refute_1_599,refute_1_600]) ).
cnf(refute_1_602,plain,
converse(complement(converse(complement(top)))) = converse(complement(converse(zero))),
inference(resolve,[$cnf( $equal(complement(converse(complement(top))),complement(converse(zero))) )],[refute_1_598,refute_1_601]) ).
cnf(refute_1_603,plain,
( converse(complement(converse(complement(top)))) != converse(complement(converse(zero)))
| top != converse(complement(converse(complement(top))))
| top = converse(complement(converse(zero))) ),
introduced(tautology,[equality,[$cnf( $equal(top,converse(complement(converse(complement(top))))) ),[1],$fot(converse(complement(converse(zero))))]]) ).
cnf(refute_1_604,plain,
( top != converse(complement(converse(complement(top))))
| top = converse(complement(converse(zero))) ),
inference(resolve,[$cnf( $equal(converse(complement(converse(complement(top)))),converse(complement(converse(zero)))) )],[refute_1_602,refute_1_603]) ).
cnf(refute_1_605,plain,
top = converse(complement(converse(zero))),
inference(resolve,[$cnf( $equal(top,converse(complement(converse(complement(top))))) )],[refute_1_590,refute_1_604]) ).
cnf(refute_1_606,plain,
( top != converse(complement(converse(zero)))
| converse(complement(converse(zero))) = top ),
inference(subst,[],[refute_1_17:[bind(X,$fot(top)),bind(Y,$fot(converse(complement(converse(zero)))))]]) ).
cnf(refute_1_607,plain,
converse(complement(converse(zero))) = top,
inference(resolve,[$cnf( $equal(top,converse(complement(converse(zero)))) )],[refute_1_605,refute_1_606]) ).
cnf(refute_1_608,plain,
( converse(complement(converse(zero))) != top
| converse(converse(complement(converse(zero)))) != complement(converse(zero))
| converse(top) = complement(converse(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(converse(complement(converse(zero)))),complement(converse(zero))) ),[0,0],$fot(top)]]) ).
cnf(refute_1_609,plain,
( converse(converse(complement(converse(zero)))) != complement(converse(zero))
| converse(top) = complement(converse(zero)) ),
inference(resolve,[$cnf( $equal(converse(complement(converse(zero))),top) )],[refute_1_607,refute_1_608]) ).
cnf(refute_1_610,plain,
converse(top) = complement(converse(zero)),
inference(resolve,[$cnf( $equal(converse(converse(complement(converse(zero)))),complement(converse(zero))) )],[refute_1_10,refute_1_609]) ).
cnf(refute_1_611,plain,
( converse(top) != complement(converse(zero))
| converse(top) != top
| top = complement(converse(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(top),complement(converse(zero))) ),[0],$fot(top)]]) ).
cnf(refute_1_612,plain,
( converse(top) != complement(converse(zero))
| top = complement(converse(zero)) ),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_1_191,refute_1_611]) ).
cnf(refute_1_613,plain,
top = complement(converse(zero)),
inference(resolve,[$cnf( $equal(converse(top),complement(converse(zero))) )],[refute_1_610,refute_1_612]) ).
cnf(refute_1_614,plain,
( top != complement(converse(zero))
| complement(converse(zero)) = top ),
inference(subst,[],[refute_1_17:[bind(X,$fot(top)),bind(Y,$fot(complement(converse(zero))))]]) ).
cnf(refute_1_615,plain,
complement(converse(zero)) = top,
inference(resolve,[$cnf( $equal(top,complement(converse(zero))) )],[refute_1_613,refute_1_614]) ).
cnf(refute_1_616,plain,
( complement(converse(zero)) != top
| zero != meet(converse(zero),complement(converse(zero)))
| zero = meet(converse(zero),top) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(converse(zero),complement(converse(zero)))) ),[1,1],$fot(top)]]) ).
cnf(refute_1_617,plain,
( zero != meet(converse(zero),complement(converse(zero)))
| zero = meet(converse(zero),top) ),
inference(resolve,[$cnf( $equal(complement(converse(zero)),top) )],[refute_1_615,refute_1_616]) ).
cnf(refute_1_618,plain,
zero = meet(converse(zero),top),
inference(resolve,[$cnf( $equal(zero,meet(converse(zero),complement(converse(zero)))) )],[refute_1_9,refute_1_617]) ).
cnf(refute_1_619,plain,
converse(zero) = join(meet(converse(zero),X1),complement(join(complement(converse(zero)),X1))),
inference(subst,[],[refute_1_69:[bind(X0,$fot(converse(zero)))]]) ).
cnf(refute_1_620,plain,
( complement(converse(zero)) != top
| converse(zero) != join(meet(converse(zero),X1),complement(join(complement(converse(zero)),X1)))
| converse(zero) = join(meet(converse(zero),X1),complement(join(top,X1))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(zero),join(meet(converse(zero),X1),complement(join(complement(converse(zero)),X1)))) ),[1,1,0,0],$fot(top)]]) ).
cnf(refute_1_621,plain,
( converse(zero) != join(meet(converse(zero),X1),complement(join(complement(converse(zero)),X1)))
| converse(zero) = join(meet(converse(zero),X1),complement(join(top,X1))) ),
inference(resolve,[$cnf( $equal(complement(converse(zero)),top) )],[refute_1_615,refute_1_620]) ).
cnf(refute_1_622,plain,
converse(zero) = join(meet(converse(zero),X1),complement(join(top,X1))),
inference(resolve,[$cnf( $equal(converse(zero),join(meet(converse(zero),X1),complement(join(complement(converse(zero)),X1)))) )],[refute_1_619,refute_1_621]) ).
cnf(refute_1_623,plain,
join(zero,meet(converse(zero),X1)) = meet(converse(zero),X1),
inference(subst,[],[refute_1_580:[bind(X_176,$fot(meet(converse(zero),X1)))]]) ).
cnf(refute_1_624,plain,
join(top,X1) = join(X1,top),
inference(subst,[],[refute_1_50:[bind(X0,$fot(top))]]) ).
cnf(refute_1_625,plain,
top = join(X1,top),
inference(subst,[],[refute_1_433:[bind(X_169,$fot(X1))]]) ).
cnf(refute_1_626,plain,
( top != join(X1,top)
| join(X1,top) = top ),
inference(subst,[],[refute_1_17:[bind(X,$fot(top)),bind(Y,$fot(join(X1,top)))]]) ).
cnf(refute_1_627,plain,
join(X1,top) = top,
inference(resolve,[$cnf( $equal(top,join(X1,top)) )],[refute_1_625,refute_1_626]) ).
cnf(refute_1_628,plain,
( join(X1,top) != top
| join(top,X1) != join(X1,top)
| join(top,X1) = top ),
introduced(tautology,[equality,[$cnf( $equal(join(top,X1),join(X1,top)) ),[1],$fot(top)]]) ).
cnf(refute_1_629,plain,
( join(top,X1) != join(X1,top)
| join(top,X1) = top ),
inference(resolve,[$cnf( $equal(join(X1,top),top) )],[refute_1_627,refute_1_628]) ).
cnf(refute_1_630,plain,
join(top,X1) = top,
inference(resolve,[$cnf( $equal(join(top,X1),join(X1,top)) )],[refute_1_624,refute_1_629]) ).
cnf(refute_1_631,plain,
complement(join(top,X1)) = complement(join(top,X1)),
introduced(tautology,[refl,[$fot(complement(join(top,X1)))]]) ).
cnf(refute_1_632,plain,
( complement(join(top,X1)) != complement(join(top,X1))
| join(top,X1) != top
| complement(join(top,X1)) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(top,X1)),complement(join(top,X1))) ),[1,0],$fot(top)]]) ).
cnf(refute_1_633,plain,
( join(top,X1) != top
| complement(join(top,X1)) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(join(top,X1)),complement(join(top,X1))) )],[refute_1_631,refute_1_632]) ).
cnf(refute_1_634,plain,
complement(join(top,X1)) = complement(top),
inference(resolve,[$cnf( $equal(join(top,X1),top) )],[refute_1_630,refute_1_633]) ).
cnf(refute_1_635,plain,
( complement(join(top,X1)) != complement(top)
| complement(top) != zero
| complement(join(top,X1)) = zero ),
inference(subst,[],[refute_1_37:[bind(X,$fot(complement(join(top,X1)))),bind(Y,$fot(complement(top))),bind(Z,$fot(zero))]]) ).
cnf(refute_1_636,plain,
( complement(top) != zero
| complement(join(top,X1)) = zero ),
inference(resolve,[$cnf( $equal(complement(join(top,X1)),complement(top)) )],[refute_1_634,refute_1_635]) ).
cnf(refute_1_637,plain,
complement(join(top,X1)) = zero,
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_1_45,refute_1_636]) ).
cnf(refute_1_638,plain,
join(complement(join(top,X1)),meet(converse(zero),X1)) = join(complement(join(top,X1)),meet(converse(zero),X1)),
introduced(tautology,[refl,[$fot(join(complement(join(top,X1)),meet(converse(zero),X1)))]]) ).
cnf(refute_1_639,plain,
( complement(join(top,X1)) != zero
| join(complement(join(top,X1)),meet(converse(zero),X1)) != join(complement(join(top,X1)),meet(converse(zero),X1))
| join(complement(join(top,X1)),meet(converse(zero),X1)) = join(zero,meet(converse(zero),X1)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(join(top,X1)),meet(converse(zero),X1)),join(complement(join(top,X1)),meet(converse(zero),X1))) ),[1,0],$fot(zero)]]) ).
cnf(refute_1_640,plain,
( complement(join(top,X1)) != zero
| join(complement(join(top,X1)),meet(converse(zero),X1)) = join(zero,meet(converse(zero),X1)) ),
inference(resolve,[$cnf( $equal(join(complement(join(top,X1)),meet(converse(zero),X1)),join(complement(join(top,X1)),meet(converse(zero),X1))) )],[refute_1_638,refute_1_639]) ).
cnf(refute_1_641,plain,
join(complement(join(top,X1)),meet(converse(zero),X1)) = join(zero,meet(converse(zero),X1)),
inference(resolve,[$cnf( $equal(complement(join(top,X1)),zero) )],[refute_1_637,refute_1_640]) ).
cnf(refute_1_642,plain,
( join(complement(join(top,X1)),meet(converse(zero),X1)) != join(zero,meet(converse(zero),X1))
| join(zero,meet(converse(zero),X1)) != meet(converse(zero),X1)
| join(complement(join(top,X1)),meet(converse(zero),X1)) = meet(converse(zero),X1) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(complement(join(top,X1)),meet(converse(zero),X1)))),bind(Y,$fot(join(zero,meet(converse(zero),X1)))),bind(Z,$fot(meet(converse(zero),X1)))]]) ).
cnf(refute_1_643,plain,
( join(zero,meet(converse(zero),X1)) != meet(converse(zero),X1)
| join(complement(join(top,X1)),meet(converse(zero),X1)) = meet(converse(zero),X1) ),
inference(resolve,[$cnf( $equal(join(complement(join(top,X1)),meet(converse(zero),X1)),join(zero,meet(converse(zero),X1))) )],[refute_1_641,refute_1_642]) ).
cnf(refute_1_644,plain,
join(complement(join(top,X1)),meet(converse(zero),X1)) = meet(converse(zero),X1),
inference(resolve,[$cnf( $equal(join(zero,meet(converse(zero),X1)),meet(converse(zero),X1)) )],[refute_1_623,refute_1_643]) ).
cnf(refute_1_645,plain,
join(meet(converse(zero),X1),complement(join(top,X1))) = join(complement(join(top,X1)),meet(converse(zero),X1)),
inference(subst,[],[refute_1_52:[bind(X0,$fot(complement(join(top,X1)))),bind(X1,$fot(meet(converse(zero),X1)))]]) ).
cnf(refute_1_646,plain,
( join(complement(join(top,X1)),meet(converse(zero),X1)) != meet(converse(zero),X1)
| join(meet(converse(zero),X1),complement(join(top,X1))) != join(complement(join(top,X1)),meet(converse(zero),X1))
| join(meet(converse(zero),X1),complement(join(top,X1))) = meet(converse(zero),X1) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(meet(converse(zero),X1),complement(join(top,X1))))),bind(Y,$fot(join(complement(join(top,X1)),meet(converse(zero),X1)))),bind(Z,$fot(meet(converse(zero),X1)))]]) ).
cnf(refute_1_647,plain,
( join(complement(join(top,X1)),meet(converse(zero),X1)) != meet(converse(zero),X1)
| join(meet(converse(zero),X1),complement(join(top,X1))) = meet(converse(zero),X1) ),
inference(resolve,[$cnf( $equal(join(meet(converse(zero),X1),complement(join(top,X1))),join(complement(join(top,X1)),meet(converse(zero),X1))) )],[refute_1_645,refute_1_646]) ).
cnf(refute_1_648,plain,
join(meet(converse(zero),X1),complement(join(top,X1))) = meet(converse(zero),X1),
inference(resolve,[$cnf( $equal(join(complement(join(top,X1)),meet(converse(zero),X1)),meet(converse(zero),X1)) )],[refute_1_644,refute_1_647]) ).
cnf(refute_1_649,plain,
( converse(zero) != join(meet(converse(zero),X1),complement(join(top,X1)))
| join(meet(converse(zero),X1),complement(join(top,X1))) != meet(converse(zero),X1)
| converse(zero) = meet(converse(zero),X1) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(zero),meet(converse(zero),X1)) ),[0],$fot(join(meet(converse(zero),X1),complement(join(top,X1))))]]) ).
cnf(refute_1_650,plain,
( converse(zero) != join(meet(converse(zero),X1),complement(join(top,X1)))
| converse(zero) = meet(converse(zero),X1) ),
inference(resolve,[$cnf( $equal(join(meet(converse(zero),X1),complement(join(top,X1))),meet(converse(zero),X1)) )],[refute_1_648,refute_1_649]) ).
cnf(refute_1_651,plain,
converse(zero) = meet(converse(zero),X1),
inference(resolve,[$cnf( $equal(converse(zero),join(meet(converse(zero),X1),complement(join(top,X1)))) )],[refute_1_622,refute_1_650]) ).
cnf(refute_1_652,plain,
( converse(zero) != meet(converse(zero),X1)
| meet(converse(zero),X1) = converse(zero) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(converse(zero))),bind(Y,$fot(meet(converse(zero),X1)))]]) ).
cnf(refute_1_653,plain,
meet(converse(zero),X1) = converse(zero),
inference(resolve,[$cnf( $equal(converse(zero),meet(converse(zero),X1)) )],[refute_1_651,refute_1_652]) ).
cnf(refute_1_654,plain,
meet(converse(zero),top) = converse(zero),
inference(subst,[],[refute_1_653:[bind(X1,$fot(top))]]) ).
cnf(refute_1_655,plain,
( meet(converse(zero),top) != converse(zero)
| zero != meet(converse(zero),top)
| zero = converse(zero) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(converse(zero),top)) ),[1],$fot(converse(zero))]]) ).
cnf(refute_1_656,plain,
( zero != meet(converse(zero),top)
| zero = converse(zero) ),
inference(resolve,[$cnf( $equal(meet(converse(zero),top),converse(zero)) )],[refute_1_654,refute_1_655]) ).
cnf(refute_1_657,plain,
zero = converse(zero),
inference(resolve,[$cnf( $equal(zero,meet(converse(zero),top)) )],[refute_1_618,refute_1_656]) ).
cnf(refute_1_658,plain,
( zero != converse(zero)
| converse(zero) = zero ),
inference(subst,[],[refute_1_17:[bind(X,$fot(zero)),bind(Y,$fot(converse(zero)))]]) ).
cnf(refute_1_659,plain,
converse(zero) = zero,
inference(resolve,[$cnf( $equal(zero,converse(zero)) )],[refute_1_657,refute_1_658]) ).
cnf(refute_1_660,plain,
( converse(composition(X_111,converse(zero))) != composition(zero,converse(X_111))
| converse(zero) != zero
| converse(composition(X_111,zero)) = composition(zero,converse(X_111)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(X_111,converse(zero))),composition(zero,converse(X_111))) ),[0,0,1],$fot(zero)]]) ).
cnf(refute_1_661,plain,
( converse(composition(X_111,converse(zero))) != composition(zero,converse(X_111))
| converse(composition(X_111,zero)) = composition(zero,converse(X_111)) ),
inference(resolve,[$cnf( $equal(converse(zero),zero) )],[refute_1_659,refute_1_660]) ).
cnf(refute_1_662,plain,
converse(composition(X_111,zero)) = composition(zero,converse(X_111)),
inference(resolve,[$cnf( $equal(converse(composition(X_111,converse(zero))),composition(zero,converse(X_111))) )],[refute_1_7,refute_1_661]) ).
cnf(refute_1_663,plain,
composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(canonicalize,[],[normalize_1_26]) ).
cnf(refute_1_664,plain,
composition(join(X_316,complement(composition(top,zero))),complement(composition(complement(composition(top,zero)),top))) = join(composition(X_316,complement(composition(complement(composition(top,zero)),top))),composition(complement(composition(top,zero)),complement(composition(complement(composition(top,zero)),top)))),
inference(subst,[],[refute_1_663:[bind(X0,$fot(X_316)),bind(X1,$fot(complement(composition(top,zero)))),bind(X2,$fot(complement(composition(complement(composition(top,zero)),top))))]]) ).
cnf(refute_1_665,plain,
join(complement(top),composition(converse(X0),complement(composition(X0,top)))) = complement(top),
inference(subst,[],[refute_1_112:[bind(X1,$fot(top))]]) ).
cnf(refute_1_666,plain,
( complement(top) != zero
| join(complement(top),composition(converse(X0),complement(composition(X0,top)))) != complement(top)
| join(zero,composition(converse(X0),complement(composition(X0,top)))) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),composition(converse(X0),complement(composition(X0,top)))),complement(top)) ),[0,0],$fot(zero)]]) ).
cnf(refute_1_667,plain,
( join(complement(top),composition(converse(X0),complement(composition(X0,top)))) != complement(top)
| join(zero,composition(converse(X0),complement(composition(X0,top)))) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_1_45,refute_1_666]) ).
cnf(refute_1_668,plain,
join(zero,composition(converse(X0),complement(composition(X0,top)))) = complement(top),
inference(resolve,[$cnf( $equal(join(complement(top),composition(converse(X0),complement(composition(X0,top)))),complement(top)) )],[refute_1_665,refute_1_667]) ).
cnf(refute_1_669,plain,
( complement(top) != zero
| join(zero,composition(converse(X0),complement(composition(X0,top)))) != complement(top)
| join(zero,composition(converse(X0),complement(composition(X0,top)))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,composition(converse(X0),complement(composition(X0,top)))),complement(top)) ),[1],$fot(zero)]]) ).
cnf(refute_1_670,plain,
( join(zero,composition(converse(X0),complement(composition(X0,top)))) != complement(top)
| join(zero,composition(converse(X0),complement(composition(X0,top)))) = zero ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_1_45,refute_1_669]) ).
cnf(refute_1_671,plain,
join(zero,composition(converse(X0),complement(composition(X0,top)))) = zero,
inference(resolve,[$cnf( $equal(join(zero,composition(converse(X0),complement(composition(X0,top)))),complement(top)) )],[refute_1_668,refute_1_670]) ).
cnf(refute_1_672,plain,
join(zero,composition(converse(X0),complement(composition(X0,top)))) = composition(converse(X0),complement(composition(X0,top))),
inference(subst,[],[refute_1_580:[bind(X_176,$fot(composition(converse(X0),complement(composition(X0,top)))))]]) ).
cnf(refute_1_673,plain,
( join(zero,composition(converse(X0),complement(composition(X0,top)))) != composition(converse(X0),complement(composition(X0,top)))
| join(zero,composition(converse(X0),complement(composition(X0,top)))) != zero
| composition(converse(X0),complement(composition(X0,top))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,composition(converse(X0),complement(composition(X0,top)))),zero) ),[0],$fot(composition(converse(X0),complement(composition(X0,top))))]]) ).
cnf(refute_1_674,plain,
( join(zero,composition(converse(X0),complement(composition(X0,top)))) != zero
| composition(converse(X0),complement(composition(X0,top))) = zero ),
inference(resolve,[$cnf( $equal(join(zero,composition(converse(X0),complement(composition(X0,top)))),composition(converse(X0),complement(composition(X0,top)))) )],[refute_1_672,refute_1_673]) ).
cnf(refute_1_675,plain,
composition(converse(X0),complement(composition(X0,top))) = zero,
inference(resolve,[$cnf( $equal(join(zero,composition(converse(X0),complement(composition(X0,top)))),zero) )],[refute_1_671,refute_1_674]) ).
cnf(refute_1_676,plain,
composition(converse(complement(composition(zero,top))),complement(composition(complement(composition(zero,top)),top))) = zero,
inference(subst,[],[refute_1_675:[bind(X0,$fot(complement(composition(zero,top))))]]) ).
cnf(refute_1_677,plain,
X_176 = join(meet(X_176,X_177),complement(join(complement(X_176),X_177))),
inference(subst,[],[refute_1_69:[bind(X0,$fot(X_176)),bind(X1,$fot(X_177))]]) ).
cnf(refute_1_678,plain,
meet(X_177,X_176) = meet(X_176,X_177),
inference(subst,[],[refute_1_461:[bind(X_137,$fot(X_177)),bind(X_138,$fot(X_176))]]) ).
cnf(refute_1_679,plain,
( meet(X_177,X_176) != meet(X_176,X_177)
| meet(X_176,X_177) = meet(X_177,X_176) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(meet(X_177,X_176))),bind(Y,$fot(meet(X_176,X_177)))]]) ).
cnf(refute_1_680,plain,
meet(X_176,X_177) = meet(X_177,X_176),
inference(resolve,[$cnf( $equal(meet(X_177,X_176),meet(X_176,X_177)) )],[refute_1_678,refute_1_679]) ).
cnf(refute_1_681,plain,
( X_176 != join(meet(X_176,X_177),complement(join(complement(X_176),X_177)))
| meet(X_176,X_177) != meet(X_177,X_176)
| X_176 = join(meet(X_177,X_176),complement(join(complement(X_176),X_177))) ),
introduced(tautology,[equality,[$cnf( $equal(X_176,join(meet(X_176,X_177),complement(join(complement(X_176),X_177)))) ),[1,0],$fot(meet(X_177,X_176))]]) ).
cnf(refute_1_682,plain,
( X_176 != join(meet(X_176,X_177),complement(join(complement(X_176),X_177)))
| X_176 = join(meet(X_177,X_176),complement(join(complement(X_176),X_177))) ),
inference(resolve,[$cnf( $equal(meet(X_176,X_177),meet(X_177,X_176)) )],[refute_1_680,refute_1_681]) ).
cnf(refute_1_683,plain,
X_176 = join(meet(X_177,X_176),complement(join(complement(X_176),X_177))),
inference(resolve,[$cnf( $equal(X_176,join(meet(X_176,X_177),complement(join(complement(X_176),X_177)))) )],[refute_1_677,refute_1_682]) ).
cnf(refute_1_684,plain,
converse(complement(composition(zero,top))) = join(meet(one,converse(complement(composition(zero,top)))),complement(join(complement(converse(complement(composition(zero,top)))),one))),
inference(subst,[],[refute_1_683:[bind(X_176,$fot(converse(complement(composition(zero,top))))),bind(X_177,$fot(one))]]) ).
cnf(refute_1_685,plain,
X_176 = join(meet(join(complement(complement(X_176)),X_214),X_176),complement(join(complement(X_176),join(complement(complement(X_176)),X_214)))),
inference(subst,[],[refute_1_683:[bind(X_177,$fot(join(complement(complement(X_176)),X_214)))]]) ).
cnf(refute_1_686,plain,
join(X_210,join(complement(X_210),X_212)) = join(join(X_210,complement(X_210)),X_212),
inference(subst,[],[refute_1_100:[bind(X0,$fot(X_210)),bind(X1,$fot(complement(X_210))),bind(X2,$fot(X_212))]]) ).
cnf(refute_1_687,plain,
top = join(X_210,complement(X_210)),
inference(subst,[],[refute_1_23:[bind(X0,$fot(X_210))]]) ).
cnf(refute_1_688,plain,
( top != join(X_210,complement(X_210))
| join(X_210,complement(X_210)) = top ),
inference(subst,[],[refute_1_17:[bind(X,$fot(top)),bind(Y,$fot(join(X_210,complement(X_210))))]]) ).
cnf(refute_1_689,plain,
join(X_210,complement(X_210)) = top,
inference(resolve,[$cnf( $equal(top,join(X_210,complement(X_210))) )],[refute_1_687,refute_1_688]) ).
cnf(refute_1_690,plain,
( join(X_210,complement(X_210)) != top
| join(X_210,join(complement(X_210),X_212)) != join(join(X_210,complement(X_210)),X_212)
| join(X_210,join(complement(X_210),X_212)) = join(top,X_212) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_210,join(complement(X_210),X_212)),join(join(X_210,complement(X_210)),X_212)) ),[1,0],$fot(top)]]) ).
cnf(refute_1_691,plain,
( join(X_210,join(complement(X_210),X_212)) != join(join(X_210,complement(X_210)),X_212)
| join(X_210,join(complement(X_210),X_212)) = join(top,X_212) ),
inference(resolve,[$cnf( $equal(join(X_210,complement(X_210)),top) )],[refute_1_689,refute_1_690]) ).
cnf(refute_1_692,plain,
join(X_210,join(complement(X_210),X_212)) = join(top,X_212),
inference(resolve,[$cnf( $equal(join(X_210,join(complement(X_210),X_212)),join(join(X_210,complement(X_210)),X_212)) )],[refute_1_686,refute_1_691]) ).
cnf(refute_1_693,plain,
join(top,X_212) = top,
inference(subst,[],[refute_1_630:[bind(X1,$fot(X_212))]]) ).
cnf(refute_1_694,plain,
( join(X_210,join(complement(X_210),X_212)) != join(top,X_212)
| join(top,X_212) != top
| join(X_210,join(complement(X_210),X_212)) = top ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_210,join(complement(X_210),X_212)),top) ),[0],$fot(join(top,X_212))]]) ).
cnf(refute_1_695,plain,
( join(X_210,join(complement(X_210),X_212)) != join(top,X_212)
| join(X_210,join(complement(X_210),X_212)) = top ),
inference(resolve,[$cnf( $equal(join(top,X_212),top) )],[refute_1_693,refute_1_694]) ).
cnf(refute_1_696,plain,
join(X_210,join(complement(X_210),X_212)) = top,
inference(resolve,[$cnf( $equal(join(X_210,join(complement(X_210),X_212)),join(top,X_212)) )],[refute_1_692,refute_1_695]) ).
cnf(refute_1_697,plain,
join(complement(X_176),join(complement(complement(X_176)),X_214)) = top,
inference(subst,[],[refute_1_696:[bind(X_210,$fot(complement(X_176))),bind(X_212,$fot(X_214))]]) ).
cnf(refute_1_698,plain,
( X_176 != join(meet(join(complement(complement(X_176)),X_214),X_176),complement(join(complement(X_176),join(complement(complement(X_176)),X_214))))
| join(complement(X_176),join(complement(complement(X_176)),X_214)) != top
| X_176 = join(meet(join(complement(complement(X_176)),X_214),X_176),complement(top)) ),
introduced(tautology,[equality,[$cnf( $equal(X_176,join(meet(join(complement(complement(X_176)),X_214),X_176),complement(join(complement(X_176),join(complement(complement(X_176)),X_214))))) ),[1,1,0],$fot(top)]]) ).
cnf(refute_1_699,plain,
( X_176 != join(meet(join(complement(complement(X_176)),X_214),X_176),complement(join(complement(X_176),join(complement(complement(X_176)),X_214))))
| X_176 = join(meet(join(complement(complement(X_176)),X_214),X_176),complement(top)) ),
inference(resolve,[$cnf( $equal(join(complement(X_176),join(complement(complement(X_176)),X_214)),top) )],[refute_1_697,refute_1_698]) ).
cnf(refute_1_700,plain,
X_176 = join(meet(join(complement(complement(X_176)),X_214),X_176),complement(top)),
inference(resolve,[$cnf( $equal(X_176,join(meet(join(complement(complement(X_176)),X_214),X_176),complement(join(complement(X_176),join(complement(complement(X_176)),X_214))))) )],[refute_1_685,refute_1_699]) ).
cnf(refute_1_701,plain,
join(zero,meet(X_176,join(X_176,X_214))) = meet(X_176,join(X_176,X_214)),
inference(subst,[],[refute_1_580:[bind(X_176,$fot(meet(X_176,join(X_176,X_214))))]]) ).
cnf(refute_1_702,plain,
join(complement(complement(X_176)),X_214) = join(complement(complement(X_176)),X_214),
introduced(tautology,[refl,[$fot(join(complement(complement(X_176)),X_214))]]) ).
cnf(refute_1_703,plain,
( complement(complement(X_176)) != X_176
| join(complement(complement(X_176)),X_214) != join(complement(complement(X_176)),X_214)
| join(complement(complement(X_176)),X_214) = join(X_176,X_214) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(complement(X_176)),X_214),join(complement(complement(X_176)),X_214)) ),[1,0],$fot(X_176)]]) ).
cnf(refute_1_704,plain,
( complement(complement(X_176)) != X_176
| join(complement(complement(X_176)),X_214) = join(X_176,X_214) ),
inference(resolve,[$cnf( $equal(join(complement(complement(X_176)),X_214),join(complement(complement(X_176)),X_214)) )],[refute_1_702,refute_1_703]) ).
cnf(refute_1_705,plain,
join(complement(complement(X_176)),X_214) = join(X_176,X_214),
inference(resolve,[$cnf( $equal(complement(complement(X_176)),X_176) )],[refute_1_518,refute_1_704]) ).
cnf(refute_1_706,plain,
meet(X_176,join(complement(complement(X_176)),X_214)) = meet(X_176,join(complement(complement(X_176)),X_214)),
introduced(tautology,[refl,[$fot(meet(X_176,join(complement(complement(X_176)),X_214)))]]) ).
cnf(refute_1_707,plain,
( join(complement(complement(X_176)),X_214) != join(X_176,X_214)
| meet(X_176,join(complement(complement(X_176)),X_214)) != meet(X_176,join(complement(complement(X_176)),X_214))
| meet(X_176,join(complement(complement(X_176)),X_214)) = meet(X_176,join(X_176,X_214)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_176,join(complement(complement(X_176)),X_214)),meet(X_176,join(complement(complement(X_176)),X_214))) ),[1,1],$fot(join(X_176,X_214))]]) ).
cnf(refute_1_708,plain,
( join(complement(complement(X_176)),X_214) != join(X_176,X_214)
| meet(X_176,join(complement(complement(X_176)),X_214)) = meet(X_176,join(X_176,X_214)) ),
inference(resolve,[$cnf( $equal(meet(X_176,join(complement(complement(X_176)),X_214)),meet(X_176,join(complement(complement(X_176)),X_214))) )],[refute_1_706,refute_1_707]) ).
cnf(refute_1_709,plain,
meet(X_176,join(complement(complement(X_176)),X_214)) = meet(X_176,join(X_176,X_214)),
inference(resolve,[$cnf( $equal(join(complement(complement(X_176)),X_214),join(X_176,X_214)) )],[refute_1_705,refute_1_708]) ).
cnf(refute_1_710,plain,
( meet(X_137,X_138) != meet(X_138,X_137)
| meet(X_138,X_137) = meet(X_137,X_138) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(meet(X_137,X_138))),bind(Y,$fot(meet(X_138,X_137)))]]) ).
cnf(refute_1_711,plain,
meet(X_138,X_137) = meet(X_137,X_138),
inference(resolve,[$cnf( $equal(meet(X_137,X_138),meet(X_138,X_137)) )],[refute_1_461,refute_1_710]) ).
cnf(refute_1_712,plain,
meet(join(complement(complement(X_176)),X_214),X_176) = meet(X_176,join(complement(complement(X_176)),X_214)),
inference(subst,[],[refute_1_711:[bind(X_137,$fot(X_176)),bind(X_138,$fot(join(complement(complement(X_176)),X_214)))]]) ).
cnf(refute_1_713,plain,
( meet(X_176,join(complement(complement(X_176)),X_214)) != meet(X_176,join(X_176,X_214))
| meet(join(complement(complement(X_176)),X_214),X_176) != meet(X_176,join(complement(complement(X_176)),X_214))
| meet(join(complement(complement(X_176)),X_214),X_176) = meet(X_176,join(X_176,X_214)) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(meet(join(complement(complement(X_176)),X_214),X_176))),bind(Y,$fot(meet(X_176,join(complement(complement(X_176)),X_214)))),bind(Z,$fot(meet(X_176,join(X_176,X_214))))]]) ).
cnf(refute_1_714,plain,
( meet(X_176,join(complement(complement(X_176)),X_214)) != meet(X_176,join(X_176,X_214))
| meet(join(complement(complement(X_176)),X_214),X_176) = meet(X_176,join(X_176,X_214)) ),
inference(resolve,[$cnf( $equal(meet(join(complement(complement(X_176)),X_214),X_176),meet(X_176,join(complement(complement(X_176)),X_214))) )],[refute_1_712,refute_1_713]) ).
cnf(refute_1_715,plain,
meet(join(complement(complement(X_176)),X_214),X_176) = meet(X_176,join(X_176,X_214)),
inference(resolve,[$cnf( $equal(meet(X_176,join(complement(complement(X_176)),X_214)),meet(X_176,join(X_176,X_214))) )],[refute_1_709,refute_1_714]) ).
cnf(refute_1_716,plain,
join(zero,meet(join(complement(complement(X_176)),X_214),X_176)) = join(zero,meet(join(complement(complement(X_176)),X_214),X_176)),
introduced(tautology,[refl,[$fot(join(zero,meet(join(complement(complement(X_176)),X_214),X_176)))]]) ).
cnf(refute_1_717,plain,
( join(zero,meet(join(complement(complement(X_176)),X_214),X_176)) != join(zero,meet(join(complement(complement(X_176)),X_214),X_176))
| meet(join(complement(complement(X_176)),X_214),X_176) != meet(X_176,join(X_176,X_214))
| join(zero,meet(join(complement(complement(X_176)),X_214),X_176)) = join(zero,meet(X_176,join(X_176,X_214))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,meet(join(complement(complement(X_176)),X_214),X_176)),join(zero,meet(join(complement(complement(X_176)),X_214),X_176))) ),[1,1],$fot(meet(X_176,join(X_176,X_214)))]]) ).
cnf(refute_1_718,plain,
( meet(join(complement(complement(X_176)),X_214),X_176) != meet(X_176,join(X_176,X_214))
| join(zero,meet(join(complement(complement(X_176)),X_214),X_176)) = join(zero,meet(X_176,join(X_176,X_214))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(join(complement(complement(X_176)),X_214),X_176)),join(zero,meet(join(complement(complement(X_176)),X_214),X_176))) )],[refute_1_716,refute_1_717]) ).
cnf(refute_1_719,plain,
join(zero,meet(join(complement(complement(X_176)),X_214),X_176)) = join(zero,meet(X_176,join(X_176,X_214))),
inference(resolve,[$cnf( $equal(meet(join(complement(complement(X_176)),X_214),X_176),meet(X_176,join(X_176,X_214))) )],[refute_1_715,refute_1_718]) ).
cnf(refute_1_720,plain,
join(complement(top),meet(join(complement(complement(X_176)),X_214),X_176)) = join(complement(top),meet(join(complement(complement(X_176)),X_214),X_176)),
introduced(tautology,[refl,[$fot(join(complement(top),meet(join(complement(complement(X_176)),X_214),X_176)))]]) ).
cnf(refute_1_721,plain,
( complement(top) != zero
| join(complement(top),meet(join(complement(complement(X_176)),X_214),X_176)) != join(complement(top),meet(join(complement(complement(X_176)),X_214),X_176))
| join(complement(top),meet(join(complement(complement(X_176)),X_214),X_176)) = join(zero,meet(join(complement(complement(X_176)),X_214),X_176)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(join(complement(complement(X_176)),X_214),X_176)),join(complement(top),meet(join(complement(complement(X_176)),X_214),X_176))) ),[1,0],$fot(zero)]]) ).
cnf(refute_1_722,plain,
( complement(top) != zero
| join(complement(top),meet(join(complement(complement(X_176)),X_214),X_176)) = join(zero,meet(join(complement(complement(X_176)),X_214),X_176)) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(join(complement(complement(X_176)),X_214),X_176)),join(complement(top),meet(join(complement(complement(X_176)),X_214),X_176))) )],[refute_1_720,refute_1_721]) ).
cnf(refute_1_723,plain,
join(complement(top),meet(join(complement(complement(X_176)),X_214),X_176)) = join(zero,meet(join(complement(complement(X_176)),X_214),X_176)),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_1_45,refute_1_722]) ).
cnf(refute_1_724,plain,
( join(complement(top),meet(join(complement(complement(X_176)),X_214),X_176)) != join(zero,meet(join(complement(complement(X_176)),X_214),X_176))
| join(zero,meet(join(complement(complement(X_176)),X_214),X_176)) != join(zero,meet(X_176,join(X_176,X_214)))
| join(complement(top),meet(join(complement(complement(X_176)),X_214),X_176)) = join(zero,meet(X_176,join(X_176,X_214))) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(complement(top),meet(join(complement(complement(X_176)),X_214),X_176)))),bind(Y,$fot(join(zero,meet(join(complement(complement(X_176)),X_214),X_176)))),bind(Z,$fot(join(zero,meet(X_176,join(X_176,X_214)))))]]) ).
cnf(refute_1_725,plain,
( join(zero,meet(join(complement(complement(X_176)),X_214),X_176)) != join(zero,meet(X_176,join(X_176,X_214)))
| join(complement(top),meet(join(complement(complement(X_176)),X_214),X_176)) = join(zero,meet(X_176,join(X_176,X_214))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(join(complement(complement(X_176)),X_214),X_176)),join(zero,meet(join(complement(complement(X_176)),X_214),X_176))) )],[refute_1_723,refute_1_724]) ).
cnf(refute_1_726,plain,
join(complement(top),meet(join(complement(complement(X_176)),X_214),X_176)) = join(zero,meet(X_176,join(X_176,X_214))),
inference(resolve,[$cnf( $equal(join(zero,meet(join(complement(complement(X_176)),X_214),X_176)),join(zero,meet(X_176,join(X_176,X_214)))) )],[refute_1_719,refute_1_725]) ).
cnf(refute_1_727,plain,
( join(complement(top),meet(join(complement(complement(X_176)),X_214),X_176)) != join(zero,meet(X_176,join(X_176,X_214)))
| join(zero,meet(X_176,join(X_176,X_214))) != meet(X_176,join(X_176,X_214))
| join(complement(top),meet(join(complement(complement(X_176)),X_214),X_176)) = meet(X_176,join(X_176,X_214)) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(complement(top),meet(join(complement(complement(X_176)),X_214),X_176)))),bind(Y,$fot(join(zero,meet(X_176,join(X_176,X_214))))),bind(Z,$fot(meet(X_176,join(X_176,X_214))))]]) ).
cnf(refute_1_728,plain,
( join(zero,meet(X_176,join(X_176,X_214))) != meet(X_176,join(X_176,X_214))
| join(complement(top),meet(join(complement(complement(X_176)),X_214),X_176)) = meet(X_176,join(X_176,X_214)) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(join(complement(complement(X_176)),X_214),X_176)),join(zero,meet(X_176,join(X_176,X_214)))) )],[refute_1_726,refute_1_727]) ).
cnf(refute_1_729,plain,
join(complement(top),meet(join(complement(complement(X_176)),X_214),X_176)) = meet(X_176,join(X_176,X_214)),
inference(resolve,[$cnf( $equal(join(zero,meet(X_176,join(X_176,X_214))),meet(X_176,join(X_176,X_214))) )],[refute_1_701,refute_1_728]) ).
cnf(refute_1_730,plain,
join(meet(join(complement(complement(X_176)),X_214),X_176),complement(top)) = join(complement(top),meet(join(complement(complement(X_176)),X_214),X_176)),
inference(subst,[],[refute_1_52:[bind(X0,$fot(complement(top))),bind(X1,$fot(meet(join(complement(complement(X_176)),X_214),X_176)))]]) ).
cnf(refute_1_731,plain,
( join(complement(top),meet(join(complement(complement(X_176)),X_214),X_176)) != meet(X_176,join(X_176,X_214))
| join(meet(join(complement(complement(X_176)),X_214),X_176),complement(top)) != join(complement(top),meet(join(complement(complement(X_176)),X_214),X_176))
| join(meet(join(complement(complement(X_176)),X_214),X_176),complement(top)) = meet(X_176,join(X_176,X_214)) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(meet(join(complement(complement(X_176)),X_214),X_176),complement(top)))),bind(Y,$fot(join(complement(top),meet(join(complement(complement(X_176)),X_214),X_176)))),bind(Z,$fot(meet(X_176,join(X_176,X_214))))]]) ).
cnf(refute_1_732,plain,
( join(complement(top),meet(join(complement(complement(X_176)),X_214),X_176)) != meet(X_176,join(X_176,X_214))
| join(meet(join(complement(complement(X_176)),X_214),X_176),complement(top)) = meet(X_176,join(X_176,X_214)) ),
inference(resolve,[$cnf( $equal(join(meet(join(complement(complement(X_176)),X_214),X_176),complement(top)),join(complement(top),meet(join(complement(complement(X_176)),X_214),X_176))) )],[refute_1_730,refute_1_731]) ).
cnf(refute_1_733,plain,
join(meet(join(complement(complement(X_176)),X_214),X_176),complement(top)) = meet(X_176,join(X_176,X_214)),
inference(resolve,[$cnf( $equal(join(complement(top),meet(join(complement(complement(X_176)),X_214),X_176)),meet(X_176,join(X_176,X_214))) )],[refute_1_729,refute_1_732]) ).
cnf(refute_1_734,plain,
( X_176 != join(meet(join(complement(complement(X_176)),X_214),X_176),complement(top))
| join(meet(join(complement(complement(X_176)),X_214),X_176),complement(top)) != meet(X_176,join(X_176,X_214))
| X_176 = meet(X_176,join(X_176,X_214)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_176,meet(X_176,join(X_176,X_214))) ),[0],$fot(join(meet(join(complement(complement(X_176)),X_214),X_176),complement(top)))]]) ).
cnf(refute_1_735,plain,
( X_176 != join(meet(join(complement(complement(X_176)),X_214),X_176),complement(top))
| X_176 = meet(X_176,join(X_176,X_214)) ),
inference(resolve,[$cnf( $equal(join(meet(join(complement(complement(X_176)),X_214),X_176),complement(top)),meet(X_176,join(X_176,X_214))) )],[refute_1_733,refute_1_734]) ).
cnf(refute_1_736,plain,
X_176 = meet(X_176,join(X_176,X_214)),
inference(resolve,[$cnf( $equal(X_176,join(meet(join(complement(complement(X_176)),X_214),X_176),complement(top))) )],[refute_1_700,refute_1_735]) ).
cnf(refute_1_737,plain,
one = meet(one,join(one,converse(X_110))),
inference(subst,[],[refute_1_736:[bind(X_176,$fot(one)),bind(X_214,$fot(converse(X_110)))]]) ).
cnf(refute_1_738,plain,
( join(one,converse(X_110)) != converse(join(one,X_110))
| one != meet(one,join(one,converse(X_110)))
| one = meet(one,converse(join(one,X_110))) ),
introduced(tautology,[equality,[$cnf( $equal(one,meet(one,join(one,converse(X_110)))) ),[1,1],$fot(converse(join(one,X_110)))]]) ).
cnf(refute_1_739,plain,
( one != meet(one,join(one,converse(X_110)))
| one = meet(one,converse(join(one,X_110))) ),
inference(resolve,[$cnf( $equal(join(one,converse(X_110)),converse(join(one,X_110))) )],[refute_1_360,refute_1_738]) ).
cnf(refute_1_740,plain,
one = meet(one,converse(join(one,X_110))),
inference(resolve,[$cnf( $equal(one,meet(one,join(one,converse(X_110)))) )],[refute_1_737,refute_1_739]) ).
cnf(refute_1_741,plain,
one = meet(one,converse(join(one,complement(composition(zero,top))))),
inference(subst,[],[refute_1_740:[bind(X_110,$fot(complement(composition(zero,top))))]]) ).
cnf(refute_1_742,plain,
complement(composition(zero,top)) = join(meet(one,complement(composition(zero,top))),complement(join(complement(complement(composition(zero,top))),one))),
inference(subst,[],[refute_1_683:[bind(X_176,$fot(complement(composition(zero,top)))),bind(X_177,$fot(one))]]) ).
cnf(refute_1_743,plain,
X_176 = join(meet(X_176,join(complement(X_138),meet(X_176,X_138))),complement(join(complement(X_176),join(complement(X_138),meet(X_176,X_138))))),
inference(subst,[],[refute_1_69:[bind(X0,$fot(X_176)),bind(X1,$fot(join(complement(X_138),meet(X_176,X_138))))]]) ).
cnf(refute_1_744,plain,
top = join(complement(X_176),join(complement(X_138),meet(X_176,X_138))),
inference(subst,[],[refute_1_236:[bind(X_137,$fot(X_176))]]) ).
cnf(refute_1_745,plain,
( top != join(complement(X_176),join(complement(X_138),meet(X_176,X_138)))
| join(complement(X_176),join(complement(X_138),meet(X_176,X_138))) = top ),
inference(subst,[],[refute_1_17:[bind(X,$fot(top)),bind(Y,$fot(join(complement(X_176),join(complement(X_138),meet(X_176,X_138)))))]]) ).
cnf(refute_1_746,plain,
join(complement(X_176),join(complement(X_138),meet(X_176,X_138))) = top,
inference(resolve,[$cnf( $equal(top,join(complement(X_176),join(complement(X_138),meet(X_176,X_138)))) )],[refute_1_744,refute_1_745]) ).
cnf(refute_1_747,plain,
( X_176 != join(meet(X_176,join(complement(X_138),meet(X_176,X_138))),complement(join(complement(X_176),join(complement(X_138),meet(X_176,X_138)))))
| join(complement(X_176),join(complement(X_138),meet(X_176,X_138))) != top
| X_176 = join(meet(X_176,join(complement(X_138),meet(X_176,X_138))),complement(top)) ),
introduced(tautology,[equality,[$cnf( $equal(X_176,join(meet(X_176,join(complement(X_138),meet(X_176,X_138))),complement(join(complement(X_176),join(complement(X_138),meet(X_176,X_138)))))) ),[1,1,0],$fot(top)]]) ).
cnf(refute_1_748,plain,
( X_176 != join(meet(X_176,join(complement(X_138),meet(X_176,X_138))),complement(join(complement(X_176),join(complement(X_138),meet(X_176,X_138)))))
| X_176 = join(meet(X_176,join(complement(X_138),meet(X_176,X_138))),complement(top)) ),
inference(resolve,[$cnf( $equal(join(complement(X_176),join(complement(X_138),meet(X_176,X_138))),top) )],[refute_1_746,refute_1_747]) ).
cnf(refute_1_749,plain,
X_176 = join(meet(X_176,join(complement(X_138),meet(X_176,X_138))),complement(top)),
inference(resolve,[$cnf( $equal(X_176,join(meet(X_176,join(complement(X_138),meet(X_176,X_138))),complement(join(complement(X_176),join(complement(X_138),meet(X_176,X_138)))))) )],[refute_1_743,refute_1_748]) ).
cnf(refute_1_750,plain,
join(complement(top),meet(X_176,join(complement(X_138),meet(X_176,X_138)))) = join(complement(top),meet(X_176,join(complement(X_138),meet(X_176,X_138)))),
introduced(tautology,[refl,[$fot(join(complement(top),meet(X_176,join(complement(X_138),meet(X_176,X_138)))))]]) ).
cnf(refute_1_751,plain,
( complement(top) != zero
| join(complement(top),meet(X_176,join(complement(X_138),meet(X_176,X_138)))) != join(complement(top),meet(X_176,join(complement(X_138),meet(X_176,X_138))))
| join(complement(top),meet(X_176,join(complement(X_138),meet(X_176,X_138)))) = join(zero,meet(X_176,join(complement(X_138),meet(X_176,X_138)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(X_176,join(complement(X_138),meet(X_176,X_138)))),join(complement(top),meet(X_176,join(complement(X_138),meet(X_176,X_138))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_1_752,plain,
( complement(top) != zero
| join(complement(top),meet(X_176,join(complement(X_138),meet(X_176,X_138)))) = join(zero,meet(X_176,join(complement(X_138),meet(X_176,X_138)))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_176,join(complement(X_138),meet(X_176,X_138)))),join(complement(top),meet(X_176,join(complement(X_138),meet(X_176,X_138))))) )],[refute_1_750,refute_1_751]) ).
cnf(refute_1_753,plain,
join(complement(top),meet(X_176,join(complement(X_138),meet(X_176,X_138)))) = join(zero,meet(X_176,join(complement(X_138),meet(X_176,X_138)))),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_1_45,refute_1_752]) ).
cnf(refute_1_754,plain,
join(meet(X_176,join(complement(X_138),meet(X_176,X_138))),complement(top)) = join(complement(top),meet(X_176,join(complement(X_138),meet(X_176,X_138)))),
inference(subst,[],[refute_1_52:[bind(X0,$fot(complement(top))),bind(X1,$fot(meet(X_176,join(complement(X_138),meet(X_176,X_138)))))]]) ).
cnf(refute_1_755,plain,
( join(complement(top),meet(X_176,join(complement(X_138),meet(X_176,X_138)))) != join(zero,meet(X_176,join(complement(X_138),meet(X_176,X_138))))
| join(meet(X_176,join(complement(X_138),meet(X_176,X_138))),complement(top)) != join(complement(top),meet(X_176,join(complement(X_138),meet(X_176,X_138))))
| join(meet(X_176,join(complement(X_138),meet(X_176,X_138))),complement(top)) = join(zero,meet(X_176,join(complement(X_138),meet(X_176,X_138)))) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(meet(X_176,join(complement(X_138),meet(X_176,X_138))),complement(top)))),bind(Y,$fot(join(complement(top),meet(X_176,join(complement(X_138),meet(X_176,X_138)))))),bind(Z,$fot(join(zero,meet(X_176,join(complement(X_138),meet(X_176,X_138))))))]]) ).
cnf(refute_1_756,plain,
( join(complement(top),meet(X_176,join(complement(X_138),meet(X_176,X_138)))) != join(zero,meet(X_176,join(complement(X_138),meet(X_176,X_138))))
| join(meet(X_176,join(complement(X_138),meet(X_176,X_138))),complement(top)) = join(zero,meet(X_176,join(complement(X_138),meet(X_176,X_138)))) ),
inference(resolve,[$cnf( $equal(join(meet(X_176,join(complement(X_138),meet(X_176,X_138))),complement(top)),join(complement(top),meet(X_176,join(complement(X_138),meet(X_176,X_138))))) )],[refute_1_754,refute_1_755]) ).
cnf(refute_1_757,plain,
join(meet(X_176,join(complement(X_138),meet(X_176,X_138))),complement(top)) = join(zero,meet(X_176,join(complement(X_138),meet(X_176,X_138)))),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_176,join(complement(X_138),meet(X_176,X_138)))),join(zero,meet(X_176,join(complement(X_138),meet(X_176,X_138))))) )],[refute_1_753,refute_1_756]) ).
cnf(refute_1_758,plain,
( X_176 != join(meet(X_176,join(complement(X_138),meet(X_176,X_138))),complement(top))
| join(meet(X_176,join(complement(X_138),meet(X_176,X_138))),complement(top)) != join(zero,meet(X_176,join(complement(X_138),meet(X_176,X_138))))
| X_176 = join(zero,meet(X_176,join(complement(X_138),meet(X_176,X_138)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_176,join(zero,meet(X_176,join(complement(X_138),meet(X_176,X_138))))) ),[0],$fot(join(meet(X_176,join(complement(X_138),meet(X_176,X_138))),complement(top)))]]) ).
cnf(refute_1_759,plain,
( X_176 != join(meet(X_176,join(complement(X_138),meet(X_176,X_138))),complement(top))
| X_176 = join(zero,meet(X_176,join(complement(X_138),meet(X_176,X_138)))) ),
inference(resolve,[$cnf( $equal(join(meet(X_176,join(complement(X_138),meet(X_176,X_138))),complement(top)),join(zero,meet(X_176,join(complement(X_138),meet(X_176,X_138))))) )],[refute_1_757,refute_1_758]) ).
cnf(refute_1_760,plain,
X_176 = join(zero,meet(X_176,join(complement(X_138),meet(X_176,X_138)))),
inference(resolve,[$cnf( $equal(X_176,join(meet(X_176,join(complement(X_138),meet(X_176,X_138))),complement(top))) )],[refute_1_749,refute_1_759]) ).
cnf(refute_1_761,plain,
join(zero,meet(X_176,join(complement(X_138),meet(X_176,X_138)))) = meet(X_176,join(complement(X_138),meet(X_176,X_138))),
inference(subst,[],[refute_1_580:[bind(X_176,$fot(meet(X_176,join(complement(X_138),meet(X_176,X_138)))))]]) ).
cnf(refute_1_762,plain,
( X_176 != join(zero,meet(X_176,join(complement(X_138),meet(X_176,X_138))))
| join(zero,meet(X_176,join(complement(X_138),meet(X_176,X_138)))) != meet(X_176,join(complement(X_138),meet(X_176,X_138)))
| X_176 = meet(X_176,join(complement(X_138),meet(X_176,X_138))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_176,meet(X_176,join(complement(X_138),meet(X_176,X_138)))) ),[0],$fot(join(zero,meet(X_176,join(complement(X_138),meet(X_176,X_138)))))]]) ).
cnf(refute_1_763,plain,
( X_176 != join(zero,meet(X_176,join(complement(X_138),meet(X_176,X_138))))
| X_176 = meet(X_176,join(complement(X_138),meet(X_176,X_138))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_176,join(complement(X_138),meet(X_176,X_138)))),meet(X_176,join(complement(X_138),meet(X_176,X_138)))) )],[refute_1_761,refute_1_762]) ).
cnf(refute_1_764,plain,
X_176 = meet(X_176,join(complement(X_138),meet(X_176,X_138))),
inference(resolve,[$cnf( $equal(X_176,join(zero,meet(X_176,join(complement(X_138),meet(X_176,X_138))))) )],[refute_1_760,refute_1_763]) ).
cnf(refute_1_765,plain,
one = meet(one,join(complement(composition(zero,top)),meet(one,composition(zero,top)))),
inference(subst,[],[refute_1_764:[bind(X_138,$fot(composition(zero,top))),bind(X_176,$fot(one))]]) ).
cnf(refute_1_766,plain,
meet(one,composition(zero,top)) = complement(complement(meet(one,composition(zero,top)))),
inference(subst,[],[refute_1_516:[bind(X_176,$fot(meet(one,composition(zero,top))))]]) ).
cnf(refute_1_767,plain,
join(complement(one),join(composition(zero,top),X_212)) = join(join(complement(one),composition(zero,top)),X_212),
inference(subst,[],[refute_1_100:[bind(X0,$fot(complement(one))),bind(X1,$fot(composition(zero,top))),bind(X2,$fot(X_212))]]) ).
cnf(refute_1_768,plain,
join(complement(one),composition(converse(X_133),complement(composition(X_133,one)))) = complement(one),
inference(subst,[],[refute_1_112:[bind(X0,$fot(X_133)),bind(X1,$fot(one))]]) ).
cnf(refute_1_769,plain,
composition(X_133,one) = X_133,
inference(subst,[],[refute_1_119:[bind(X0,$fot(X_133))]]) ).
cnf(refute_1_770,plain,
( composition(X_133,one) != X_133
| join(complement(one),composition(converse(X_133),complement(composition(X_133,one)))) != complement(one)
| join(complement(one),composition(converse(X_133),complement(X_133))) = complement(one) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(one),composition(converse(X_133),complement(composition(X_133,one)))),complement(one)) ),[0,1,1,0],$fot(X_133)]]) ).
cnf(refute_1_771,plain,
( join(complement(one),composition(converse(X_133),complement(composition(X_133,one)))) != complement(one)
| join(complement(one),composition(converse(X_133),complement(X_133))) = complement(one) ),
inference(resolve,[$cnf( $equal(composition(X_133,one),X_133) )],[refute_1_769,refute_1_770]) ).
cnf(refute_1_772,plain,
join(complement(one),composition(converse(X_133),complement(X_133))) = complement(one),
inference(resolve,[$cnf( $equal(join(complement(one),composition(converse(X_133),complement(composition(X_133,one)))),complement(one)) )],[refute_1_768,refute_1_771]) ).
cnf(refute_1_773,plain,
join(complement(one),composition(converse(converse(zero)),complement(converse(zero)))) = complement(one),
inference(subst,[],[refute_1_772:[bind(X_133,$fot(converse(zero)))]]) ).
cnf(refute_1_774,plain,
( complement(converse(zero)) != top
| join(complement(one),composition(converse(converse(zero)),complement(converse(zero)))) != complement(one)
| join(complement(one),composition(converse(converse(zero)),top)) = complement(one) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(one),composition(converse(converse(zero)),complement(converse(zero)))),complement(one)) ),[0,1,1],$fot(top)]]) ).
cnf(refute_1_775,plain,
( join(complement(one),composition(converse(converse(zero)),complement(converse(zero)))) != complement(one)
| join(complement(one),composition(converse(converse(zero)),top)) = complement(one) ),
inference(resolve,[$cnf( $equal(complement(converse(zero)),top) )],[refute_1_615,refute_1_774]) ).
cnf(refute_1_776,plain,
join(complement(one),composition(converse(converse(zero)),top)) = complement(one),
inference(resolve,[$cnf( $equal(join(complement(one),composition(converse(converse(zero)),complement(converse(zero)))),complement(one)) )],[refute_1_773,refute_1_775]) ).
cnf(refute_1_777,plain,
composition(zero,converse(top)) = composition(zero,converse(top)),
introduced(tautology,[refl,[$fot(composition(zero,converse(top)))]]) ).
cnf(refute_1_778,plain,
( composition(zero,converse(top)) != composition(zero,converse(top))
| converse(top) != top
| composition(zero,converse(top)) = composition(zero,top) ),
introduced(tautology,[equality,[$cnf( $equal(composition(zero,converse(top)),composition(zero,converse(top))) ),[1,1],$fot(top)]]) ).
cnf(refute_1_779,plain,
( converse(top) != top
| composition(zero,converse(top)) = composition(zero,top) ),
inference(resolve,[$cnf( $equal(composition(zero,converse(top)),composition(zero,converse(top))) )],[refute_1_777,refute_1_778]) ).
cnf(refute_1_780,plain,
composition(zero,converse(top)) = composition(zero,top),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_1_191,refute_1_779]) ).
cnf(refute_1_781,plain,
converse(composition(top,converse(zero))) = composition(zero,converse(top)),
inference(subst,[],[refute_1_6:[bind(X0,$fot(zero)),bind(X_111,$fot(top))]]) ).
cnf(refute_1_782,plain,
converse(composition(converse(top),X_112)) = composition(converse(X_112),top),
inference(subst,[],[refute_1_117:[bind(X0,$fot(top))]]) ).
cnf(refute_1_783,plain,
( converse(composition(converse(top),X_112)) != composition(converse(X_112),top)
| converse(top) != top
| converse(composition(top,X_112)) = composition(converse(X_112),top) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(top),X_112)),composition(converse(X_112),top)) ),[0,0,0],$fot(top)]]) ).
cnf(refute_1_784,plain,
( converse(composition(converse(top),X_112)) != composition(converse(X_112),top)
| converse(composition(top,X_112)) = composition(converse(X_112),top) ),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_1_191,refute_1_783]) ).
cnf(refute_1_785,plain,
converse(composition(top,X_112)) = composition(converse(X_112),top),
inference(resolve,[$cnf( $equal(converse(composition(converse(top),X_112)),composition(converse(X_112),top)) )],[refute_1_782,refute_1_784]) ).
cnf(refute_1_786,plain,
( converse(composition(top,X_112)) != composition(converse(X_112),top)
| composition(converse(X_112),top) = converse(composition(top,X_112)) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(converse(composition(top,X_112)))),bind(Y,$fot(composition(converse(X_112),top)))]]) ).
cnf(refute_1_787,plain,
composition(converse(X_112),top) = converse(composition(top,X_112)),
inference(resolve,[$cnf( $equal(converse(composition(top,X_112)),composition(converse(X_112),top)) )],[refute_1_785,refute_1_786]) ).
cnf(refute_1_788,plain,
composition(converse(converse(zero)),top) = converse(composition(top,converse(zero))),
inference(subst,[],[refute_1_787:[bind(X_112,$fot(converse(zero)))]]) ).
cnf(refute_1_789,plain,
( composition(converse(converse(zero)),top) != converse(composition(top,converse(zero)))
| converse(composition(top,converse(zero))) != composition(zero,converse(top))
| composition(converse(converse(zero)),top) = composition(zero,converse(top)) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(composition(converse(converse(zero)),top))),bind(Y,$fot(converse(composition(top,converse(zero))))),bind(Z,$fot(composition(zero,converse(top))))]]) ).
cnf(refute_1_790,plain,
( converse(composition(top,converse(zero))) != composition(zero,converse(top))
| composition(converse(converse(zero)),top) = composition(zero,converse(top)) ),
inference(resolve,[$cnf( $equal(composition(converse(converse(zero)),top),converse(composition(top,converse(zero)))) )],[refute_1_788,refute_1_789]) ).
cnf(refute_1_791,plain,
composition(converse(converse(zero)),top) = composition(zero,converse(top)),
inference(resolve,[$cnf( $equal(converse(composition(top,converse(zero))),composition(zero,converse(top))) )],[refute_1_781,refute_1_790]) ).
cnf(refute_1_792,plain,
( composition(converse(converse(zero)),top) != composition(zero,converse(top))
| composition(zero,converse(top)) != composition(zero,top)
| composition(converse(converse(zero)),top) = composition(zero,top) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(composition(converse(converse(zero)),top))),bind(Y,$fot(composition(zero,converse(top)))),bind(Z,$fot(composition(zero,top)))]]) ).
cnf(refute_1_793,plain,
( composition(zero,converse(top)) != composition(zero,top)
| composition(converse(converse(zero)),top) = composition(zero,top) ),
inference(resolve,[$cnf( $equal(composition(converse(converse(zero)),top),composition(zero,converse(top))) )],[refute_1_791,refute_1_792]) ).
cnf(refute_1_794,plain,
composition(converse(converse(zero)),top) = composition(zero,top),
inference(resolve,[$cnf( $equal(composition(zero,converse(top)),composition(zero,top)) )],[refute_1_780,refute_1_793]) ).
cnf(refute_1_795,plain,
join(complement(one),composition(converse(converse(zero)),top)) = join(complement(one),composition(converse(converse(zero)),top)),
introduced(tautology,[refl,[$fot(join(complement(one),composition(converse(converse(zero)),top)))]]) ).
cnf(refute_1_796,plain,
( composition(converse(converse(zero)),top) != composition(zero,top)
| join(complement(one),composition(converse(converse(zero)),top)) != join(complement(one),composition(converse(converse(zero)),top))
| join(complement(one),composition(converse(converse(zero)),top)) = join(complement(one),composition(zero,top)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(one),composition(converse(converse(zero)),top)),join(complement(one),composition(converse(converse(zero)),top))) ),[1,1],$fot(composition(zero,top))]]) ).
cnf(refute_1_797,plain,
( composition(converse(converse(zero)),top) != composition(zero,top)
| join(complement(one),composition(converse(converse(zero)),top)) = join(complement(one),composition(zero,top)) ),
inference(resolve,[$cnf( $equal(join(complement(one),composition(converse(converse(zero)),top)),join(complement(one),composition(converse(converse(zero)),top))) )],[refute_1_795,refute_1_796]) ).
cnf(refute_1_798,plain,
join(complement(one),composition(converse(converse(zero)),top)) = join(complement(one),composition(zero,top)),
inference(resolve,[$cnf( $equal(composition(converse(converse(zero)),top),composition(zero,top)) )],[refute_1_794,refute_1_797]) ).
cnf(refute_1_799,plain,
( join(complement(one),composition(converse(converse(zero)),top)) != complement(one)
| join(complement(one),composition(converse(converse(zero)),top)) != join(complement(one),composition(zero,top))
| join(complement(one),composition(zero,top)) = complement(one) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(one),composition(converse(converse(zero)),top)),complement(one)) ),[0],$fot(join(complement(one),composition(zero,top)))]]) ).
cnf(refute_1_800,plain,
( join(complement(one),composition(converse(converse(zero)),top)) != complement(one)
| join(complement(one),composition(zero,top)) = complement(one) ),
inference(resolve,[$cnf( $equal(join(complement(one),composition(converse(converse(zero)),top)),join(complement(one),composition(zero,top))) )],[refute_1_798,refute_1_799]) ).
cnf(refute_1_801,plain,
join(complement(one),composition(zero,top)) = complement(one),
inference(resolve,[$cnf( $equal(join(complement(one),composition(converse(converse(zero)),top)),complement(one)) )],[refute_1_776,refute_1_800]) ).
cnf(refute_1_802,plain,
( join(complement(one),composition(zero,top)) != complement(one)
| join(complement(one),join(composition(zero,top),X_212)) != join(join(complement(one),composition(zero,top)),X_212)
| join(complement(one),join(composition(zero,top),X_212)) = join(complement(one),X_212) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(one),join(composition(zero,top),X_212)),join(join(complement(one),composition(zero,top)),X_212)) ),[1,0],$fot(complement(one))]]) ).
cnf(refute_1_803,plain,
( join(complement(one),join(composition(zero,top),X_212)) != join(join(complement(one),composition(zero,top)),X_212)
| join(complement(one),join(composition(zero,top),X_212)) = join(complement(one),X_212) ),
inference(resolve,[$cnf( $equal(join(complement(one),composition(zero,top)),complement(one)) )],[refute_1_801,refute_1_802]) ).
cnf(refute_1_804,plain,
join(complement(one),join(composition(zero,top),X_212)) = join(complement(one),X_212),
inference(resolve,[$cnf( $equal(join(complement(one),join(composition(zero,top),X_212)),join(join(complement(one),composition(zero,top)),X_212)) )],[refute_1_767,refute_1_803]) ).
cnf(refute_1_805,plain,
join(complement(one),join(composition(zero,top),complement(composition(zero,top)))) = join(complement(one),complement(composition(zero,top))),
inference(subst,[],[refute_1_804:[bind(X_212,$fot(complement(composition(zero,top))))]]) ).
cnf(refute_1_806,plain,
top = join(composition(zero,top),complement(composition(zero,top))),
inference(subst,[],[refute_1_23:[bind(X0,$fot(composition(zero,top)))]]) ).
cnf(refute_1_807,plain,
( top != join(composition(zero,top),complement(composition(zero,top)))
| join(composition(zero,top),complement(composition(zero,top))) = top ),
inference(subst,[],[refute_1_17:[bind(X,$fot(top)),bind(Y,$fot(join(composition(zero,top),complement(composition(zero,top)))))]]) ).
cnf(refute_1_808,plain,
join(composition(zero,top),complement(composition(zero,top))) = top,
inference(resolve,[$cnf( $equal(top,join(composition(zero,top),complement(composition(zero,top)))) )],[refute_1_806,refute_1_807]) ).
cnf(refute_1_809,plain,
( join(complement(one),join(composition(zero,top),complement(composition(zero,top)))) != join(complement(one),complement(composition(zero,top)))
| join(composition(zero,top),complement(composition(zero,top))) != top
| join(complement(one),top) = join(complement(one),complement(composition(zero,top))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(one),join(composition(zero,top),complement(composition(zero,top)))),join(complement(one),complement(composition(zero,top)))) ),[0,1],$fot(top)]]) ).
cnf(refute_1_810,plain,
( join(complement(one),join(composition(zero,top),complement(composition(zero,top)))) != join(complement(one),complement(composition(zero,top)))
| join(complement(one),top) = join(complement(one),complement(composition(zero,top))) ),
inference(resolve,[$cnf( $equal(join(composition(zero,top),complement(composition(zero,top))),top) )],[refute_1_808,refute_1_809]) ).
cnf(refute_1_811,plain,
join(complement(one),top) = join(complement(one),complement(composition(zero,top))),
inference(resolve,[$cnf( $equal(join(complement(one),join(composition(zero,top),complement(composition(zero,top)))),join(complement(one),complement(composition(zero,top)))) )],[refute_1_805,refute_1_810]) ).
cnf(refute_1_812,plain,
( top != join(X_169,top)
| join(X_169,top) = top ),
inference(subst,[],[refute_1_17:[bind(X,$fot(top)),bind(Y,$fot(join(X_169,top)))]]) ).
cnf(refute_1_813,plain,
join(X_169,top) = top,
inference(resolve,[$cnf( $equal(top,join(X_169,top)) )],[refute_1_433,refute_1_812]) ).
cnf(refute_1_814,plain,
join(complement(one),top) = top,
inference(subst,[],[refute_1_813:[bind(X_169,$fot(complement(one)))]]) ).
cnf(refute_1_815,plain,
( join(complement(one),top) != join(complement(one),complement(composition(zero,top)))
| join(complement(one),top) != top
| top = join(complement(one),complement(composition(zero,top))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(one),top),join(complement(one),complement(composition(zero,top)))) ),[0],$fot(top)]]) ).
cnf(refute_1_816,plain,
( join(complement(one),top) != join(complement(one),complement(composition(zero,top)))
| top = join(complement(one),complement(composition(zero,top))) ),
inference(resolve,[$cnf( $equal(join(complement(one),top),top) )],[refute_1_814,refute_1_815]) ).
cnf(refute_1_817,plain,
join(complement(X0),complement(X1)) = join(zero,complement(complement(join(complement(X0),complement(X1))))),
inference(subst,[],[refute_1_492:[bind(X_176,$fot(join(complement(X0),complement(X1))))]]) ).
cnf(refute_1_818,plain,
( complement(join(complement(X0),complement(X1))) != meet(X0,X1)
| join(complement(X0),complement(X1)) != join(zero,complement(complement(join(complement(X0),complement(X1)))))
| join(complement(X0),complement(X1)) = join(zero,complement(meet(X0,X1))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X0),complement(X1)),join(zero,complement(complement(join(complement(X0),complement(X1)))))) ),[1,1,0],$fot(meet(X0,X1))]]) ).
cnf(refute_1_819,plain,
( join(complement(X0),complement(X1)) != join(zero,complement(complement(join(complement(X0),complement(X1)))))
| join(complement(X0),complement(X1)) = join(zero,complement(meet(X0,X1))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X0),complement(X1))),meet(X0,X1)) )],[refute_1_59,refute_1_818]) ).
cnf(refute_1_820,plain,
join(complement(X0),complement(X1)) = join(zero,complement(meet(X0,X1))),
inference(resolve,[$cnf( $equal(join(complement(X0),complement(X1)),join(zero,complement(complement(join(complement(X0),complement(X1)))))) )],[refute_1_817,refute_1_819]) ).
cnf(refute_1_821,plain,
join(zero,complement(meet(X0,X1))) = complement(meet(X0,X1)),
inference(subst,[],[refute_1_504:[bind(X_181,$fot(meet(X0,X1)))]]) ).
cnf(refute_1_822,plain,
( join(complement(X0),complement(X1)) != join(zero,complement(meet(X0,X1)))
| join(zero,complement(meet(X0,X1))) != complement(meet(X0,X1))
| join(complement(X0),complement(X1)) = complement(meet(X0,X1)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(complement(X0),complement(X1)),complement(meet(X0,X1))) ),[0],$fot(join(zero,complement(meet(X0,X1))))]]) ).
cnf(refute_1_823,plain,
( join(complement(X0),complement(X1)) != join(zero,complement(meet(X0,X1)))
| join(complement(X0),complement(X1)) = complement(meet(X0,X1)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(meet(X0,X1))),complement(meet(X0,X1))) )],[refute_1_821,refute_1_822]) ).
cnf(refute_1_824,plain,
join(complement(X0),complement(X1)) = complement(meet(X0,X1)),
inference(resolve,[$cnf( $equal(join(complement(X0),complement(X1)),join(zero,complement(meet(X0,X1)))) )],[refute_1_820,refute_1_823]) ).
cnf(refute_1_825,plain,
join(complement(one),complement(composition(zero,top))) = complement(meet(one,composition(zero,top))),
inference(subst,[],[refute_1_824:[bind(X0,$fot(one)),bind(X1,$fot(composition(zero,top)))]]) ).
cnf(refute_1_826,plain,
( join(complement(one),complement(composition(zero,top))) != complement(meet(one,composition(zero,top)))
| top != join(complement(one),complement(composition(zero,top)))
| top = complement(meet(one,composition(zero,top))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(one),complement(composition(zero,top)))) ),[1],$fot(complement(meet(one,composition(zero,top))))]]) ).
cnf(refute_1_827,plain,
( top != join(complement(one),complement(composition(zero,top)))
| top = complement(meet(one,composition(zero,top))) ),
inference(resolve,[$cnf( $equal(join(complement(one),complement(composition(zero,top))),complement(meet(one,composition(zero,top)))) )],[refute_1_825,refute_1_826]) ).
cnf(refute_1_828,plain,
( join(complement(one),top) != join(complement(one),complement(composition(zero,top)))
| top = complement(meet(one,composition(zero,top))) ),
inference(resolve,[$cnf( $equal(top,join(complement(one),complement(composition(zero,top)))) )],[refute_1_816,refute_1_827]) ).
cnf(refute_1_829,plain,
top = complement(meet(one,composition(zero,top))),
inference(resolve,[$cnf( $equal(join(complement(one),top),join(complement(one),complement(composition(zero,top)))) )],[refute_1_811,refute_1_828]) ).
cnf(refute_1_830,plain,
( top != complement(meet(one,composition(zero,top)))
| complement(meet(one,composition(zero,top))) = top ),
inference(subst,[],[refute_1_17:[bind(X,$fot(top)),bind(Y,$fot(complement(meet(one,composition(zero,top)))))]]) ).
cnf(refute_1_831,plain,
complement(meet(one,composition(zero,top))) = top,
inference(resolve,[$cnf( $equal(top,complement(meet(one,composition(zero,top)))) )],[refute_1_829,refute_1_830]) ).
cnf(refute_1_832,plain,
( complement(meet(one,composition(zero,top))) != top
| meet(one,composition(zero,top)) != complement(complement(meet(one,composition(zero,top))))
| meet(one,composition(zero,top)) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(meet(one,composition(zero,top)),complement(complement(meet(one,composition(zero,top))))) ),[1,0],$fot(top)]]) ).
cnf(refute_1_833,plain,
( meet(one,composition(zero,top)) != complement(complement(meet(one,composition(zero,top))))
| meet(one,composition(zero,top)) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(meet(one,composition(zero,top))),top) )],[refute_1_831,refute_1_832]) ).
cnf(refute_1_834,plain,
meet(one,composition(zero,top)) = complement(top),
inference(resolve,[$cnf( $equal(meet(one,composition(zero,top)),complement(complement(meet(one,composition(zero,top))))) )],[refute_1_766,refute_1_833]) ).
cnf(refute_1_835,plain,
( complement(top) != zero
| meet(one,composition(zero,top)) != complement(top)
| meet(one,composition(zero,top)) = zero ),
introduced(tautology,[equality,[$cnf( $equal(meet(one,composition(zero,top)),complement(top)) ),[1],$fot(zero)]]) ).
cnf(refute_1_836,plain,
( meet(one,composition(zero,top)) != complement(top)
| meet(one,composition(zero,top)) = zero ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_1_45,refute_1_835]) ).
cnf(refute_1_837,plain,
meet(one,composition(zero,top)) = zero,
inference(resolve,[$cnf( $equal(meet(one,composition(zero,top)),complement(top)) )],[refute_1_834,refute_1_836]) ).
cnf(refute_1_838,plain,
( meet(one,composition(zero,top)) != zero
| one != meet(one,join(complement(composition(zero,top)),meet(one,composition(zero,top))))
| one = meet(one,join(complement(composition(zero,top)),zero)) ),
introduced(tautology,[equality,[$cnf( $equal(one,meet(one,join(complement(composition(zero,top)),meet(one,composition(zero,top))))) ),[1,1,1],$fot(zero)]]) ).
cnf(refute_1_839,plain,
( one != meet(one,join(complement(composition(zero,top)),meet(one,composition(zero,top))))
| one = meet(one,join(complement(composition(zero,top)),zero)) ),
inference(resolve,[$cnf( $equal(meet(one,composition(zero,top)),zero) )],[refute_1_837,refute_1_838]) ).
cnf(refute_1_840,plain,
one = meet(one,join(complement(composition(zero,top)),zero)),
inference(resolve,[$cnf( $equal(one,meet(one,join(complement(composition(zero,top)),meet(one,composition(zero,top))))) )],[refute_1_765,refute_1_839]) ).
cnf(refute_1_841,plain,
X1 = join(meet(X1,X1),complement(join(complement(X1),X1))),
inference(subst,[],[refute_1_69:[bind(X0,$fot(X1))]]) ).
cnf(refute_1_842,plain,
meet(X1,X1) = X1,
inference(subst,[],[refute_1_563:[bind(X_138,$fot(X1))]]) ).
cnf(refute_1_843,plain,
( X1 != join(meet(X1,X1),complement(join(complement(X1),X1)))
| meet(X1,X1) != X1
| X1 = join(X1,complement(join(complement(X1),X1))) ),
introduced(tautology,[equality,[$cnf( $equal(X1,join(meet(X1,X1),complement(join(complement(X1),X1)))) ),[1,0],$fot(X1)]]) ).
cnf(refute_1_844,plain,
( X1 != join(meet(X1,X1),complement(join(complement(X1),X1)))
| X1 = join(X1,complement(join(complement(X1),X1))) ),
inference(resolve,[$cnf( $equal(meet(X1,X1),X1) )],[refute_1_842,refute_1_843]) ).
cnf(refute_1_845,plain,
X1 = join(X1,complement(join(complement(X1),X1))),
inference(resolve,[$cnf( $equal(X1,join(meet(X1,X1),complement(join(complement(X1),X1)))) )],[refute_1_841,refute_1_844]) ).
cnf(refute_1_846,plain,
join(X1,complement(X1)) = top,
inference(subst,[],[refute_1_25:[bind(X0,$fot(X1))]]) ).
cnf(refute_1_847,plain,
join(complement(X1),X1) = join(X1,complement(X1)),
inference(subst,[],[refute_1_52:[bind(X0,$fot(X1)),bind(X1,$fot(complement(X1)))]]) ).
cnf(refute_1_848,plain,
( join(X1,complement(X1)) != top
| join(complement(X1),X1) != join(X1,complement(X1))
| join(complement(X1),X1) = top ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(complement(X1),X1))),bind(Y,$fot(join(X1,complement(X1)))),bind(Z,$fot(top))]]) ).
cnf(refute_1_849,plain,
( join(X1,complement(X1)) != top
| join(complement(X1),X1) = top ),
inference(resolve,[$cnf( $equal(join(complement(X1),X1),join(X1,complement(X1))) )],[refute_1_847,refute_1_848]) ).
cnf(refute_1_850,plain,
join(complement(X1),X1) = top,
inference(resolve,[$cnf( $equal(join(X1,complement(X1)),top) )],[refute_1_846,refute_1_849]) ).
cnf(refute_1_851,plain,
complement(join(complement(X1),X1)) = complement(join(complement(X1),X1)),
introduced(tautology,[refl,[$fot(complement(join(complement(X1),X1)))]]) ).
cnf(refute_1_852,plain,
( complement(join(complement(X1),X1)) != complement(join(complement(X1),X1))
| join(complement(X1),X1) != top
| complement(join(complement(X1),X1)) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(X1),X1)),complement(join(complement(X1),X1))) ),[1,0],$fot(top)]]) ).
cnf(refute_1_853,plain,
( join(complement(X1),X1) != top
| complement(join(complement(X1),X1)) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X1),X1)),complement(join(complement(X1),X1))) )],[refute_1_851,refute_1_852]) ).
cnf(refute_1_854,plain,
complement(join(complement(X1),X1)) = complement(top),
inference(resolve,[$cnf( $equal(join(complement(X1),X1),top) )],[refute_1_850,refute_1_853]) ).
cnf(refute_1_855,plain,
( complement(join(complement(X1),X1)) != complement(top)
| complement(top) != zero
| complement(join(complement(X1),X1)) = zero ),
inference(subst,[],[refute_1_37:[bind(X,$fot(complement(join(complement(X1),X1)))),bind(Y,$fot(complement(top))),bind(Z,$fot(zero))]]) ).
cnf(refute_1_856,plain,
( complement(top) != zero
| complement(join(complement(X1),X1)) = zero ),
inference(resolve,[$cnf( $equal(complement(join(complement(X1),X1)),complement(top)) )],[refute_1_854,refute_1_855]) ).
cnf(refute_1_857,plain,
complement(join(complement(X1),X1)) = zero,
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_1_45,refute_1_856]) ).
cnf(refute_1_858,plain,
join(X1,complement(join(complement(X1),X1))) = join(X1,complement(join(complement(X1),X1))),
introduced(tautology,[refl,[$fot(join(X1,complement(join(complement(X1),X1))))]]) ).
cnf(refute_1_859,plain,
( complement(join(complement(X1),X1)) != zero
| join(X1,complement(join(complement(X1),X1))) != join(X1,complement(join(complement(X1),X1)))
| join(X1,complement(join(complement(X1),X1))) = join(X1,zero) ),
introduced(tautology,[equality,[$cnf( $equal(join(X1,complement(join(complement(X1),X1))),join(X1,complement(join(complement(X1),X1)))) ),[1,1],$fot(zero)]]) ).
cnf(refute_1_860,plain,
( complement(join(complement(X1),X1)) != zero
| join(X1,complement(join(complement(X1),X1))) = join(X1,zero) ),
inference(resolve,[$cnf( $equal(join(X1,complement(join(complement(X1),X1))),join(X1,complement(join(complement(X1),X1)))) )],[refute_1_858,refute_1_859]) ).
cnf(refute_1_861,plain,
join(X1,complement(join(complement(X1),X1))) = join(X1,zero),
inference(resolve,[$cnf( $equal(complement(join(complement(X1),X1)),zero) )],[refute_1_857,refute_1_860]) ).
cnf(refute_1_862,plain,
( X1 != join(X1,complement(join(complement(X1),X1)))
| join(X1,complement(join(complement(X1),X1))) != join(X1,zero)
| X1 = join(X1,zero) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X1,join(X1,zero)) ),[0],$fot(join(X1,complement(join(complement(X1),X1))))]]) ).
cnf(refute_1_863,plain,
( X1 != join(X1,complement(join(complement(X1),X1)))
| X1 = join(X1,zero) ),
inference(resolve,[$cnf( $equal(join(X1,complement(join(complement(X1),X1))),join(X1,zero)) )],[refute_1_861,refute_1_862]) ).
cnf(refute_1_864,plain,
X1 = join(X1,zero),
inference(resolve,[$cnf( $equal(X1,join(X1,complement(join(complement(X1),X1)))) )],[refute_1_845,refute_1_863]) ).
cnf(refute_1_865,plain,
( X1 != join(X1,zero)
| join(X1,zero) = X1 ),
inference(subst,[],[refute_1_17:[bind(X,$fot(X1)),bind(Y,$fot(join(X1,zero)))]]) ).
cnf(refute_1_866,plain,
join(X1,zero) = X1,
inference(resolve,[$cnf( $equal(X1,join(X1,zero)) )],[refute_1_864,refute_1_865]) ).
cnf(refute_1_867,plain,
join(complement(composition(zero,top)),zero) = complement(composition(zero,top)),
inference(subst,[],[refute_1_866:[bind(X1,$fot(complement(composition(zero,top))))]]) ).
cnf(refute_1_868,plain,
meet(one,join(complement(composition(zero,top)),zero)) = meet(one,join(complement(composition(zero,top)),zero)),
introduced(tautology,[refl,[$fot(meet(one,join(complement(composition(zero,top)),zero)))]]) ).
cnf(refute_1_869,plain,
( join(complement(composition(zero,top)),zero) != complement(composition(zero,top))
| meet(one,join(complement(composition(zero,top)),zero)) != meet(one,join(complement(composition(zero,top)),zero))
| meet(one,join(complement(composition(zero,top)),zero)) = meet(one,complement(composition(zero,top))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(one,join(complement(composition(zero,top)),zero)),meet(one,join(complement(composition(zero,top)),zero))) ),[1,1],$fot(complement(composition(zero,top)))]]) ).
cnf(refute_1_870,plain,
( join(complement(composition(zero,top)),zero) != complement(composition(zero,top))
| meet(one,join(complement(composition(zero,top)),zero)) = meet(one,complement(composition(zero,top))) ),
inference(resolve,[$cnf( $equal(meet(one,join(complement(composition(zero,top)),zero)),meet(one,join(complement(composition(zero,top)),zero))) )],[refute_1_868,refute_1_869]) ).
cnf(refute_1_871,plain,
meet(one,join(complement(composition(zero,top)),zero)) = meet(one,complement(composition(zero,top))),
inference(resolve,[$cnf( $equal(join(complement(composition(zero,top)),zero),complement(composition(zero,top))) )],[refute_1_867,refute_1_870]) ).
cnf(refute_1_872,plain,
( meet(one,join(complement(composition(zero,top)),zero)) != meet(one,complement(composition(zero,top)))
| one != meet(one,join(complement(composition(zero,top)),zero))
| one = meet(one,complement(composition(zero,top))) ),
introduced(tautology,[equality,[$cnf( $equal(one,meet(one,join(complement(composition(zero,top)),zero))) ),[1],$fot(meet(one,complement(composition(zero,top))))]]) ).
cnf(refute_1_873,plain,
( one != meet(one,join(complement(composition(zero,top)),zero))
| one = meet(one,complement(composition(zero,top))) ),
inference(resolve,[$cnf( $equal(meet(one,join(complement(composition(zero,top)),zero)),meet(one,complement(composition(zero,top)))) )],[refute_1_871,refute_1_872]) ).
cnf(refute_1_874,plain,
one = meet(one,complement(composition(zero,top))),
inference(resolve,[$cnf( $equal(one,meet(one,join(complement(composition(zero,top)),zero))) )],[refute_1_840,refute_1_873]) ).
cnf(refute_1_875,plain,
( one != meet(one,complement(composition(zero,top)))
| meet(one,complement(composition(zero,top))) = one ),
inference(subst,[],[refute_1_17:[bind(X,$fot(one)),bind(Y,$fot(meet(one,complement(composition(zero,top)))))]]) ).
cnf(refute_1_876,plain,
meet(one,complement(composition(zero,top))) = one,
inference(resolve,[$cnf( $equal(one,meet(one,complement(composition(zero,top)))) )],[refute_1_874,refute_1_875]) ).
cnf(refute_1_877,plain,
( complement(composition(zero,top)) != join(meet(one,complement(composition(zero,top))),complement(join(complement(complement(composition(zero,top))),one)))
| meet(one,complement(composition(zero,top))) != one
| complement(composition(zero,top)) = join(one,complement(join(complement(complement(composition(zero,top))),one))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(composition(zero,top)),join(meet(one,complement(composition(zero,top))),complement(join(complement(complement(composition(zero,top))),one)))) ),[1,0],$fot(one)]]) ).
cnf(refute_1_878,plain,
( complement(composition(zero,top)) != join(meet(one,complement(composition(zero,top))),complement(join(complement(complement(composition(zero,top))),one)))
| complement(composition(zero,top)) = join(one,complement(join(complement(complement(composition(zero,top))),one))) ),
inference(resolve,[$cnf( $equal(meet(one,complement(composition(zero,top))),one) )],[refute_1_876,refute_1_877]) ).
cnf(refute_1_879,plain,
complement(composition(zero,top)) = join(one,complement(join(complement(complement(composition(zero,top))),one))),
inference(resolve,[$cnf( $equal(complement(composition(zero,top)),join(meet(one,complement(composition(zero,top))),complement(join(complement(complement(composition(zero,top))),one)))) )],[refute_1_742,refute_1_878]) ).
cnf(refute_1_880,plain,
join(X_177,complement(X_176)) = join(complement(X_176),X_177),
inference(subst,[],[refute_1_50:[bind(X0,$fot(X_177)),bind(X1,$fot(complement(X_176)))]]) ).
cnf(refute_1_881,plain,
( join(X_177,complement(X_176)) != join(complement(X_176),X_177)
| join(complement(X_176),X_177) = join(X_177,complement(X_176)) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(join(X_177,complement(X_176)))),bind(Y,$fot(join(complement(X_176),X_177)))]]) ).
cnf(refute_1_882,plain,
join(complement(X_176),X_177) = join(X_177,complement(X_176)),
inference(resolve,[$cnf( $equal(join(X_177,complement(X_176)),join(complement(X_176),X_177)) )],[refute_1_880,refute_1_881]) ).
cnf(refute_1_883,plain,
( X_176 != join(meet(X_176,X_177),complement(join(complement(X_176),X_177)))
| join(complement(X_176),X_177) != join(X_177,complement(X_176))
| X_176 = join(meet(X_176,X_177),complement(join(X_177,complement(X_176)))) ),
introduced(tautology,[equality,[$cnf( $equal(X_176,join(meet(X_176,X_177),complement(join(complement(X_176),X_177)))) ),[1,1,0],$fot(join(X_177,complement(X_176)))]]) ).
cnf(refute_1_884,plain,
( X_176 != join(meet(X_176,X_177),complement(join(complement(X_176),X_177)))
| X_176 = join(meet(X_176,X_177),complement(join(X_177,complement(X_176)))) ),
inference(resolve,[$cnf( $equal(join(complement(X_176),X_177),join(X_177,complement(X_176))) )],[refute_1_882,refute_1_883]) ).
cnf(refute_1_885,plain,
X_176 = join(meet(X_176,X_177),complement(join(X_177,complement(X_176)))),
inference(resolve,[$cnf( $equal(X_176,join(meet(X_176,X_177),complement(join(complement(X_176),X_177)))) )],[refute_1_677,refute_1_884]) ).
cnf(refute_1_886,plain,
join(one,complement(composition(zero,top))) = join(meet(join(one,complement(composition(zero,top))),one),complement(join(one,complement(join(one,complement(composition(zero,top))))))),
inference(subst,[],[refute_1_885:[bind(X_176,$fot(join(one,complement(composition(zero,top))))),bind(X_177,$fot(one))]]) ).
cnf(refute_1_887,plain,
join(one,join(meet(one,composition(zero,top)),X_212)) = join(join(one,meet(one,composition(zero,top))),X_212),
inference(subst,[],[refute_1_100:[bind(X0,$fot(one)),bind(X1,$fot(meet(one,composition(zero,top)))),bind(X2,$fot(X_212))]]) ).
cnf(refute_1_888,plain,
one = join(meet(one,composition(zero,top)),complement(join(complement(one),composition(zero,top)))),
inference(subst,[],[refute_1_69:[bind(X0,$fot(one)),bind(X1,$fot(composition(zero,top)))]]) ).
cnf(refute_1_889,plain,
( join(complement(one),composition(zero,top)) != complement(one)
| one != join(meet(one,composition(zero,top)),complement(join(complement(one),composition(zero,top))))
| one = join(meet(one,composition(zero,top)),complement(complement(one))) ),
introduced(tautology,[equality,[$cnf( $equal(one,join(meet(one,composition(zero,top)),complement(join(complement(one),composition(zero,top))))) ),[1,1,0],$fot(complement(one))]]) ).
cnf(refute_1_890,plain,
( one != join(meet(one,composition(zero,top)),complement(join(complement(one),composition(zero,top))))
| one = join(meet(one,composition(zero,top)),complement(complement(one))) ),
inference(resolve,[$cnf( $equal(join(complement(one),composition(zero,top)),complement(one)) )],[refute_1_801,refute_1_889]) ).
cnf(refute_1_891,plain,
one = join(meet(one,composition(zero,top)),complement(complement(one))),
inference(resolve,[$cnf( $equal(one,join(meet(one,composition(zero,top)),complement(join(complement(one),composition(zero,top))))) )],[refute_1_888,refute_1_890]) ).
cnf(refute_1_892,plain,
complement(complement(one)) = one,
inference(subst,[],[refute_1_518:[bind(X_176,$fot(one))]]) ).
cnf(refute_1_893,plain,
join(complement(complement(one)),meet(one,composition(zero,top))) = join(complement(complement(one)),meet(one,composition(zero,top))),
introduced(tautology,[refl,[$fot(join(complement(complement(one)),meet(one,composition(zero,top))))]]) ).
cnf(refute_1_894,plain,
( complement(complement(one)) != one
| join(complement(complement(one)),meet(one,composition(zero,top))) != join(complement(complement(one)),meet(one,composition(zero,top)))
| join(complement(complement(one)),meet(one,composition(zero,top))) = join(one,meet(one,composition(zero,top))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(complement(one)),meet(one,composition(zero,top))),join(complement(complement(one)),meet(one,composition(zero,top)))) ),[1,0],$fot(one)]]) ).
cnf(refute_1_895,plain,
( complement(complement(one)) != one
| join(complement(complement(one)),meet(one,composition(zero,top))) = join(one,meet(one,composition(zero,top))) ),
inference(resolve,[$cnf( $equal(join(complement(complement(one)),meet(one,composition(zero,top))),join(complement(complement(one)),meet(one,composition(zero,top)))) )],[refute_1_893,refute_1_894]) ).
cnf(refute_1_896,plain,
join(complement(complement(one)),meet(one,composition(zero,top))) = join(one,meet(one,composition(zero,top))),
inference(resolve,[$cnf( $equal(complement(complement(one)),one) )],[refute_1_892,refute_1_895]) ).
cnf(refute_1_897,plain,
join(meet(one,composition(zero,top)),complement(complement(one))) = join(complement(complement(one)),meet(one,composition(zero,top))),
inference(subst,[],[refute_1_52:[bind(X0,$fot(complement(complement(one)))),bind(X1,$fot(meet(one,composition(zero,top))))]]) ).
cnf(refute_1_898,plain,
( join(complement(complement(one)),meet(one,composition(zero,top))) != join(one,meet(one,composition(zero,top)))
| join(meet(one,composition(zero,top)),complement(complement(one))) != join(complement(complement(one)),meet(one,composition(zero,top)))
| join(meet(one,composition(zero,top)),complement(complement(one))) = join(one,meet(one,composition(zero,top))) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(meet(one,composition(zero,top)),complement(complement(one))))),bind(Y,$fot(join(complement(complement(one)),meet(one,composition(zero,top))))),bind(Z,$fot(join(one,meet(one,composition(zero,top)))))]]) ).
cnf(refute_1_899,plain,
( join(complement(complement(one)),meet(one,composition(zero,top))) != join(one,meet(one,composition(zero,top)))
| join(meet(one,composition(zero,top)),complement(complement(one))) = join(one,meet(one,composition(zero,top))) ),
inference(resolve,[$cnf( $equal(join(meet(one,composition(zero,top)),complement(complement(one))),join(complement(complement(one)),meet(one,composition(zero,top)))) )],[refute_1_897,refute_1_898]) ).
cnf(refute_1_900,plain,
join(meet(one,composition(zero,top)),complement(complement(one))) = join(one,meet(one,composition(zero,top))),
inference(resolve,[$cnf( $equal(join(complement(complement(one)),meet(one,composition(zero,top))),join(one,meet(one,composition(zero,top)))) )],[refute_1_896,refute_1_899]) ).
cnf(refute_1_901,plain,
( join(meet(one,composition(zero,top)),complement(complement(one))) != join(one,meet(one,composition(zero,top)))
| one != join(meet(one,composition(zero,top)),complement(complement(one)))
| one = join(one,meet(one,composition(zero,top))) ),
introduced(tautology,[equality,[$cnf( $equal(one,join(meet(one,composition(zero,top)),complement(complement(one)))) ),[1],$fot(join(one,meet(one,composition(zero,top))))]]) ).
cnf(refute_1_902,plain,
( one != join(meet(one,composition(zero,top)),complement(complement(one)))
| one = join(one,meet(one,composition(zero,top))) ),
inference(resolve,[$cnf( $equal(join(meet(one,composition(zero,top)),complement(complement(one))),join(one,meet(one,composition(zero,top)))) )],[refute_1_900,refute_1_901]) ).
cnf(refute_1_903,plain,
one = join(one,meet(one,composition(zero,top))),
inference(resolve,[$cnf( $equal(one,join(meet(one,composition(zero,top)),complement(complement(one)))) )],[refute_1_891,refute_1_902]) ).
cnf(refute_1_904,plain,
( one != join(one,meet(one,composition(zero,top)))
| join(one,meet(one,composition(zero,top))) = one ),
inference(subst,[],[refute_1_17:[bind(X,$fot(one)),bind(Y,$fot(join(one,meet(one,composition(zero,top)))))]]) ).
cnf(refute_1_905,plain,
join(one,meet(one,composition(zero,top))) = one,
inference(resolve,[$cnf( $equal(one,join(one,meet(one,composition(zero,top)))) )],[refute_1_903,refute_1_904]) ).
cnf(refute_1_906,plain,
( join(one,join(meet(one,composition(zero,top)),X_212)) != join(join(one,meet(one,composition(zero,top))),X_212)
| join(one,meet(one,composition(zero,top))) != one
| join(one,join(meet(one,composition(zero,top)),X_212)) = join(one,X_212) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(meet(one,composition(zero,top)),X_212)),join(join(one,meet(one,composition(zero,top))),X_212)) ),[1,0],$fot(one)]]) ).
cnf(refute_1_907,plain,
( join(one,join(meet(one,composition(zero,top)),X_212)) != join(join(one,meet(one,composition(zero,top))),X_212)
| join(one,join(meet(one,composition(zero,top)),X_212)) = join(one,X_212) ),
inference(resolve,[$cnf( $equal(join(one,meet(one,composition(zero,top))),one) )],[refute_1_905,refute_1_906]) ).
cnf(refute_1_908,plain,
join(one,join(meet(one,composition(zero,top)),X_212)) = join(one,X_212),
inference(resolve,[$cnf( $equal(join(one,join(meet(one,composition(zero,top)),X_212)),join(join(one,meet(one,composition(zero,top))),X_212)) )],[refute_1_887,refute_1_907]) ).
cnf(refute_1_909,plain,
join(one,join(meet(one,composition(zero,top)),complement(join(complement(composition(zero,top)),one)))) = join(one,complement(join(complement(composition(zero,top)),one))),
inference(subst,[],[refute_1_908:[bind(X_212,$fot(complement(join(complement(composition(zero,top)),one))))]]) ).
cnf(refute_1_910,plain,
composition(zero,top) = join(meet(one,composition(zero,top)),complement(join(complement(composition(zero,top)),one))),
inference(subst,[],[refute_1_683:[bind(X_176,$fot(composition(zero,top))),bind(X_177,$fot(one))]]) ).
cnf(refute_1_911,plain,
( composition(zero,top) != join(meet(one,composition(zero,top)),complement(join(complement(composition(zero,top)),one)))
| join(meet(one,composition(zero,top)),complement(join(complement(composition(zero,top)),one))) = composition(zero,top) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(composition(zero,top))),bind(Y,$fot(join(meet(one,composition(zero,top)),complement(join(complement(composition(zero,top)),one)))))]]) ).
cnf(refute_1_912,plain,
join(meet(one,composition(zero,top)),complement(join(complement(composition(zero,top)),one))) = composition(zero,top),
inference(resolve,[$cnf( $equal(composition(zero,top),join(meet(one,composition(zero,top)),complement(join(complement(composition(zero,top)),one)))) )],[refute_1_910,refute_1_911]) ).
cnf(refute_1_913,plain,
( join(meet(one,composition(zero,top)),complement(join(complement(composition(zero,top)),one))) != composition(zero,top)
| join(one,join(meet(one,composition(zero,top)),complement(join(complement(composition(zero,top)),one)))) != join(one,complement(join(complement(composition(zero,top)),one)))
| join(one,composition(zero,top)) = join(one,complement(join(complement(composition(zero,top)),one))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(meet(one,composition(zero,top)),complement(join(complement(composition(zero,top)),one)))),join(one,complement(join(complement(composition(zero,top)),one)))) ),[0,1],$fot(composition(zero,top))]]) ).
cnf(refute_1_914,plain,
( join(one,join(meet(one,composition(zero,top)),complement(join(complement(composition(zero,top)),one)))) != join(one,complement(join(complement(composition(zero,top)),one)))
| join(one,composition(zero,top)) = join(one,complement(join(complement(composition(zero,top)),one))) ),
inference(resolve,[$cnf( $equal(join(meet(one,composition(zero,top)),complement(join(complement(composition(zero,top)),one))),composition(zero,top)) )],[refute_1_912,refute_1_913]) ).
cnf(refute_1_915,plain,
join(one,composition(zero,top)) = join(one,complement(join(complement(composition(zero,top)),one))),
inference(resolve,[$cnf( $equal(join(one,join(meet(one,composition(zero,top)),complement(join(complement(composition(zero,top)),one)))),join(one,complement(join(complement(composition(zero,top)),one)))) )],[refute_1_909,refute_1_914]) ).
cnf(refute_1_916,plain,
converse(join(converse(X0),join(one,one))) = join(X0,converse(join(one,one))),
inference(subst,[],[refute_1_75:[bind(X_110,$fot(join(one,one)))]]) ).
cnf(refute_1_917,plain,
( converse(join(converse(X0),join(one,one))) != join(X0,converse(join(one,one)))
| converse(join(one,one)) != join(one,one)
| converse(join(converse(X0),join(one,one))) = join(X0,join(one,one)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(X0),join(one,one))),join(X0,converse(join(one,one)))) ),[1,1],$fot(join(one,one))]]) ).
cnf(refute_1_918,plain,
( converse(join(converse(X0),join(one,one))) != join(X0,converse(join(one,one)))
| converse(join(converse(X0),join(one,one))) = join(X0,join(one,one)) ),
inference(resolve,[$cnf( $equal(converse(join(one,one)),join(one,one)) )],[refute_1_355,refute_1_917]) ).
cnf(refute_1_919,plain,
converse(join(converse(X0),join(one,one))) = join(X0,join(one,one)),
inference(resolve,[$cnf( $equal(converse(join(converse(X0),join(one,one))),join(X0,converse(join(one,one)))) )],[refute_1_916,refute_1_918]) ).
cnf(refute_1_920,plain,
join(converse(one),X0) = join(converse(one),X0),
introduced(tautology,[refl,[$fot(join(converse(one),X0))]]) ).
cnf(refute_1_921,plain,
( converse(one) != one
| join(converse(one),X0) != join(converse(one),X0)
| join(converse(one),X0) = join(one,X0) ),
introduced(tautology,[equality,[$cnf( $equal(join(converse(one),X0),join(converse(one),X0)) ),[1,0],$fot(one)]]) ).
cnf(refute_1_922,plain,
( converse(one) != one
| join(converse(one),X0) = join(one,X0) ),
inference(resolve,[$cnf( $equal(join(converse(one),X0),join(converse(one),X0)) )],[refute_1_920,refute_1_921]) ).
cnf(refute_1_923,plain,
join(converse(one),X0) = join(one,X0),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_1_136,refute_1_922]) ).
cnf(refute_1_924,plain,
join(one,join(converse(one),X0)) = join(one,join(converse(one),X0)),
introduced(tautology,[refl,[$fot(join(one,join(converse(one),X0)))]]) ).
cnf(refute_1_925,plain,
( join(converse(one),X0) != join(one,X0)
| join(one,join(converse(one),X0)) != join(one,join(converse(one),X0))
| join(one,join(converse(one),X0)) = join(one,join(one,X0)) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(converse(one),X0)),join(one,join(converse(one),X0))) ),[1,1],$fot(join(one,X0))]]) ).
cnf(refute_1_926,plain,
( join(converse(one),X0) != join(one,X0)
| join(one,join(converse(one),X0)) = join(one,join(one,X0)) ),
inference(resolve,[$cnf( $equal(join(one,join(converse(one),X0)),join(one,join(converse(one),X0))) )],[refute_1_924,refute_1_925]) ).
cnf(refute_1_927,plain,
join(one,join(converse(one),X0)) = join(one,join(one,X0)),
inference(resolve,[$cnf( $equal(join(converse(one),X0),join(one,X0)) )],[refute_1_923,refute_1_926]) ).
cnf(refute_1_928,plain,
converse(join(one,join(X_109,converse(X0)))) = join(one,converse(join(X_109,converse(X0)))),
inference(subst,[],[refute_1_351:[bind(X_110,$fot(join(X_109,converse(X0))))]]) ).
cnf(refute_1_929,plain,
( converse(join(X_109,converse(X0))) != join(converse(X_109),X0)
| converse(join(one,join(X_109,converse(X0)))) != join(one,converse(join(X_109,converse(X0))))
| converse(join(one,join(X_109,converse(X0)))) = join(one,join(converse(X_109),X0)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(one,join(X_109,converse(X0)))),join(one,converse(join(X_109,converse(X0))))) ),[1,1],$fot(join(converse(X_109),X0))]]) ).
cnf(refute_1_930,plain,
( converse(join(one,join(X_109,converse(X0)))) != join(one,converse(join(X_109,converse(X0))))
| converse(join(one,join(X_109,converse(X0)))) = join(one,join(converse(X_109),X0)) ),
inference(resolve,[$cnf( $equal(converse(join(X_109,converse(X0))),join(converse(X_109),X0)) )],[refute_1_203,refute_1_929]) ).
cnf(refute_1_931,plain,
converse(join(one,join(X_109,converse(X0)))) = join(one,join(converse(X_109),X0)),
inference(resolve,[$cnf( $equal(converse(join(one,join(X_109,converse(X0)))),join(one,converse(join(X_109,converse(X0))))) )],[refute_1_928,refute_1_930]) ).
cnf(refute_1_932,plain,
converse(join(one,join(one,converse(X0)))) = join(one,join(converse(one),X0)),
inference(subst,[],[refute_1_931:[bind(X_109,$fot(one))]]) ).
cnf(refute_1_933,plain,
converse(join(one,join(X1,X0))) = join(one,converse(join(X1,X0))),
inference(subst,[],[refute_1_351:[bind(X_110,$fot(join(X1,X0)))]]) ).
cnf(refute_1_934,plain,
( converse(join(X0,X1)) != converse(join(X1,X0))
| converse(join(X1,X0)) = converse(join(X0,X1)) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(converse(join(X0,X1)))),bind(Y,$fot(converse(join(X1,X0))))]]) ).
cnf(refute_1_935,plain,
converse(join(X1,X0)) = converse(join(X0,X1)),
inference(resolve,[$cnf( $equal(converse(join(X0,X1)),converse(join(X1,X0))) )],[refute_1_95,refute_1_934]) ).
cnf(refute_1_936,plain,
( converse(join(X1,X0)) != converse(join(X0,X1))
| converse(join(one,join(X1,X0))) != join(one,converse(join(X1,X0)))
| converse(join(one,join(X1,X0))) = join(one,converse(join(X0,X1))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(one,join(X1,X0))),join(one,converse(join(X1,X0)))) ),[1,1],$fot(converse(join(X0,X1)))]]) ).
cnf(refute_1_937,plain,
( converse(join(one,join(X1,X0))) != join(one,converse(join(X1,X0)))
| converse(join(one,join(X1,X0))) = join(one,converse(join(X0,X1))) ),
inference(resolve,[$cnf( $equal(converse(join(X1,X0)),converse(join(X0,X1))) )],[refute_1_935,refute_1_936]) ).
cnf(refute_1_938,plain,
converse(join(one,join(X1,X0))) = join(one,converse(join(X0,X1))),
inference(resolve,[$cnf( $equal(converse(join(one,join(X1,X0))),join(one,converse(join(X1,X0)))) )],[refute_1_933,refute_1_937]) ).
cnf(refute_1_939,plain,
join(one,converse(join(X0,X1))) = converse(join(one,join(X0,X1))),
inference(subst,[],[refute_1_360:[bind(X_110,$fot(join(X0,X1)))]]) ).
cnf(refute_1_940,plain,
( converse(join(one,join(X1,X0))) != join(one,converse(join(X0,X1)))
| join(one,converse(join(X0,X1))) != converse(join(one,join(X0,X1)))
| converse(join(one,join(X1,X0))) = converse(join(one,join(X0,X1))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(join(one,join(X1,X0))),converse(join(one,join(X0,X1)))) ),[0],$fot(join(one,converse(join(X0,X1))))]]) ).
cnf(refute_1_941,plain,
( converse(join(one,join(X1,X0))) != join(one,converse(join(X0,X1)))
| converse(join(one,join(X1,X0))) = converse(join(one,join(X0,X1))) ),
inference(resolve,[$cnf( $equal(join(one,converse(join(X0,X1))),converse(join(one,join(X0,X1)))) )],[refute_1_939,refute_1_940]) ).
cnf(refute_1_942,plain,
converse(join(one,join(X1,X0))) = converse(join(one,join(X0,X1))),
inference(resolve,[$cnf( $equal(converse(join(one,join(X1,X0))),join(one,converse(join(X0,X1)))) )],[refute_1_938,refute_1_941]) ).
cnf(refute_1_943,plain,
( converse(join(one,join(X1,X0))) != converse(join(one,join(X0,X1)))
| converse(join(one,join(X0,X1))) = converse(join(one,join(X1,X0))) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(converse(join(one,join(X1,X0))))),bind(Y,$fot(converse(join(one,join(X0,X1)))))]]) ).
cnf(refute_1_944,plain,
converse(join(one,join(X0,X1))) = converse(join(one,join(X1,X0))),
inference(resolve,[$cnf( $equal(converse(join(one,join(X1,X0))),converse(join(one,join(X0,X1)))) )],[refute_1_942,refute_1_943]) ).
cnf(refute_1_945,plain,
converse(join(one,join(converse(X0),one))) = converse(join(one,join(one,converse(X0)))),
inference(subst,[],[refute_1_944:[bind(X0,$fot(converse(X0))),bind(X1,$fot(one))]]) ).
cnf(refute_1_946,plain,
( converse(join(one,join(converse(X0),one))) != converse(join(one,join(one,converse(X0))))
| converse(join(one,join(one,converse(X0)))) != join(one,join(converse(one),X0))
| converse(join(one,join(converse(X0),one))) = join(one,join(converse(one),X0)) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(converse(join(one,join(converse(X0),one))))),bind(Y,$fot(converse(join(one,join(one,converse(X0)))))),bind(Z,$fot(join(one,join(converse(one),X0))))]]) ).
cnf(refute_1_947,plain,
( converse(join(one,join(one,converse(X0)))) != join(one,join(converse(one),X0))
| converse(join(one,join(converse(X0),one))) = join(one,join(converse(one),X0)) ),
inference(resolve,[$cnf( $equal(converse(join(one,join(converse(X0),one))),converse(join(one,join(one,converse(X0))))) )],[refute_1_945,refute_1_946]) ).
cnf(refute_1_948,plain,
converse(join(one,join(converse(X0),one))) = join(one,join(converse(one),X0)),
inference(resolve,[$cnf( $equal(converse(join(one,join(one,converse(X0)))),join(one,join(converse(one),X0))) )],[refute_1_932,refute_1_947]) ).
cnf(refute_1_949,plain,
converse(join(join(X_120,X_121),X1)) = join(converse(join(X_120,X_121)),converse(X1)),
inference(subst,[],[refute_1_71:[bind(X0,$fot(join(X_120,X_121)))]]) ).
cnf(refute_1_950,plain,
( converse(join(X_120,X_121)) != converse(join(X_121,X_120))
| converse(join(join(X_120,X_121),X1)) != join(converse(join(X_120,X_121)),converse(X1))
| converse(join(join(X_120,X_121),X1)) = join(converse(join(X_121,X_120)),converse(X1)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(join(X_120,X_121),X1)),join(converse(join(X_120,X_121)),converse(X1))) ),[1,0],$fot(converse(join(X_121,X_120)))]]) ).
cnf(refute_1_951,plain,
( converse(join(join(X_120,X_121),X1)) != join(converse(join(X_120,X_121)),converse(X1))
| converse(join(join(X_120,X_121),X1)) = join(converse(join(X_121,X_120)),converse(X1)) ),
inference(resolve,[$cnf( $equal(converse(join(X_120,X_121)),converse(join(X_121,X_120))) )],[refute_1_96,refute_1_950]) ).
cnf(refute_1_952,plain,
converse(join(join(X_120,X_121),X1)) = join(converse(join(X_121,X_120)),converse(X1)),
inference(resolve,[$cnf( $equal(converse(join(join(X_120,X_121),X1)),join(converse(join(X_120,X_121)),converse(X1))) )],[refute_1_949,refute_1_951]) ).
cnf(refute_1_953,plain,
join(join(X_120,X_121),X1) = join(X_120,join(X_121,X1)),
inference(subst,[],[refute_1_102:[bind(X0,$fot(X_120)),bind(X1,$fot(X_121)),bind(X2,$fot(X1))]]) ).
cnf(refute_1_954,plain,
converse(join(join(X_120,X_121),X1)) = converse(join(join(X_120,X_121),X1)),
introduced(tautology,[refl,[$fot(converse(join(join(X_120,X_121),X1)))]]) ).
cnf(refute_1_955,plain,
( converse(join(join(X_120,X_121),X1)) != converse(join(join(X_120,X_121),X1))
| join(join(X_120,X_121),X1) != join(X_120,join(X_121,X1))
| converse(join(join(X_120,X_121),X1)) = converse(join(X_120,join(X_121,X1))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(join(X_120,X_121),X1)),converse(join(join(X_120,X_121),X1))) ),[1,0],$fot(join(X_120,join(X_121,X1)))]]) ).
cnf(refute_1_956,plain,
( join(join(X_120,X_121),X1) != join(X_120,join(X_121,X1))
| converse(join(join(X_120,X_121),X1)) = converse(join(X_120,join(X_121,X1))) ),
inference(resolve,[$cnf( $equal(converse(join(join(X_120,X_121),X1)),converse(join(join(X_120,X_121),X1))) )],[refute_1_954,refute_1_955]) ).
cnf(refute_1_957,plain,
converse(join(join(X_120,X_121),X1)) = converse(join(X_120,join(X_121,X1))),
inference(resolve,[$cnf( $equal(join(join(X_120,X_121),X1),join(X_120,join(X_121,X1))) )],[refute_1_953,refute_1_956]) ).
cnf(refute_1_958,plain,
( converse(join(join(X_120,X_121),X1)) != converse(join(X_120,join(X_121,X1)))
| converse(join(join(X_120,X_121),X1)) != join(converse(join(X_121,X_120)),converse(X1))
| converse(join(X_120,join(X_121,X1))) = join(converse(join(X_121,X_120)),converse(X1)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(join(X_120,X_121),X1)),join(converse(join(X_121,X_120)),converse(X1))) ),[0],$fot(converse(join(X_120,join(X_121,X1))))]]) ).
cnf(refute_1_959,plain,
( converse(join(join(X_120,X_121),X1)) != join(converse(join(X_121,X_120)),converse(X1))
| converse(join(X_120,join(X_121,X1))) = join(converse(join(X_121,X_120)),converse(X1)) ),
inference(resolve,[$cnf( $equal(converse(join(join(X_120,X_121),X1)),converse(join(X_120,join(X_121,X1)))) )],[refute_1_957,refute_1_958]) ).
cnf(refute_1_960,plain,
join(join(X_121,X_120),X1) = join(X_121,join(X_120,X1)),
inference(subst,[],[refute_1_102:[bind(X0,$fot(X_121)),bind(X1,$fot(X_120)),bind(X2,$fot(X1))]]) ).
cnf(refute_1_961,plain,
converse(join(join(X_121,X_120),X1)) = converse(join(join(X_121,X_120),X1)),
introduced(tautology,[refl,[$fot(converse(join(join(X_121,X_120),X1)))]]) ).
cnf(refute_1_962,plain,
( converse(join(join(X_121,X_120),X1)) != converse(join(join(X_121,X_120),X1))
| join(join(X_121,X_120),X1) != join(X_121,join(X_120,X1))
| converse(join(join(X_121,X_120),X1)) = converse(join(X_121,join(X_120,X1))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(join(X_121,X_120),X1)),converse(join(join(X_121,X_120),X1))) ),[1,0],$fot(join(X_121,join(X_120,X1)))]]) ).
cnf(refute_1_963,plain,
( join(join(X_121,X_120),X1) != join(X_121,join(X_120,X1))
| converse(join(join(X_121,X_120),X1)) = converse(join(X_121,join(X_120,X1))) ),
inference(resolve,[$cnf( $equal(converse(join(join(X_121,X_120),X1)),converse(join(join(X_121,X_120),X1))) )],[refute_1_961,refute_1_962]) ).
cnf(refute_1_964,plain,
converse(join(join(X_121,X_120),X1)) = converse(join(X_121,join(X_120,X1))),
inference(resolve,[$cnf( $equal(join(join(X_121,X_120),X1),join(X_121,join(X_120,X1))) )],[refute_1_960,refute_1_963]) ).
cnf(refute_1_965,plain,
join(converse(join(X_121,X_120)),converse(X1)) = converse(join(join(X_121,X_120),X1)),
inference(subst,[],[refute_1_91:[bind(X0,$fot(join(X_121,X_120)))]]) ).
cnf(refute_1_966,plain,
( converse(join(join(X_121,X_120),X1)) != converse(join(X_121,join(X_120,X1)))
| join(converse(join(X_121,X_120)),converse(X1)) != converse(join(join(X_121,X_120),X1))
| join(converse(join(X_121,X_120)),converse(X1)) = converse(join(X_121,join(X_120,X1))) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(converse(join(X_121,X_120)),converse(X1)))),bind(Y,$fot(converse(join(join(X_121,X_120),X1)))),bind(Z,$fot(converse(join(X_121,join(X_120,X1)))))]]) ).
cnf(refute_1_967,plain,
( converse(join(join(X_121,X_120),X1)) != converse(join(X_121,join(X_120,X1)))
| join(converse(join(X_121,X_120)),converse(X1)) = converse(join(X_121,join(X_120,X1))) ),
inference(resolve,[$cnf( $equal(join(converse(join(X_121,X_120)),converse(X1)),converse(join(join(X_121,X_120),X1))) )],[refute_1_965,refute_1_966]) ).
cnf(refute_1_968,plain,
join(converse(join(X_121,X_120)),converse(X1)) = converse(join(X_121,join(X_120,X1))),
inference(resolve,[$cnf( $equal(converse(join(join(X_121,X_120),X1)),converse(join(X_121,join(X_120,X1)))) )],[refute_1_964,refute_1_967]) ).
cnf(refute_1_969,plain,
( converse(join(X_120,join(X_121,X1))) != join(converse(join(X_121,X_120)),converse(X1))
| join(converse(join(X_121,X_120)),converse(X1)) != converse(join(X_121,join(X_120,X1)))
| converse(join(X_120,join(X_121,X1))) = converse(join(X_121,join(X_120,X1))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(join(X_120,join(X_121,X1))),converse(join(X_121,join(X_120,X1)))) ),[0],$fot(join(converse(join(X_121,X_120)),converse(X1)))]]) ).
cnf(refute_1_970,plain,
( converse(join(X_120,join(X_121,X1))) != join(converse(join(X_121,X_120)),converse(X1))
| converse(join(X_120,join(X_121,X1))) = converse(join(X_121,join(X_120,X1))) ),
inference(resolve,[$cnf( $equal(join(converse(join(X_121,X_120)),converse(X1)),converse(join(X_121,join(X_120,X1)))) )],[refute_1_968,refute_1_969]) ).
cnf(refute_1_971,plain,
( converse(join(join(X_120,X_121),X1)) != join(converse(join(X_121,X_120)),converse(X1))
| converse(join(X_120,join(X_121,X1))) = converse(join(X_121,join(X_120,X1))) ),
inference(resolve,[$cnf( $equal(converse(join(X_120,join(X_121,X1))),join(converse(join(X_121,X_120)),converse(X1))) )],[refute_1_959,refute_1_970]) ).
cnf(refute_1_972,plain,
converse(join(X_120,join(X_121,X1))) = converse(join(X_121,join(X_120,X1))),
inference(resolve,[$cnf( $equal(converse(join(join(X_120,X_121),X1)),join(converse(join(X_121,X_120)),converse(X1))) )],[refute_1_952,refute_1_971]) ).
cnf(refute_1_973,plain,
( converse(join(X_120,join(X_121,X1))) != converse(join(X_121,join(X_120,X1)))
| converse(join(X_121,join(X_120,X1))) = converse(join(X_120,join(X_121,X1))) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(converse(join(X_120,join(X_121,X1))))),bind(Y,$fot(converse(join(X_121,join(X_120,X1)))))]]) ).
cnf(refute_1_974,plain,
converse(join(X_121,join(X_120,X1))) = converse(join(X_120,join(X_121,X1))),
inference(resolve,[$cnf( $equal(converse(join(X_120,join(X_121,X1))),converse(join(X_121,join(X_120,X1)))) )],[refute_1_972,refute_1_973]) ).
cnf(refute_1_975,plain,
converse(join(converse(X0),join(one,one))) = converse(join(one,join(converse(X0),one))),
inference(subst,[],[refute_1_974:[bind(X1,$fot(one)),bind(X_120,$fot(one)),bind(X_121,$fot(converse(X0)))]]) ).
cnf(refute_1_976,plain,
( converse(join(converse(X0),join(one,one))) != converse(join(one,join(converse(X0),one)))
| converse(join(one,join(converse(X0),one))) != join(one,join(converse(one),X0))
| converse(join(converse(X0),join(one,one))) = join(one,join(converse(one),X0)) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(converse(join(converse(X0),join(one,one))))),bind(Y,$fot(converse(join(one,join(converse(X0),one))))),bind(Z,$fot(join(one,join(converse(one),X0))))]]) ).
cnf(refute_1_977,plain,
( converse(join(one,join(converse(X0),one))) != join(one,join(converse(one),X0))
| converse(join(converse(X0),join(one,one))) = join(one,join(converse(one),X0)) ),
inference(resolve,[$cnf( $equal(converse(join(converse(X0),join(one,one))),converse(join(one,join(converse(X0),one)))) )],[refute_1_975,refute_1_976]) ).
cnf(refute_1_978,plain,
converse(join(converse(X0),join(one,one))) = join(one,join(converse(one),X0)),
inference(resolve,[$cnf( $equal(converse(join(one,join(converse(X0),one))),join(one,join(converse(one),X0))) )],[refute_1_948,refute_1_977]) ).
cnf(refute_1_979,plain,
( converse(join(converse(X0),join(one,one))) != join(one,join(converse(one),X0))
| join(one,join(converse(one),X0)) != join(one,join(one,X0))
| converse(join(converse(X0),join(one,one))) = join(one,join(one,X0)) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(converse(join(converse(X0),join(one,one))))),bind(Y,$fot(join(one,join(converse(one),X0)))),bind(Z,$fot(join(one,join(one,X0))))]]) ).
cnf(refute_1_980,plain,
( join(one,join(converse(one),X0)) != join(one,join(one,X0))
| converse(join(converse(X0),join(one,one))) = join(one,join(one,X0)) ),
inference(resolve,[$cnf( $equal(converse(join(converse(X0),join(one,one))),join(one,join(converse(one),X0))) )],[refute_1_978,refute_1_979]) ).
cnf(refute_1_981,plain,
converse(join(converse(X0),join(one,one))) = join(one,join(one,X0)),
inference(resolve,[$cnf( $equal(join(one,join(converse(one),X0)),join(one,join(one,X0))) )],[refute_1_927,refute_1_980]) ).
cnf(refute_1_982,plain,
( converse(join(converse(X0),join(one,one))) != join(X0,join(one,one))
| converse(join(converse(X0),join(one,one))) != join(one,join(one,X0))
| join(one,join(one,X0)) = join(X0,join(one,one)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(X0),join(one,one))),join(X0,join(one,one))) ),[0],$fot(join(one,join(one,X0)))]]) ).
cnf(refute_1_983,plain,
( converse(join(converse(X0),join(one,one))) != join(X0,join(one,one))
| join(one,join(one,X0)) = join(X0,join(one,one)) ),
inference(resolve,[$cnf( $equal(converse(join(converse(X0),join(one,one))),join(one,join(one,X0))) )],[refute_1_981,refute_1_982]) ).
cnf(refute_1_984,plain,
join(one,join(one,X0)) = join(X0,join(one,one)),
inference(resolve,[$cnf( $equal(converse(join(converse(X0),join(one,one))),join(X0,join(one,one))) )],[refute_1_919,refute_1_983]) ).
cnf(refute_1_985,plain,
join(complement(join(complement(X_137),complement(X_138))),complement(join(complement(X_137),complement(X_138)))) = complement(join(complement(X_137),complement(X_138))),
inference(subst,[],[refute_1_166:[bind(X_134,$fot(join(complement(X_137),complement(X_138))))]]) ).
cnf(refute_1_986,plain,
( complement(join(complement(X_137),complement(X_138))) != meet(X_137,X_138)
| join(complement(join(complement(X_137),complement(X_138))),complement(join(complement(X_137),complement(X_138)))) != complement(join(complement(X_137),complement(X_138)))
| join(meet(X_137,X_138),complement(join(complement(X_137),complement(X_138)))) = complement(join(complement(X_137),complement(X_138))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(join(complement(X_137),complement(X_138))),complement(join(complement(X_137),complement(X_138)))),complement(join(complement(X_137),complement(X_138)))) ),[0,0],$fot(meet(X_137,X_138))]]) ).
cnf(refute_1_987,plain,
( join(complement(join(complement(X_137),complement(X_138))),complement(join(complement(X_137),complement(X_138)))) != complement(join(complement(X_137),complement(X_138)))
| join(meet(X_137,X_138),complement(join(complement(X_137),complement(X_138)))) = complement(join(complement(X_137),complement(X_138))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_137),complement(X_138))),meet(X_137,X_138)) )],[refute_1_19,refute_1_986]) ).
cnf(refute_1_988,plain,
join(meet(X_137,X_138),complement(join(complement(X_137),complement(X_138)))) = complement(join(complement(X_137),complement(X_138))),
inference(resolve,[$cnf( $equal(join(complement(join(complement(X_137),complement(X_138))),complement(join(complement(X_137),complement(X_138)))),complement(join(complement(X_137),complement(X_138)))) )],[refute_1_985,refute_1_987]) ).
cnf(refute_1_989,plain,
join(meet(X_137,X_138),complement(join(complement(X_137),complement(X_138)))) = join(meet(X_137,X_138),complement(join(complement(X_137),complement(X_138)))),
introduced(tautology,[refl,[$fot(join(meet(X_137,X_138),complement(join(complement(X_137),complement(X_138)))))]]) ).
cnf(refute_1_990,plain,
( complement(join(complement(X_137),complement(X_138))) != meet(X_137,X_138)
| join(meet(X_137,X_138),complement(join(complement(X_137),complement(X_138)))) != join(meet(X_137,X_138),complement(join(complement(X_137),complement(X_138))))
| join(meet(X_137,X_138),complement(join(complement(X_137),complement(X_138)))) = join(meet(X_137,X_138),meet(X_137,X_138)) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_137,X_138),complement(join(complement(X_137),complement(X_138)))),join(meet(X_137,X_138),complement(join(complement(X_137),complement(X_138))))) ),[1,1],$fot(meet(X_137,X_138))]]) ).
cnf(refute_1_991,plain,
( complement(join(complement(X_137),complement(X_138))) != meet(X_137,X_138)
| join(meet(X_137,X_138),complement(join(complement(X_137),complement(X_138)))) = join(meet(X_137,X_138),meet(X_137,X_138)) ),
inference(resolve,[$cnf( $equal(join(meet(X_137,X_138),complement(join(complement(X_137),complement(X_138)))),join(meet(X_137,X_138),complement(join(complement(X_137),complement(X_138))))) )],[refute_1_989,refute_1_990]) ).
cnf(refute_1_992,plain,
join(meet(X_137,X_138),complement(join(complement(X_137),complement(X_138)))) = join(meet(X_137,X_138),meet(X_137,X_138)),
inference(resolve,[$cnf( $equal(complement(join(complement(X_137),complement(X_138))),meet(X_137,X_138)) )],[refute_1_19,refute_1_991]) ).
cnf(refute_1_993,plain,
( join(meet(X_137,X_138),complement(join(complement(X_137),complement(X_138)))) != complement(join(complement(X_137),complement(X_138)))
| join(meet(X_137,X_138),complement(join(complement(X_137),complement(X_138)))) != join(meet(X_137,X_138),meet(X_137,X_138))
| join(meet(X_137,X_138),meet(X_137,X_138)) = complement(join(complement(X_137),complement(X_138))) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_137,X_138),complement(join(complement(X_137),complement(X_138)))),complement(join(complement(X_137),complement(X_138)))) ),[0],$fot(join(meet(X_137,X_138),meet(X_137,X_138)))]]) ).
cnf(refute_1_994,plain,
( join(meet(X_137,X_138),complement(join(complement(X_137),complement(X_138)))) != complement(join(complement(X_137),complement(X_138)))
| join(meet(X_137,X_138),meet(X_137,X_138)) = complement(join(complement(X_137),complement(X_138))) ),
inference(resolve,[$cnf( $equal(join(meet(X_137,X_138),complement(join(complement(X_137),complement(X_138)))),join(meet(X_137,X_138),meet(X_137,X_138))) )],[refute_1_992,refute_1_993]) ).
cnf(refute_1_995,plain,
( complement(join(complement(X_137),complement(X_138))) != meet(X_137,X_138)
| join(meet(X_137,X_138),meet(X_137,X_138)) != complement(join(complement(X_137),complement(X_138)))
| join(meet(X_137,X_138),meet(X_137,X_138)) = meet(X_137,X_138) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_137,X_138),meet(X_137,X_138)),complement(join(complement(X_137),complement(X_138)))) ),[1],$fot(meet(X_137,X_138))]]) ).
cnf(refute_1_996,plain,
( join(meet(X_137,X_138),meet(X_137,X_138)) != complement(join(complement(X_137),complement(X_138)))
| join(meet(X_137,X_138),meet(X_137,X_138)) = meet(X_137,X_138) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_137),complement(X_138))),meet(X_137,X_138)) )],[refute_1_19,refute_1_995]) ).
cnf(refute_1_997,plain,
( join(meet(X_137,X_138),complement(join(complement(X_137),complement(X_138)))) != complement(join(complement(X_137),complement(X_138)))
| join(meet(X_137,X_138),meet(X_137,X_138)) = meet(X_137,X_138) ),
inference(resolve,[$cnf( $equal(join(meet(X_137,X_138),meet(X_137,X_138)),complement(join(complement(X_137),complement(X_138)))) )],[refute_1_994,refute_1_996]) ).
cnf(refute_1_998,plain,
join(meet(X_137,X_138),meet(X_137,X_138)) = meet(X_137,X_138),
inference(resolve,[$cnf( $equal(join(meet(X_137,X_138),complement(join(complement(X_137),complement(X_138)))),complement(join(complement(X_137),complement(X_138)))) )],[refute_1_988,refute_1_997]) ).
cnf(refute_1_999,plain,
join(meet(X_143,X_144),meet(X_143,X_144)) = meet(X_143,X_144),
inference(subst,[],[refute_1_998:[bind(X_137,$fot(X_143)),bind(X_138,$fot(X_144))]]) ).
cnf(refute_1_1000,plain,
meet(X_144,X_143) = meet(X_143,X_144),
inference(subst,[],[refute_1_461:[bind(X_137,$fot(X_144)),bind(X_138,$fot(X_143))]]) ).
cnf(refute_1_1001,plain,
( meet(X_144,X_143) != meet(X_143,X_144)
| meet(X_143,X_144) = meet(X_144,X_143) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(meet(X_144,X_143))),bind(Y,$fot(meet(X_143,X_144)))]]) ).
cnf(refute_1_1002,plain,
meet(X_143,X_144) = meet(X_144,X_143),
inference(resolve,[$cnf( $equal(meet(X_144,X_143),meet(X_143,X_144)) )],[refute_1_1000,refute_1_1001]) ).
cnf(refute_1_1003,plain,
( join(meet(X_143,X_144),meet(X_143,X_144)) != meet(X_143,X_144)
| meet(X_143,X_144) != meet(X_144,X_143)
| join(meet(X_143,X_144),meet(X_144,X_143)) = meet(X_143,X_144) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_143,X_144),meet(X_143,X_144)),meet(X_143,X_144)) ),[0,1],$fot(meet(X_144,X_143))]]) ).
cnf(refute_1_1004,plain,
( join(meet(X_143,X_144),meet(X_143,X_144)) != meet(X_143,X_144)
| join(meet(X_143,X_144),meet(X_144,X_143)) = meet(X_143,X_144) ),
inference(resolve,[$cnf( $equal(meet(X_143,X_144),meet(X_144,X_143)) )],[refute_1_1002,refute_1_1003]) ).
cnf(refute_1_1005,plain,
join(meet(X_143,X_144),meet(X_144,X_143)) = meet(X_143,X_144),
inference(resolve,[$cnf( $equal(join(meet(X_143,X_144),meet(X_143,X_144)),meet(X_143,X_144)) )],[refute_1_999,refute_1_1004]) ).
cnf(refute_1_1006,plain,
join(meet(top,X_144),meet(X_144,top)) = meet(top,X_144),
inference(subst,[],[refute_1_1005:[bind(X_143,$fot(top))]]) ).
cnf(refute_1_1007,plain,
meet(top,X_144) = X_144,
inference(subst,[],[refute_1_522:[bind(X1,$fot(X_144))]]) ).
cnf(refute_1_1008,plain,
( join(meet(top,X_144),meet(X_144,top)) != meet(top,X_144)
| meet(top,X_144) != X_144
| join(X_144,meet(X_144,top)) = meet(top,X_144) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(top,X_144),meet(X_144,top)),meet(top,X_144)) ),[0,0],$fot(X_144)]]) ).
cnf(refute_1_1009,plain,
( join(meet(top,X_144),meet(X_144,top)) != meet(top,X_144)
| join(X_144,meet(X_144,top)) = meet(top,X_144) ),
inference(resolve,[$cnf( $equal(meet(top,X_144),X_144) )],[refute_1_1007,refute_1_1008]) ).
cnf(refute_1_1010,plain,
join(X_144,meet(X_144,top)) = meet(top,X_144),
inference(resolve,[$cnf( $equal(join(meet(top,X_144),meet(X_144,top)),meet(top,X_144)) )],[refute_1_1006,refute_1_1009]) ).
cnf(refute_1_1011,plain,
join(zero,meet(X_176,top)) = meet(X_176,top),
inference(subst,[],[refute_1_580:[bind(X_176,$fot(meet(X_176,top)))]]) ).
cnf(refute_1_1012,plain,
( X_176 != join(zero,meet(X_176,top))
| join(zero,meet(X_176,top)) != meet(X_176,top)
| X_176 = meet(X_176,top) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_176,meet(X_176,top)) ),[0],$fot(join(zero,meet(X_176,top)))]]) ).
cnf(refute_1_1013,plain,
( X_176 != join(zero,meet(X_176,top))
| X_176 = meet(X_176,top) ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_176,top)),meet(X_176,top)) )],[refute_1_1011,refute_1_1012]) ).
cnf(refute_1_1014,plain,
X_176 = meet(X_176,top),
inference(resolve,[$cnf( $equal(X_176,join(zero,meet(X_176,top))) )],[refute_1_450,refute_1_1013]) ).
cnf(refute_1_1015,plain,
( X_176 != meet(X_176,top)
| meet(X_176,top) = X_176 ),
inference(subst,[],[refute_1_17:[bind(X,$fot(X_176)),bind(Y,$fot(meet(X_176,top)))]]) ).
cnf(refute_1_1016,plain,
meet(X_176,top) = X_176,
inference(resolve,[$cnf( $equal(X_176,meet(X_176,top)) )],[refute_1_1014,refute_1_1015]) ).
cnf(refute_1_1017,plain,
meet(X_144,top) = X_144,
inference(subst,[],[refute_1_1016:[bind(X_176,$fot(X_144))]]) ).
cnf(refute_1_1018,plain,
join(X_144,meet(X_144,top)) = join(X_144,meet(X_144,top)),
introduced(tautology,[refl,[$fot(join(X_144,meet(X_144,top)))]]) ).
cnf(refute_1_1019,plain,
( join(X_144,meet(X_144,top)) != join(X_144,meet(X_144,top))
| meet(X_144,top) != X_144
| join(X_144,meet(X_144,top)) = join(X_144,X_144) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_144,meet(X_144,top)),join(X_144,meet(X_144,top))) ),[1,1],$fot(X_144)]]) ).
cnf(refute_1_1020,plain,
( meet(X_144,top) != X_144
| join(X_144,meet(X_144,top)) = join(X_144,X_144) ),
inference(resolve,[$cnf( $equal(join(X_144,meet(X_144,top)),join(X_144,meet(X_144,top))) )],[refute_1_1018,refute_1_1019]) ).
cnf(refute_1_1021,plain,
join(X_144,meet(X_144,top)) = join(X_144,X_144),
inference(resolve,[$cnf( $equal(meet(X_144,top),X_144) )],[refute_1_1017,refute_1_1020]) ).
cnf(refute_1_1022,plain,
( join(X_144,meet(X_144,top)) != join(X_144,X_144)
| join(X_144,meet(X_144,top)) != meet(top,X_144)
| join(X_144,X_144) = meet(top,X_144) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_144,meet(X_144,top)),meet(top,X_144)) ),[0],$fot(join(X_144,X_144))]]) ).
cnf(refute_1_1023,plain,
( join(X_144,meet(X_144,top)) != meet(top,X_144)
| join(X_144,X_144) = meet(top,X_144) ),
inference(resolve,[$cnf( $equal(join(X_144,meet(X_144,top)),join(X_144,X_144)) )],[refute_1_1021,refute_1_1022]) ).
cnf(refute_1_1024,plain,
( join(X_144,X_144) != meet(top,X_144)
| meet(top,X_144) != X_144
| join(X_144,X_144) = X_144 ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_144,X_144),X_144) ),[0],$fot(meet(top,X_144))]]) ).
cnf(refute_1_1025,plain,
( join(X_144,X_144) != meet(top,X_144)
| join(X_144,X_144) = X_144 ),
inference(resolve,[$cnf( $equal(meet(top,X_144),X_144) )],[refute_1_1007,refute_1_1024]) ).
cnf(refute_1_1026,plain,
( join(X_144,meet(X_144,top)) != meet(top,X_144)
| join(X_144,X_144) = X_144 ),
inference(resolve,[$cnf( $equal(join(X_144,X_144),meet(top,X_144)) )],[refute_1_1023,refute_1_1025]) ).
cnf(refute_1_1027,plain,
join(X_144,X_144) = X_144,
inference(resolve,[$cnf( $equal(join(X_144,meet(X_144,top)),meet(top,X_144)) )],[refute_1_1010,refute_1_1026]) ).
cnf(refute_1_1028,plain,
join(one,one) = one,
inference(subst,[],[refute_1_1027:[bind(X_144,$fot(one))]]) ).
cnf(refute_1_1029,plain,
join(X0,join(one,one)) = join(X0,join(one,one)),
introduced(tautology,[refl,[$fot(join(X0,join(one,one)))]]) ).
cnf(refute_1_1030,plain,
( join(X0,join(one,one)) != join(X0,join(one,one))
| join(one,one) != one
| join(X0,join(one,one)) = join(X0,one) ),
introduced(tautology,[equality,[$cnf( $equal(join(X0,join(one,one)),join(X0,join(one,one))) ),[1,1],$fot(one)]]) ).
cnf(refute_1_1031,plain,
( join(one,one) != one
| join(X0,join(one,one)) = join(X0,one) ),
inference(resolve,[$cnf( $equal(join(X0,join(one,one)),join(X0,join(one,one))) )],[refute_1_1029,refute_1_1030]) ).
cnf(refute_1_1032,plain,
join(X0,join(one,one)) = join(X0,one),
inference(resolve,[$cnf( $equal(join(one,one),one) )],[refute_1_1028,refute_1_1031]) ).
cnf(refute_1_1033,plain,
( join(X0,join(one,one)) != join(X0,one)
| join(one,join(one,X0)) != join(X0,join(one,one))
| join(one,join(one,X0)) = join(X0,one) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(one,X0)),join(X0,join(one,one))) ),[1],$fot(join(X0,one))]]) ).
cnf(refute_1_1034,plain,
( join(one,join(one,X0)) != join(X0,join(one,one))
| join(one,join(one,X0)) = join(X0,one) ),
inference(resolve,[$cnf( $equal(join(X0,join(one,one)),join(X0,one)) )],[refute_1_1032,refute_1_1033]) ).
cnf(refute_1_1035,plain,
join(one,join(one,X0)) = join(X0,one),
inference(resolve,[$cnf( $equal(join(one,join(one,X0)),join(X0,join(one,one))) )],[refute_1_984,refute_1_1034]) ).
cnf(refute_1_1036,plain,
join(X_211,join(X_211,X_212)) = join(join(X_211,X_211),X_212),
inference(subst,[],[refute_1_100:[bind(X0,$fot(X_211)),bind(X1,$fot(X_211)),bind(X2,$fot(X_212))]]) ).
cnf(refute_1_1037,plain,
join(X_211,X_211) = X_211,
inference(subst,[],[refute_1_1027:[bind(X_144,$fot(X_211))]]) ).
cnf(refute_1_1038,plain,
( join(X_211,X_211) != X_211
| join(X_211,join(X_211,X_212)) != join(join(X_211,X_211),X_212)
| join(X_211,join(X_211,X_212)) = join(X_211,X_212) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_211,join(X_211,X_212)),join(join(X_211,X_211),X_212)) ),[1,0],$fot(X_211)]]) ).
cnf(refute_1_1039,plain,
( join(X_211,join(X_211,X_212)) != join(join(X_211,X_211),X_212)
| join(X_211,join(X_211,X_212)) = join(X_211,X_212) ),
inference(resolve,[$cnf( $equal(join(X_211,X_211),X_211) )],[refute_1_1037,refute_1_1038]) ).
cnf(refute_1_1040,plain,
join(X_211,join(X_211,X_212)) = join(X_211,X_212),
inference(resolve,[$cnf( $equal(join(X_211,join(X_211,X_212)),join(join(X_211,X_211),X_212)) )],[refute_1_1036,refute_1_1039]) ).
cnf(refute_1_1041,plain,
join(one,join(one,X0)) = join(one,X0),
inference(subst,[],[refute_1_1040:[bind(X_211,$fot(one)),bind(X_212,$fot(X0))]]) ).
cnf(refute_1_1042,plain,
( join(one,join(one,X0)) != join(X0,one)
| join(one,join(one,X0)) != join(one,X0)
| join(one,X0) = join(X0,one) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(one,X0)),join(X0,one)) ),[0],$fot(join(one,X0))]]) ).
cnf(refute_1_1043,plain,
( join(one,join(one,X0)) != join(X0,one)
| join(one,X0) = join(X0,one) ),
inference(resolve,[$cnf( $equal(join(one,join(one,X0)),join(one,X0)) )],[refute_1_1041,refute_1_1042]) ).
cnf(refute_1_1044,plain,
join(one,X0) = join(X0,one),
inference(resolve,[$cnf( $equal(join(one,join(one,X0)),join(X0,one)) )],[refute_1_1035,refute_1_1043]) ).
cnf(refute_1_1045,plain,
( join(one,X0) != join(X0,one)
| join(X0,one) = join(one,X0) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(join(one,X0))),bind(Y,$fot(join(X0,one)))]]) ).
cnf(refute_1_1046,plain,
join(X0,one) = join(one,X0),
inference(resolve,[$cnf( $equal(join(one,X0),join(X0,one)) )],[refute_1_1044,refute_1_1045]) ).
cnf(refute_1_1047,plain,
join(complement(composition(zero,top)),one) = join(one,complement(composition(zero,top))),
inference(subst,[],[refute_1_1046:[bind(X0,$fot(complement(composition(zero,top))))]]) ).
cnf(refute_1_1048,plain,
complement(join(complement(composition(zero,top)),one)) = complement(join(complement(composition(zero,top)),one)),
introduced(tautology,[refl,[$fot(complement(join(complement(composition(zero,top)),one)))]]) ).
cnf(refute_1_1049,plain,
( complement(join(complement(composition(zero,top)),one)) != complement(join(complement(composition(zero,top)),one))
| join(complement(composition(zero,top)),one) != join(one,complement(composition(zero,top)))
| complement(join(complement(composition(zero,top)),one)) = complement(join(one,complement(composition(zero,top)))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(composition(zero,top)),one)),complement(join(complement(composition(zero,top)),one))) ),[1,0],$fot(join(one,complement(composition(zero,top))))]]) ).
cnf(refute_1_1050,plain,
( join(complement(composition(zero,top)),one) != join(one,complement(composition(zero,top)))
| complement(join(complement(composition(zero,top)),one)) = complement(join(one,complement(composition(zero,top)))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(composition(zero,top)),one)),complement(join(complement(composition(zero,top)),one))) )],[refute_1_1048,refute_1_1049]) ).
cnf(refute_1_1051,plain,
complement(join(complement(composition(zero,top)),one)) = complement(join(one,complement(composition(zero,top)))),
inference(resolve,[$cnf( $equal(join(complement(composition(zero,top)),one),join(one,complement(composition(zero,top)))) )],[refute_1_1047,refute_1_1050]) ).
cnf(refute_1_1052,plain,
join(one,complement(join(complement(composition(zero,top)),one))) = join(one,complement(join(complement(composition(zero,top)),one))),
introduced(tautology,[refl,[$fot(join(one,complement(join(complement(composition(zero,top)),one))))]]) ).
cnf(refute_1_1053,plain,
( complement(join(complement(composition(zero,top)),one)) != complement(join(one,complement(composition(zero,top))))
| join(one,complement(join(complement(composition(zero,top)),one))) != join(one,complement(join(complement(composition(zero,top)),one)))
| join(one,complement(join(complement(composition(zero,top)),one))) = join(one,complement(join(one,complement(composition(zero,top))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,complement(join(complement(composition(zero,top)),one))),join(one,complement(join(complement(composition(zero,top)),one)))) ),[1,1],$fot(complement(join(one,complement(composition(zero,top)))))]]) ).
cnf(refute_1_1054,plain,
( complement(join(complement(composition(zero,top)),one)) != complement(join(one,complement(composition(zero,top))))
| join(one,complement(join(complement(composition(zero,top)),one))) = join(one,complement(join(one,complement(composition(zero,top))))) ),
inference(resolve,[$cnf( $equal(join(one,complement(join(complement(composition(zero,top)),one))),join(one,complement(join(complement(composition(zero,top)),one)))) )],[refute_1_1052,refute_1_1053]) ).
cnf(refute_1_1055,plain,
join(one,complement(join(complement(composition(zero,top)),one))) = join(one,complement(join(one,complement(composition(zero,top))))),
inference(resolve,[$cnf( $equal(complement(join(complement(composition(zero,top)),one)),complement(join(one,complement(composition(zero,top))))) )],[refute_1_1051,refute_1_1054]) ).
cnf(refute_1_1056,plain,
( join(one,complement(join(complement(composition(zero,top)),one))) != join(one,complement(join(one,complement(composition(zero,top)))))
| join(one,composition(zero,top)) != join(one,complement(join(complement(composition(zero,top)),one)))
| join(one,composition(zero,top)) = join(one,complement(join(one,complement(composition(zero,top))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,composition(zero,top)),join(one,complement(join(complement(composition(zero,top)),one)))) ),[1],$fot(join(one,complement(join(one,complement(composition(zero,top))))))]]) ).
cnf(refute_1_1057,plain,
( join(one,composition(zero,top)) != join(one,complement(join(complement(composition(zero,top)),one)))
| join(one,composition(zero,top)) = join(one,complement(join(one,complement(composition(zero,top))))) ),
inference(resolve,[$cnf( $equal(join(one,complement(join(complement(composition(zero,top)),one))),join(one,complement(join(one,complement(composition(zero,top)))))) )],[refute_1_1055,refute_1_1056]) ).
cnf(refute_1_1058,plain,
join(one,composition(zero,top)) = join(one,complement(join(one,complement(composition(zero,top))))),
inference(resolve,[$cnf( $equal(join(one,composition(zero,top)),join(one,complement(join(complement(composition(zero,top)),one)))) )],[refute_1_915,refute_1_1057]) ).
cnf(refute_1_1059,plain,
( join(one,composition(zero,top)) != join(one,complement(join(one,complement(composition(zero,top)))))
| join(one,complement(join(one,complement(composition(zero,top))))) = join(one,composition(zero,top)) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(join(one,composition(zero,top)))),bind(Y,$fot(join(one,complement(join(one,complement(composition(zero,top)))))))]]) ).
cnf(refute_1_1060,plain,
join(one,complement(join(one,complement(composition(zero,top))))) = join(one,composition(zero,top)),
inference(resolve,[$cnf( $equal(join(one,composition(zero,top)),join(one,complement(join(one,complement(composition(zero,top)))))) )],[refute_1_1058,refute_1_1059]) ).
cnf(refute_1_1061,plain,
( join(one,complement(composition(zero,top))) != join(meet(join(one,complement(composition(zero,top))),one),complement(join(one,complement(join(one,complement(composition(zero,top)))))))
| join(one,complement(join(one,complement(composition(zero,top))))) != join(one,composition(zero,top))
| join(one,complement(composition(zero,top))) = join(meet(join(one,complement(composition(zero,top))),one),complement(join(one,composition(zero,top)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,complement(composition(zero,top))),join(meet(join(one,complement(composition(zero,top))),one),complement(join(one,complement(join(one,complement(composition(zero,top)))))))) ),[1,1,0],$fot(join(one,composition(zero,top)))]]) ).
cnf(refute_1_1062,plain,
( join(one,complement(composition(zero,top))) != join(meet(join(one,complement(composition(zero,top))),one),complement(join(one,complement(join(one,complement(composition(zero,top)))))))
| join(one,complement(composition(zero,top))) = join(meet(join(one,complement(composition(zero,top))),one),complement(join(one,composition(zero,top)))) ),
inference(resolve,[$cnf( $equal(join(one,complement(join(one,complement(composition(zero,top))))),join(one,composition(zero,top))) )],[refute_1_1060,refute_1_1061]) ).
cnf(refute_1_1063,plain,
join(one,complement(composition(zero,top))) = join(meet(join(one,complement(composition(zero,top))),one),complement(join(one,composition(zero,top)))),
inference(resolve,[$cnf( $equal(join(one,complement(composition(zero,top))),join(meet(join(one,complement(composition(zero,top))),one),complement(join(one,complement(join(one,complement(composition(zero,top)))))))) )],[refute_1_886,refute_1_1062]) ).
cnf(refute_1_1064,plain,
join(complement(join(one,composition(zero,top))),one) = join(one,complement(join(one,composition(zero,top)))),
inference(subst,[],[refute_1_1046:[bind(X0,$fot(complement(join(one,composition(zero,top)))))]]) ).
cnf(refute_1_1065,plain,
( X_176 != meet(X_176,join(X_176,X_214))
| meet(X_176,join(X_176,X_214)) = X_176 ),
inference(subst,[],[refute_1_17:[bind(X,$fot(X_176)),bind(Y,$fot(meet(X_176,join(X_176,X_214))))]]) ).
cnf(refute_1_1066,plain,
meet(X_176,join(X_176,X_214)) = X_176,
inference(resolve,[$cnf( $equal(X_176,meet(X_176,join(X_176,X_214))) )],[refute_1_736,refute_1_1065]) ).
cnf(refute_1_1067,plain,
meet(one,join(one,complement(composition(zero,top)))) = one,
inference(subst,[],[refute_1_1066:[bind(X_176,$fot(one)),bind(X_214,$fot(complement(composition(zero,top))))]]) ).
cnf(refute_1_1068,plain,
meet(join(one,complement(composition(zero,top))),one) = meet(one,join(one,complement(composition(zero,top)))),
inference(subst,[],[refute_1_711:[bind(X_137,$fot(one)),bind(X_138,$fot(join(one,complement(composition(zero,top)))))]]) ).
cnf(refute_1_1069,plain,
( meet(join(one,complement(composition(zero,top))),one) != meet(one,join(one,complement(composition(zero,top))))
| meet(one,join(one,complement(composition(zero,top)))) != one
| meet(join(one,complement(composition(zero,top))),one) = one ),
inference(subst,[],[refute_1_37:[bind(X,$fot(meet(join(one,complement(composition(zero,top))),one))),bind(Y,$fot(meet(one,join(one,complement(composition(zero,top)))))),bind(Z,$fot(one))]]) ).
cnf(refute_1_1070,plain,
( meet(one,join(one,complement(composition(zero,top)))) != one
| meet(join(one,complement(composition(zero,top))),one) = one ),
inference(resolve,[$cnf( $equal(meet(join(one,complement(composition(zero,top))),one),meet(one,join(one,complement(composition(zero,top))))) )],[refute_1_1068,refute_1_1069]) ).
cnf(refute_1_1071,plain,
meet(join(one,complement(composition(zero,top))),one) = one,
inference(resolve,[$cnf( $equal(meet(one,join(one,complement(composition(zero,top)))),one) )],[refute_1_1067,refute_1_1070]) ).
cnf(refute_1_1072,plain,
join(complement(join(one,composition(zero,top))),meet(join(one,complement(composition(zero,top))),one)) = join(complement(join(one,composition(zero,top))),meet(join(one,complement(composition(zero,top))),one)),
introduced(tautology,[refl,[$fot(join(complement(join(one,composition(zero,top))),meet(join(one,complement(composition(zero,top))),one)))]]) ).
cnf(refute_1_1073,plain,
( join(complement(join(one,composition(zero,top))),meet(join(one,complement(composition(zero,top))),one)) != join(complement(join(one,composition(zero,top))),meet(join(one,complement(composition(zero,top))),one))
| meet(join(one,complement(composition(zero,top))),one) != one
| join(complement(join(one,composition(zero,top))),meet(join(one,complement(composition(zero,top))),one)) = join(complement(join(one,composition(zero,top))),one) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(join(one,composition(zero,top))),meet(join(one,complement(composition(zero,top))),one)),join(complement(join(one,composition(zero,top))),meet(join(one,complement(composition(zero,top))),one))) ),[1,1],$fot(one)]]) ).
cnf(refute_1_1074,plain,
( meet(join(one,complement(composition(zero,top))),one) != one
| join(complement(join(one,composition(zero,top))),meet(join(one,complement(composition(zero,top))),one)) = join(complement(join(one,composition(zero,top))),one) ),
inference(resolve,[$cnf( $equal(join(complement(join(one,composition(zero,top))),meet(join(one,complement(composition(zero,top))),one)),join(complement(join(one,composition(zero,top))),meet(join(one,complement(composition(zero,top))),one))) )],[refute_1_1072,refute_1_1073]) ).
cnf(refute_1_1075,plain,
join(complement(join(one,composition(zero,top))),meet(join(one,complement(composition(zero,top))),one)) = join(complement(join(one,composition(zero,top))),one),
inference(resolve,[$cnf( $equal(meet(join(one,complement(composition(zero,top))),one),one) )],[refute_1_1071,refute_1_1074]) ).
cnf(refute_1_1076,plain,
( join(complement(join(one,composition(zero,top))),meet(join(one,complement(composition(zero,top))),one)) != join(complement(join(one,composition(zero,top))),one)
| join(complement(join(one,composition(zero,top))),one) != join(one,complement(join(one,composition(zero,top))))
| join(complement(join(one,composition(zero,top))),meet(join(one,complement(composition(zero,top))),one)) = join(one,complement(join(one,composition(zero,top)))) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(complement(join(one,composition(zero,top))),meet(join(one,complement(composition(zero,top))),one)))),bind(Y,$fot(join(complement(join(one,composition(zero,top))),one))),bind(Z,$fot(join(one,complement(join(one,composition(zero,top))))))]]) ).
cnf(refute_1_1077,plain,
( join(complement(join(one,composition(zero,top))),one) != join(one,complement(join(one,composition(zero,top))))
| join(complement(join(one,composition(zero,top))),meet(join(one,complement(composition(zero,top))),one)) = join(one,complement(join(one,composition(zero,top)))) ),
inference(resolve,[$cnf( $equal(join(complement(join(one,composition(zero,top))),meet(join(one,complement(composition(zero,top))),one)),join(complement(join(one,composition(zero,top))),one)) )],[refute_1_1075,refute_1_1076]) ).
cnf(refute_1_1078,plain,
join(complement(join(one,composition(zero,top))),meet(join(one,complement(composition(zero,top))),one)) = join(one,complement(join(one,composition(zero,top)))),
inference(resolve,[$cnf( $equal(join(complement(join(one,composition(zero,top))),one),join(one,complement(join(one,composition(zero,top))))) )],[refute_1_1064,refute_1_1077]) ).
cnf(refute_1_1079,plain,
join(meet(join(one,complement(composition(zero,top))),one),complement(join(one,composition(zero,top)))) = join(complement(join(one,composition(zero,top))),meet(join(one,complement(composition(zero,top))),one)),
inference(subst,[],[refute_1_52:[bind(X0,$fot(complement(join(one,composition(zero,top))))),bind(X1,$fot(meet(join(one,complement(composition(zero,top))),one)))]]) ).
cnf(refute_1_1080,plain,
( join(complement(join(one,composition(zero,top))),meet(join(one,complement(composition(zero,top))),one)) != join(one,complement(join(one,composition(zero,top))))
| join(meet(join(one,complement(composition(zero,top))),one),complement(join(one,composition(zero,top)))) != join(complement(join(one,composition(zero,top))),meet(join(one,complement(composition(zero,top))),one))
| join(meet(join(one,complement(composition(zero,top))),one),complement(join(one,composition(zero,top)))) = join(one,complement(join(one,composition(zero,top)))) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(meet(join(one,complement(composition(zero,top))),one),complement(join(one,composition(zero,top)))))),bind(Y,$fot(join(complement(join(one,composition(zero,top))),meet(join(one,complement(composition(zero,top))),one)))),bind(Z,$fot(join(one,complement(join(one,composition(zero,top))))))]]) ).
cnf(refute_1_1081,plain,
( join(complement(join(one,composition(zero,top))),meet(join(one,complement(composition(zero,top))),one)) != join(one,complement(join(one,composition(zero,top))))
| join(meet(join(one,complement(composition(zero,top))),one),complement(join(one,composition(zero,top)))) = join(one,complement(join(one,composition(zero,top)))) ),
inference(resolve,[$cnf( $equal(join(meet(join(one,complement(composition(zero,top))),one),complement(join(one,composition(zero,top)))),join(complement(join(one,composition(zero,top))),meet(join(one,complement(composition(zero,top))),one))) )],[refute_1_1079,refute_1_1080]) ).
cnf(refute_1_1082,plain,
join(meet(join(one,complement(composition(zero,top))),one),complement(join(one,composition(zero,top)))) = join(one,complement(join(one,composition(zero,top)))),
inference(resolve,[$cnf( $equal(join(complement(join(one,composition(zero,top))),meet(join(one,complement(composition(zero,top))),one)),join(one,complement(join(one,composition(zero,top))))) )],[refute_1_1078,refute_1_1081]) ).
cnf(refute_1_1083,plain,
( join(meet(join(one,complement(composition(zero,top))),one),complement(join(one,composition(zero,top)))) != join(one,complement(join(one,composition(zero,top))))
| join(one,complement(composition(zero,top))) != join(meet(join(one,complement(composition(zero,top))),one),complement(join(one,composition(zero,top))))
| join(one,complement(composition(zero,top))) = join(one,complement(join(one,composition(zero,top)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,complement(composition(zero,top))),join(meet(join(one,complement(composition(zero,top))),one),complement(join(one,composition(zero,top))))) ),[1],$fot(join(one,complement(join(one,composition(zero,top)))))]]) ).
cnf(refute_1_1084,plain,
( join(one,complement(composition(zero,top))) != join(meet(join(one,complement(composition(zero,top))),one),complement(join(one,composition(zero,top))))
| join(one,complement(composition(zero,top))) = join(one,complement(join(one,composition(zero,top)))) ),
inference(resolve,[$cnf( $equal(join(meet(join(one,complement(composition(zero,top))),one),complement(join(one,composition(zero,top)))),join(one,complement(join(one,composition(zero,top))))) )],[refute_1_1082,refute_1_1083]) ).
cnf(refute_1_1085,plain,
join(one,complement(composition(zero,top))) = join(one,complement(join(one,composition(zero,top)))),
inference(resolve,[$cnf( $equal(join(one,complement(composition(zero,top))),join(meet(join(one,complement(composition(zero,top))),one),complement(join(one,composition(zero,top))))) )],[refute_1_1063,refute_1_1084]) ).
cnf(refute_1_1086,plain,
( join(one,complement(composition(zero,top))) != join(one,complement(join(one,composition(zero,top))))
| join(one,complement(join(one,composition(zero,top)))) = join(one,complement(composition(zero,top))) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(join(one,complement(composition(zero,top))))),bind(Y,$fot(join(one,complement(join(one,composition(zero,top))))))]]) ).
cnf(refute_1_1087,plain,
join(one,complement(join(one,composition(zero,top)))) = join(one,complement(composition(zero,top))),
inference(resolve,[$cnf( $equal(join(one,complement(composition(zero,top))),join(one,complement(join(one,composition(zero,top))))) )],[refute_1_1085,refute_1_1086]) ).
cnf(refute_1_1088,plain,
complement(complement(composition(zero,top))) = composition(zero,top),
inference(subst,[],[refute_1_518:[bind(X_176,$fot(composition(zero,top)))]]) ).
cnf(refute_1_1089,plain,
join(one,complement(complement(composition(zero,top)))) = join(one,complement(complement(composition(zero,top)))),
introduced(tautology,[refl,[$fot(join(one,complement(complement(composition(zero,top)))))]]) ).
cnf(refute_1_1090,plain,
( complement(complement(composition(zero,top))) != composition(zero,top)
| join(one,complement(complement(composition(zero,top)))) != join(one,complement(complement(composition(zero,top))))
| join(one,complement(complement(composition(zero,top)))) = join(one,composition(zero,top)) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,complement(complement(composition(zero,top)))),join(one,complement(complement(composition(zero,top))))) ),[1,1],$fot(composition(zero,top))]]) ).
cnf(refute_1_1091,plain,
( complement(complement(composition(zero,top))) != composition(zero,top)
| join(one,complement(complement(composition(zero,top)))) = join(one,composition(zero,top)) ),
inference(resolve,[$cnf( $equal(join(one,complement(complement(composition(zero,top)))),join(one,complement(complement(composition(zero,top))))) )],[refute_1_1089,refute_1_1090]) ).
cnf(refute_1_1092,plain,
join(one,complement(complement(composition(zero,top)))) = join(one,composition(zero,top)),
inference(resolve,[$cnf( $equal(complement(complement(composition(zero,top))),composition(zero,top)) )],[refute_1_1088,refute_1_1091]) ).
cnf(refute_1_1093,plain,
join(complement(complement(composition(zero,top))),one) = join(one,complement(complement(composition(zero,top)))),
inference(subst,[],[refute_1_1046:[bind(X0,$fot(complement(complement(composition(zero,top)))))]]) ).
cnf(refute_1_1094,plain,
( join(complement(complement(composition(zero,top))),one) != join(one,complement(complement(composition(zero,top))))
| join(one,complement(complement(composition(zero,top)))) != join(one,composition(zero,top))
| join(complement(complement(composition(zero,top))),one) = join(one,composition(zero,top)) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(complement(complement(composition(zero,top))),one))),bind(Y,$fot(join(one,complement(complement(composition(zero,top)))))),bind(Z,$fot(join(one,composition(zero,top))))]]) ).
cnf(refute_1_1095,plain,
( join(one,complement(complement(composition(zero,top)))) != join(one,composition(zero,top))
| join(complement(complement(composition(zero,top))),one) = join(one,composition(zero,top)) ),
inference(resolve,[$cnf( $equal(join(complement(complement(composition(zero,top))),one),join(one,complement(complement(composition(zero,top))))) )],[refute_1_1093,refute_1_1094]) ).
cnf(refute_1_1096,plain,
join(complement(complement(composition(zero,top))),one) = join(one,composition(zero,top)),
inference(resolve,[$cnf( $equal(join(one,complement(complement(composition(zero,top)))),join(one,composition(zero,top))) )],[refute_1_1092,refute_1_1095]) ).
cnf(refute_1_1097,plain,
complement(join(complement(complement(composition(zero,top))),one)) = complement(join(complement(complement(composition(zero,top))),one)),
introduced(tautology,[refl,[$fot(complement(join(complement(complement(composition(zero,top))),one)))]]) ).
cnf(refute_1_1098,plain,
( complement(join(complement(complement(composition(zero,top))),one)) != complement(join(complement(complement(composition(zero,top))),one))
| join(complement(complement(composition(zero,top))),one) != join(one,composition(zero,top))
| complement(join(complement(complement(composition(zero,top))),one)) = complement(join(one,composition(zero,top))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(complement(composition(zero,top))),one)),complement(join(complement(complement(composition(zero,top))),one))) ),[1,0],$fot(join(one,composition(zero,top)))]]) ).
cnf(refute_1_1099,plain,
( join(complement(complement(composition(zero,top))),one) != join(one,composition(zero,top))
| complement(join(complement(complement(composition(zero,top))),one)) = complement(join(one,composition(zero,top))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(complement(composition(zero,top))),one)),complement(join(complement(complement(composition(zero,top))),one))) )],[refute_1_1097,refute_1_1098]) ).
cnf(refute_1_1100,plain,
complement(join(complement(complement(composition(zero,top))),one)) = complement(join(one,composition(zero,top))),
inference(resolve,[$cnf( $equal(join(complement(complement(composition(zero,top))),one),join(one,composition(zero,top))) )],[refute_1_1096,refute_1_1099]) ).
cnf(refute_1_1101,plain,
join(one,complement(join(complement(complement(composition(zero,top))),one))) = join(one,complement(join(complement(complement(composition(zero,top))),one))),
introduced(tautology,[refl,[$fot(join(one,complement(join(complement(complement(composition(zero,top))),one))))]]) ).
cnf(refute_1_1102,plain,
( complement(join(complement(complement(composition(zero,top))),one)) != complement(join(one,composition(zero,top)))
| join(one,complement(join(complement(complement(composition(zero,top))),one))) != join(one,complement(join(complement(complement(composition(zero,top))),one)))
| join(one,complement(join(complement(complement(composition(zero,top))),one))) = join(one,complement(join(one,composition(zero,top)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,complement(join(complement(complement(composition(zero,top))),one))),join(one,complement(join(complement(complement(composition(zero,top))),one)))) ),[1,1],$fot(complement(join(one,composition(zero,top))))]]) ).
cnf(refute_1_1103,plain,
( complement(join(complement(complement(composition(zero,top))),one)) != complement(join(one,composition(zero,top)))
| join(one,complement(join(complement(complement(composition(zero,top))),one))) = join(one,complement(join(one,composition(zero,top)))) ),
inference(resolve,[$cnf( $equal(join(one,complement(join(complement(complement(composition(zero,top))),one))),join(one,complement(join(complement(complement(composition(zero,top))),one)))) )],[refute_1_1101,refute_1_1102]) ).
cnf(refute_1_1104,plain,
join(one,complement(join(complement(complement(composition(zero,top))),one))) = join(one,complement(join(one,composition(zero,top)))),
inference(resolve,[$cnf( $equal(complement(join(complement(complement(composition(zero,top))),one)),complement(join(one,composition(zero,top)))) )],[refute_1_1100,refute_1_1103]) ).
cnf(refute_1_1105,plain,
( join(one,complement(join(complement(complement(composition(zero,top))),one))) != join(one,complement(join(one,composition(zero,top))))
| join(one,complement(join(one,composition(zero,top)))) != join(one,complement(composition(zero,top)))
| join(one,complement(join(complement(complement(composition(zero,top))),one))) = join(one,complement(composition(zero,top))) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(one,complement(join(complement(complement(composition(zero,top))),one))))),bind(Y,$fot(join(one,complement(join(one,composition(zero,top)))))),bind(Z,$fot(join(one,complement(composition(zero,top)))))]]) ).
cnf(refute_1_1106,plain,
( join(one,complement(join(one,composition(zero,top)))) != join(one,complement(composition(zero,top)))
| join(one,complement(join(complement(complement(composition(zero,top))),one))) = join(one,complement(composition(zero,top))) ),
inference(resolve,[$cnf( $equal(join(one,complement(join(complement(complement(composition(zero,top))),one))),join(one,complement(join(one,composition(zero,top))))) )],[refute_1_1104,refute_1_1105]) ).
cnf(refute_1_1107,plain,
join(one,complement(join(complement(complement(composition(zero,top))),one))) = join(one,complement(composition(zero,top))),
inference(resolve,[$cnf( $equal(join(one,complement(join(one,composition(zero,top)))),join(one,complement(composition(zero,top)))) )],[refute_1_1087,refute_1_1106]) ).
cnf(refute_1_1108,plain,
( complement(composition(zero,top)) != join(one,complement(join(complement(complement(composition(zero,top))),one)))
| join(one,complement(join(complement(complement(composition(zero,top))),one))) != join(one,complement(composition(zero,top)))
| complement(composition(zero,top)) = join(one,complement(composition(zero,top))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(composition(zero,top)),join(one,complement(composition(zero,top)))) ),[0],$fot(join(one,complement(join(complement(complement(composition(zero,top))),one))))]]) ).
cnf(refute_1_1109,plain,
( complement(composition(zero,top)) != join(one,complement(join(complement(complement(composition(zero,top))),one)))
| complement(composition(zero,top)) = join(one,complement(composition(zero,top))) ),
inference(resolve,[$cnf( $equal(join(one,complement(join(complement(complement(composition(zero,top))),one))),join(one,complement(composition(zero,top)))) )],[refute_1_1107,refute_1_1108]) ).
cnf(refute_1_1110,plain,
complement(composition(zero,top)) = join(one,complement(composition(zero,top))),
inference(resolve,[$cnf( $equal(complement(composition(zero,top)),join(one,complement(join(complement(complement(composition(zero,top))),one)))) )],[refute_1_879,refute_1_1109]) ).
cnf(refute_1_1111,plain,
( complement(composition(zero,top)) != join(one,complement(composition(zero,top)))
| join(one,complement(composition(zero,top))) = complement(composition(zero,top)) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(complement(composition(zero,top)))),bind(Y,$fot(join(one,complement(composition(zero,top)))))]]) ).
cnf(refute_1_1112,plain,
join(one,complement(composition(zero,top))) = complement(composition(zero,top)),
inference(resolve,[$cnf( $equal(complement(composition(zero,top)),join(one,complement(composition(zero,top)))) )],[refute_1_1110,refute_1_1111]) ).
cnf(refute_1_1113,plain,
( join(one,complement(composition(zero,top))) != complement(composition(zero,top))
| one != meet(one,converse(join(one,complement(composition(zero,top)))))
| one = meet(one,converse(complement(composition(zero,top)))) ),
introduced(tautology,[equality,[$cnf( $equal(one,meet(one,converse(join(one,complement(composition(zero,top)))))) ),[1,1,0],$fot(complement(composition(zero,top)))]]) ).
cnf(refute_1_1114,plain,
( one != meet(one,converse(join(one,complement(composition(zero,top)))))
| one = meet(one,converse(complement(composition(zero,top)))) ),
inference(resolve,[$cnf( $equal(join(one,complement(composition(zero,top))),complement(composition(zero,top))) )],[refute_1_1112,refute_1_1113]) ).
cnf(refute_1_1115,plain,
one = meet(one,converse(complement(composition(zero,top)))),
inference(resolve,[$cnf( $equal(one,meet(one,converse(join(one,complement(composition(zero,top)))))) )],[refute_1_741,refute_1_1114]) ).
cnf(refute_1_1116,plain,
( one != meet(one,converse(complement(composition(zero,top))))
| meet(one,converse(complement(composition(zero,top)))) = one ),
inference(subst,[],[refute_1_17:[bind(X,$fot(one)),bind(Y,$fot(meet(one,converse(complement(composition(zero,top))))))]]) ).
cnf(refute_1_1117,plain,
meet(one,converse(complement(composition(zero,top)))) = one,
inference(resolve,[$cnf( $equal(one,meet(one,converse(complement(composition(zero,top))))) )],[refute_1_1115,refute_1_1116]) ).
cnf(refute_1_1118,plain,
( converse(complement(composition(zero,top))) != join(meet(one,converse(complement(composition(zero,top)))),complement(join(complement(converse(complement(composition(zero,top)))),one)))
| meet(one,converse(complement(composition(zero,top)))) != one
| converse(complement(composition(zero,top))) = join(one,complement(join(complement(converse(complement(composition(zero,top)))),one))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(complement(composition(zero,top))),join(meet(one,converse(complement(composition(zero,top)))),complement(join(complement(converse(complement(composition(zero,top)))),one)))) ),[1,0],$fot(one)]]) ).
cnf(refute_1_1119,plain,
( converse(complement(composition(zero,top))) != join(meet(one,converse(complement(composition(zero,top)))),complement(join(complement(converse(complement(composition(zero,top)))),one)))
| converse(complement(composition(zero,top))) = join(one,complement(join(complement(converse(complement(composition(zero,top)))),one))) ),
inference(resolve,[$cnf( $equal(meet(one,converse(complement(composition(zero,top)))),one) )],[refute_1_1117,refute_1_1118]) ).
cnf(refute_1_1120,plain,
converse(complement(composition(zero,top))) = join(one,complement(join(complement(converse(complement(composition(zero,top)))),one))),
inference(resolve,[$cnf( $equal(converse(complement(composition(zero,top))),join(meet(one,converse(complement(composition(zero,top)))),complement(join(complement(converse(complement(composition(zero,top)))),one)))) )],[refute_1_684,refute_1_1119]) ).
cnf(refute_1_1121,plain,
join(complement(converse(complement(composition(zero,top)))),one) = join(one,complement(converse(complement(composition(zero,top))))),
inference(subst,[],[refute_1_1046:[bind(X0,$fot(complement(converse(complement(composition(zero,top))))))]]) ).
cnf(refute_1_1122,plain,
complement(join(complement(converse(complement(composition(zero,top)))),one)) = complement(join(complement(converse(complement(composition(zero,top)))),one)),
introduced(tautology,[refl,[$fot(complement(join(complement(converse(complement(composition(zero,top)))),one)))]]) ).
cnf(refute_1_1123,plain,
( complement(join(complement(converse(complement(composition(zero,top)))),one)) != complement(join(complement(converse(complement(composition(zero,top)))),one))
| join(complement(converse(complement(composition(zero,top)))),one) != join(one,complement(converse(complement(composition(zero,top)))))
| complement(join(complement(converse(complement(composition(zero,top)))),one)) = complement(join(one,complement(converse(complement(composition(zero,top)))))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(converse(complement(composition(zero,top)))),one)),complement(join(complement(converse(complement(composition(zero,top)))),one))) ),[1,0],$fot(join(one,complement(converse(complement(composition(zero,top))))))]]) ).
cnf(refute_1_1124,plain,
( join(complement(converse(complement(composition(zero,top)))),one) != join(one,complement(converse(complement(composition(zero,top)))))
| complement(join(complement(converse(complement(composition(zero,top)))),one)) = complement(join(one,complement(converse(complement(composition(zero,top)))))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(converse(complement(composition(zero,top)))),one)),complement(join(complement(converse(complement(composition(zero,top)))),one))) )],[refute_1_1122,refute_1_1123]) ).
cnf(refute_1_1125,plain,
complement(join(complement(converse(complement(composition(zero,top)))),one)) = complement(join(one,complement(converse(complement(composition(zero,top)))))),
inference(resolve,[$cnf( $equal(join(complement(converse(complement(composition(zero,top)))),one),join(one,complement(converse(complement(composition(zero,top)))))) )],[refute_1_1121,refute_1_1124]) ).
cnf(refute_1_1126,plain,
join(one,complement(join(complement(converse(complement(composition(zero,top)))),one))) = join(one,complement(join(complement(converse(complement(composition(zero,top)))),one))),
introduced(tautology,[refl,[$fot(join(one,complement(join(complement(converse(complement(composition(zero,top)))),one))))]]) ).
cnf(refute_1_1127,plain,
( complement(join(complement(converse(complement(composition(zero,top)))),one)) != complement(join(one,complement(converse(complement(composition(zero,top))))))
| join(one,complement(join(complement(converse(complement(composition(zero,top)))),one))) != join(one,complement(join(complement(converse(complement(composition(zero,top)))),one)))
| join(one,complement(join(complement(converse(complement(composition(zero,top)))),one))) = join(one,complement(join(one,complement(converse(complement(composition(zero,top))))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,complement(join(complement(converse(complement(composition(zero,top)))),one))),join(one,complement(join(complement(converse(complement(composition(zero,top)))),one)))) ),[1,1],$fot(complement(join(one,complement(converse(complement(composition(zero,top)))))))]]) ).
cnf(refute_1_1128,plain,
( complement(join(complement(converse(complement(composition(zero,top)))),one)) != complement(join(one,complement(converse(complement(composition(zero,top))))))
| join(one,complement(join(complement(converse(complement(composition(zero,top)))),one))) = join(one,complement(join(one,complement(converse(complement(composition(zero,top))))))) ),
inference(resolve,[$cnf( $equal(join(one,complement(join(complement(converse(complement(composition(zero,top)))),one))),join(one,complement(join(complement(converse(complement(composition(zero,top)))),one)))) )],[refute_1_1126,refute_1_1127]) ).
cnf(refute_1_1129,plain,
join(one,complement(join(complement(converse(complement(composition(zero,top)))),one))) = join(one,complement(join(one,complement(converse(complement(composition(zero,top))))))),
inference(resolve,[$cnf( $equal(complement(join(complement(converse(complement(composition(zero,top)))),one)),complement(join(one,complement(converse(complement(composition(zero,top))))))) )],[refute_1_1125,refute_1_1128]) ).
cnf(refute_1_1130,plain,
( converse(complement(composition(zero,top))) != join(one,complement(join(complement(converse(complement(composition(zero,top)))),one)))
| join(one,complement(join(complement(converse(complement(composition(zero,top)))),one))) != join(one,complement(join(one,complement(converse(complement(composition(zero,top)))))))
| converse(complement(composition(zero,top))) = join(one,complement(join(one,complement(converse(complement(composition(zero,top))))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(complement(composition(zero,top))),join(one,complement(join(one,complement(converse(complement(composition(zero,top)))))))) ),[0],$fot(join(one,complement(join(complement(converse(complement(composition(zero,top)))),one))))]]) ).
cnf(refute_1_1131,plain,
( converse(complement(composition(zero,top))) != join(one,complement(join(complement(converse(complement(composition(zero,top)))),one)))
| converse(complement(composition(zero,top))) = join(one,complement(join(one,complement(converse(complement(composition(zero,top))))))) ),
inference(resolve,[$cnf( $equal(join(one,complement(join(complement(converse(complement(composition(zero,top)))),one))),join(one,complement(join(one,complement(converse(complement(composition(zero,top)))))))) )],[refute_1_1129,refute_1_1130]) ).
cnf(refute_1_1132,plain,
converse(complement(composition(zero,top))) = join(one,complement(join(one,complement(converse(complement(composition(zero,top))))))),
inference(resolve,[$cnf( $equal(converse(complement(composition(zero,top))),join(one,complement(join(complement(converse(complement(composition(zero,top)))),one)))) )],[refute_1_1120,refute_1_1131]) ).
cnf(refute_1_1133,plain,
join(one,complement(composition(top,zero))) = join(meet(join(one,complement(composition(top,zero))),one),complement(join(one,complement(join(one,complement(composition(top,zero))))))),
inference(subst,[],[refute_1_885:[bind(X_176,$fot(join(one,complement(composition(top,zero))))),bind(X_177,$fot(one))]]) ).
cnf(refute_1_1134,plain,
join(one,join(meet(one,composition(top,zero)),X_212)) = join(join(one,meet(one,composition(top,zero))),X_212),
inference(subst,[],[refute_1_100:[bind(X0,$fot(one)),bind(X1,$fot(meet(one,composition(top,zero)))),bind(X2,$fot(X_212))]]) ).
cnf(refute_1_1135,plain,
one = join(meet(one,composition(top,zero)),complement(join(complement(one),composition(top,zero)))),
inference(subst,[],[refute_1_69:[bind(X0,$fot(one)),bind(X1,$fot(composition(top,zero)))]]) ).
cnf(refute_1_1136,plain,
join(complement(one),composition(converse(top),complement(top))) = complement(one),
inference(subst,[],[refute_1_772:[bind(X_133,$fot(top))]]) ).
cnf(refute_1_1137,plain,
( complement(top) != zero
| join(complement(one),composition(converse(top),complement(top))) != complement(one)
| join(complement(one),composition(converse(top),zero)) = complement(one) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(one),composition(converse(top),complement(top))),complement(one)) ),[0,1,1],$fot(zero)]]) ).
cnf(refute_1_1138,plain,
( join(complement(one),composition(converse(top),complement(top))) != complement(one)
| join(complement(one),composition(converse(top),zero)) = complement(one) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_1_45,refute_1_1137]) ).
cnf(refute_1_1139,plain,
join(complement(one),composition(converse(top),zero)) = complement(one),
inference(resolve,[$cnf( $equal(join(complement(one),composition(converse(top),complement(top))),complement(one)) )],[refute_1_1136,refute_1_1138]) ).
cnf(refute_1_1140,plain,
composition(converse(top),zero) = composition(converse(top),zero),
introduced(tautology,[refl,[$fot(composition(converse(top),zero))]]) ).
cnf(refute_1_1141,plain,
( composition(converse(top),zero) != composition(converse(top),zero)
| converse(top) != top
| composition(converse(top),zero) = composition(top,zero) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(top),zero),composition(converse(top),zero)) ),[1,0],$fot(top)]]) ).
cnf(refute_1_1142,plain,
( converse(top) != top
| composition(converse(top),zero) = composition(top,zero) ),
inference(resolve,[$cnf( $equal(composition(converse(top),zero),composition(converse(top),zero)) )],[refute_1_1140,refute_1_1141]) ).
cnf(refute_1_1143,plain,
composition(converse(top),zero) = composition(top,zero),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_1_191,refute_1_1142]) ).
cnf(refute_1_1144,plain,
join(complement(one),composition(converse(top),zero)) = join(complement(one),composition(converse(top),zero)),
introduced(tautology,[refl,[$fot(join(complement(one),composition(converse(top),zero)))]]) ).
cnf(refute_1_1145,plain,
( composition(converse(top),zero) != composition(top,zero)
| join(complement(one),composition(converse(top),zero)) != join(complement(one),composition(converse(top),zero))
| join(complement(one),composition(converse(top),zero)) = join(complement(one),composition(top,zero)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(one),composition(converse(top),zero)),join(complement(one),composition(converse(top),zero))) ),[1,1],$fot(composition(top,zero))]]) ).
cnf(refute_1_1146,plain,
( composition(converse(top),zero) != composition(top,zero)
| join(complement(one),composition(converse(top),zero)) = join(complement(one),composition(top,zero)) ),
inference(resolve,[$cnf( $equal(join(complement(one),composition(converse(top),zero)),join(complement(one),composition(converse(top),zero))) )],[refute_1_1144,refute_1_1145]) ).
cnf(refute_1_1147,plain,
join(complement(one),composition(converse(top),zero)) = join(complement(one),composition(top,zero)),
inference(resolve,[$cnf( $equal(composition(converse(top),zero),composition(top,zero)) )],[refute_1_1143,refute_1_1146]) ).
cnf(refute_1_1148,plain,
( join(complement(one),composition(converse(top),zero)) != complement(one)
| join(complement(one),composition(converse(top),zero)) != join(complement(one),composition(top,zero))
| join(complement(one),composition(top,zero)) = complement(one) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(one),composition(converse(top),zero)),complement(one)) ),[0],$fot(join(complement(one),composition(top,zero)))]]) ).
cnf(refute_1_1149,plain,
( join(complement(one),composition(converse(top),zero)) != complement(one)
| join(complement(one),composition(top,zero)) = complement(one) ),
inference(resolve,[$cnf( $equal(join(complement(one),composition(converse(top),zero)),join(complement(one),composition(top,zero))) )],[refute_1_1147,refute_1_1148]) ).
cnf(refute_1_1150,plain,
join(complement(one),composition(top,zero)) = complement(one),
inference(resolve,[$cnf( $equal(join(complement(one),composition(converse(top),zero)),complement(one)) )],[refute_1_1139,refute_1_1149]) ).
cnf(refute_1_1151,plain,
( join(complement(one),composition(top,zero)) != complement(one)
| one != join(meet(one,composition(top,zero)),complement(join(complement(one),composition(top,zero))))
| one = join(meet(one,composition(top,zero)),complement(complement(one))) ),
introduced(tautology,[equality,[$cnf( $equal(one,join(meet(one,composition(top,zero)),complement(join(complement(one),composition(top,zero))))) ),[1,1,0],$fot(complement(one))]]) ).
cnf(refute_1_1152,plain,
( one != join(meet(one,composition(top,zero)),complement(join(complement(one),composition(top,zero))))
| one = join(meet(one,composition(top,zero)),complement(complement(one))) ),
inference(resolve,[$cnf( $equal(join(complement(one),composition(top,zero)),complement(one)) )],[refute_1_1150,refute_1_1151]) ).
cnf(refute_1_1153,plain,
one = join(meet(one,composition(top,zero)),complement(complement(one))),
inference(resolve,[$cnf( $equal(one,join(meet(one,composition(top,zero)),complement(join(complement(one),composition(top,zero))))) )],[refute_1_1135,refute_1_1152]) ).
cnf(refute_1_1154,plain,
join(meet(one,composition(top,zero)),complement(complement(one))) = join(complement(complement(one)),meet(one,composition(top,zero))),
inference(subst,[],[refute_1_52:[bind(X0,$fot(complement(complement(one)))),bind(X1,$fot(meet(one,composition(top,zero))))]]) ).
cnf(refute_1_1155,plain,
( join(meet(one,composition(top,zero)),complement(complement(one))) != join(complement(complement(one)),meet(one,composition(top,zero)))
| one != join(meet(one,composition(top,zero)),complement(complement(one)))
| one = join(complement(complement(one)),meet(one,composition(top,zero))) ),
introduced(tautology,[equality,[$cnf( $equal(one,join(meet(one,composition(top,zero)),complement(complement(one)))) ),[1],$fot(join(complement(complement(one)),meet(one,composition(top,zero))))]]) ).
cnf(refute_1_1156,plain,
( one != join(meet(one,composition(top,zero)),complement(complement(one)))
| one = join(complement(complement(one)),meet(one,composition(top,zero))) ),
inference(resolve,[$cnf( $equal(join(meet(one,composition(top,zero)),complement(complement(one))),join(complement(complement(one)),meet(one,composition(top,zero)))) )],[refute_1_1154,refute_1_1155]) ).
cnf(refute_1_1157,plain,
one = join(complement(complement(one)),meet(one,composition(top,zero))),
inference(resolve,[$cnf( $equal(one,join(meet(one,composition(top,zero)),complement(complement(one)))) )],[refute_1_1153,refute_1_1156]) ).
cnf(refute_1_1158,plain,
join(complement(complement(one)),meet(one,composition(top,zero))) = join(complement(complement(one)),meet(one,composition(top,zero))),
introduced(tautology,[refl,[$fot(join(complement(complement(one)),meet(one,composition(top,zero))))]]) ).
cnf(refute_1_1159,plain,
( complement(complement(one)) != one
| join(complement(complement(one)),meet(one,composition(top,zero))) != join(complement(complement(one)),meet(one,composition(top,zero)))
| join(complement(complement(one)),meet(one,composition(top,zero))) = join(one,meet(one,composition(top,zero))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(complement(one)),meet(one,composition(top,zero))),join(complement(complement(one)),meet(one,composition(top,zero)))) ),[1,0],$fot(one)]]) ).
cnf(refute_1_1160,plain,
( complement(complement(one)) != one
| join(complement(complement(one)),meet(one,composition(top,zero))) = join(one,meet(one,composition(top,zero))) ),
inference(resolve,[$cnf( $equal(join(complement(complement(one)),meet(one,composition(top,zero))),join(complement(complement(one)),meet(one,composition(top,zero)))) )],[refute_1_1158,refute_1_1159]) ).
cnf(refute_1_1161,plain,
join(complement(complement(one)),meet(one,composition(top,zero))) = join(one,meet(one,composition(top,zero))),
inference(resolve,[$cnf( $equal(complement(complement(one)),one) )],[refute_1_892,refute_1_1160]) ).
cnf(refute_1_1162,plain,
( join(complement(complement(one)),meet(one,composition(top,zero))) != join(one,meet(one,composition(top,zero)))
| one != join(complement(complement(one)),meet(one,composition(top,zero)))
| one = join(one,meet(one,composition(top,zero))) ),
introduced(tautology,[equality,[$cnf( $equal(one,join(complement(complement(one)),meet(one,composition(top,zero)))) ),[1],$fot(join(one,meet(one,composition(top,zero))))]]) ).
cnf(refute_1_1163,plain,
( one != join(complement(complement(one)),meet(one,composition(top,zero)))
| one = join(one,meet(one,composition(top,zero))) ),
inference(resolve,[$cnf( $equal(join(complement(complement(one)),meet(one,composition(top,zero))),join(one,meet(one,composition(top,zero)))) )],[refute_1_1161,refute_1_1162]) ).
cnf(refute_1_1164,plain,
one = join(one,meet(one,composition(top,zero))),
inference(resolve,[$cnf( $equal(one,join(complement(complement(one)),meet(one,composition(top,zero)))) )],[refute_1_1157,refute_1_1163]) ).
cnf(refute_1_1165,plain,
( one != join(one,meet(one,composition(top,zero)))
| join(one,meet(one,composition(top,zero))) = one ),
inference(subst,[],[refute_1_17:[bind(X,$fot(one)),bind(Y,$fot(join(one,meet(one,composition(top,zero)))))]]) ).
cnf(refute_1_1166,plain,
join(one,meet(one,composition(top,zero))) = one,
inference(resolve,[$cnf( $equal(one,join(one,meet(one,composition(top,zero)))) )],[refute_1_1164,refute_1_1165]) ).
cnf(refute_1_1167,plain,
( join(one,join(meet(one,composition(top,zero)),X_212)) != join(join(one,meet(one,composition(top,zero))),X_212)
| join(one,meet(one,composition(top,zero))) != one
| join(one,join(meet(one,composition(top,zero)),X_212)) = join(one,X_212) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(meet(one,composition(top,zero)),X_212)),join(join(one,meet(one,composition(top,zero))),X_212)) ),[1,0],$fot(one)]]) ).
cnf(refute_1_1168,plain,
( join(one,join(meet(one,composition(top,zero)),X_212)) != join(join(one,meet(one,composition(top,zero))),X_212)
| join(one,join(meet(one,composition(top,zero)),X_212)) = join(one,X_212) ),
inference(resolve,[$cnf( $equal(join(one,meet(one,composition(top,zero))),one) )],[refute_1_1166,refute_1_1167]) ).
cnf(refute_1_1169,plain,
join(one,join(meet(one,composition(top,zero)),X_212)) = join(one,X_212),
inference(resolve,[$cnf( $equal(join(one,join(meet(one,composition(top,zero)),X_212)),join(join(one,meet(one,composition(top,zero))),X_212)) )],[refute_1_1134,refute_1_1168]) ).
cnf(refute_1_1170,plain,
join(one,join(meet(one,composition(top,zero)),complement(join(complement(composition(top,zero)),one)))) = join(one,complement(join(complement(composition(top,zero)),one))),
inference(subst,[],[refute_1_1169:[bind(X_212,$fot(complement(join(complement(composition(top,zero)),one))))]]) ).
cnf(refute_1_1171,plain,
composition(top,zero) = join(meet(one,composition(top,zero)),complement(join(complement(composition(top,zero)),one))),
inference(subst,[],[refute_1_683:[bind(X_176,$fot(composition(top,zero))),bind(X_177,$fot(one))]]) ).
cnf(refute_1_1172,plain,
( composition(top,zero) != join(meet(one,composition(top,zero)),complement(join(complement(composition(top,zero)),one)))
| join(meet(one,composition(top,zero)),complement(join(complement(composition(top,zero)),one))) = composition(top,zero) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(composition(top,zero))),bind(Y,$fot(join(meet(one,composition(top,zero)),complement(join(complement(composition(top,zero)),one)))))]]) ).
cnf(refute_1_1173,plain,
join(meet(one,composition(top,zero)),complement(join(complement(composition(top,zero)),one))) = composition(top,zero),
inference(resolve,[$cnf( $equal(composition(top,zero),join(meet(one,composition(top,zero)),complement(join(complement(composition(top,zero)),one)))) )],[refute_1_1171,refute_1_1172]) ).
cnf(refute_1_1174,plain,
( join(meet(one,composition(top,zero)),complement(join(complement(composition(top,zero)),one))) != composition(top,zero)
| join(one,join(meet(one,composition(top,zero)),complement(join(complement(composition(top,zero)),one)))) != join(one,complement(join(complement(composition(top,zero)),one)))
| join(one,composition(top,zero)) = join(one,complement(join(complement(composition(top,zero)),one))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(meet(one,composition(top,zero)),complement(join(complement(composition(top,zero)),one)))),join(one,complement(join(complement(composition(top,zero)),one)))) ),[0,1],$fot(composition(top,zero))]]) ).
cnf(refute_1_1175,plain,
( join(one,join(meet(one,composition(top,zero)),complement(join(complement(composition(top,zero)),one)))) != join(one,complement(join(complement(composition(top,zero)),one)))
| join(one,composition(top,zero)) = join(one,complement(join(complement(composition(top,zero)),one))) ),
inference(resolve,[$cnf( $equal(join(meet(one,composition(top,zero)),complement(join(complement(composition(top,zero)),one))),composition(top,zero)) )],[refute_1_1173,refute_1_1174]) ).
cnf(refute_1_1176,plain,
join(one,composition(top,zero)) = join(one,complement(join(complement(composition(top,zero)),one))),
inference(resolve,[$cnf( $equal(join(one,join(meet(one,composition(top,zero)),complement(join(complement(composition(top,zero)),one)))),join(one,complement(join(complement(composition(top,zero)),one)))) )],[refute_1_1170,refute_1_1175]) ).
cnf(refute_1_1177,plain,
join(complement(composition(top,zero)),one) = join(one,complement(composition(top,zero))),
inference(subst,[],[refute_1_1046:[bind(X0,$fot(complement(composition(top,zero))))]]) ).
cnf(refute_1_1178,plain,
complement(join(complement(composition(top,zero)),one)) = complement(join(complement(composition(top,zero)),one)),
introduced(tautology,[refl,[$fot(complement(join(complement(composition(top,zero)),one)))]]) ).
cnf(refute_1_1179,plain,
( complement(join(complement(composition(top,zero)),one)) != complement(join(complement(composition(top,zero)),one))
| join(complement(composition(top,zero)),one) != join(one,complement(composition(top,zero)))
| complement(join(complement(composition(top,zero)),one)) = complement(join(one,complement(composition(top,zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(composition(top,zero)),one)),complement(join(complement(composition(top,zero)),one))) ),[1,0],$fot(join(one,complement(composition(top,zero))))]]) ).
cnf(refute_1_1180,plain,
( join(complement(composition(top,zero)),one) != join(one,complement(composition(top,zero)))
| complement(join(complement(composition(top,zero)),one)) = complement(join(one,complement(composition(top,zero)))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(composition(top,zero)),one)),complement(join(complement(composition(top,zero)),one))) )],[refute_1_1178,refute_1_1179]) ).
cnf(refute_1_1181,plain,
complement(join(complement(composition(top,zero)),one)) = complement(join(one,complement(composition(top,zero)))),
inference(resolve,[$cnf( $equal(join(complement(composition(top,zero)),one),join(one,complement(composition(top,zero)))) )],[refute_1_1177,refute_1_1180]) ).
cnf(refute_1_1182,plain,
join(one,complement(join(complement(composition(top,zero)),one))) = join(one,complement(join(complement(composition(top,zero)),one))),
introduced(tautology,[refl,[$fot(join(one,complement(join(complement(composition(top,zero)),one))))]]) ).
cnf(refute_1_1183,plain,
( complement(join(complement(composition(top,zero)),one)) != complement(join(one,complement(composition(top,zero))))
| join(one,complement(join(complement(composition(top,zero)),one))) != join(one,complement(join(complement(composition(top,zero)),one)))
| join(one,complement(join(complement(composition(top,zero)),one))) = join(one,complement(join(one,complement(composition(top,zero))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,complement(join(complement(composition(top,zero)),one))),join(one,complement(join(complement(composition(top,zero)),one)))) ),[1,1],$fot(complement(join(one,complement(composition(top,zero)))))]]) ).
cnf(refute_1_1184,plain,
( complement(join(complement(composition(top,zero)),one)) != complement(join(one,complement(composition(top,zero))))
| join(one,complement(join(complement(composition(top,zero)),one))) = join(one,complement(join(one,complement(composition(top,zero))))) ),
inference(resolve,[$cnf( $equal(join(one,complement(join(complement(composition(top,zero)),one))),join(one,complement(join(complement(composition(top,zero)),one)))) )],[refute_1_1182,refute_1_1183]) ).
cnf(refute_1_1185,plain,
join(one,complement(join(complement(composition(top,zero)),one))) = join(one,complement(join(one,complement(composition(top,zero))))),
inference(resolve,[$cnf( $equal(complement(join(complement(composition(top,zero)),one)),complement(join(one,complement(composition(top,zero))))) )],[refute_1_1181,refute_1_1184]) ).
cnf(refute_1_1186,plain,
( join(one,complement(join(complement(composition(top,zero)),one))) != join(one,complement(join(one,complement(composition(top,zero)))))
| join(one,composition(top,zero)) != join(one,complement(join(complement(composition(top,zero)),one)))
| join(one,composition(top,zero)) = join(one,complement(join(one,complement(composition(top,zero))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,composition(top,zero)),join(one,complement(join(complement(composition(top,zero)),one)))) ),[1],$fot(join(one,complement(join(one,complement(composition(top,zero))))))]]) ).
cnf(refute_1_1187,plain,
( join(one,composition(top,zero)) != join(one,complement(join(complement(composition(top,zero)),one)))
| join(one,composition(top,zero)) = join(one,complement(join(one,complement(composition(top,zero))))) ),
inference(resolve,[$cnf( $equal(join(one,complement(join(complement(composition(top,zero)),one))),join(one,complement(join(one,complement(composition(top,zero)))))) )],[refute_1_1185,refute_1_1186]) ).
cnf(refute_1_1188,plain,
join(one,composition(top,zero)) = join(one,complement(join(one,complement(composition(top,zero))))),
inference(resolve,[$cnf( $equal(join(one,composition(top,zero)),join(one,complement(join(complement(composition(top,zero)),one)))) )],[refute_1_1176,refute_1_1187]) ).
cnf(refute_1_1189,plain,
( join(one,composition(top,zero)) != join(one,complement(join(one,complement(composition(top,zero)))))
| join(one,complement(join(one,complement(composition(top,zero))))) = join(one,composition(top,zero)) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(join(one,composition(top,zero)))),bind(Y,$fot(join(one,complement(join(one,complement(composition(top,zero)))))))]]) ).
cnf(refute_1_1190,plain,
join(one,complement(join(one,complement(composition(top,zero))))) = join(one,composition(top,zero)),
inference(resolve,[$cnf( $equal(join(one,composition(top,zero)),join(one,complement(join(one,complement(composition(top,zero)))))) )],[refute_1_1188,refute_1_1189]) ).
cnf(refute_1_1191,plain,
( join(one,complement(composition(top,zero))) != join(meet(join(one,complement(composition(top,zero))),one),complement(join(one,complement(join(one,complement(composition(top,zero)))))))
| join(one,complement(join(one,complement(composition(top,zero))))) != join(one,composition(top,zero))
| join(one,complement(composition(top,zero))) = join(meet(join(one,complement(composition(top,zero))),one),complement(join(one,composition(top,zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,complement(composition(top,zero))),join(meet(join(one,complement(composition(top,zero))),one),complement(join(one,complement(join(one,complement(composition(top,zero)))))))) ),[1,1,0],$fot(join(one,composition(top,zero)))]]) ).
cnf(refute_1_1192,plain,
( join(one,complement(composition(top,zero))) != join(meet(join(one,complement(composition(top,zero))),one),complement(join(one,complement(join(one,complement(composition(top,zero)))))))
| join(one,complement(composition(top,zero))) = join(meet(join(one,complement(composition(top,zero))),one),complement(join(one,composition(top,zero)))) ),
inference(resolve,[$cnf( $equal(join(one,complement(join(one,complement(composition(top,zero))))),join(one,composition(top,zero))) )],[refute_1_1190,refute_1_1191]) ).
cnf(refute_1_1193,plain,
join(one,complement(composition(top,zero))) = join(meet(join(one,complement(composition(top,zero))),one),complement(join(one,composition(top,zero)))),
inference(resolve,[$cnf( $equal(join(one,complement(composition(top,zero))),join(meet(join(one,complement(composition(top,zero))),one),complement(join(one,complement(join(one,complement(composition(top,zero)))))))) )],[refute_1_1133,refute_1_1192]) ).
cnf(refute_1_1194,plain,
join(complement(join(one,composition(top,zero))),one) = join(one,complement(join(one,composition(top,zero)))),
inference(subst,[],[refute_1_1046:[bind(X0,$fot(complement(join(one,composition(top,zero)))))]]) ).
cnf(refute_1_1195,plain,
meet(one,join(one,complement(composition(top,zero)))) = one,
inference(subst,[],[refute_1_1066:[bind(X_176,$fot(one)),bind(X_214,$fot(complement(composition(top,zero))))]]) ).
cnf(refute_1_1196,plain,
meet(join(one,complement(composition(top,zero))),one) = meet(one,join(one,complement(composition(top,zero)))),
inference(subst,[],[refute_1_711:[bind(X_137,$fot(one)),bind(X_138,$fot(join(one,complement(composition(top,zero)))))]]) ).
cnf(refute_1_1197,plain,
( meet(join(one,complement(composition(top,zero))),one) != meet(one,join(one,complement(composition(top,zero))))
| meet(one,join(one,complement(composition(top,zero)))) != one
| meet(join(one,complement(composition(top,zero))),one) = one ),
inference(subst,[],[refute_1_37:[bind(X,$fot(meet(join(one,complement(composition(top,zero))),one))),bind(Y,$fot(meet(one,join(one,complement(composition(top,zero)))))),bind(Z,$fot(one))]]) ).
cnf(refute_1_1198,plain,
( meet(one,join(one,complement(composition(top,zero)))) != one
| meet(join(one,complement(composition(top,zero))),one) = one ),
inference(resolve,[$cnf( $equal(meet(join(one,complement(composition(top,zero))),one),meet(one,join(one,complement(composition(top,zero))))) )],[refute_1_1196,refute_1_1197]) ).
cnf(refute_1_1199,plain,
meet(join(one,complement(composition(top,zero))),one) = one,
inference(resolve,[$cnf( $equal(meet(one,join(one,complement(composition(top,zero)))),one) )],[refute_1_1195,refute_1_1198]) ).
cnf(refute_1_1200,plain,
join(complement(join(one,composition(top,zero))),meet(join(one,complement(composition(top,zero))),one)) = join(complement(join(one,composition(top,zero))),meet(join(one,complement(composition(top,zero))),one)),
introduced(tautology,[refl,[$fot(join(complement(join(one,composition(top,zero))),meet(join(one,complement(composition(top,zero))),one)))]]) ).
cnf(refute_1_1201,plain,
( join(complement(join(one,composition(top,zero))),meet(join(one,complement(composition(top,zero))),one)) != join(complement(join(one,composition(top,zero))),meet(join(one,complement(composition(top,zero))),one))
| meet(join(one,complement(composition(top,zero))),one) != one
| join(complement(join(one,composition(top,zero))),meet(join(one,complement(composition(top,zero))),one)) = join(complement(join(one,composition(top,zero))),one) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(join(one,composition(top,zero))),meet(join(one,complement(composition(top,zero))),one)),join(complement(join(one,composition(top,zero))),meet(join(one,complement(composition(top,zero))),one))) ),[1,1],$fot(one)]]) ).
cnf(refute_1_1202,plain,
( meet(join(one,complement(composition(top,zero))),one) != one
| join(complement(join(one,composition(top,zero))),meet(join(one,complement(composition(top,zero))),one)) = join(complement(join(one,composition(top,zero))),one) ),
inference(resolve,[$cnf( $equal(join(complement(join(one,composition(top,zero))),meet(join(one,complement(composition(top,zero))),one)),join(complement(join(one,composition(top,zero))),meet(join(one,complement(composition(top,zero))),one))) )],[refute_1_1200,refute_1_1201]) ).
cnf(refute_1_1203,plain,
join(complement(join(one,composition(top,zero))),meet(join(one,complement(composition(top,zero))),one)) = join(complement(join(one,composition(top,zero))),one),
inference(resolve,[$cnf( $equal(meet(join(one,complement(composition(top,zero))),one),one) )],[refute_1_1199,refute_1_1202]) ).
cnf(refute_1_1204,plain,
( join(complement(join(one,composition(top,zero))),meet(join(one,complement(composition(top,zero))),one)) != join(complement(join(one,composition(top,zero))),one)
| join(complement(join(one,composition(top,zero))),one) != join(one,complement(join(one,composition(top,zero))))
| join(complement(join(one,composition(top,zero))),meet(join(one,complement(composition(top,zero))),one)) = join(one,complement(join(one,composition(top,zero)))) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(complement(join(one,composition(top,zero))),meet(join(one,complement(composition(top,zero))),one)))),bind(Y,$fot(join(complement(join(one,composition(top,zero))),one))),bind(Z,$fot(join(one,complement(join(one,composition(top,zero))))))]]) ).
cnf(refute_1_1205,plain,
( join(complement(join(one,composition(top,zero))),one) != join(one,complement(join(one,composition(top,zero))))
| join(complement(join(one,composition(top,zero))),meet(join(one,complement(composition(top,zero))),one)) = join(one,complement(join(one,composition(top,zero)))) ),
inference(resolve,[$cnf( $equal(join(complement(join(one,composition(top,zero))),meet(join(one,complement(composition(top,zero))),one)),join(complement(join(one,composition(top,zero))),one)) )],[refute_1_1203,refute_1_1204]) ).
cnf(refute_1_1206,plain,
join(complement(join(one,composition(top,zero))),meet(join(one,complement(composition(top,zero))),one)) = join(one,complement(join(one,composition(top,zero)))),
inference(resolve,[$cnf( $equal(join(complement(join(one,composition(top,zero))),one),join(one,complement(join(one,composition(top,zero))))) )],[refute_1_1194,refute_1_1205]) ).
cnf(refute_1_1207,plain,
join(meet(join(one,complement(composition(top,zero))),one),complement(join(one,composition(top,zero)))) = join(complement(join(one,composition(top,zero))),meet(join(one,complement(composition(top,zero))),one)),
inference(subst,[],[refute_1_52:[bind(X0,$fot(complement(join(one,composition(top,zero))))),bind(X1,$fot(meet(join(one,complement(composition(top,zero))),one)))]]) ).
cnf(refute_1_1208,plain,
( join(complement(join(one,composition(top,zero))),meet(join(one,complement(composition(top,zero))),one)) != join(one,complement(join(one,composition(top,zero))))
| join(meet(join(one,complement(composition(top,zero))),one),complement(join(one,composition(top,zero)))) != join(complement(join(one,composition(top,zero))),meet(join(one,complement(composition(top,zero))),one))
| join(meet(join(one,complement(composition(top,zero))),one),complement(join(one,composition(top,zero)))) = join(one,complement(join(one,composition(top,zero)))) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(meet(join(one,complement(composition(top,zero))),one),complement(join(one,composition(top,zero)))))),bind(Y,$fot(join(complement(join(one,composition(top,zero))),meet(join(one,complement(composition(top,zero))),one)))),bind(Z,$fot(join(one,complement(join(one,composition(top,zero))))))]]) ).
cnf(refute_1_1209,plain,
( join(complement(join(one,composition(top,zero))),meet(join(one,complement(composition(top,zero))),one)) != join(one,complement(join(one,composition(top,zero))))
| join(meet(join(one,complement(composition(top,zero))),one),complement(join(one,composition(top,zero)))) = join(one,complement(join(one,composition(top,zero)))) ),
inference(resolve,[$cnf( $equal(join(meet(join(one,complement(composition(top,zero))),one),complement(join(one,composition(top,zero)))),join(complement(join(one,composition(top,zero))),meet(join(one,complement(composition(top,zero))),one))) )],[refute_1_1207,refute_1_1208]) ).
cnf(refute_1_1210,plain,
join(meet(join(one,complement(composition(top,zero))),one),complement(join(one,composition(top,zero)))) = join(one,complement(join(one,composition(top,zero)))),
inference(resolve,[$cnf( $equal(join(complement(join(one,composition(top,zero))),meet(join(one,complement(composition(top,zero))),one)),join(one,complement(join(one,composition(top,zero))))) )],[refute_1_1206,refute_1_1209]) ).
cnf(refute_1_1211,plain,
( join(meet(join(one,complement(composition(top,zero))),one),complement(join(one,composition(top,zero)))) != join(one,complement(join(one,composition(top,zero))))
| join(one,complement(composition(top,zero))) != join(meet(join(one,complement(composition(top,zero))),one),complement(join(one,composition(top,zero))))
| join(one,complement(composition(top,zero))) = join(one,complement(join(one,composition(top,zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,complement(composition(top,zero))),join(meet(join(one,complement(composition(top,zero))),one),complement(join(one,composition(top,zero))))) ),[1],$fot(join(one,complement(join(one,composition(top,zero)))))]]) ).
cnf(refute_1_1212,plain,
( join(one,complement(composition(top,zero))) != join(meet(join(one,complement(composition(top,zero))),one),complement(join(one,composition(top,zero))))
| join(one,complement(composition(top,zero))) = join(one,complement(join(one,composition(top,zero)))) ),
inference(resolve,[$cnf( $equal(join(meet(join(one,complement(composition(top,zero))),one),complement(join(one,composition(top,zero)))),join(one,complement(join(one,composition(top,zero))))) )],[refute_1_1210,refute_1_1211]) ).
cnf(refute_1_1213,plain,
join(one,complement(composition(top,zero))) = join(one,complement(join(one,composition(top,zero)))),
inference(resolve,[$cnf( $equal(join(one,complement(composition(top,zero))),join(meet(join(one,complement(composition(top,zero))),one),complement(join(one,composition(top,zero))))) )],[refute_1_1193,refute_1_1212]) ).
cnf(refute_1_1214,plain,
complement(composition(top,zero)) = join(meet(one,complement(composition(top,zero))),complement(join(complement(complement(composition(top,zero))),one))),
inference(subst,[],[refute_1_683:[bind(X_176,$fot(complement(composition(top,zero)))),bind(X_177,$fot(one))]]) ).
cnf(refute_1_1215,plain,
one = meet(one,join(complement(composition(top,zero)),meet(one,composition(top,zero)))),
inference(subst,[],[refute_1_764:[bind(X_138,$fot(composition(top,zero))),bind(X_176,$fot(one))]]) ).
cnf(refute_1_1216,plain,
meet(one,composition(top,zero)) = complement(complement(meet(one,composition(top,zero)))),
inference(subst,[],[refute_1_516:[bind(X_176,$fot(meet(one,composition(top,zero))))]]) ).
cnf(refute_1_1217,plain,
join(complement(one),join(composition(top,zero),X_212)) = join(join(complement(one),composition(top,zero)),X_212),
inference(subst,[],[refute_1_100:[bind(X0,$fot(complement(one))),bind(X1,$fot(composition(top,zero))),bind(X2,$fot(X_212))]]) ).
cnf(refute_1_1218,plain,
( join(complement(one),composition(top,zero)) != complement(one)
| join(complement(one),join(composition(top,zero),X_212)) != join(join(complement(one),composition(top,zero)),X_212)
| join(complement(one),join(composition(top,zero),X_212)) = join(complement(one),X_212) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(one),join(composition(top,zero),X_212)),join(join(complement(one),composition(top,zero)),X_212)) ),[1,0],$fot(complement(one))]]) ).
cnf(refute_1_1219,plain,
( join(complement(one),join(composition(top,zero),X_212)) != join(join(complement(one),composition(top,zero)),X_212)
| join(complement(one),join(composition(top,zero),X_212)) = join(complement(one),X_212) ),
inference(resolve,[$cnf( $equal(join(complement(one),composition(top,zero)),complement(one)) )],[refute_1_1150,refute_1_1218]) ).
cnf(refute_1_1220,plain,
join(complement(one),join(composition(top,zero),X_212)) = join(complement(one),X_212),
inference(resolve,[$cnf( $equal(join(complement(one),join(composition(top,zero),X_212)),join(join(complement(one),composition(top,zero)),X_212)) )],[refute_1_1217,refute_1_1219]) ).
cnf(refute_1_1221,plain,
join(complement(one),join(composition(top,zero),complement(composition(top,zero)))) = join(complement(one),complement(composition(top,zero))),
inference(subst,[],[refute_1_1220:[bind(X_212,$fot(complement(composition(top,zero))))]]) ).
cnf(refute_1_1222,plain,
top = join(composition(top,zero),complement(composition(top,zero))),
inference(subst,[],[refute_1_23:[bind(X0,$fot(composition(top,zero)))]]) ).
cnf(refute_1_1223,plain,
( top != join(composition(top,zero),complement(composition(top,zero)))
| join(composition(top,zero),complement(composition(top,zero))) = top ),
inference(subst,[],[refute_1_17:[bind(X,$fot(top)),bind(Y,$fot(join(composition(top,zero),complement(composition(top,zero)))))]]) ).
cnf(refute_1_1224,plain,
join(composition(top,zero),complement(composition(top,zero))) = top,
inference(resolve,[$cnf( $equal(top,join(composition(top,zero),complement(composition(top,zero)))) )],[refute_1_1222,refute_1_1223]) ).
cnf(refute_1_1225,plain,
( join(complement(one),join(composition(top,zero),complement(composition(top,zero)))) != join(complement(one),complement(composition(top,zero)))
| join(composition(top,zero),complement(composition(top,zero))) != top
| join(complement(one),top) = join(complement(one),complement(composition(top,zero))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(one),join(composition(top,zero),complement(composition(top,zero)))),join(complement(one),complement(composition(top,zero)))) ),[0,1],$fot(top)]]) ).
cnf(refute_1_1226,plain,
( join(complement(one),join(composition(top,zero),complement(composition(top,zero)))) != join(complement(one),complement(composition(top,zero)))
| join(complement(one),top) = join(complement(one),complement(composition(top,zero))) ),
inference(resolve,[$cnf( $equal(join(composition(top,zero),complement(composition(top,zero))),top) )],[refute_1_1224,refute_1_1225]) ).
cnf(refute_1_1227,plain,
join(complement(one),top) = join(complement(one),complement(composition(top,zero))),
inference(resolve,[$cnf( $equal(join(complement(one),join(composition(top,zero),complement(composition(top,zero)))),join(complement(one),complement(composition(top,zero)))) )],[refute_1_1221,refute_1_1226]) ).
cnf(refute_1_1228,plain,
( join(complement(one),top) != join(complement(one),complement(composition(top,zero)))
| join(complement(one),top) != top
| top = join(complement(one),complement(composition(top,zero))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(one),top),join(complement(one),complement(composition(top,zero)))) ),[0],$fot(top)]]) ).
cnf(refute_1_1229,plain,
( join(complement(one),top) != join(complement(one),complement(composition(top,zero)))
| top = join(complement(one),complement(composition(top,zero))) ),
inference(resolve,[$cnf( $equal(join(complement(one),top),top) )],[refute_1_814,refute_1_1228]) ).
cnf(refute_1_1230,plain,
join(complement(one),complement(composition(top,zero))) = complement(meet(one,composition(top,zero))),
inference(subst,[],[refute_1_824:[bind(X0,$fot(one)),bind(X1,$fot(composition(top,zero)))]]) ).
cnf(refute_1_1231,plain,
( join(complement(one),complement(composition(top,zero))) != complement(meet(one,composition(top,zero)))
| top != join(complement(one),complement(composition(top,zero)))
| top = complement(meet(one,composition(top,zero))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(one),complement(composition(top,zero)))) ),[1],$fot(complement(meet(one,composition(top,zero))))]]) ).
cnf(refute_1_1232,plain,
( top != join(complement(one),complement(composition(top,zero)))
| top = complement(meet(one,composition(top,zero))) ),
inference(resolve,[$cnf( $equal(join(complement(one),complement(composition(top,zero))),complement(meet(one,composition(top,zero)))) )],[refute_1_1230,refute_1_1231]) ).
cnf(refute_1_1233,plain,
( join(complement(one),top) != join(complement(one),complement(composition(top,zero)))
| top = complement(meet(one,composition(top,zero))) ),
inference(resolve,[$cnf( $equal(top,join(complement(one),complement(composition(top,zero)))) )],[refute_1_1229,refute_1_1232]) ).
cnf(refute_1_1234,plain,
top = complement(meet(one,composition(top,zero))),
inference(resolve,[$cnf( $equal(join(complement(one),top),join(complement(one),complement(composition(top,zero)))) )],[refute_1_1227,refute_1_1233]) ).
cnf(refute_1_1235,plain,
( top != complement(meet(one,composition(top,zero)))
| complement(meet(one,composition(top,zero))) = top ),
inference(subst,[],[refute_1_17:[bind(X,$fot(top)),bind(Y,$fot(complement(meet(one,composition(top,zero)))))]]) ).
cnf(refute_1_1236,plain,
complement(meet(one,composition(top,zero))) = top,
inference(resolve,[$cnf( $equal(top,complement(meet(one,composition(top,zero)))) )],[refute_1_1234,refute_1_1235]) ).
cnf(refute_1_1237,plain,
( complement(meet(one,composition(top,zero))) != top
| meet(one,composition(top,zero)) != complement(complement(meet(one,composition(top,zero))))
| meet(one,composition(top,zero)) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(meet(one,composition(top,zero)),complement(complement(meet(one,composition(top,zero))))) ),[1,0],$fot(top)]]) ).
cnf(refute_1_1238,plain,
( meet(one,composition(top,zero)) != complement(complement(meet(one,composition(top,zero))))
| meet(one,composition(top,zero)) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(meet(one,composition(top,zero))),top) )],[refute_1_1236,refute_1_1237]) ).
cnf(refute_1_1239,plain,
meet(one,composition(top,zero)) = complement(top),
inference(resolve,[$cnf( $equal(meet(one,composition(top,zero)),complement(complement(meet(one,composition(top,zero))))) )],[refute_1_1216,refute_1_1238]) ).
cnf(refute_1_1240,plain,
( complement(top) != zero
| meet(one,composition(top,zero)) != complement(top)
| meet(one,composition(top,zero)) = zero ),
introduced(tautology,[equality,[$cnf( $equal(meet(one,composition(top,zero)),complement(top)) ),[1],$fot(zero)]]) ).
cnf(refute_1_1241,plain,
( meet(one,composition(top,zero)) != complement(top)
| meet(one,composition(top,zero)) = zero ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_1_45,refute_1_1240]) ).
cnf(refute_1_1242,plain,
meet(one,composition(top,zero)) = zero,
inference(resolve,[$cnf( $equal(meet(one,composition(top,zero)),complement(top)) )],[refute_1_1239,refute_1_1241]) ).
cnf(refute_1_1243,plain,
( meet(one,composition(top,zero)) != zero
| one != meet(one,join(complement(composition(top,zero)),meet(one,composition(top,zero))))
| one = meet(one,join(complement(composition(top,zero)),zero)) ),
introduced(tautology,[equality,[$cnf( $equal(one,meet(one,join(complement(composition(top,zero)),meet(one,composition(top,zero))))) ),[1,1,1],$fot(zero)]]) ).
cnf(refute_1_1244,plain,
( one != meet(one,join(complement(composition(top,zero)),meet(one,composition(top,zero))))
| one = meet(one,join(complement(composition(top,zero)),zero)) ),
inference(resolve,[$cnf( $equal(meet(one,composition(top,zero)),zero) )],[refute_1_1242,refute_1_1243]) ).
cnf(refute_1_1245,plain,
one = meet(one,join(complement(composition(top,zero)),zero)),
inference(resolve,[$cnf( $equal(one,meet(one,join(complement(composition(top,zero)),meet(one,composition(top,zero))))) )],[refute_1_1215,refute_1_1244]) ).
cnf(refute_1_1246,plain,
join(complement(composition(top,zero)),zero) = complement(composition(top,zero)),
inference(subst,[],[refute_1_866:[bind(X1,$fot(complement(composition(top,zero))))]]) ).
cnf(refute_1_1247,plain,
meet(one,join(complement(composition(top,zero)),zero)) = meet(one,join(complement(composition(top,zero)),zero)),
introduced(tautology,[refl,[$fot(meet(one,join(complement(composition(top,zero)),zero)))]]) ).
cnf(refute_1_1248,plain,
( join(complement(composition(top,zero)),zero) != complement(composition(top,zero))
| meet(one,join(complement(composition(top,zero)),zero)) != meet(one,join(complement(composition(top,zero)),zero))
| meet(one,join(complement(composition(top,zero)),zero)) = meet(one,complement(composition(top,zero))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(one,join(complement(composition(top,zero)),zero)),meet(one,join(complement(composition(top,zero)),zero))) ),[1,1],$fot(complement(composition(top,zero)))]]) ).
cnf(refute_1_1249,plain,
( join(complement(composition(top,zero)),zero) != complement(composition(top,zero))
| meet(one,join(complement(composition(top,zero)),zero)) = meet(one,complement(composition(top,zero))) ),
inference(resolve,[$cnf( $equal(meet(one,join(complement(composition(top,zero)),zero)),meet(one,join(complement(composition(top,zero)),zero))) )],[refute_1_1247,refute_1_1248]) ).
cnf(refute_1_1250,plain,
meet(one,join(complement(composition(top,zero)),zero)) = meet(one,complement(composition(top,zero))),
inference(resolve,[$cnf( $equal(join(complement(composition(top,zero)),zero),complement(composition(top,zero))) )],[refute_1_1246,refute_1_1249]) ).
cnf(refute_1_1251,plain,
( meet(one,join(complement(composition(top,zero)),zero)) != meet(one,complement(composition(top,zero)))
| one != meet(one,join(complement(composition(top,zero)),zero))
| one = meet(one,complement(composition(top,zero))) ),
introduced(tautology,[equality,[$cnf( $equal(one,meet(one,join(complement(composition(top,zero)),zero))) ),[1],$fot(meet(one,complement(composition(top,zero))))]]) ).
cnf(refute_1_1252,plain,
( one != meet(one,join(complement(composition(top,zero)),zero))
| one = meet(one,complement(composition(top,zero))) ),
inference(resolve,[$cnf( $equal(meet(one,join(complement(composition(top,zero)),zero)),meet(one,complement(composition(top,zero)))) )],[refute_1_1250,refute_1_1251]) ).
cnf(refute_1_1253,plain,
one = meet(one,complement(composition(top,zero))),
inference(resolve,[$cnf( $equal(one,meet(one,join(complement(composition(top,zero)),zero))) )],[refute_1_1245,refute_1_1252]) ).
cnf(refute_1_1254,plain,
( one != meet(one,complement(composition(top,zero)))
| meet(one,complement(composition(top,zero))) = one ),
inference(subst,[],[refute_1_17:[bind(X,$fot(one)),bind(Y,$fot(meet(one,complement(composition(top,zero)))))]]) ).
cnf(refute_1_1255,plain,
meet(one,complement(composition(top,zero))) = one,
inference(resolve,[$cnf( $equal(one,meet(one,complement(composition(top,zero)))) )],[refute_1_1253,refute_1_1254]) ).
cnf(refute_1_1256,plain,
( complement(composition(top,zero)) != join(meet(one,complement(composition(top,zero))),complement(join(complement(complement(composition(top,zero))),one)))
| meet(one,complement(composition(top,zero))) != one
| complement(composition(top,zero)) = join(one,complement(join(complement(complement(composition(top,zero))),one))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(composition(top,zero)),join(meet(one,complement(composition(top,zero))),complement(join(complement(complement(composition(top,zero))),one)))) ),[1,0],$fot(one)]]) ).
cnf(refute_1_1257,plain,
( complement(composition(top,zero)) != join(meet(one,complement(composition(top,zero))),complement(join(complement(complement(composition(top,zero))),one)))
| complement(composition(top,zero)) = join(one,complement(join(complement(complement(composition(top,zero))),one))) ),
inference(resolve,[$cnf( $equal(meet(one,complement(composition(top,zero))),one) )],[refute_1_1255,refute_1_1256]) ).
cnf(refute_1_1258,plain,
complement(composition(top,zero)) = join(one,complement(join(complement(complement(composition(top,zero))),one))),
inference(resolve,[$cnf( $equal(complement(composition(top,zero)),join(meet(one,complement(composition(top,zero))),complement(join(complement(complement(composition(top,zero))),one)))) )],[refute_1_1214,refute_1_1257]) ).
cnf(refute_1_1259,plain,
( join(one,complement(composition(top,zero))) != join(one,complement(join(one,composition(top,zero))))
| join(one,complement(join(one,composition(top,zero)))) = join(one,complement(composition(top,zero))) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(join(one,complement(composition(top,zero))))),bind(Y,$fot(join(one,complement(join(one,composition(top,zero))))))]]) ).
cnf(refute_1_1260,plain,
join(one,complement(join(one,composition(top,zero)))) = join(one,complement(composition(top,zero))),
inference(resolve,[$cnf( $equal(join(one,complement(composition(top,zero))),join(one,complement(join(one,composition(top,zero))))) )],[refute_1_1213,refute_1_1259]) ).
cnf(refute_1_1261,plain,
complement(complement(composition(top,zero))) = composition(top,zero),
inference(subst,[],[refute_1_518:[bind(X_176,$fot(composition(top,zero)))]]) ).
cnf(refute_1_1262,plain,
join(one,complement(complement(composition(top,zero)))) = join(one,complement(complement(composition(top,zero)))),
introduced(tautology,[refl,[$fot(join(one,complement(complement(composition(top,zero)))))]]) ).
cnf(refute_1_1263,plain,
( complement(complement(composition(top,zero))) != composition(top,zero)
| join(one,complement(complement(composition(top,zero)))) != join(one,complement(complement(composition(top,zero))))
| join(one,complement(complement(composition(top,zero)))) = join(one,composition(top,zero)) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,complement(complement(composition(top,zero)))),join(one,complement(complement(composition(top,zero))))) ),[1,1],$fot(composition(top,zero))]]) ).
cnf(refute_1_1264,plain,
( complement(complement(composition(top,zero))) != composition(top,zero)
| join(one,complement(complement(composition(top,zero)))) = join(one,composition(top,zero)) ),
inference(resolve,[$cnf( $equal(join(one,complement(complement(composition(top,zero)))),join(one,complement(complement(composition(top,zero))))) )],[refute_1_1262,refute_1_1263]) ).
cnf(refute_1_1265,plain,
join(one,complement(complement(composition(top,zero)))) = join(one,composition(top,zero)),
inference(resolve,[$cnf( $equal(complement(complement(composition(top,zero))),composition(top,zero)) )],[refute_1_1261,refute_1_1264]) ).
cnf(refute_1_1266,plain,
join(complement(complement(composition(top,zero))),one) = join(one,complement(complement(composition(top,zero)))),
inference(subst,[],[refute_1_1046:[bind(X0,$fot(complement(complement(composition(top,zero)))))]]) ).
cnf(refute_1_1267,plain,
( join(complement(complement(composition(top,zero))),one) != join(one,complement(complement(composition(top,zero))))
| join(one,complement(complement(composition(top,zero)))) != join(one,composition(top,zero))
| join(complement(complement(composition(top,zero))),one) = join(one,composition(top,zero)) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(complement(complement(composition(top,zero))),one))),bind(Y,$fot(join(one,complement(complement(composition(top,zero)))))),bind(Z,$fot(join(one,composition(top,zero))))]]) ).
cnf(refute_1_1268,plain,
( join(one,complement(complement(composition(top,zero)))) != join(one,composition(top,zero))
| join(complement(complement(composition(top,zero))),one) = join(one,composition(top,zero)) ),
inference(resolve,[$cnf( $equal(join(complement(complement(composition(top,zero))),one),join(one,complement(complement(composition(top,zero))))) )],[refute_1_1266,refute_1_1267]) ).
cnf(refute_1_1269,plain,
join(complement(complement(composition(top,zero))),one) = join(one,composition(top,zero)),
inference(resolve,[$cnf( $equal(join(one,complement(complement(composition(top,zero)))),join(one,composition(top,zero))) )],[refute_1_1265,refute_1_1268]) ).
cnf(refute_1_1270,plain,
complement(join(complement(complement(composition(top,zero))),one)) = complement(join(complement(complement(composition(top,zero))),one)),
introduced(tautology,[refl,[$fot(complement(join(complement(complement(composition(top,zero))),one)))]]) ).
cnf(refute_1_1271,plain,
( complement(join(complement(complement(composition(top,zero))),one)) != complement(join(complement(complement(composition(top,zero))),one))
| join(complement(complement(composition(top,zero))),one) != join(one,composition(top,zero))
| complement(join(complement(complement(composition(top,zero))),one)) = complement(join(one,composition(top,zero))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(complement(composition(top,zero))),one)),complement(join(complement(complement(composition(top,zero))),one))) ),[1,0],$fot(join(one,composition(top,zero)))]]) ).
cnf(refute_1_1272,plain,
( join(complement(complement(composition(top,zero))),one) != join(one,composition(top,zero))
| complement(join(complement(complement(composition(top,zero))),one)) = complement(join(one,composition(top,zero))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(complement(composition(top,zero))),one)),complement(join(complement(complement(composition(top,zero))),one))) )],[refute_1_1270,refute_1_1271]) ).
cnf(refute_1_1273,plain,
complement(join(complement(complement(composition(top,zero))),one)) = complement(join(one,composition(top,zero))),
inference(resolve,[$cnf( $equal(join(complement(complement(composition(top,zero))),one),join(one,composition(top,zero))) )],[refute_1_1269,refute_1_1272]) ).
cnf(refute_1_1274,plain,
join(one,complement(join(complement(complement(composition(top,zero))),one))) = join(one,complement(join(complement(complement(composition(top,zero))),one))),
introduced(tautology,[refl,[$fot(join(one,complement(join(complement(complement(composition(top,zero))),one))))]]) ).
cnf(refute_1_1275,plain,
( complement(join(complement(complement(composition(top,zero))),one)) != complement(join(one,composition(top,zero)))
| join(one,complement(join(complement(complement(composition(top,zero))),one))) != join(one,complement(join(complement(complement(composition(top,zero))),one)))
| join(one,complement(join(complement(complement(composition(top,zero))),one))) = join(one,complement(join(one,composition(top,zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,complement(join(complement(complement(composition(top,zero))),one))),join(one,complement(join(complement(complement(composition(top,zero))),one)))) ),[1,1],$fot(complement(join(one,composition(top,zero))))]]) ).
cnf(refute_1_1276,plain,
( complement(join(complement(complement(composition(top,zero))),one)) != complement(join(one,composition(top,zero)))
| join(one,complement(join(complement(complement(composition(top,zero))),one))) = join(one,complement(join(one,composition(top,zero)))) ),
inference(resolve,[$cnf( $equal(join(one,complement(join(complement(complement(composition(top,zero))),one))),join(one,complement(join(complement(complement(composition(top,zero))),one)))) )],[refute_1_1274,refute_1_1275]) ).
cnf(refute_1_1277,plain,
join(one,complement(join(complement(complement(composition(top,zero))),one))) = join(one,complement(join(one,composition(top,zero)))),
inference(resolve,[$cnf( $equal(complement(join(complement(complement(composition(top,zero))),one)),complement(join(one,composition(top,zero)))) )],[refute_1_1273,refute_1_1276]) ).
cnf(refute_1_1278,plain,
( join(one,complement(join(complement(complement(composition(top,zero))),one))) != join(one,complement(join(one,composition(top,zero))))
| join(one,complement(join(one,composition(top,zero)))) != join(one,complement(composition(top,zero)))
| join(one,complement(join(complement(complement(composition(top,zero))),one))) = join(one,complement(composition(top,zero))) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(one,complement(join(complement(complement(composition(top,zero))),one))))),bind(Y,$fot(join(one,complement(join(one,composition(top,zero)))))),bind(Z,$fot(join(one,complement(composition(top,zero)))))]]) ).
cnf(refute_1_1279,plain,
( join(one,complement(join(one,composition(top,zero)))) != join(one,complement(composition(top,zero)))
| join(one,complement(join(complement(complement(composition(top,zero))),one))) = join(one,complement(composition(top,zero))) ),
inference(resolve,[$cnf( $equal(join(one,complement(join(complement(complement(composition(top,zero))),one))),join(one,complement(join(one,composition(top,zero))))) )],[refute_1_1277,refute_1_1278]) ).
cnf(refute_1_1280,plain,
join(one,complement(join(complement(complement(composition(top,zero))),one))) = join(one,complement(composition(top,zero))),
inference(resolve,[$cnf( $equal(join(one,complement(join(one,composition(top,zero)))),join(one,complement(composition(top,zero)))) )],[refute_1_1260,refute_1_1279]) ).
cnf(refute_1_1281,plain,
( complement(composition(top,zero)) != join(one,complement(join(complement(complement(composition(top,zero))),one)))
| join(one,complement(join(complement(complement(composition(top,zero))),one))) != join(one,complement(composition(top,zero)))
| complement(composition(top,zero)) = join(one,complement(composition(top,zero))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(composition(top,zero)),join(one,complement(composition(top,zero)))) ),[0],$fot(join(one,complement(join(complement(complement(composition(top,zero))),one))))]]) ).
cnf(refute_1_1282,plain,
( complement(composition(top,zero)) != join(one,complement(join(complement(complement(composition(top,zero))),one)))
| complement(composition(top,zero)) = join(one,complement(composition(top,zero))) ),
inference(resolve,[$cnf( $equal(join(one,complement(join(complement(complement(composition(top,zero))),one))),join(one,complement(composition(top,zero)))) )],[refute_1_1280,refute_1_1281]) ).
cnf(refute_1_1283,plain,
complement(composition(top,zero)) = join(one,complement(composition(top,zero))),
inference(resolve,[$cnf( $equal(complement(composition(top,zero)),join(one,complement(join(complement(complement(composition(top,zero))),one)))) )],[refute_1_1258,refute_1_1282]) ).
cnf(refute_1_1284,plain,
( complement(composition(top,zero)) != join(one,complement(composition(top,zero)))
| join(one,complement(composition(top,zero))) = complement(composition(top,zero)) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(complement(composition(top,zero)))),bind(Y,$fot(join(one,complement(composition(top,zero)))))]]) ).
cnf(refute_1_1285,plain,
join(one,complement(composition(top,zero))) = complement(composition(top,zero)),
inference(resolve,[$cnf( $equal(complement(composition(top,zero)),join(one,complement(composition(top,zero)))) )],[refute_1_1283,refute_1_1284]) ).
cnf(refute_1_1286,plain,
( join(one,complement(composition(top,zero))) != complement(composition(top,zero))
| join(one,complement(composition(top,zero))) != join(one,complement(join(one,composition(top,zero))))
| complement(composition(top,zero)) = join(one,complement(join(one,composition(top,zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,complement(composition(top,zero))),join(one,complement(join(one,composition(top,zero))))) ),[0],$fot(complement(composition(top,zero)))]]) ).
cnf(refute_1_1287,plain,
( join(one,complement(composition(top,zero))) != join(one,complement(join(one,composition(top,zero))))
| complement(composition(top,zero)) = join(one,complement(join(one,composition(top,zero)))) ),
inference(resolve,[$cnf( $equal(join(one,complement(composition(top,zero))),complement(composition(top,zero))) )],[refute_1_1285,refute_1_1286]) ).
cnf(refute_1_1288,plain,
complement(composition(top,zero)) = join(one,complement(join(one,composition(top,zero)))),
inference(resolve,[$cnf( $equal(join(one,complement(composition(top,zero))),join(one,complement(join(one,composition(top,zero))))) )],[refute_1_1213,refute_1_1287]) ).
cnf(refute_1_1289,plain,
( complement(composition(top,zero)) != join(one,complement(join(one,composition(top,zero))))
| join(one,complement(join(one,composition(top,zero)))) = complement(composition(top,zero)) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(complement(composition(top,zero)))),bind(Y,$fot(join(one,complement(join(one,composition(top,zero))))))]]) ).
cnf(refute_1_1290,plain,
join(one,complement(join(one,composition(top,zero)))) = complement(composition(top,zero)),
inference(resolve,[$cnf( $equal(complement(composition(top,zero)),join(one,complement(join(one,composition(top,zero))))) )],[refute_1_1288,refute_1_1289]) ).
cnf(refute_1_1291,plain,
converse(converse(join(one,complement(converse(complement(composition(zero,top))))))) = join(one,complement(converse(complement(composition(zero,top))))),
inference(subst,[],[refute_1_3:[bind(X0,$fot(join(one,complement(converse(complement(composition(zero,top)))))))]]) ).
cnf(refute_1_1292,plain,
join(meet(X_177,X_176),join(meet(X_177,X_176),complement(join(complement(X_176),X_177)))) = join(meet(X_177,X_176),complement(join(complement(X_176),X_177))),
inference(subst,[],[refute_1_1040:[bind(X_211,$fot(meet(X_177,X_176))),bind(X_212,$fot(complement(join(complement(X_176),X_177))))]]) ).
cnf(refute_1_1293,plain,
( X_176 != join(meet(X_177,X_176),complement(join(complement(X_176),X_177)))
| join(meet(X_177,X_176),complement(join(complement(X_176),X_177))) = X_176 ),
inference(subst,[],[refute_1_17:[bind(X,$fot(X_176)),bind(Y,$fot(join(meet(X_177,X_176),complement(join(complement(X_176),X_177)))))]]) ).
cnf(refute_1_1294,plain,
join(meet(X_177,X_176),complement(join(complement(X_176),X_177))) = X_176,
inference(resolve,[$cnf( $equal(X_176,join(meet(X_177,X_176),complement(join(complement(X_176),X_177)))) )],[refute_1_683,refute_1_1293]) ).
cnf(refute_1_1295,plain,
( join(meet(X_177,X_176),complement(join(complement(X_176),X_177))) != X_176
| join(meet(X_177,X_176),join(meet(X_177,X_176),complement(join(complement(X_176),X_177)))) != join(meet(X_177,X_176),complement(join(complement(X_176),X_177)))
| join(meet(X_177,X_176),X_176) = join(meet(X_177,X_176),complement(join(complement(X_176),X_177))) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_177,X_176),join(meet(X_177,X_176),complement(join(complement(X_176),X_177)))),join(meet(X_177,X_176),complement(join(complement(X_176),X_177)))) ),[0,1],$fot(X_176)]]) ).
cnf(refute_1_1296,plain,
( join(meet(X_177,X_176),join(meet(X_177,X_176),complement(join(complement(X_176),X_177)))) != join(meet(X_177,X_176),complement(join(complement(X_176),X_177)))
| join(meet(X_177,X_176),X_176) = join(meet(X_177,X_176),complement(join(complement(X_176),X_177))) ),
inference(resolve,[$cnf( $equal(join(meet(X_177,X_176),complement(join(complement(X_176),X_177))),X_176) )],[refute_1_1294,refute_1_1295]) ).
cnf(refute_1_1297,plain,
join(meet(X_177,X_176),X_176) = join(meet(X_177,X_176),complement(join(complement(X_176),X_177))),
inference(resolve,[$cnf( $equal(join(meet(X_177,X_176),join(meet(X_177,X_176),complement(join(complement(X_176),X_177)))),join(meet(X_177,X_176),complement(join(complement(X_176),X_177)))) )],[refute_1_1292,refute_1_1296]) ).
cnf(refute_1_1298,plain,
join(meet(X_177,X_176),X_176) = join(X_176,meet(X_177,X_176)),
inference(subst,[],[refute_1_52:[bind(X0,$fot(X_176)),bind(X1,$fot(meet(X_177,X_176)))]]) ).
cnf(refute_1_1299,plain,
( join(meet(X_177,X_176),X_176) != join(X_176,meet(X_177,X_176))
| join(meet(X_177,X_176),X_176) != join(meet(X_177,X_176),complement(join(complement(X_176),X_177)))
| join(X_176,meet(X_177,X_176)) = join(meet(X_177,X_176),complement(join(complement(X_176),X_177))) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_177,X_176),X_176),join(meet(X_177,X_176),complement(join(complement(X_176),X_177)))) ),[0],$fot(join(X_176,meet(X_177,X_176)))]]) ).
cnf(refute_1_1300,plain,
( join(meet(X_177,X_176),X_176) != join(meet(X_177,X_176),complement(join(complement(X_176),X_177)))
| join(X_176,meet(X_177,X_176)) = join(meet(X_177,X_176),complement(join(complement(X_176),X_177))) ),
inference(resolve,[$cnf( $equal(join(meet(X_177,X_176),X_176),join(X_176,meet(X_177,X_176))) )],[refute_1_1298,refute_1_1299]) ).
cnf(refute_1_1301,plain,
( join(X_176,meet(X_177,X_176)) != join(meet(X_177,X_176),complement(join(complement(X_176),X_177)))
| join(meet(X_177,X_176),complement(join(complement(X_176),X_177))) != X_176
| join(X_176,meet(X_177,X_176)) = X_176 ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_176,meet(X_177,X_176)),X_176) ),[0],$fot(join(meet(X_177,X_176),complement(join(complement(X_176),X_177))))]]) ).
cnf(refute_1_1302,plain,
( join(X_176,meet(X_177,X_176)) != join(meet(X_177,X_176),complement(join(complement(X_176),X_177)))
| join(X_176,meet(X_177,X_176)) = X_176 ),
inference(resolve,[$cnf( $equal(join(meet(X_177,X_176),complement(join(complement(X_176),X_177))),X_176) )],[refute_1_1294,refute_1_1301]) ).
cnf(refute_1_1303,plain,
( join(meet(X_177,X_176),X_176) != join(meet(X_177,X_176),complement(join(complement(X_176),X_177)))
| join(X_176,meet(X_177,X_176)) = X_176 ),
inference(resolve,[$cnf( $equal(join(X_176,meet(X_177,X_176)),join(meet(X_177,X_176),complement(join(complement(X_176),X_177)))) )],[refute_1_1300,refute_1_1302]) ).
cnf(refute_1_1304,plain,
join(X_176,meet(X_177,X_176)) = X_176,
inference(resolve,[$cnf( $equal(join(meet(X_177,X_176),X_176),join(meet(X_177,X_176),complement(join(complement(X_176),X_177)))) )],[refute_1_1297,refute_1_1303]) ).
cnf(refute_1_1305,plain,
join(converse(join(one,complement(converse(complement(composition(zero,top)))))),meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top)))))))) = converse(join(one,complement(converse(complement(composition(zero,top)))))),
inference(subst,[],[refute_1_1304:[bind(X_176,$fot(converse(join(one,complement(converse(complement(composition(zero,top)))))))),bind(X_177,$fot(composition(zero,top)))]]) ).
cnf(refute_1_1306,plain,
composition(zero,top) = join(meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top)),complement(join(complement(composition(zero,top)),converse(join(one,complement(converse(complement(composition(zero,top))))))))),
inference(subst,[],[refute_1_683:[bind(X_176,$fot(composition(zero,top))),bind(X_177,$fot(converse(join(one,complement(converse(complement(composition(zero,top))))))))]]) ).
cnf(refute_1_1307,plain,
converse(top) = join(X_154,join(one,converse(complement(converse(join(one,X_154)))))),
inference(subst,[],[refute_1_106:[bind(X_120,$fot(X_154)),bind(X_121,$fot(one))]]) ).
cnf(refute_1_1308,plain,
converse(join(one,complement(converse(join(one,X_154))))) = join(one,converse(complement(converse(join(one,X_154))))),
inference(subst,[],[refute_1_351:[bind(X_110,$fot(complement(converse(join(one,X_154)))))]]) ).
cnf(refute_1_1309,plain,
( converse(join(one,complement(converse(join(one,X_154))))) != join(one,converse(complement(converse(join(one,X_154)))))
| join(one,converse(complement(converse(join(one,X_154))))) = converse(join(one,complement(converse(join(one,X_154))))) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(converse(join(one,complement(converse(join(one,X_154))))))),bind(Y,$fot(join(one,converse(complement(converse(join(one,X_154)))))))]]) ).
cnf(refute_1_1310,plain,
join(one,converse(complement(converse(join(one,X_154))))) = converse(join(one,complement(converse(join(one,X_154))))),
inference(resolve,[$cnf( $equal(converse(join(one,complement(converse(join(one,X_154))))),join(one,converse(complement(converse(join(one,X_154)))))) )],[refute_1_1308,refute_1_1309]) ).
cnf(refute_1_1311,plain,
( converse(top) != join(X_154,join(one,converse(complement(converse(join(one,X_154))))))
| join(one,converse(complement(converse(join(one,X_154))))) != converse(join(one,complement(converse(join(one,X_154)))))
| converse(top) = join(X_154,converse(join(one,complement(converse(join(one,X_154)))))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(top),join(X_154,join(one,converse(complement(converse(join(one,X_154))))))) ),[1,1],$fot(converse(join(one,complement(converse(join(one,X_154))))))]]) ).
cnf(refute_1_1312,plain,
( converse(top) != join(X_154,join(one,converse(complement(converse(join(one,X_154))))))
| converse(top) = join(X_154,converse(join(one,complement(converse(join(one,X_154)))))) ),
inference(resolve,[$cnf( $equal(join(one,converse(complement(converse(join(one,X_154))))),converse(join(one,complement(converse(join(one,X_154)))))) )],[refute_1_1310,refute_1_1311]) ).
cnf(refute_1_1313,plain,
converse(top) = join(X_154,converse(join(one,complement(converse(join(one,X_154)))))),
inference(resolve,[$cnf( $equal(converse(top),join(X_154,join(one,converse(complement(converse(join(one,X_154))))))) )],[refute_1_1307,refute_1_1312]) ).
cnf(refute_1_1314,plain,
( converse(top) != join(X_154,converse(join(one,complement(converse(join(one,X_154))))))
| converse(top) != top
| top = join(X_154,converse(join(one,complement(converse(join(one,X_154)))))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(top),join(X_154,converse(join(one,complement(converse(join(one,X_154))))))) ),[0],$fot(top)]]) ).
cnf(refute_1_1315,plain,
( converse(top) != join(X_154,converse(join(one,complement(converse(join(one,X_154))))))
| top = join(X_154,converse(join(one,complement(converse(join(one,X_154)))))) ),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_1_191,refute_1_1314]) ).
cnf(refute_1_1316,plain,
top = join(X_154,converse(join(one,complement(converse(join(one,X_154)))))),
inference(resolve,[$cnf( $equal(converse(top),join(X_154,converse(join(one,complement(converse(join(one,X_154))))))) )],[refute_1_1313,refute_1_1315]) ).
cnf(refute_1_1317,plain,
top = join(complement(composition(zero,top)),converse(join(one,complement(converse(join(one,complement(composition(zero,top)))))))),
inference(subst,[],[refute_1_1316:[bind(X_154,$fot(complement(composition(zero,top))))]]) ).
cnf(refute_1_1318,plain,
( join(one,complement(composition(zero,top))) != complement(composition(zero,top))
| top != join(complement(composition(zero,top)),converse(join(one,complement(converse(join(one,complement(composition(zero,top))))))))
| top = join(complement(composition(zero,top)),converse(join(one,complement(converse(complement(composition(zero,top))))))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(composition(zero,top)),converse(join(one,complement(converse(join(one,complement(composition(zero,top))))))))) ),[1,1,0,1,0,0],$fot(complement(composition(zero,top)))]]) ).
cnf(refute_1_1319,plain,
( top != join(complement(composition(zero,top)),converse(join(one,complement(converse(join(one,complement(composition(zero,top))))))))
| top = join(complement(composition(zero,top)),converse(join(one,complement(converse(complement(composition(zero,top))))))) ),
inference(resolve,[$cnf( $equal(join(one,complement(composition(zero,top))),complement(composition(zero,top))) )],[refute_1_1112,refute_1_1318]) ).
cnf(refute_1_1320,plain,
top = join(complement(composition(zero,top)),converse(join(one,complement(converse(complement(composition(zero,top))))))),
inference(resolve,[$cnf( $equal(top,join(complement(composition(zero,top)),converse(join(one,complement(converse(join(one,complement(composition(zero,top))))))))) )],[refute_1_1317,refute_1_1319]) ).
cnf(refute_1_1321,plain,
( top != join(complement(composition(zero,top)),converse(join(one,complement(converse(complement(composition(zero,top)))))))
| join(complement(composition(zero,top)),converse(join(one,complement(converse(complement(composition(zero,top))))))) = top ),
inference(subst,[],[refute_1_17:[bind(X,$fot(top)),bind(Y,$fot(join(complement(composition(zero,top)),converse(join(one,complement(converse(complement(composition(zero,top)))))))))]]) ).
cnf(refute_1_1322,plain,
join(complement(composition(zero,top)),converse(join(one,complement(converse(complement(composition(zero,top))))))) = top,
inference(resolve,[$cnf( $equal(top,join(complement(composition(zero,top)),converse(join(one,complement(converse(complement(composition(zero,top)))))))) )],[refute_1_1320,refute_1_1321]) ).
cnf(refute_1_1323,plain,
( composition(zero,top) != join(meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top)),complement(join(complement(composition(zero,top)),converse(join(one,complement(converse(complement(composition(zero,top)))))))))
| join(complement(composition(zero,top)),converse(join(one,complement(converse(complement(composition(zero,top))))))) != top
| composition(zero,top) = join(meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top)),complement(top)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(zero,top),join(meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top)),complement(join(complement(composition(zero,top)),converse(join(one,complement(converse(complement(composition(zero,top)))))))))) ),[1,1,0],$fot(top)]]) ).
cnf(refute_1_1324,plain,
( composition(zero,top) != join(meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top)),complement(join(complement(composition(zero,top)),converse(join(one,complement(converse(complement(composition(zero,top)))))))))
| composition(zero,top) = join(meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top)),complement(top)) ),
inference(resolve,[$cnf( $equal(join(complement(composition(zero,top)),converse(join(one,complement(converse(complement(composition(zero,top))))))),top) )],[refute_1_1322,refute_1_1323]) ).
cnf(refute_1_1325,plain,
composition(zero,top) = join(meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top)),complement(top)),
inference(resolve,[$cnf( $equal(composition(zero,top),join(meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top)),complement(join(complement(composition(zero,top)),converse(join(one,complement(converse(complement(composition(zero,top)))))))))) )],[refute_1_1306,refute_1_1324]) ).
cnf(refute_1_1326,plain,
join(zero,meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top)))))))) = meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top))))))),
inference(subst,[],[refute_1_580:[bind(X_176,$fot(meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top)))))))))]]) ).
cnf(refute_1_1327,plain,
meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top)) = meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top))))))),
inference(subst,[],[refute_1_711:[bind(X_137,$fot(composition(zero,top))),bind(X_138,$fot(converse(join(one,complement(converse(complement(composition(zero,top))))))))]]) ).
cnf(refute_1_1328,plain,
join(zero,meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top))) = join(zero,meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top))),
introduced(tautology,[refl,[$fot(join(zero,meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top))))]]) ).
cnf(refute_1_1329,plain,
( join(zero,meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top))) != join(zero,meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top)))
| meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top)) != meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top)))))))
| join(zero,meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top))) = join(zero,meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top)))))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top))),join(zero,meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top)))) ),[1,1],$fot(meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top))))))))]]) ).
cnf(refute_1_1330,plain,
( meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top)) != meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top)))))))
| join(zero,meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top))) = join(zero,meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top)))))))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top))),join(zero,meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top)))) )],[refute_1_1328,refute_1_1329]) ).
cnf(refute_1_1331,plain,
join(zero,meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top))) = join(zero,meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top)))))))),
inference(resolve,[$cnf( $equal(meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top)),meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top)))))))) )],[refute_1_1327,refute_1_1330]) ).
cnf(refute_1_1332,plain,
join(complement(top),meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top))) = join(complement(top),meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top))),
introduced(tautology,[refl,[$fot(join(complement(top),meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top))))]]) ).
cnf(refute_1_1333,plain,
( complement(top) != zero
| join(complement(top),meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top))) != join(complement(top),meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top)))
| join(complement(top),meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top))) = join(zero,meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top))),join(complement(top),meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top)))) ),[1,0],$fot(zero)]]) ).
cnf(refute_1_1334,plain,
( complement(top) != zero
| join(complement(top),meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top))) = join(zero,meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top))),join(complement(top),meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top)))) )],[refute_1_1332,refute_1_1333]) ).
cnf(refute_1_1335,plain,
join(complement(top),meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top))) = join(zero,meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top))),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_1_45,refute_1_1334]) ).
cnf(refute_1_1336,plain,
( join(complement(top),meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top))) != join(zero,meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top)))
| join(zero,meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top))) != join(zero,meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top))))))))
| join(complement(top),meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top))) = join(zero,meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top)))))))) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(complement(top),meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top))))),bind(Y,$fot(join(zero,meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top))))),bind(Z,$fot(join(zero,meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top))))))))))]]) ).
cnf(refute_1_1337,plain,
( join(zero,meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top))) != join(zero,meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top))))))))
| join(complement(top),meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top))) = join(zero,meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top)))))))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top))),join(zero,meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top)))) )],[refute_1_1335,refute_1_1336]) ).
cnf(refute_1_1338,plain,
join(complement(top),meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top))) = join(zero,meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top)))))))),
inference(resolve,[$cnf( $equal(join(zero,meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top))),join(zero,meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top))))))))) )],[refute_1_1331,refute_1_1337]) ).
cnf(refute_1_1339,plain,
( join(complement(top),meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top))) != join(zero,meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top))))))))
| join(zero,meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top)))))))) != meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top)))))))
| join(complement(top),meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top))) = meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top))))))) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(complement(top),meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top))))),bind(Y,$fot(join(zero,meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top)))))))))),bind(Z,$fot(meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top)))))))))]]) ).
cnf(refute_1_1340,plain,
( join(zero,meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top)))))))) != meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top)))))))
| join(complement(top),meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top))) = meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top))))))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top))),join(zero,meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top))))))))) )],[refute_1_1338,refute_1_1339]) ).
cnf(refute_1_1341,plain,
join(complement(top),meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top))) = meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top))))))),
inference(resolve,[$cnf( $equal(join(zero,meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top)))))))),meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top)))))))) )],[refute_1_1326,refute_1_1340]) ).
cnf(refute_1_1342,plain,
join(meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top)),complement(top)) = join(complement(top),meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top))),
inference(subst,[],[refute_1_52:[bind(X0,$fot(complement(top))),bind(X1,$fot(meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top))))]]) ).
cnf(refute_1_1343,plain,
( join(complement(top),meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top))) != meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top)))))))
| join(meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top)),complement(top)) != join(complement(top),meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top)))
| join(meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top)),complement(top)) = meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top))))))) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top)),complement(top)))),bind(Y,$fot(join(complement(top),meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top))))),bind(Z,$fot(meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top)))))))))]]) ).
cnf(refute_1_1344,plain,
( join(complement(top),meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top))) != meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top)))))))
| join(meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top)),complement(top)) = meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top))))))) ),
inference(resolve,[$cnf( $equal(join(meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top)),complement(top)),join(complement(top),meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top)))) )],[refute_1_1342,refute_1_1343]) ).
cnf(refute_1_1345,plain,
join(meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top)),complement(top)) = meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top))))))),
inference(resolve,[$cnf( $equal(join(complement(top),meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top))),meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top)))))))) )],[refute_1_1341,refute_1_1344]) ).
cnf(refute_1_1346,plain,
( composition(zero,top) != join(meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top)),complement(top))
| join(meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top)),complement(top)) != meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top)))))))
| composition(zero,top) = meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top))))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(zero,top),meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top)))))))) ),[0],$fot(join(meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top)),complement(top)))]]) ).
cnf(refute_1_1347,plain,
( composition(zero,top) != join(meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top)),complement(top))
| composition(zero,top) = meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top))))))) ),
inference(resolve,[$cnf( $equal(join(meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top)),complement(top)),meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top)))))))) )],[refute_1_1345,refute_1_1346]) ).
cnf(refute_1_1348,plain,
composition(zero,top) = meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top))))))),
inference(resolve,[$cnf( $equal(composition(zero,top),join(meet(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top)),complement(top))) )],[refute_1_1325,refute_1_1347]) ).
cnf(refute_1_1349,plain,
( composition(zero,top) != meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top)))))))
| meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top))))))) = composition(zero,top) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(composition(zero,top))),bind(Y,$fot(meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top)))))))))]]) ).
cnf(refute_1_1350,plain,
meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top))))))) = composition(zero,top),
inference(resolve,[$cnf( $equal(composition(zero,top),meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top)))))))) )],[refute_1_1348,refute_1_1349]) ).
cnf(refute_1_1351,plain,
( join(converse(join(one,complement(converse(complement(composition(zero,top)))))),meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top)))))))) != converse(join(one,complement(converse(complement(composition(zero,top))))))
| meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top))))))) != composition(zero,top)
| join(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top)) = converse(join(one,complement(converse(complement(composition(zero,top)))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(converse(join(one,complement(converse(complement(composition(zero,top)))))),meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top)))))))),converse(join(one,complement(converse(complement(composition(zero,top))))))) ),[0,1],$fot(composition(zero,top))]]) ).
cnf(refute_1_1352,plain,
( join(converse(join(one,complement(converse(complement(composition(zero,top)))))),meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top)))))))) != converse(join(one,complement(converse(complement(composition(zero,top))))))
| join(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top)) = converse(join(one,complement(converse(complement(composition(zero,top)))))) ),
inference(resolve,[$cnf( $equal(meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top))))))),composition(zero,top)) )],[refute_1_1350,refute_1_1351]) ).
cnf(refute_1_1353,plain,
join(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top)) = converse(join(one,complement(converse(complement(composition(zero,top)))))),
inference(resolve,[$cnf( $equal(join(converse(join(one,complement(converse(complement(composition(zero,top)))))),meet(composition(zero,top),converse(join(one,complement(converse(complement(composition(zero,top)))))))),converse(join(one,complement(converse(complement(composition(zero,top))))))) )],[refute_1_1305,refute_1_1352]) ).
cnf(refute_1_1354,plain,
converse(join(one,join(complement(converse(complement(composition(zero,top)))),composition(top,zero)))) = converse(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top))))))),
inference(subst,[],[refute_1_944:[bind(X0,$fot(complement(converse(complement(composition(zero,top)))))),bind(X1,$fot(composition(top,zero)))]]) ).
cnf(refute_1_1355,plain,
converse(join(X0,join(X_210,X_211))) = converse(join(join(X_210,X_211),X0)),
inference(subst,[],[refute_1_95:[bind(X1,$fot(join(X_210,X_211)))]]) ).
cnf(refute_1_1356,plain,
join(X_210,join(X_211,X0)) = join(join(X_210,X_211),X0),
inference(subst,[],[refute_1_100:[bind(X0,$fot(X_210)),bind(X1,$fot(X_211)),bind(X2,$fot(X0))]]) ).
cnf(refute_1_1357,plain,
( join(X_210,join(X_211,X0)) != join(join(X_210,X_211),X0)
| join(join(X_210,X_211),X0) = join(X_210,join(X_211,X0)) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(join(X_210,join(X_211,X0)))),bind(Y,$fot(join(join(X_210,X_211),X0)))]]) ).
cnf(refute_1_1358,plain,
join(join(X_210,X_211),X0) = join(X_210,join(X_211,X0)),
inference(resolve,[$cnf( $equal(join(X_210,join(X_211,X0)),join(join(X_210,X_211),X0)) )],[refute_1_1356,refute_1_1357]) ).
cnf(refute_1_1359,plain,
( converse(join(X0,join(X_210,X_211))) != converse(join(join(X_210,X_211),X0))
| join(join(X_210,X_211),X0) != join(X_210,join(X_211,X0))
| converse(join(X0,join(X_210,X_211))) = converse(join(X_210,join(X_211,X0))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(X0,join(X_210,X_211))),converse(join(join(X_210,X_211),X0))) ),[1,0],$fot(join(X_210,join(X_211,X0)))]]) ).
cnf(refute_1_1360,plain,
( converse(join(X0,join(X_210,X_211))) != converse(join(join(X_210,X_211),X0))
| converse(join(X0,join(X_210,X_211))) = converse(join(X_210,join(X_211,X0))) ),
inference(resolve,[$cnf( $equal(join(join(X_210,X_211),X0),join(X_210,join(X_211,X0))) )],[refute_1_1358,refute_1_1359]) ).
cnf(refute_1_1361,plain,
converse(join(X0,join(X_210,X_211))) = converse(join(X_210,join(X_211,X0))),
inference(resolve,[$cnf( $equal(converse(join(X0,join(X_210,X_211))),converse(join(join(X_210,X_211),X0))) )],[refute_1_1355,refute_1_1360]) ).
cnf(refute_1_1362,plain,
converse(join(composition(top,zero),join(one,complement(converse(complement(composition(zero,top))))))) = converse(join(one,join(complement(converse(complement(composition(zero,top)))),composition(top,zero)))),
inference(subst,[],[refute_1_1361:[bind(X0,$fot(composition(top,zero))),bind(X_210,$fot(one)),bind(X_211,$fot(complement(converse(complement(composition(zero,top))))))]]) ).
cnf(refute_1_1363,plain,
( converse(join(composition(top,zero),join(one,complement(converse(complement(composition(zero,top))))))) != converse(join(one,join(complement(converse(complement(composition(zero,top)))),composition(top,zero))))
| converse(join(one,join(complement(converse(complement(composition(zero,top)))),composition(top,zero)))) != converse(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top)))))))
| converse(join(composition(top,zero),join(one,complement(converse(complement(composition(zero,top))))))) = converse(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top))))))) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(converse(join(composition(top,zero),join(one,complement(converse(complement(composition(zero,top))))))))),bind(Y,$fot(converse(join(one,join(complement(converse(complement(composition(zero,top)))),composition(top,zero)))))),bind(Z,$fot(converse(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top)))))))))]]) ).
cnf(refute_1_1364,plain,
( converse(join(one,join(complement(converse(complement(composition(zero,top)))),composition(top,zero)))) != converse(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top)))))))
| converse(join(composition(top,zero),join(one,complement(converse(complement(composition(zero,top))))))) = converse(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top))))))) ),
inference(resolve,[$cnf( $equal(converse(join(composition(top,zero),join(one,complement(converse(complement(composition(zero,top))))))),converse(join(one,join(complement(converse(complement(composition(zero,top)))),composition(top,zero))))) )],[refute_1_1362,refute_1_1363]) ).
cnf(refute_1_1365,plain,
converse(join(composition(top,zero),join(one,complement(converse(complement(composition(zero,top))))))) = converse(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top))))))),
inference(resolve,[$cnf( $equal(converse(join(one,join(complement(converse(complement(composition(zero,top)))),composition(top,zero)))),converse(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top)))))))) )],[refute_1_1354,refute_1_1364]) ).
cnf(refute_1_1366,plain,
converse(join(join(one,complement(converse(complement(composition(zero,top))))),composition(top,zero))) = converse(join(composition(top,zero),join(one,complement(converse(complement(composition(zero,top))))))),
inference(subst,[],[refute_1_935:[bind(X0,$fot(composition(top,zero))),bind(X1,$fot(join(one,complement(converse(complement(composition(zero,top)))))))]]) ).
cnf(refute_1_1367,plain,
( converse(join(composition(top,zero),join(one,complement(converse(complement(composition(zero,top))))))) != converse(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top)))))))
| converse(join(join(one,complement(converse(complement(composition(zero,top))))),composition(top,zero))) != converse(join(composition(top,zero),join(one,complement(converse(complement(composition(zero,top)))))))
| converse(join(join(one,complement(converse(complement(composition(zero,top))))),composition(top,zero))) = converse(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top))))))) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(converse(join(join(one,complement(converse(complement(composition(zero,top))))),composition(top,zero))))),bind(Y,$fot(converse(join(composition(top,zero),join(one,complement(converse(complement(composition(zero,top))))))))),bind(Z,$fot(converse(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top)))))))))]]) ).
cnf(refute_1_1368,plain,
( converse(join(composition(top,zero),join(one,complement(converse(complement(composition(zero,top))))))) != converse(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top)))))))
| converse(join(join(one,complement(converse(complement(composition(zero,top))))),composition(top,zero))) = converse(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top))))))) ),
inference(resolve,[$cnf( $equal(converse(join(join(one,complement(converse(complement(composition(zero,top))))),composition(top,zero))),converse(join(composition(top,zero),join(one,complement(converse(complement(composition(zero,top)))))))) )],[refute_1_1366,refute_1_1367]) ).
cnf(refute_1_1369,plain,
converse(join(join(one,complement(converse(complement(composition(zero,top))))),composition(top,zero))) = converse(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top))))))),
inference(resolve,[$cnf( $equal(converse(join(composition(top,zero),join(one,complement(converse(complement(composition(zero,top))))))),converse(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top)))))))) )],[refute_1_1365,refute_1_1368]) ).
cnf(refute_1_1370,plain,
converse(join(X0,composition(top,zero))) = join(converse(X0),converse(composition(top,zero))),
inference(subst,[],[refute_1_71:[bind(X1,$fot(composition(top,zero)))]]) ).
cnf(refute_1_1371,plain,
converse(composition(top,zero)) = composition(zero,converse(top)),
inference(subst,[],[refute_1_662:[bind(X_111,$fot(top))]]) ).
cnf(refute_1_1372,plain,
( converse(composition(top,zero)) != composition(zero,converse(top))
| converse(top) != top
| converse(composition(top,zero)) = composition(zero,top) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(top,zero)),composition(zero,converse(top))) ),[1,1],$fot(top)]]) ).
cnf(refute_1_1373,plain,
( converse(composition(top,zero)) != composition(zero,converse(top))
| converse(composition(top,zero)) = composition(zero,top) ),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_1_191,refute_1_1372]) ).
cnf(refute_1_1374,plain,
converse(composition(top,zero)) = composition(zero,top),
inference(resolve,[$cnf( $equal(converse(composition(top,zero)),composition(zero,converse(top))) )],[refute_1_1371,refute_1_1373]) ).
cnf(refute_1_1375,plain,
( converse(composition(top,zero)) != composition(zero,top)
| converse(join(X0,composition(top,zero))) != join(converse(X0),converse(composition(top,zero)))
| converse(join(X0,composition(top,zero))) = join(converse(X0),composition(zero,top)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(X0,composition(top,zero))),join(converse(X0),converse(composition(top,zero)))) ),[1,1],$fot(composition(zero,top))]]) ).
cnf(refute_1_1376,plain,
( converse(join(X0,composition(top,zero))) != join(converse(X0),converse(composition(top,zero)))
| converse(join(X0,composition(top,zero))) = join(converse(X0),composition(zero,top)) ),
inference(resolve,[$cnf( $equal(converse(composition(top,zero)),composition(zero,top)) )],[refute_1_1374,refute_1_1375]) ).
cnf(refute_1_1377,plain,
converse(join(X0,composition(top,zero))) = join(converse(X0),composition(zero,top)),
inference(resolve,[$cnf( $equal(converse(join(X0,composition(top,zero))),join(converse(X0),converse(composition(top,zero)))) )],[refute_1_1370,refute_1_1376]) ).
cnf(refute_1_1378,plain,
( converse(join(X0,composition(top,zero))) != join(converse(X0),composition(zero,top))
| join(converse(X0),composition(zero,top)) = converse(join(X0,composition(top,zero))) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(converse(join(X0,composition(top,zero))))),bind(Y,$fot(join(converse(X0),composition(zero,top))))]]) ).
cnf(refute_1_1379,plain,
join(converse(X0),composition(zero,top)) = converse(join(X0,composition(top,zero))),
inference(resolve,[$cnf( $equal(converse(join(X0,composition(top,zero))),join(converse(X0),composition(zero,top))) )],[refute_1_1377,refute_1_1378]) ).
cnf(refute_1_1380,plain,
join(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top)) = converse(join(join(one,complement(converse(complement(composition(zero,top))))),composition(top,zero))),
inference(subst,[],[refute_1_1379:[bind(X0,$fot(join(one,complement(converse(complement(composition(zero,top)))))))]]) ).
cnf(refute_1_1381,plain,
( converse(join(join(one,complement(converse(complement(composition(zero,top))))),composition(top,zero))) != converse(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top)))))))
| join(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top)) != converse(join(join(one,complement(converse(complement(composition(zero,top))))),composition(top,zero)))
| join(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top)) = converse(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top))))))) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top)))),bind(Y,$fot(converse(join(join(one,complement(converse(complement(composition(zero,top))))),composition(top,zero))))),bind(Z,$fot(converse(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top)))))))))]]) ).
cnf(refute_1_1382,plain,
( converse(join(join(one,complement(converse(complement(composition(zero,top))))),composition(top,zero))) != converse(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top)))))))
| join(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top)) = converse(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top))))))) ),
inference(resolve,[$cnf( $equal(join(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top)),converse(join(join(one,complement(converse(complement(composition(zero,top))))),composition(top,zero)))) )],[refute_1_1380,refute_1_1381]) ).
cnf(refute_1_1383,plain,
join(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top)) = converse(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top))))))),
inference(resolve,[$cnf( $equal(converse(join(join(one,complement(converse(complement(composition(zero,top))))),composition(top,zero))),converse(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top)))))))) )],[refute_1_1369,refute_1_1382]) ).
cnf(refute_1_1384,plain,
( join(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top)) != converse(join(one,complement(converse(complement(composition(zero,top))))))
| join(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top)) != converse(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top)))))))
| converse(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top))))))) = converse(join(one,complement(converse(complement(composition(zero,top)))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top)),converse(join(one,complement(converse(complement(composition(zero,top))))))) ),[0],$fot(converse(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top))))))))]]) ).
cnf(refute_1_1385,plain,
( join(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top)) != converse(join(one,complement(converse(complement(composition(zero,top))))))
| converse(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top))))))) = converse(join(one,complement(converse(complement(composition(zero,top)))))) ),
inference(resolve,[$cnf( $equal(join(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top)),converse(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top)))))))) )],[refute_1_1383,refute_1_1384]) ).
cnf(refute_1_1386,plain,
converse(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top))))))) = converse(join(one,complement(converse(complement(composition(zero,top)))))),
inference(resolve,[$cnf( $equal(join(converse(join(one,complement(converse(complement(composition(zero,top)))))),composition(zero,top)),converse(join(one,complement(converse(complement(composition(zero,top))))))) )],[refute_1_1353,refute_1_1385]) ).
cnf(refute_1_1387,plain,
converse(join(one,composition(top,zero))) = join(one,converse(composition(top,zero))),
inference(subst,[],[refute_1_351:[bind(X_110,$fot(composition(top,zero)))]]) ).
cnf(refute_1_1388,plain,
( converse(composition(top,zero)) != composition(zero,top)
| converse(join(one,composition(top,zero))) != join(one,converse(composition(top,zero)))
| converse(join(one,composition(top,zero))) = join(one,composition(zero,top)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(one,composition(top,zero))),join(one,converse(composition(top,zero)))) ),[1,1],$fot(composition(zero,top))]]) ).
cnf(refute_1_1389,plain,
( converse(join(one,composition(top,zero))) != join(one,converse(composition(top,zero)))
| converse(join(one,composition(top,zero))) = join(one,composition(zero,top)) ),
inference(resolve,[$cnf( $equal(converse(composition(top,zero)),composition(zero,top)) )],[refute_1_1374,refute_1_1388]) ).
cnf(refute_1_1390,plain,
converse(join(one,composition(top,zero))) = join(one,composition(zero,top)),
inference(resolve,[$cnf( $equal(converse(join(one,composition(top,zero))),join(one,converse(composition(top,zero)))) )],[refute_1_1387,refute_1_1389]) ).
cnf(refute_1_1391,plain,
composition(top,zero) = join(meet(converse(complement(composition(zero,top))),composition(top,zero)),complement(join(complement(composition(top,zero)),converse(complement(composition(zero,top)))))),
inference(subst,[],[refute_1_683:[bind(X_176,$fot(composition(top,zero))),bind(X_177,$fot(converse(complement(composition(zero,top)))))]]) ).
cnf(refute_1_1392,plain,
join(converse(complement(composition(zero,top))),meet(complement(composition(top,zero)),converse(complement(composition(zero,top))))) = converse(complement(composition(zero,top))),
inference(subst,[],[refute_1_1304:[bind(X_176,$fot(converse(complement(composition(zero,top))))),bind(X_177,$fot(complement(composition(top,zero))))]]) ).
cnf(refute_1_1393,plain,
complement(X_194) = meet(complement(X_194),converse(complement(converse(complement(complement(X_194)))))),
inference(subst,[],[refute_1_584:[bind(X_176,$fot(complement(X_194)))]]) ).
cnf(refute_1_1394,plain,
X_194 = complement(complement(X_194)),
inference(subst,[],[refute_1_516:[bind(X_176,$fot(X_194))]]) ).
cnf(refute_1_1395,plain,
( X_194 != complement(complement(X_194))
| complement(complement(X_194)) = X_194 ),
inference(subst,[],[refute_1_17:[bind(X,$fot(X_194)),bind(Y,$fot(complement(complement(X_194))))]]) ).
cnf(refute_1_1396,plain,
complement(complement(X_194)) = X_194,
inference(resolve,[$cnf( $equal(X_194,complement(complement(X_194))) )],[refute_1_1394,refute_1_1395]) ).
cnf(refute_1_1397,plain,
( complement(X_194) != meet(complement(X_194),converse(complement(converse(complement(complement(X_194))))))
| complement(complement(X_194)) != X_194
| complement(X_194) = meet(complement(X_194),converse(complement(converse(X_194)))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(X_194),meet(complement(X_194),converse(complement(converse(complement(complement(X_194))))))) ),[1,1,0,0,0],$fot(X_194)]]) ).
cnf(refute_1_1398,plain,
( complement(X_194) != meet(complement(X_194),converse(complement(converse(complement(complement(X_194))))))
| complement(X_194) = meet(complement(X_194),converse(complement(converse(X_194)))) ),
inference(resolve,[$cnf( $equal(complement(complement(X_194)),X_194) )],[refute_1_1396,refute_1_1397]) ).
cnf(refute_1_1399,plain,
complement(X_194) = meet(complement(X_194),converse(complement(converse(X_194)))),
inference(resolve,[$cnf( $equal(complement(X_194),meet(complement(X_194),converse(complement(converse(complement(complement(X_194))))))) )],[refute_1_1393,refute_1_1398]) ).
cnf(refute_1_1400,plain,
complement(composition(top,zero)) = meet(complement(composition(top,zero)),converse(complement(converse(composition(top,zero))))),
inference(subst,[],[refute_1_1399:[bind(X_194,$fot(composition(top,zero)))]]) ).
cnf(refute_1_1401,plain,
( complement(composition(top,zero)) != meet(complement(composition(top,zero)),converse(complement(converse(composition(top,zero)))))
| converse(composition(top,zero)) != composition(zero,top)
| complement(composition(top,zero)) = meet(complement(composition(top,zero)),converse(complement(composition(zero,top)))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(composition(top,zero)),meet(complement(composition(top,zero)),converse(complement(converse(composition(top,zero)))))) ),[1,1,0,0],$fot(composition(zero,top))]]) ).
cnf(refute_1_1402,plain,
( complement(composition(top,zero)) != meet(complement(composition(top,zero)),converse(complement(converse(composition(top,zero)))))
| complement(composition(top,zero)) = meet(complement(composition(top,zero)),converse(complement(composition(zero,top)))) ),
inference(resolve,[$cnf( $equal(converse(composition(top,zero)),composition(zero,top)) )],[refute_1_1374,refute_1_1401]) ).
cnf(refute_1_1403,plain,
complement(composition(top,zero)) = meet(complement(composition(top,zero)),converse(complement(composition(zero,top)))),
inference(resolve,[$cnf( $equal(complement(composition(top,zero)),meet(complement(composition(top,zero)),converse(complement(converse(composition(top,zero)))))) )],[refute_1_1400,refute_1_1402]) ).
cnf(refute_1_1404,plain,
( complement(composition(top,zero)) != meet(complement(composition(top,zero)),converse(complement(composition(zero,top))))
| meet(complement(composition(top,zero)),converse(complement(composition(zero,top)))) = complement(composition(top,zero)) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(complement(composition(top,zero)))),bind(Y,$fot(meet(complement(composition(top,zero)),converse(complement(composition(zero,top))))))]]) ).
cnf(refute_1_1405,plain,
meet(complement(composition(top,zero)),converse(complement(composition(zero,top)))) = complement(composition(top,zero)),
inference(resolve,[$cnf( $equal(complement(composition(top,zero)),meet(complement(composition(top,zero)),converse(complement(composition(zero,top))))) )],[refute_1_1403,refute_1_1404]) ).
cnf(refute_1_1406,plain,
( join(converse(complement(composition(zero,top))),meet(complement(composition(top,zero)),converse(complement(composition(zero,top))))) != converse(complement(composition(zero,top)))
| meet(complement(composition(top,zero)),converse(complement(composition(zero,top)))) != complement(composition(top,zero))
| join(converse(complement(composition(zero,top))),complement(composition(top,zero))) = converse(complement(composition(zero,top))) ),
introduced(tautology,[equality,[$cnf( $equal(join(converse(complement(composition(zero,top))),meet(complement(composition(top,zero)),converse(complement(composition(zero,top))))),converse(complement(composition(zero,top)))) ),[0,1],$fot(complement(composition(top,zero)))]]) ).
cnf(refute_1_1407,plain,
( join(converse(complement(composition(zero,top))),meet(complement(composition(top,zero)),converse(complement(composition(zero,top))))) != converse(complement(composition(zero,top)))
| join(converse(complement(composition(zero,top))),complement(composition(top,zero))) = converse(complement(composition(zero,top))) ),
inference(resolve,[$cnf( $equal(meet(complement(composition(top,zero)),converse(complement(composition(zero,top)))),complement(composition(top,zero))) )],[refute_1_1405,refute_1_1406]) ).
cnf(refute_1_1408,plain,
join(converse(complement(composition(zero,top))),complement(composition(top,zero))) = converse(complement(composition(zero,top))),
inference(resolve,[$cnf( $equal(join(converse(complement(composition(zero,top))),meet(complement(composition(top,zero)),converse(complement(composition(zero,top))))),converse(complement(composition(zero,top)))) )],[refute_1_1392,refute_1_1407]) ).
cnf(refute_1_1409,plain,
join(converse(complement(composition(zero,top))),complement(composition(top,zero))) = join(complement(composition(top,zero)),converse(complement(composition(zero,top)))),
inference(subst,[],[refute_1_52:[bind(X0,$fot(complement(composition(top,zero)))),bind(X1,$fot(converse(complement(composition(zero,top)))))]]) ).
cnf(refute_1_1410,plain,
( join(converse(complement(composition(zero,top))),complement(composition(top,zero))) != converse(complement(composition(zero,top)))
| join(converse(complement(composition(zero,top))),complement(composition(top,zero))) != join(complement(composition(top,zero)),converse(complement(composition(zero,top))))
| join(complement(composition(top,zero)),converse(complement(composition(zero,top)))) = converse(complement(composition(zero,top))) ),
introduced(tautology,[equality,[$cnf( $equal(join(converse(complement(composition(zero,top))),complement(composition(top,zero))),converse(complement(composition(zero,top)))) ),[0],$fot(join(complement(composition(top,zero)),converse(complement(composition(zero,top)))))]]) ).
cnf(refute_1_1411,plain,
( join(converse(complement(composition(zero,top))),complement(composition(top,zero))) != converse(complement(composition(zero,top)))
| join(complement(composition(top,zero)),converse(complement(composition(zero,top)))) = converse(complement(composition(zero,top))) ),
inference(resolve,[$cnf( $equal(join(converse(complement(composition(zero,top))),complement(composition(top,zero))),join(complement(composition(top,zero)),converse(complement(composition(zero,top))))) )],[refute_1_1409,refute_1_1410]) ).
cnf(refute_1_1412,plain,
join(complement(composition(top,zero)),converse(complement(composition(zero,top)))) = converse(complement(composition(zero,top))),
inference(resolve,[$cnf( $equal(join(converse(complement(composition(zero,top))),complement(composition(top,zero))),converse(complement(composition(zero,top)))) )],[refute_1_1408,refute_1_1411]) ).
cnf(refute_1_1413,plain,
( composition(top,zero) != join(meet(converse(complement(composition(zero,top))),composition(top,zero)),complement(join(complement(composition(top,zero)),converse(complement(composition(zero,top))))))
| join(complement(composition(top,zero)),converse(complement(composition(zero,top)))) != converse(complement(composition(zero,top)))
| composition(top,zero) = join(meet(converse(complement(composition(zero,top))),composition(top,zero)),complement(converse(complement(composition(zero,top))))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(top,zero),join(meet(converse(complement(composition(zero,top))),composition(top,zero)),complement(join(complement(composition(top,zero)),converse(complement(composition(zero,top))))))) ),[1,1,0],$fot(converse(complement(composition(zero,top))))]]) ).
cnf(refute_1_1414,plain,
( composition(top,zero) != join(meet(converse(complement(composition(zero,top))),composition(top,zero)),complement(join(complement(composition(top,zero)),converse(complement(composition(zero,top))))))
| composition(top,zero) = join(meet(converse(complement(composition(zero,top))),composition(top,zero)),complement(converse(complement(composition(zero,top))))) ),
inference(resolve,[$cnf( $equal(join(complement(composition(top,zero)),converse(complement(composition(zero,top)))),converse(complement(composition(zero,top)))) )],[refute_1_1412,refute_1_1413]) ).
cnf(refute_1_1415,plain,
composition(top,zero) = join(meet(converse(complement(composition(zero,top))),composition(top,zero)),complement(converse(complement(composition(zero,top))))),
inference(resolve,[$cnf( $equal(composition(top,zero),join(meet(converse(complement(composition(zero,top))),composition(top,zero)),complement(join(complement(composition(top,zero)),converse(complement(composition(zero,top))))))) )],[refute_1_1391,refute_1_1414]) ).
cnf(refute_1_1416,plain,
join(complement(converse(complement(composition(zero,top)))),composition(top,zero)) = join(composition(top,zero),complement(converse(complement(composition(zero,top))))),
inference(subst,[],[refute_1_52:[bind(X0,$fot(composition(top,zero))),bind(X1,$fot(complement(converse(complement(composition(zero,top))))))]]) ).
cnf(refute_1_1417,plain,
join(join(complement(X_200),meet(X_200,X_275)),meet(X_275,join(complement(X_200),meet(X_200,X_275)))) = join(complement(X_200),meet(X_200,X_275)),
inference(subst,[],[refute_1_1304:[bind(X_176,$fot(join(complement(X_200),meet(X_200,X_275)))),bind(X_177,$fot(X_275))]]) ).
cnf(refute_1_1418,plain,
X_201 = meet(X_201,join(complement(X_200),meet(X_201,X_200))),
inference(subst,[],[refute_1_764:[bind(X_138,$fot(X_200)),bind(X_176,$fot(X_201))]]) ).
cnf(refute_1_1419,plain,
meet(X_200,X_201) = meet(X_201,X_200),
inference(subst,[],[refute_1_461:[bind(X_137,$fot(X_200)),bind(X_138,$fot(X_201))]]) ).
cnf(refute_1_1420,plain,
( meet(X_200,X_201) != meet(X_201,X_200)
| meet(X_201,X_200) = meet(X_200,X_201) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(meet(X_200,X_201))),bind(Y,$fot(meet(X_201,X_200)))]]) ).
cnf(refute_1_1421,plain,
meet(X_201,X_200) = meet(X_200,X_201),
inference(resolve,[$cnf( $equal(meet(X_200,X_201),meet(X_201,X_200)) )],[refute_1_1419,refute_1_1420]) ).
cnf(refute_1_1422,plain,
( X_201 != meet(X_201,join(complement(X_200),meet(X_201,X_200)))
| meet(X_201,X_200) != meet(X_200,X_201)
| X_201 = meet(X_201,join(complement(X_200),meet(X_200,X_201))) ),
introduced(tautology,[equality,[$cnf( $equal(X_201,meet(X_201,join(complement(X_200),meet(X_201,X_200)))) ),[1,1,1],$fot(meet(X_200,X_201))]]) ).
cnf(refute_1_1423,plain,
( X_201 != meet(X_201,join(complement(X_200),meet(X_201,X_200)))
| X_201 = meet(X_201,join(complement(X_200),meet(X_200,X_201))) ),
inference(resolve,[$cnf( $equal(meet(X_201,X_200),meet(X_200,X_201)) )],[refute_1_1421,refute_1_1422]) ).
cnf(refute_1_1424,plain,
X_201 = meet(X_201,join(complement(X_200),meet(X_200,X_201))),
inference(resolve,[$cnf( $equal(X_201,meet(X_201,join(complement(X_200),meet(X_201,X_200)))) )],[refute_1_1418,refute_1_1423]) ).
cnf(refute_1_1425,plain,
X_275 = meet(X_275,join(complement(X_200),meet(X_200,X_275))),
inference(subst,[],[refute_1_1424:[bind(X_201,$fot(X_275))]]) ).
cnf(refute_1_1426,plain,
( X_275 != meet(X_275,join(complement(X_200),meet(X_200,X_275)))
| meet(X_275,join(complement(X_200),meet(X_200,X_275))) = X_275 ),
inference(subst,[],[refute_1_17:[bind(X,$fot(X_275)),bind(Y,$fot(meet(X_275,join(complement(X_200),meet(X_200,X_275)))))]]) ).
cnf(refute_1_1427,plain,
meet(X_275,join(complement(X_200),meet(X_200,X_275))) = X_275,
inference(resolve,[$cnf( $equal(X_275,meet(X_275,join(complement(X_200),meet(X_200,X_275)))) )],[refute_1_1425,refute_1_1426]) ).
cnf(refute_1_1428,plain,
( join(join(complement(X_200),meet(X_200,X_275)),meet(X_275,join(complement(X_200),meet(X_200,X_275)))) != join(complement(X_200),meet(X_200,X_275))
| meet(X_275,join(complement(X_200),meet(X_200,X_275))) != X_275
| join(join(complement(X_200),meet(X_200,X_275)),X_275) = join(complement(X_200),meet(X_200,X_275)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(complement(X_200),meet(X_200,X_275)),meet(X_275,join(complement(X_200),meet(X_200,X_275)))),join(complement(X_200),meet(X_200,X_275))) ),[0,1],$fot(X_275)]]) ).
cnf(refute_1_1429,plain,
( join(join(complement(X_200),meet(X_200,X_275)),meet(X_275,join(complement(X_200),meet(X_200,X_275)))) != join(complement(X_200),meet(X_200,X_275))
| join(join(complement(X_200),meet(X_200,X_275)),X_275) = join(complement(X_200),meet(X_200,X_275)) ),
inference(resolve,[$cnf( $equal(meet(X_275,join(complement(X_200),meet(X_200,X_275))),X_275) )],[refute_1_1427,refute_1_1428]) ).
cnf(refute_1_1430,plain,
join(join(complement(X_200),meet(X_200,X_275)),X_275) = join(complement(X_200),meet(X_200,X_275)),
inference(resolve,[$cnf( $equal(join(join(complement(X_200),meet(X_200,X_275)),meet(X_275,join(complement(X_200),meet(X_200,X_275)))),join(complement(X_200),meet(X_200,X_275))) )],[refute_1_1417,refute_1_1429]) ).
cnf(refute_1_1431,plain,
join(X_275,meet(X_200,X_275)) = X_275,
inference(subst,[],[refute_1_1304:[bind(X_176,$fot(X_275)),bind(X_177,$fot(X_200))]]) ).
cnf(refute_1_1432,plain,
join(complement(X_200),join(X_275,meet(X_200,X_275))) = join(complement(X_200),join(X_275,meet(X_200,X_275))),
introduced(tautology,[refl,[$fot(join(complement(X_200),join(X_275,meet(X_200,X_275))))]]) ).
cnf(refute_1_1433,plain,
( join(X_275,meet(X_200,X_275)) != X_275
| join(complement(X_200),join(X_275,meet(X_200,X_275))) != join(complement(X_200),join(X_275,meet(X_200,X_275)))
| join(complement(X_200),join(X_275,meet(X_200,X_275))) = join(complement(X_200),X_275) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_200),join(X_275,meet(X_200,X_275))),join(complement(X_200),join(X_275,meet(X_200,X_275)))) ),[1,1],$fot(X_275)]]) ).
cnf(refute_1_1434,plain,
( join(X_275,meet(X_200,X_275)) != X_275
| join(complement(X_200),join(X_275,meet(X_200,X_275))) = join(complement(X_200),X_275) ),
inference(resolve,[$cnf( $equal(join(complement(X_200),join(X_275,meet(X_200,X_275))),join(complement(X_200),join(X_275,meet(X_200,X_275)))) )],[refute_1_1432,refute_1_1433]) ).
cnf(refute_1_1435,plain,
join(complement(X_200),join(X_275,meet(X_200,X_275))) = join(complement(X_200),X_275),
inference(resolve,[$cnf( $equal(join(X_275,meet(X_200,X_275)),X_275) )],[refute_1_1431,refute_1_1434]) ).
cnf(refute_1_1436,plain,
join(X_210,join(X_211,X_212)) = join(join(X_210,X_211),X_212),
inference(subst,[],[refute_1_100:[bind(X0,$fot(X_210)),bind(X1,$fot(X_211)),bind(X2,$fot(X_212))]]) ).
cnf(refute_1_1437,plain,
join(X_212,X_211) = join(X_211,X_212),
inference(subst,[],[refute_1_50:[bind(X0,$fot(X_212)),bind(X1,$fot(X_211))]]) ).
cnf(refute_1_1438,plain,
( join(X_212,X_211) != join(X_211,X_212)
| join(X_211,X_212) = join(X_212,X_211) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(join(X_212,X_211))),bind(Y,$fot(join(X_211,X_212)))]]) ).
cnf(refute_1_1439,plain,
join(X_211,X_212) = join(X_212,X_211),
inference(resolve,[$cnf( $equal(join(X_212,X_211),join(X_211,X_212)) )],[refute_1_1437,refute_1_1438]) ).
cnf(refute_1_1440,plain,
( join(X_210,join(X_211,X_212)) != join(join(X_210,X_211),X_212)
| join(X_211,X_212) != join(X_212,X_211)
| join(X_210,join(X_212,X_211)) = join(join(X_210,X_211),X_212) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_210,join(X_211,X_212)),join(join(X_210,X_211),X_212)) ),[0,1],$fot(join(X_212,X_211))]]) ).
cnf(refute_1_1441,plain,
( join(X_210,join(X_211,X_212)) != join(join(X_210,X_211),X_212)
| join(X_210,join(X_212,X_211)) = join(join(X_210,X_211),X_212) ),
inference(resolve,[$cnf( $equal(join(X_211,X_212),join(X_212,X_211)) )],[refute_1_1439,refute_1_1440]) ).
cnf(refute_1_1442,plain,
join(X_210,join(X_212,X_211)) = join(join(X_210,X_211),X_212),
inference(resolve,[$cnf( $equal(join(X_210,join(X_211,X_212)),join(join(X_210,X_211),X_212)) )],[refute_1_1436,refute_1_1441]) ).
cnf(refute_1_1443,plain,
join(join(X_210,X_211),X_212) = join(X_210,join(X_211,X_212)),
inference(subst,[],[refute_1_102:[bind(X0,$fot(X_210)),bind(X1,$fot(X_211)),bind(X2,$fot(X_212))]]) ).
cnf(refute_1_1444,plain,
( join(X_210,join(X_212,X_211)) != join(join(X_210,X_211),X_212)
| join(join(X_210,X_211),X_212) != join(X_210,join(X_211,X_212))
| join(X_210,join(X_212,X_211)) = join(X_210,join(X_211,X_212)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_210,join(X_212,X_211)),join(X_210,join(X_211,X_212))) ),[0],$fot(join(join(X_210,X_211),X_212))]]) ).
cnf(refute_1_1445,plain,
( join(X_210,join(X_212,X_211)) != join(join(X_210,X_211),X_212)
| join(X_210,join(X_212,X_211)) = join(X_210,join(X_211,X_212)) ),
inference(resolve,[$cnf( $equal(join(join(X_210,X_211),X_212),join(X_210,join(X_211,X_212))) )],[refute_1_1443,refute_1_1444]) ).
cnf(refute_1_1446,plain,
join(X_210,join(X_212,X_211)) = join(X_210,join(X_211,X_212)),
inference(resolve,[$cnf( $equal(join(X_210,join(X_212,X_211)),join(join(X_210,X_211),X_212)) )],[refute_1_1442,refute_1_1445]) ).
cnf(refute_1_1447,plain,
( join(X_210,join(X_212,X_211)) != join(X_210,join(X_211,X_212))
| join(X_210,join(X_211,X_212)) = join(X_210,join(X_212,X_211)) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(join(X_210,join(X_212,X_211)))),bind(Y,$fot(join(X_210,join(X_211,X_212))))]]) ).
cnf(refute_1_1448,plain,
join(X_210,join(X_211,X_212)) = join(X_210,join(X_212,X_211)),
inference(resolve,[$cnf( $equal(join(X_210,join(X_212,X_211)),join(X_210,join(X_211,X_212))) )],[refute_1_1446,refute_1_1447]) ).
cnf(refute_1_1449,plain,
join(complement(X_200),join(meet(X_200,X_275),X_275)) = join(complement(X_200),join(X_275,meet(X_200,X_275))),
inference(subst,[],[refute_1_1448:[bind(X_210,$fot(complement(X_200))),bind(X_211,$fot(meet(X_200,X_275))),bind(X_212,$fot(X_275))]]) ).
cnf(refute_1_1450,plain,
join(join(complement(X_200),meet(X_200,X_275)),X_275) = join(complement(X_200),join(meet(X_200,X_275),X_275)),
inference(subst,[],[refute_1_102:[bind(X0,$fot(complement(X_200))),bind(X1,$fot(meet(X_200,X_275))),bind(X2,$fot(X_275))]]) ).
cnf(refute_1_1451,plain,
( join(complement(X_200),join(meet(X_200,X_275),X_275)) != join(complement(X_200),join(X_275,meet(X_200,X_275)))
| join(join(complement(X_200),meet(X_200,X_275)),X_275) != join(complement(X_200),join(meet(X_200,X_275),X_275))
| join(join(complement(X_200),meet(X_200,X_275)),X_275) = join(complement(X_200),join(X_275,meet(X_200,X_275))) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(join(complement(X_200),meet(X_200,X_275)),X_275))),bind(Y,$fot(join(complement(X_200),join(meet(X_200,X_275),X_275)))),bind(Z,$fot(join(complement(X_200),join(X_275,meet(X_200,X_275)))))]]) ).
cnf(refute_1_1452,plain,
( join(complement(X_200),join(meet(X_200,X_275),X_275)) != join(complement(X_200),join(X_275,meet(X_200,X_275)))
| join(join(complement(X_200),meet(X_200,X_275)),X_275) = join(complement(X_200),join(X_275,meet(X_200,X_275))) ),
inference(resolve,[$cnf( $equal(join(join(complement(X_200),meet(X_200,X_275)),X_275),join(complement(X_200),join(meet(X_200,X_275),X_275))) )],[refute_1_1450,refute_1_1451]) ).
cnf(refute_1_1453,plain,
join(join(complement(X_200),meet(X_200,X_275)),X_275) = join(complement(X_200),join(X_275,meet(X_200,X_275))),
inference(resolve,[$cnf( $equal(join(complement(X_200),join(meet(X_200,X_275),X_275)),join(complement(X_200),join(X_275,meet(X_200,X_275)))) )],[refute_1_1449,refute_1_1452]) ).
cnf(refute_1_1454,plain,
( join(complement(X_200),join(X_275,meet(X_200,X_275))) != join(complement(X_200),X_275)
| join(join(complement(X_200),meet(X_200,X_275)),X_275) != join(complement(X_200),join(X_275,meet(X_200,X_275)))
| join(join(complement(X_200),meet(X_200,X_275)),X_275) = join(complement(X_200),X_275) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(join(complement(X_200),meet(X_200,X_275)),X_275))),bind(Y,$fot(join(complement(X_200),join(X_275,meet(X_200,X_275))))),bind(Z,$fot(join(complement(X_200),X_275)))]]) ).
cnf(refute_1_1455,plain,
( join(complement(X_200),join(X_275,meet(X_200,X_275))) != join(complement(X_200),X_275)
| join(join(complement(X_200),meet(X_200,X_275)),X_275) = join(complement(X_200),X_275) ),
inference(resolve,[$cnf( $equal(join(join(complement(X_200),meet(X_200,X_275)),X_275),join(complement(X_200),join(X_275,meet(X_200,X_275)))) )],[refute_1_1453,refute_1_1454]) ).
cnf(refute_1_1456,plain,
join(join(complement(X_200),meet(X_200,X_275)),X_275) = join(complement(X_200),X_275),
inference(resolve,[$cnf( $equal(join(complement(X_200),join(X_275,meet(X_200,X_275))),join(complement(X_200),X_275)) )],[refute_1_1435,refute_1_1455]) ).
cnf(refute_1_1457,plain,
( join(join(complement(X_200),meet(X_200,X_275)),X_275) != join(complement(X_200),X_275)
| join(join(complement(X_200),meet(X_200,X_275)),X_275) != join(complement(X_200),meet(X_200,X_275))
| join(complement(X_200),X_275) = join(complement(X_200),meet(X_200,X_275)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(complement(X_200),meet(X_200,X_275)),X_275),join(complement(X_200),meet(X_200,X_275))) ),[0],$fot(join(complement(X_200),X_275))]]) ).
cnf(refute_1_1458,plain,
( join(join(complement(X_200),meet(X_200,X_275)),X_275) != join(complement(X_200),meet(X_200,X_275))
| join(complement(X_200),X_275) = join(complement(X_200),meet(X_200,X_275)) ),
inference(resolve,[$cnf( $equal(join(join(complement(X_200),meet(X_200,X_275)),X_275),join(complement(X_200),X_275)) )],[refute_1_1456,refute_1_1457]) ).
cnf(refute_1_1459,plain,
join(complement(X_200),X_275) = join(complement(X_200),meet(X_200,X_275)),
inference(resolve,[$cnf( $equal(join(join(complement(X_200),meet(X_200,X_275)),X_275),join(complement(X_200),meet(X_200,X_275))) )],[refute_1_1430,refute_1_1458]) ).
cnf(refute_1_1460,plain,
( join(complement(X_200),X_275) != join(complement(X_200),meet(X_200,X_275))
| join(complement(X_200),meet(X_200,X_275)) = join(complement(X_200),X_275) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(join(complement(X_200),X_275))),bind(Y,$fot(join(complement(X_200),meet(X_200,X_275))))]]) ).
cnf(refute_1_1461,plain,
join(complement(X_200),meet(X_200,X_275)) = join(complement(X_200),X_275),
inference(resolve,[$cnf( $equal(join(complement(X_200),X_275),join(complement(X_200),meet(X_200,X_275))) )],[refute_1_1459,refute_1_1460]) ).
cnf(refute_1_1462,plain,
join(complement(converse(complement(composition(zero,top)))),meet(converse(complement(composition(zero,top))),composition(top,zero))) = join(complement(converse(complement(composition(zero,top)))),composition(top,zero)),
inference(subst,[],[refute_1_1461:[bind(X_200,$fot(converse(complement(composition(zero,top))))),bind(X_275,$fot(composition(top,zero)))]]) ).
cnf(refute_1_1463,plain,
( join(complement(converse(complement(composition(zero,top)))),composition(top,zero)) != join(composition(top,zero),complement(converse(complement(composition(zero,top)))))
| join(complement(converse(complement(composition(zero,top)))),meet(converse(complement(composition(zero,top))),composition(top,zero))) != join(complement(converse(complement(composition(zero,top)))),composition(top,zero))
| join(complement(converse(complement(composition(zero,top)))),meet(converse(complement(composition(zero,top))),composition(top,zero))) = join(composition(top,zero),complement(converse(complement(composition(zero,top))))) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(complement(converse(complement(composition(zero,top)))),meet(converse(complement(composition(zero,top))),composition(top,zero))))),bind(Y,$fot(join(complement(converse(complement(composition(zero,top)))),composition(top,zero)))),bind(Z,$fot(join(composition(top,zero),complement(converse(complement(composition(zero,top)))))))]]) ).
cnf(refute_1_1464,plain,
( join(complement(converse(complement(composition(zero,top)))),composition(top,zero)) != join(composition(top,zero),complement(converse(complement(composition(zero,top)))))
| join(complement(converse(complement(composition(zero,top)))),meet(converse(complement(composition(zero,top))),composition(top,zero))) = join(composition(top,zero),complement(converse(complement(composition(zero,top))))) ),
inference(resolve,[$cnf( $equal(join(complement(converse(complement(composition(zero,top)))),meet(converse(complement(composition(zero,top))),composition(top,zero))),join(complement(converse(complement(composition(zero,top)))),composition(top,zero))) )],[refute_1_1462,refute_1_1463]) ).
cnf(refute_1_1465,plain,
join(complement(converse(complement(composition(zero,top)))),meet(converse(complement(composition(zero,top))),composition(top,zero))) = join(composition(top,zero),complement(converse(complement(composition(zero,top))))),
inference(resolve,[$cnf( $equal(join(complement(converse(complement(composition(zero,top)))),composition(top,zero)),join(composition(top,zero),complement(converse(complement(composition(zero,top)))))) )],[refute_1_1416,refute_1_1464]) ).
cnf(refute_1_1466,plain,
join(meet(converse(complement(composition(zero,top))),composition(top,zero)),complement(converse(complement(composition(zero,top))))) = join(complement(converse(complement(composition(zero,top)))),meet(converse(complement(composition(zero,top))),composition(top,zero))),
inference(subst,[],[refute_1_52:[bind(X0,$fot(complement(converse(complement(composition(zero,top)))))),bind(X1,$fot(meet(converse(complement(composition(zero,top))),composition(top,zero))))]]) ).
cnf(refute_1_1467,plain,
( join(complement(converse(complement(composition(zero,top)))),meet(converse(complement(composition(zero,top))),composition(top,zero))) != join(composition(top,zero),complement(converse(complement(composition(zero,top)))))
| join(meet(converse(complement(composition(zero,top))),composition(top,zero)),complement(converse(complement(composition(zero,top))))) != join(complement(converse(complement(composition(zero,top)))),meet(converse(complement(composition(zero,top))),composition(top,zero)))
| join(meet(converse(complement(composition(zero,top))),composition(top,zero)),complement(converse(complement(composition(zero,top))))) = join(composition(top,zero),complement(converse(complement(composition(zero,top))))) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(meet(converse(complement(composition(zero,top))),composition(top,zero)),complement(converse(complement(composition(zero,top))))))),bind(Y,$fot(join(complement(converse(complement(composition(zero,top)))),meet(converse(complement(composition(zero,top))),composition(top,zero))))),bind(Z,$fot(join(composition(top,zero),complement(converse(complement(composition(zero,top)))))))]]) ).
cnf(refute_1_1468,plain,
( join(complement(converse(complement(composition(zero,top)))),meet(converse(complement(composition(zero,top))),composition(top,zero))) != join(composition(top,zero),complement(converse(complement(composition(zero,top)))))
| join(meet(converse(complement(composition(zero,top))),composition(top,zero)),complement(converse(complement(composition(zero,top))))) = join(composition(top,zero),complement(converse(complement(composition(zero,top))))) ),
inference(resolve,[$cnf( $equal(join(meet(converse(complement(composition(zero,top))),composition(top,zero)),complement(converse(complement(composition(zero,top))))),join(complement(converse(complement(composition(zero,top)))),meet(converse(complement(composition(zero,top))),composition(top,zero)))) )],[refute_1_1466,refute_1_1467]) ).
cnf(refute_1_1469,plain,
join(meet(converse(complement(composition(zero,top))),composition(top,zero)),complement(converse(complement(composition(zero,top))))) = join(composition(top,zero),complement(converse(complement(composition(zero,top))))),
inference(resolve,[$cnf( $equal(join(complement(converse(complement(composition(zero,top)))),meet(converse(complement(composition(zero,top))),composition(top,zero))),join(composition(top,zero),complement(converse(complement(composition(zero,top)))))) )],[refute_1_1465,refute_1_1468]) ).
cnf(refute_1_1470,plain,
( composition(top,zero) != join(meet(converse(complement(composition(zero,top))),composition(top,zero)),complement(converse(complement(composition(zero,top)))))
| join(meet(converse(complement(composition(zero,top))),composition(top,zero)),complement(converse(complement(composition(zero,top))))) != join(composition(top,zero),complement(converse(complement(composition(zero,top)))))
| composition(top,zero) = join(composition(top,zero),complement(converse(complement(composition(zero,top))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(top,zero),join(composition(top,zero),complement(converse(complement(composition(zero,top)))))) ),[0],$fot(join(meet(converse(complement(composition(zero,top))),composition(top,zero)),complement(converse(complement(composition(zero,top))))))]]) ).
cnf(refute_1_1471,plain,
( composition(top,zero) != join(meet(converse(complement(composition(zero,top))),composition(top,zero)),complement(converse(complement(composition(zero,top)))))
| composition(top,zero) = join(composition(top,zero),complement(converse(complement(composition(zero,top))))) ),
inference(resolve,[$cnf( $equal(join(meet(converse(complement(composition(zero,top))),composition(top,zero)),complement(converse(complement(composition(zero,top))))),join(composition(top,zero),complement(converse(complement(composition(zero,top)))))) )],[refute_1_1469,refute_1_1470]) ).
cnf(refute_1_1472,plain,
composition(top,zero) = join(composition(top,zero),complement(converse(complement(composition(zero,top))))),
inference(resolve,[$cnf( $equal(composition(top,zero),join(meet(converse(complement(composition(zero,top))),composition(top,zero)),complement(converse(complement(composition(zero,top)))))) )],[refute_1_1415,refute_1_1471]) ).
cnf(refute_1_1473,plain,
( composition(top,zero) != join(composition(top,zero),complement(converse(complement(composition(zero,top)))))
| join(composition(top,zero),complement(converse(complement(composition(zero,top))))) = composition(top,zero) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(composition(top,zero))),bind(Y,$fot(join(composition(top,zero),complement(converse(complement(composition(zero,top)))))))]]) ).
cnf(refute_1_1474,plain,
join(composition(top,zero),complement(converse(complement(composition(zero,top))))) = composition(top,zero),
inference(resolve,[$cnf( $equal(composition(top,zero),join(composition(top,zero),complement(converse(complement(composition(zero,top)))))) )],[refute_1_1472,refute_1_1473]) ).
cnf(refute_1_1475,plain,
join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top)))))) = join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top)))))),
introduced(tautology,[refl,[$fot(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top)))))))]]) ).
cnf(refute_1_1476,plain,
( join(composition(top,zero),complement(converse(complement(composition(zero,top))))) != composition(top,zero)
| join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top)))))) != join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top))))))
| join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top)))))) = join(one,composition(top,zero)) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top)))))),join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top))))))) ),[1,1],$fot(composition(top,zero))]]) ).
cnf(refute_1_1477,plain,
( join(composition(top,zero),complement(converse(complement(composition(zero,top))))) != composition(top,zero)
| join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top)))))) = join(one,composition(top,zero)) ),
inference(resolve,[$cnf( $equal(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top)))))),join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top))))))) )],[refute_1_1475,refute_1_1476]) ).
cnf(refute_1_1478,plain,
join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top)))))) = join(one,composition(top,zero)),
inference(resolve,[$cnf( $equal(join(composition(top,zero),complement(converse(complement(composition(zero,top))))),composition(top,zero)) )],[refute_1_1474,refute_1_1477]) ).
cnf(refute_1_1479,plain,
converse(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top))))))) = converse(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top))))))),
introduced(tautology,[refl,[$fot(converse(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top))))))))]]) ).
cnf(refute_1_1480,plain,
( converse(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top))))))) != converse(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top)))))))
| join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top)))))) != join(one,composition(top,zero))
| converse(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top))))))) = converse(join(one,composition(top,zero))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top))))))),converse(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top)))))))) ),[1,0],$fot(join(one,composition(top,zero)))]]) ).
cnf(refute_1_1481,plain,
( join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top)))))) != join(one,composition(top,zero))
| converse(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top))))))) = converse(join(one,composition(top,zero))) ),
inference(resolve,[$cnf( $equal(converse(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top))))))),converse(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top)))))))) )],[refute_1_1479,refute_1_1480]) ).
cnf(refute_1_1482,plain,
converse(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top))))))) = converse(join(one,composition(top,zero))),
inference(resolve,[$cnf( $equal(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top)))))),join(one,composition(top,zero))) )],[refute_1_1478,refute_1_1481]) ).
cnf(refute_1_1483,plain,
( converse(join(one,composition(top,zero))) != join(one,composition(zero,top))
| converse(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top))))))) != converse(join(one,composition(top,zero)))
| converse(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top))))))) = join(one,composition(zero,top)) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(converse(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top))))))))),bind(Y,$fot(converse(join(one,composition(top,zero))))),bind(Z,$fot(join(one,composition(zero,top))))]]) ).
cnf(refute_1_1484,plain,
( converse(join(one,composition(top,zero))) != join(one,composition(zero,top))
| converse(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top))))))) = join(one,composition(zero,top)) ),
inference(resolve,[$cnf( $equal(converse(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top))))))),converse(join(one,composition(top,zero)))) )],[refute_1_1482,refute_1_1483]) ).
cnf(refute_1_1485,plain,
converse(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top))))))) = join(one,composition(zero,top)),
inference(resolve,[$cnf( $equal(converse(join(one,composition(top,zero))),join(one,composition(zero,top))) )],[refute_1_1390,refute_1_1484]) ).
cnf(refute_1_1486,plain,
( converse(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top))))))) != converse(join(one,complement(converse(complement(composition(zero,top))))))
| converse(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top))))))) != join(one,composition(zero,top))
| join(one,composition(zero,top)) = converse(join(one,complement(converse(complement(composition(zero,top)))))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top))))))),converse(join(one,complement(converse(complement(composition(zero,top))))))) ),[0],$fot(join(one,composition(zero,top)))]]) ).
cnf(refute_1_1487,plain,
( converse(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top))))))) != converse(join(one,complement(converse(complement(composition(zero,top))))))
| join(one,composition(zero,top)) = converse(join(one,complement(converse(complement(composition(zero,top)))))) ),
inference(resolve,[$cnf( $equal(converse(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top))))))),join(one,composition(zero,top))) )],[refute_1_1485,refute_1_1486]) ).
cnf(refute_1_1488,plain,
join(one,composition(zero,top)) = converse(join(one,complement(converse(complement(composition(zero,top)))))),
inference(resolve,[$cnf( $equal(converse(join(one,join(composition(top,zero),complement(converse(complement(composition(zero,top))))))),converse(join(one,complement(converse(complement(composition(zero,top))))))) )],[refute_1_1386,refute_1_1487]) ).
cnf(refute_1_1489,plain,
( join(one,composition(zero,top)) != converse(join(one,complement(converse(complement(composition(zero,top))))))
| converse(join(one,complement(converse(complement(composition(zero,top)))))) = join(one,composition(zero,top)) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(join(one,composition(zero,top)))),bind(Y,$fot(converse(join(one,complement(converse(complement(composition(zero,top))))))))]]) ).
cnf(refute_1_1490,plain,
converse(join(one,complement(converse(complement(composition(zero,top)))))) = join(one,composition(zero,top)),
inference(resolve,[$cnf( $equal(join(one,composition(zero,top)),converse(join(one,complement(converse(complement(composition(zero,top))))))) )],[refute_1_1488,refute_1_1489]) ).
cnf(refute_1_1491,plain,
( converse(converse(join(one,complement(converse(complement(composition(zero,top))))))) != join(one,complement(converse(complement(composition(zero,top)))))
| converse(join(one,complement(converse(complement(composition(zero,top)))))) != join(one,composition(zero,top))
| converse(join(one,composition(zero,top))) = join(one,complement(converse(complement(composition(zero,top))))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(converse(join(one,complement(converse(complement(composition(zero,top))))))),join(one,complement(converse(complement(composition(zero,top)))))) ),[0,0],$fot(join(one,composition(zero,top)))]]) ).
cnf(refute_1_1492,plain,
( converse(converse(join(one,complement(converse(complement(composition(zero,top))))))) != join(one,complement(converse(complement(composition(zero,top)))))
| converse(join(one,composition(zero,top))) = join(one,complement(converse(complement(composition(zero,top))))) ),
inference(resolve,[$cnf( $equal(converse(join(one,complement(converse(complement(composition(zero,top)))))),join(one,composition(zero,top))) )],[refute_1_1490,refute_1_1491]) ).
cnf(refute_1_1493,plain,
converse(join(one,composition(zero,top))) = join(one,complement(converse(complement(composition(zero,top))))),
inference(resolve,[$cnf( $equal(converse(converse(join(one,complement(converse(complement(composition(zero,top))))))),join(one,complement(converse(complement(composition(zero,top)))))) )],[refute_1_1291,refute_1_1492]) ).
cnf(refute_1_1494,plain,
converse(join(one,composition(zero,top))) = join(one,converse(composition(zero,top))),
inference(subst,[],[refute_1_351:[bind(X_110,$fot(composition(zero,top)))]]) ).
cnf(refute_1_1495,plain,
converse(converse(composition(top,zero))) = composition(top,zero),
inference(subst,[],[refute_1_3:[bind(X0,$fot(composition(top,zero)))]]) ).
cnf(refute_1_1496,plain,
( converse(composition(top,zero)) != composition(zero,top)
| converse(converse(composition(top,zero))) != composition(top,zero)
| converse(composition(zero,top)) = composition(top,zero) ),
introduced(tautology,[equality,[$cnf( $equal(converse(converse(composition(top,zero))),composition(top,zero)) ),[0,0],$fot(composition(zero,top))]]) ).
cnf(refute_1_1497,plain,
( converse(converse(composition(top,zero))) != composition(top,zero)
| converse(composition(zero,top)) = composition(top,zero) ),
inference(resolve,[$cnf( $equal(converse(composition(top,zero)),composition(zero,top)) )],[refute_1_1374,refute_1_1496]) ).
cnf(refute_1_1498,plain,
converse(composition(zero,top)) = composition(top,zero),
inference(resolve,[$cnf( $equal(converse(converse(composition(top,zero))),composition(top,zero)) )],[refute_1_1495,refute_1_1497]) ).
cnf(refute_1_1499,plain,
( converse(composition(zero,top)) != composition(top,zero)
| converse(join(one,composition(zero,top))) != join(one,converse(composition(zero,top)))
| converse(join(one,composition(zero,top))) = join(one,composition(top,zero)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(one,composition(zero,top))),join(one,converse(composition(zero,top)))) ),[1,1],$fot(composition(top,zero))]]) ).
cnf(refute_1_1500,plain,
( converse(join(one,composition(zero,top))) != join(one,converse(composition(zero,top)))
| converse(join(one,composition(zero,top))) = join(one,composition(top,zero)) ),
inference(resolve,[$cnf( $equal(converse(composition(zero,top)),composition(top,zero)) )],[refute_1_1498,refute_1_1499]) ).
cnf(refute_1_1501,plain,
converse(join(one,composition(zero,top))) = join(one,composition(top,zero)),
inference(resolve,[$cnf( $equal(converse(join(one,composition(zero,top))),join(one,converse(composition(zero,top)))) )],[refute_1_1494,refute_1_1500]) ).
cnf(refute_1_1502,plain,
( converse(join(one,composition(zero,top))) != join(one,complement(converse(complement(composition(zero,top)))))
| converse(join(one,composition(zero,top))) != join(one,composition(top,zero))
| join(one,composition(top,zero)) = join(one,complement(converse(complement(composition(zero,top))))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(one,composition(zero,top))),join(one,complement(converse(complement(composition(zero,top)))))) ),[0],$fot(join(one,composition(top,zero)))]]) ).
cnf(refute_1_1503,plain,
( converse(join(one,composition(zero,top))) != join(one,complement(converse(complement(composition(zero,top)))))
| join(one,composition(top,zero)) = join(one,complement(converse(complement(composition(zero,top))))) ),
inference(resolve,[$cnf( $equal(converse(join(one,composition(zero,top))),join(one,composition(top,zero))) )],[refute_1_1501,refute_1_1502]) ).
cnf(refute_1_1504,plain,
join(one,composition(top,zero)) = join(one,complement(converse(complement(composition(zero,top))))),
inference(resolve,[$cnf( $equal(converse(join(one,composition(zero,top))),join(one,complement(converse(complement(composition(zero,top)))))) )],[refute_1_1493,refute_1_1503]) ).
cnf(refute_1_1505,plain,
( join(one,composition(top,zero)) != join(one,complement(converse(complement(composition(zero,top)))))
| join(one,complement(converse(complement(composition(zero,top))))) = join(one,composition(top,zero)) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(join(one,composition(top,zero)))),bind(Y,$fot(join(one,complement(converse(complement(composition(zero,top)))))))]]) ).
cnf(refute_1_1506,plain,
join(one,complement(converse(complement(composition(zero,top))))) = join(one,composition(top,zero)),
inference(resolve,[$cnf( $equal(join(one,composition(top,zero)),join(one,complement(converse(complement(composition(zero,top)))))) )],[refute_1_1504,refute_1_1505]) ).
cnf(refute_1_1507,plain,
complement(join(one,complement(converse(complement(composition(zero,top)))))) = complement(join(one,complement(converse(complement(composition(zero,top)))))),
introduced(tautology,[refl,[$fot(complement(join(one,complement(converse(complement(composition(zero,top)))))))]]) ).
cnf(refute_1_1508,plain,
( complement(join(one,complement(converse(complement(composition(zero,top)))))) != complement(join(one,complement(converse(complement(composition(zero,top))))))
| join(one,complement(converse(complement(composition(zero,top))))) != join(one,composition(top,zero))
| complement(join(one,complement(converse(complement(composition(zero,top)))))) = complement(join(one,composition(top,zero))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(one,complement(converse(complement(composition(zero,top)))))),complement(join(one,complement(converse(complement(composition(zero,top))))))) ),[1,0],$fot(join(one,composition(top,zero)))]]) ).
cnf(refute_1_1509,plain,
( join(one,complement(converse(complement(composition(zero,top))))) != join(one,composition(top,zero))
| complement(join(one,complement(converse(complement(composition(zero,top)))))) = complement(join(one,composition(top,zero))) ),
inference(resolve,[$cnf( $equal(complement(join(one,complement(converse(complement(composition(zero,top)))))),complement(join(one,complement(converse(complement(composition(zero,top))))))) )],[refute_1_1507,refute_1_1508]) ).
cnf(refute_1_1510,plain,
complement(join(one,complement(converse(complement(composition(zero,top)))))) = complement(join(one,composition(top,zero))),
inference(resolve,[$cnf( $equal(join(one,complement(converse(complement(composition(zero,top))))),join(one,composition(top,zero))) )],[refute_1_1506,refute_1_1509]) ).
cnf(refute_1_1511,plain,
join(one,complement(join(one,complement(converse(complement(composition(zero,top))))))) = join(one,complement(join(one,complement(converse(complement(composition(zero,top))))))),
introduced(tautology,[refl,[$fot(join(one,complement(join(one,complement(converse(complement(composition(zero,top))))))))]]) ).
cnf(refute_1_1512,plain,
( complement(join(one,complement(converse(complement(composition(zero,top)))))) != complement(join(one,composition(top,zero)))
| join(one,complement(join(one,complement(converse(complement(composition(zero,top))))))) != join(one,complement(join(one,complement(converse(complement(composition(zero,top)))))))
| join(one,complement(join(one,complement(converse(complement(composition(zero,top))))))) = join(one,complement(join(one,composition(top,zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,complement(join(one,complement(converse(complement(composition(zero,top))))))),join(one,complement(join(one,complement(converse(complement(composition(zero,top)))))))) ),[1,1],$fot(complement(join(one,composition(top,zero))))]]) ).
cnf(refute_1_1513,plain,
( complement(join(one,complement(converse(complement(composition(zero,top)))))) != complement(join(one,composition(top,zero)))
| join(one,complement(join(one,complement(converse(complement(composition(zero,top))))))) = join(one,complement(join(one,composition(top,zero)))) ),
inference(resolve,[$cnf( $equal(join(one,complement(join(one,complement(converse(complement(composition(zero,top))))))),join(one,complement(join(one,complement(converse(complement(composition(zero,top)))))))) )],[refute_1_1511,refute_1_1512]) ).
cnf(refute_1_1514,plain,
join(one,complement(join(one,complement(converse(complement(composition(zero,top))))))) = join(one,complement(join(one,composition(top,zero)))),
inference(resolve,[$cnf( $equal(complement(join(one,complement(converse(complement(composition(zero,top)))))),complement(join(one,composition(top,zero)))) )],[refute_1_1510,refute_1_1513]) ).
cnf(refute_1_1515,plain,
( join(one,complement(join(one,complement(converse(complement(composition(zero,top))))))) != join(one,complement(join(one,composition(top,zero))))
| join(one,complement(join(one,composition(top,zero)))) != complement(composition(top,zero))
| join(one,complement(join(one,complement(converse(complement(composition(zero,top))))))) = complement(composition(top,zero)) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(one,complement(join(one,complement(converse(complement(composition(zero,top))))))))),bind(Y,$fot(join(one,complement(join(one,composition(top,zero)))))),bind(Z,$fot(complement(composition(top,zero))))]]) ).
cnf(refute_1_1516,plain,
( join(one,complement(join(one,composition(top,zero)))) != complement(composition(top,zero))
| join(one,complement(join(one,complement(converse(complement(composition(zero,top))))))) = complement(composition(top,zero)) ),
inference(resolve,[$cnf( $equal(join(one,complement(join(one,complement(converse(complement(composition(zero,top))))))),join(one,complement(join(one,composition(top,zero))))) )],[refute_1_1514,refute_1_1515]) ).
cnf(refute_1_1517,plain,
join(one,complement(join(one,complement(converse(complement(composition(zero,top))))))) = complement(composition(top,zero)),
inference(resolve,[$cnf( $equal(join(one,complement(join(one,composition(top,zero)))),complement(composition(top,zero))) )],[refute_1_1290,refute_1_1516]) ).
cnf(refute_1_1518,plain,
( converse(complement(composition(zero,top))) != join(one,complement(join(one,complement(converse(complement(composition(zero,top)))))))
| join(one,complement(join(one,complement(converse(complement(composition(zero,top))))))) != complement(composition(top,zero))
| converse(complement(composition(zero,top))) = complement(composition(top,zero)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(complement(composition(zero,top))),complement(composition(top,zero))) ),[0],$fot(join(one,complement(join(one,complement(converse(complement(composition(zero,top))))))))]]) ).
cnf(refute_1_1519,plain,
( converse(complement(composition(zero,top))) != join(one,complement(join(one,complement(converse(complement(composition(zero,top)))))))
| converse(complement(composition(zero,top))) = complement(composition(top,zero)) ),
inference(resolve,[$cnf( $equal(join(one,complement(join(one,complement(converse(complement(composition(zero,top))))))),complement(composition(top,zero))) )],[refute_1_1517,refute_1_1518]) ).
cnf(refute_1_1520,plain,
converse(complement(composition(zero,top))) = complement(composition(top,zero)),
inference(resolve,[$cnf( $equal(converse(complement(composition(zero,top))),join(one,complement(join(one,complement(converse(complement(composition(zero,top)))))))) )],[refute_1_1132,refute_1_1519]) ).
cnf(refute_1_1521,plain,
( composition(converse(complement(composition(zero,top))),complement(composition(complement(composition(zero,top)),top))) != zero
| converse(complement(composition(zero,top))) != complement(composition(top,zero))
| composition(complement(composition(top,zero)),complement(composition(complement(composition(zero,top)),top))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(complement(composition(zero,top))),complement(composition(complement(composition(zero,top)),top))),zero) ),[0,0],$fot(complement(composition(top,zero)))]]) ).
cnf(refute_1_1522,plain,
( composition(converse(complement(composition(zero,top))),complement(composition(complement(composition(zero,top)),top))) != zero
| composition(complement(composition(top,zero)),complement(composition(complement(composition(zero,top)),top))) = zero ),
inference(resolve,[$cnf( $equal(converse(complement(composition(zero,top))),complement(composition(top,zero))) )],[refute_1_1520,refute_1_1521]) ).
cnf(refute_1_1523,plain,
composition(complement(composition(top,zero)),complement(composition(complement(composition(zero,top)),top))) = zero,
inference(resolve,[$cnf( $equal(composition(converse(complement(composition(zero,top))),complement(composition(complement(composition(zero,top)),top))),zero) )],[refute_1_676,refute_1_1522]) ).
cnf(refute_1_1524,plain,
composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
inference(canonicalize,[],[normalize_1_28]) ).
cnf(refute_1_1525,plain,
composition(converse(X1),composition(converse(X0),X_124)) = composition(composition(converse(X1),converse(X0)),X_124),
inference(subst,[],[refute_1_1524:[bind(X0,$fot(converse(X1))),bind(X1,$fot(converse(X0))),bind(X2,$fot(X_124))]]) ).
cnf(refute_1_1526,plain,
( converse(composition(X0,X1)) != composition(converse(X1),converse(X0))
| composition(converse(X1),converse(X0)) = converse(composition(X0,X1)) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(converse(composition(X0,X1)))),bind(Y,$fot(composition(converse(X1),converse(X0))))]]) ).
cnf(refute_1_1527,plain,
composition(converse(X1),converse(X0)) = converse(composition(X0,X1)),
inference(resolve,[$cnf( $equal(converse(composition(X0,X1)),composition(converse(X1),converse(X0))) )],[refute_1_1,refute_1_1526]) ).
cnf(refute_1_1528,plain,
( composition(converse(X1),composition(converse(X0),X_124)) != composition(composition(converse(X1),converse(X0)),X_124)
| composition(converse(X1),converse(X0)) != converse(composition(X0,X1))
| composition(converse(X1),composition(converse(X0),X_124)) = composition(converse(composition(X0,X1)),X_124) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(X1),composition(converse(X0),X_124)),composition(composition(converse(X1),converse(X0)),X_124)) ),[1,0],$fot(converse(composition(X0,X1)))]]) ).
cnf(refute_1_1529,plain,
( composition(converse(X1),composition(converse(X0),X_124)) != composition(composition(converse(X1),converse(X0)),X_124)
| composition(converse(X1),composition(converse(X0),X_124)) = composition(converse(composition(X0,X1)),X_124) ),
inference(resolve,[$cnf( $equal(composition(converse(X1),converse(X0)),converse(composition(X0,X1))) )],[refute_1_1527,refute_1_1528]) ).
cnf(refute_1_1530,plain,
composition(converse(X1),composition(converse(X0),X_124)) = composition(converse(composition(X0,X1)),X_124),
inference(resolve,[$cnf( $equal(composition(converse(X1),composition(converse(X0),X_124)),composition(composition(converse(X1),converse(X0)),X_124)) )],[refute_1_1525,refute_1_1529]) ).
cnf(refute_1_1531,plain,
composition(converse(top),composition(converse(complement(composition(top,top))),X_284)) = composition(converse(composition(complement(composition(top,top)),top)),X_284),
inference(subst,[],[refute_1_1530:[bind(X0,$fot(complement(composition(top,top)))),bind(X1,$fot(top)),bind(X_124,$fot(X_284))]]) ).
cnf(refute_1_1532,plain,
composition(converse(converse(complement(composition(top,top)))),complement(composition(converse(complement(composition(top,top))),top))) = zero,
inference(subst,[],[refute_1_675:[bind(X0,$fot(converse(complement(composition(top,top)))))]]) ).
cnf(refute_1_1533,plain,
converse(composition(converse(X_193),complement(composition(X_193,top)))) = composition(converse(complement(composition(X_193,top))),converse(converse(X_193))),
inference(subst,[],[refute_1_1:[bind(X0,$fot(converse(X_193))),bind(X1,$fot(complement(composition(X_193,top))))]]) ).
cnf(refute_1_1534,plain,
composition(converse(X_193),complement(composition(X_193,top))) = zero,
inference(subst,[],[refute_1_675:[bind(X0,$fot(X_193))]]) ).
cnf(refute_1_1535,plain,
( composition(converse(X_193),complement(composition(X_193,top))) != zero
| converse(composition(converse(X_193),complement(composition(X_193,top)))) != composition(converse(complement(composition(X_193,top))),converse(converse(X_193)))
| converse(zero) = composition(converse(complement(composition(X_193,top))),converse(converse(X_193))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(X_193),complement(composition(X_193,top)))),composition(converse(complement(composition(X_193,top))),converse(converse(X_193)))) ),[0,0],$fot(zero)]]) ).
cnf(refute_1_1536,plain,
( converse(composition(converse(X_193),complement(composition(X_193,top)))) != composition(converse(complement(composition(X_193,top))),converse(converse(X_193)))
| converse(zero) = composition(converse(complement(composition(X_193,top))),converse(converse(X_193))) ),
inference(resolve,[$cnf( $equal(composition(converse(X_193),complement(composition(X_193,top))),zero) )],[refute_1_1534,refute_1_1535]) ).
cnf(refute_1_1537,plain,
converse(zero) = composition(converse(complement(composition(X_193,top))),converse(converse(X_193))),
inference(resolve,[$cnf( $equal(converse(composition(converse(X_193),complement(composition(X_193,top)))),composition(converse(complement(composition(X_193,top))),converse(converse(X_193)))) )],[refute_1_1533,refute_1_1536]) ).
cnf(refute_1_1538,plain,
( converse(zero) != composition(converse(complement(composition(X_193,top))),converse(converse(X_193)))
| converse(zero) != zero
| zero = composition(converse(complement(composition(X_193,top))),converse(converse(X_193))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(zero),composition(converse(complement(composition(X_193,top))),converse(converse(X_193)))) ),[0],$fot(zero)]]) ).
cnf(refute_1_1539,plain,
( converse(zero) != composition(converse(complement(composition(X_193,top))),converse(converse(X_193)))
| zero = composition(converse(complement(composition(X_193,top))),converse(converse(X_193))) ),
inference(resolve,[$cnf( $equal(converse(zero),zero) )],[refute_1_659,refute_1_1538]) ).
cnf(refute_1_1540,plain,
converse(composition(converse(X_193),complement(composition(X_193,top)))) = composition(converse(complement(composition(X_193,top))),X_193),
inference(subst,[],[refute_1_117:[bind(X0,$fot(X_193)),bind(X_112,$fot(complement(composition(X_193,top))))]]) ).
cnf(refute_1_1541,plain,
composition(converse(complement(composition(X_193,top))),converse(converse(X_193))) = converse(composition(converse(X_193),complement(composition(X_193,top)))),
inference(subst,[],[refute_1_1527:[bind(X0,$fot(converse(X_193))),bind(X1,$fot(complement(composition(X_193,top))))]]) ).
cnf(refute_1_1542,plain,
( composition(converse(complement(composition(X_193,top))),converse(converse(X_193))) != converse(composition(converse(X_193),complement(composition(X_193,top))))
| converse(composition(converse(X_193),complement(composition(X_193,top)))) != composition(converse(complement(composition(X_193,top))),X_193)
| composition(converse(complement(composition(X_193,top))),converse(converse(X_193))) = composition(converse(complement(composition(X_193,top))),X_193) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(composition(converse(complement(composition(X_193,top))),converse(converse(X_193))))),bind(Y,$fot(converse(composition(converse(X_193),complement(composition(X_193,top)))))),bind(Z,$fot(composition(converse(complement(composition(X_193,top))),X_193)))]]) ).
cnf(refute_1_1543,plain,
( converse(composition(converse(X_193),complement(composition(X_193,top)))) != composition(converse(complement(composition(X_193,top))),X_193)
| composition(converse(complement(composition(X_193,top))),converse(converse(X_193))) = composition(converse(complement(composition(X_193,top))),X_193) ),
inference(resolve,[$cnf( $equal(composition(converse(complement(composition(X_193,top))),converse(converse(X_193))),converse(composition(converse(X_193),complement(composition(X_193,top))))) )],[refute_1_1541,refute_1_1542]) ).
cnf(refute_1_1544,plain,
composition(converse(complement(composition(X_193,top))),converse(converse(X_193))) = composition(converse(complement(composition(X_193,top))),X_193),
inference(resolve,[$cnf( $equal(converse(composition(converse(X_193),complement(composition(X_193,top)))),composition(converse(complement(composition(X_193,top))),X_193)) )],[refute_1_1540,refute_1_1543]) ).
cnf(refute_1_1545,plain,
( composition(converse(complement(composition(X_193,top))),converse(converse(X_193))) != composition(converse(complement(composition(X_193,top))),X_193)
| zero != composition(converse(complement(composition(X_193,top))),converse(converse(X_193)))
| zero = composition(converse(complement(composition(X_193,top))),X_193) ),
introduced(tautology,[equality,[$cnf( $equal(zero,composition(converse(complement(composition(X_193,top))),converse(converse(X_193)))) ),[1],$fot(composition(converse(complement(composition(X_193,top))),X_193))]]) ).
cnf(refute_1_1546,plain,
( zero != composition(converse(complement(composition(X_193,top))),converse(converse(X_193)))
| zero = composition(converse(complement(composition(X_193,top))),X_193) ),
inference(resolve,[$cnf( $equal(composition(converse(complement(composition(X_193,top))),converse(converse(X_193))),composition(converse(complement(composition(X_193,top))),X_193)) )],[refute_1_1544,refute_1_1545]) ).
cnf(refute_1_1547,plain,
( converse(zero) != composition(converse(complement(composition(X_193,top))),converse(converse(X_193)))
| zero = composition(converse(complement(composition(X_193,top))),X_193) ),
inference(resolve,[$cnf( $equal(zero,composition(converse(complement(composition(X_193,top))),converse(converse(X_193)))) )],[refute_1_1539,refute_1_1546]) ).
cnf(refute_1_1548,plain,
zero = composition(converse(complement(composition(X_193,top))),X_193),
inference(resolve,[$cnf( $equal(converse(zero),composition(converse(complement(composition(X_193,top))),converse(converse(X_193)))) )],[refute_1_1537,refute_1_1547]) ).
cnf(refute_1_1549,plain,
zero = composition(converse(complement(composition(top,top))),top),
inference(subst,[],[refute_1_1548:[bind(X_193,$fot(top))]]) ).
cnf(refute_1_1550,plain,
( zero != composition(converse(complement(composition(top,top))),top)
| composition(converse(complement(composition(top,top))),top) = zero ),
inference(subst,[],[refute_1_17:[bind(X,$fot(zero)),bind(Y,$fot(composition(converse(complement(composition(top,top))),top)))]]) ).
cnf(refute_1_1551,plain,
composition(converse(complement(composition(top,top))),top) = zero,
inference(resolve,[$cnf( $equal(zero,composition(converse(complement(composition(top,top))),top)) )],[refute_1_1549,refute_1_1550]) ).
cnf(refute_1_1552,plain,
( composition(converse(complement(composition(top,top))),top) != zero
| composition(converse(converse(complement(composition(top,top)))),complement(composition(converse(complement(composition(top,top))),top))) != zero
| composition(converse(converse(complement(composition(top,top)))),complement(zero)) = zero ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(converse(complement(composition(top,top)))),complement(composition(converse(complement(composition(top,top))),top))),zero) ),[0,1,0],$fot(zero)]]) ).
cnf(refute_1_1553,plain,
( composition(converse(converse(complement(composition(top,top)))),complement(composition(converse(complement(composition(top,top))),top))) != zero
| composition(converse(converse(complement(composition(top,top)))),complement(zero)) = zero ),
inference(resolve,[$cnf( $equal(composition(converse(complement(composition(top,top))),top),zero) )],[refute_1_1551,refute_1_1552]) ).
cnf(refute_1_1554,plain,
composition(converse(converse(complement(composition(top,top)))),complement(zero)) = zero,
inference(resolve,[$cnf( $equal(composition(converse(converse(complement(composition(top,top)))),complement(composition(converse(complement(composition(top,top))),top))),zero) )],[refute_1_1532,refute_1_1553]) ).
cnf(refute_1_1555,plain,
top = join(complement(zero),join(complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero))))),
inference(subst,[],[refute_1_236:[bind(X_137,$fot(zero)),bind(X_138,$fot(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))))]]) ).
cnf(refute_1_1556,plain,
zero = join(meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),complement(join(complement(zero),composition(converse(skolemFOFtoCNF_X0_1),complement(zero))))),
inference(subst,[],[refute_1_69:[bind(X0,$fot(zero)),bind(X1,$fot(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))))]]) ).
cnf(refute_1_1557,plain,
join(complement(zero),composition(converse(skolemFOFtoCNF_X0_1),complement(composition(skolemFOFtoCNF_X0_1,zero)))) = complement(zero),
inference(subst,[],[refute_1_112:[bind(X0,$fot(skolemFOFtoCNF_X0_1)),bind(X1,$fot(zero))]]) ).
cnf(refute_1_1558,plain,
composition(skolemFOFtoCNF_X0_1,zero) = zero,
inference(canonicalize,[],[normalize_1_29]) ).
cnf(refute_1_1559,plain,
( composition(skolemFOFtoCNF_X0_1,zero) != zero
| join(complement(zero),composition(converse(skolemFOFtoCNF_X0_1),complement(composition(skolemFOFtoCNF_X0_1,zero)))) != complement(zero)
| join(complement(zero),composition(converse(skolemFOFtoCNF_X0_1),complement(zero))) = complement(zero) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(zero),composition(converse(skolemFOFtoCNF_X0_1),complement(composition(skolemFOFtoCNF_X0_1,zero)))),complement(zero)) ),[0,1,1,0],$fot(zero)]]) ).
cnf(refute_1_1560,plain,
( join(complement(zero),composition(converse(skolemFOFtoCNF_X0_1),complement(composition(skolemFOFtoCNF_X0_1,zero)))) != complement(zero)
| join(complement(zero),composition(converse(skolemFOFtoCNF_X0_1),complement(zero))) = complement(zero) ),
inference(resolve,[$cnf( $equal(composition(skolemFOFtoCNF_X0_1,zero),zero) )],[refute_1_1558,refute_1_1559]) ).
cnf(refute_1_1561,plain,
join(complement(zero),composition(converse(skolemFOFtoCNF_X0_1),complement(zero))) = complement(zero),
inference(resolve,[$cnf( $equal(join(complement(zero),composition(converse(skolemFOFtoCNF_X0_1),complement(composition(skolemFOFtoCNF_X0_1,zero)))),complement(zero)) )],[refute_1_1557,refute_1_1560]) ).
cnf(refute_1_1562,plain,
( join(complement(zero),composition(converse(skolemFOFtoCNF_X0_1),complement(zero))) != complement(zero)
| zero != join(meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),complement(join(complement(zero),composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))))
| zero = join(meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),complement(complement(zero))) ),
introduced(tautology,[equality,[$cnf( $equal(zero,join(meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),complement(join(complement(zero),composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))))) ),[1,1,0],$fot(complement(zero))]]) ).
cnf(refute_1_1563,plain,
( zero != join(meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),complement(join(complement(zero),composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))))
| zero = join(meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),complement(complement(zero))) ),
inference(resolve,[$cnf( $equal(join(complement(zero),composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),complement(zero)) )],[refute_1_1561,refute_1_1562]) ).
cnf(refute_1_1564,plain,
zero = join(meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),complement(complement(zero))),
inference(resolve,[$cnf( $equal(zero,join(meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),complement(join(complement(zero),composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))))) )],[refute_1_1556,refute_1_1563]) ).
cnf(refute_1_1565,plain,
join(meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),complement(complement(zero))) = join(complement(complement(zero)),meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))),
inference(subst,[],[refute_1_52:[bind(X0,$fot(complement(complement(zero)))),bind(X1,$fot(meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))))]]) ).
cnf(refute_1_1566,plain,
( join(meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),complement(complement(zero))) != join(complement(complement(zero)),meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero))))
| zero != join(meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),complement(complement(zero)))
| zero = join(complement(complement(zero)),meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(zero,join(meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),complement(complement(zero)))) ),[1],$fot(join(complement(complement(zero)),meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))))]]) ).
cnf(refute_1_1567,plain,
( zero != join(meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),complement(complement(zero)))
| zero = join(complement(complement(zero)),meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))) ),
inference(resolve,[$cnf( $equal(join(meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),complement(complement(zero))),join(complement(complement(zero)),meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero))))) )],[refute_1_1565,refute_1_1566]) ).
cnf(refute_1_1568,plain,
zero = join(complement(complement(zero)),meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))),
inference(resolve,[$cnf( $equal(zero,join(meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),complement(complement(zero)))) )],[refute_1_1564,refute_1_1567]) ).
cnf(refute_1_1569,plain,
zero = meet(top,complement(top)),
inference(subst,[],[refute_1_8:[bind(X0,$fot(top))]]) ).
cnf(refute_1_1570,plain,
( complement(top) != zero
| zero != meet(top,complement(top))
| zero = meet(top,zero) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(top,complement(top))) ),[1,1],$fot(zero)]]) ).
cnf(refute_1_1571,plain,
( zero != meet(top,complement(top))
| zero = meet(top,zero) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_1_45,refute_1_1570]) ).
cnf(refute_1_1572,plain,
zero = meet(top,zero),
inference(resolve,[$cnf( $equal(zero,meet(top,complement(top))) )],[refute_1_1569,refute_1_1571]) ).
cnf(refute_1_1573,plain,
meet(top,zero) = complement(complement(zero)),
inference(subst,[],[refute_1_512:[bind(X1,$fot(zero))]]) ).
cnf(refute_1_1574,plain,
( meet(top,zero) != complement(complement(zero))
| zero != meet(top,zero)
| zero = complement(complement(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(top,zero)) ),[1],$fot(complement(complement(zero)))]]) ).
cnf(refute_1_1575,plain,
( zero != meet(top,zero)
| zero = complement(complement(zero)) ),
inference(resolve,[$cnf( $equal(meet(top,zero),complement(complement(zero))) )],[refute_1_1573,refute_1_1574]) ).
cnf(refute_1_1576,plain,
zero = complement(complement(zero)),
inference(resolve,[$cnf( $equal(zero,meet(top,zero)) )],[refute_1_1572,refute_1_1575]) ).
cnf(refute_1_1577,plain,
( zero != complement(complement(zero))
| complement(complement(zero)) = zero ),
inference(subst,[],[refute_1_17:[bind(X,$fot(zero)),bind(Y,$fot(complement(complement(zero))))]]) ).
cnf(refute_1_1578,plain,
complement(complement(zero)) = zero,
inference(resolve,[$cnf( $equal(zero,complement(complement(zero))) )],[refute_1_1576,refute_1_1577]) ).
cnf(refute_1_1579,plain,
join(complement(complement(zero)),meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))) = join(complement(complement(zero)),meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))),
introduced(tautology,[refl,[$fot(join(complement(complement(zero)),meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))))]]) ).
cnf(refute_1_1580,plain,
( complement(complement(zero)) != zero
| join(complement(complement(zero)),meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))) != join(complement(complement(zero)),meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero))))
| join(complement(complement(zero)),meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))) = join(zero,meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(complement(zero)),meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))),join(complement(complement(zero)),meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_1_1581,plain,
( complement(complement(zero)) != zero
| join(complement(complement(zero)),meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))) = join(zero,meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))) ),
inference(resolve,[$cnf( $equal(join(complement(complement(zero)),meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))),join(complement(complement(zero)),meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero))))) )],[refute_1_1579,refute_1_1580]) ).
cnf(refute_1_1582,plain,
join(complement(complement(zero)),meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))) = join(zero,meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))),
inference(resolve,[$cnf( $equal(complement(complement(zero)),zero) )],[refute_1_1578,refute_1_1581]) ).
cnf(refute_1_1583,plain,
( join(complement(complement(zero)),meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))) != join(zero,meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero))))
| zero != join(complement(complement(zero)),meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero))))
| zero = join(zero,meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(zero,join(complement(complement(zero)),meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero))))) ),[1],$fot(join(zero,meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))))]]) ).
cnf(refute_1_1584,plain,
( zero != join(complement(complement(zero)),meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero))))
| zero = join(zero,meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))) ),
inference(resolve,[$cnf( $equal(join(complement(complement(zero)),meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))),join(zero,meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero))))) )],[refute_1_1582,refute_1_1583]) ).
cnf(refute_1_1585,plain,
zero = join(zero,meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))),
inference(resolve,[$cnf( $equal(zero,join(complement(complement(zero)),meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero))))) )],[refute_1_1568,refute_1_1584]) ).
cnf(refute_1_1586,plain,
join(zero,meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))) = meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),
inference(subst,[],[refute_1_580:[bind(X_176,$fot(meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))))]]) ).
cnf(refute_1_1587,plain,
( join(zero,meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))) != meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))
| zero != join(zero,meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero))))
| zero = meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero))) ),
introduced(tautology,[equality,[$cnf( $equal(zero,join(zero,meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero))))) ),[1],$fot(meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero))))]]) ).
cnf(refute_1_1588,plain,
( zero != join(zero,meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero))))
| zero = meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))),meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))) )],[refute_1_1586,refute_1_1587]) ).
cnf(refute_1_1589,plain,
zero = meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),
inference(resolve,[$cnf( $equal(zero,join(zero,meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero))))) )],[refute_1_1585,refute_1_1588]) ).
cnf(refute_1_1590,plain,
( zero != meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))
| meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero))) = zero ),
inference(subst,[],[refute_1_17:[bind(X,$fot(zero)),bind(Y,$fot(meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))))]]) ).
cnf(refute_1_1591,plain,
meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero))) = zero,
inference(resolve,[$cnf( $equal(zero,meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))) )],[refute_1_1589,refute_1_1590]) ).
cnf(refute_1_1592,plain,
( meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero))) != zero
| top != join(complement(zero),join(complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))))
| top = join(complement(zero),join(complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),zero)) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(zero),join(complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))))) ),[1,1,1],$fot(zero)]]) ).
cnf(refute_1_1593,plain,
( top != join(complement(zero),join(complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))))
| top = join(complement(zero),join(complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),zero)) ),
inference(resolve,[$cnf( $equal(meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),zero) )],[refute_1_1591,refute_1_1592]) ).
cnf(refute_1_1594,plain,
top = join(complement(zero),join(complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),zero)),
inference(resolve,[$cnf( $equal(top,join(complement(zero),join(complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))))) )],[refute_1_1555,refute_1_1593]) ).
cnf(refute_1_1595,plain,
complement(meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))) = complement(meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))),
introduced(tautology,[refl,[$fot(complement(meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))))]]) ).
cnf(refute_1_1596,plain,
( complement(meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))) != complement(meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero))))
| meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero))) != zero
| complement(meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))) = complement(zero) ),
introduced(tautology,[equality,[$cnf( $equal(complement(meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))),complement(meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_1_1597,plain,
( meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero))) != zero
| complement(meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))) = complement(zero) ),
inference(resolve,[$cnf( $equal(complement(meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))),complement(meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero))))) )],[refute_1_1595,refute_1_1596]) ).
cnf(refute_1_1598,plain,
complement(meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))) = complement(zero),
inference(resolve,[$cnf( $equal(meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),zero) )],[refute_1_1591,refute_1_1597]) ).
cnf(refute_1_1599,plain,
join(complement(zero),complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))) = complement(meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))),
inference(subst,[],[refute_1_824:[bind(X0,$fot(zero)),bind(X1,$fot(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))))]]) ).
cnf(refute_1_1600,plain,
( complement(meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))) != complement(zero)
| join(complement(zero),complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))) != complement(meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero))))
| join(complement(zero),complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))) = complement(zero) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(complement(zero),complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))))),bind(Y,$fot(complement(meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))))),bind(Z,$fot(complement(zero)))]]) ).
cnf(refute_1_1601,plain,
( complement(meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))) != complement(zero)
| join(complement(zero),complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))) = complement(zero) ),
inference(resolve,[$cnf( $equal(join(complement(zero),complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))),complement(meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero))))) )],[refute_1_1599,refute_1_1600]) ).
cnf(refute_1_1602,plain,
join(complement(zero),complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))) = complement(zero),
inference(resolve,[$cnf( $equal(complement(meet(zero,composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))),complement(zero)) )],[refute_1_1598,refute_1_1601]) ).
cnf(refute_1_1603,plain,
join(zero,complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))) = complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),
inference(subst,[],[refute_1_580:[bind(X_176,$fot(complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))))]]) ).
cnf(refute_1_1604,plain,
join(complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),zero) = join(zero,complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))),
inference(subst,[],[refute_1_52:[bind(X0,$fot(zero)),bind(X1,$fot(complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))))]]) ).
cnf(refute_1_1605,plain,
( join(complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),zero) != join(zero,complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))))
| join(zero,complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))) != complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))
| join(complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),zero) = complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),zero))),bind(Y,$fot(join(zero,complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))))),bind(Z,$fot(complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))))]]) ).
cnf(refute_1_1606,plain,
( join(zero,complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))) != complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))
| join(complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),zero) = complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))) ),
inference(resolve,[$cnf( $equal(join(complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),zero),join(zero,complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))))) )],[refute_1_1604,refute_1_1605]) ).
cnf(refute_1_1607,plain,
join(complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),zero) = complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),
inference(resolve,[$cnf( $equal(join(zero,complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))),complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))) )],[refute_1_1603,refute_1_1606]) ).
cnf(refute_1_1608,plain,
join(complement(zero),join(complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),zero)) = join(complement(zero),join(complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),zero)),
introduced(tautology,[refl,[$fot(join(complement(zero),join(complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),zero)))]]) ).
cnf(refute_1_1609,plain,
( join(complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),zero) != complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))
| join(complement(zero),join(complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),zero)) != join(complement(zero),join(complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),zero))
| join(complement(zero),join(complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),zero)) = join(complement(zero),complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(zero),join(complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),zero)),join(complement(zero),join(complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),zero))) ),[1,1],$fot(complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))))]]) ).
cnf(refute_1_1610,plain,
( join(complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),zero) != complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))
| join(complement(zero),join(complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),zero)) = join(complement(zero),complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))) ),
inference(resolve,[$cnf( $equal(join(complement(zero),join(complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),zero)),join(complement(zero),join(complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),zero))) )],[refute_1_1608,refute_1_1609]) ).
cnf(refute_1_1611,plain,
join(complement(zero),join(complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),zero)) = join(complement(zero),complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))),
inference(resolve,[$cnf( $equal(join(complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),zero),complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))) )],[refute_1_1607,refute_1_1610]) ).
cnf(refute_1_1612,plain,
( join(complement(zero),complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))) != complement(zero)
| join(complement(zero),join(complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),zero)) != join(complement(zero),complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))))
| join(complement(zero),join(complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),zero)) = complement(zero) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(complement(zero),join(complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),zero)))),bind(Y,$fot(join(complement(zero),complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))))),bind(Z,$fot(complement(zero)))]]) ).
cnf(refute_1_1613,plain,
( join(complement(zero),complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))) != complement(zero)
| join(complement(zero),join(complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),zero)) = complement(zero) ),
inference(resolve,[$cnf( $equal(join(complement(zero),join(complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),zero)),join(complement(zero),complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))))) )],[refute_1_1611,refute_1_1612]) ).
cnf(refute_1_1614,plain,
join(complement(zero),join(complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),zero)) = complement(zero),
inference(resolve,[$cnf( $equal(join(complement(zero),complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero)))),complement(zero)) )],[refute_1_1602,refute_1_1613]) ).
cnf(refute_1_1615,plain,
( join(complement(zero),join(complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),zero)) != complement(zero)
| top != join(complement(zero),join(complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),zero))
| top = complement(zero) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(zero),join(complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),zero))) ),[1],$fot(complement(zero))]]) ).
cnf(refute_1_1616,plain,
( top != join(complement(zero),join(complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),zero))
| top = complement(zero) ),
inference(resolve,[$cnf( $equal(join(complement(zero),join(complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),zero)),complement(zero)) )],[refute_1_1614,refute_1_1615]) ).
cnf(refute_1_1617,plain,
top = complement(zero),
inference(resolve,[$cnf( $equal(top,join(complement(zero),join(complement(composition(converse(skolemFOFtoCNF_X0_1),complement(zero))),zero))) )],[refute_1_1594,refute_1_1616]) ).
cnf(refute_1_1618,plain,
( top != complement(zero)
| complement(zero) = top ),
inference(subst,[],[refute_1_17:[bind(X,$fot(top)),bind(Y,$fot(complement(zero)))]]) ).
cnf(refute_1_1619,plain,
complement(zero) = top,
inference(resolve,[$cnf( $equal(top,complement(zero)) )],[refute_1_1617,refute_1_1618]) ).
cnf(refute_1_1620,plain,
composition(complement(composition(top,top)),complement(zero)) = composition(complement(composition(top,top)),complement(zero)),
introduced(tautology,[refl,[$fot(composition(complement(composition(top,top)),complement(zero)))]]) ).
cnf(refute_1_1621,plain,
( complement(zero) != top
| composition(complement(composition(top,top)),complement(zero)) != composition(complement(composition(top,top)),complement(zero))
| composition(complement(composition(top,top)),complement(zero)) = composition(complement(composition(top,top)),top) ),
introduced(tautology,[equality,[$cnf( $equal(composition(complement(composition(top,top)),complement(zero)),composition(complement(composition(top,top)),complement(zero))) ),[1,1],$fot(top)]]) ).
cnf(refute_1_1622,plain,
( complement(zero) != top
| composition(complement(composition(top,top)),complement(zero)) = composition(complement(composition(top,top)),top) ),
inference(resolve,[$cnf( $equal(composition(complement(composition(top,top)),complement(zero)),composition(complement(composition(top,top)),complement(zero))) )],[refute_1_1620,refute_1_1621]) ).
cnf(refute_1_1623,plain,
composition(complement(composition(top,top)),complement(zero)) = composition(complement(composition(top,top)),top),
inference(resolve,[$cnf( $equal(complement(zero),top) )],[refute_1_1619,refute_1_1622]) ).
cnf(refute_1_1624,plain,
converse(converse(complement(composition(top,top)))) = complement(composition(top,top)),
inference(subst,[],[refute_1_3:[bind(X0,$fot(complement(composition(top,top))))]]) ).
cnf(refute_1_1625,plain,
composition(converse(converse(complement(composition(top,top)))),complement(zero)) = composition(converse(converse(complement(composition(top,top)))),complement(zero)),
introduced(tautology,[refl,[$fot(composition(converse(converse(complement(composition(top,top)))),complement(zero)))]]) ).
cnf(refute_1_1626,plain,
( composition(converse(converse(complement(composition(top,top)))),complement(zero)) != composition(converse(converse(complement(composition(top,top)))),complement(zero))
| converse(converse(complement(composition(top,top)))) != complement(composition(top,top))
| composition(converse(converse(complement(composition(top,top)))),complement(zero)) = composition(complement(composition(top,top)),complement(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(converse(complement(composition(top,top)))),complement(zero)),composition(converse(converse(complement(composition(top,top)))),complement(zero))) ),[1,0],$fot(complement(composition(top,top)))]]) ).
cnf(refute_1_1627,plain,
( converse(converse(complement(composition(top,top)))) != complement(composition(top,top))
| composition(converse(converse(complement(composition(top,top)))),complement(zero)) = composition(complement(composition(top,top)),complement(zero)) ),
inference(resolve,[$cnf( $equal(composition(converse(converse(complement(composition(top,top)))),complement(zero)),composition(converse(converse(complement(composition(top,top)))),complement(zero))) )],[refute_1_1625,refute_1_1626]) ).
cnf(refute_1_1628,plain,
composition(converse(converse(complement(composition(top,top)))),complement(zero)) = composition(complement(composition(top,top)),complement(zero)),
inference(resolve,[$cnf( $equal(converse(converse(complement(composition(top,top)))),complement(composition(top,top))) )],[refute_1_1624,refute_1_1627]) ).
cnf(refute_1_1629,plain,
( composition(complement(composition(top,top)),complement(zero)) != composition(complement(composition(top,top)),top)
| composition(converse(converse(complement(composition(top,top)))),complement(zero)) != composition(complement(composition(top,top)),complement(zero))
| composition(converse(converse(complement(composition(top,top)))),complement(zero)) = composition(complement(composition(top,top)),top) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(composition(converse(converse(complement(composition(top,top)))),complement(zero)))),bind(Y,$fot(composition(complement(composition(top,top)),complement(zero)))),bind(Z,$fot(composition(complement(composition(top,top)),top)))]]) ).
cnf(refute_1_1630,plain,
( composition(complement(composition(top,top)),complement(zero)) != composition(complement(composition(top,top)),top)
| composition(converse(converse(complement(composition(top,top)))),complement(zero)) = composition(complement(composition(top,top)),top) ),
inference(resolve,[$cnf( $equal(composition(converse(converse(complement(composition(top,top)))),complement(zero)),composition(complement(composition(top,top)),complement(zero))) )],[refute_1_1628,refute_1_1629]) ).
cnf(refute_1_1631,plain,
composition(converse(converse(complement(composition(top,top)))),complement(zero)) = composition(complement(composition(top,top)),top),
inference(resolve,[$cnf( $equal(composition(complement(composition(top,top)),complement(zero)),composition(complement(composition(top,top)),top)) )],[refute_1_1623,refute_1_1630]) ).
cnf(refute_1_1632,plain,
( composition(converse(converse(complement(composition(top,top)))),complement(zero)) != composition(complement(composition(top,top)),top)
| composition(converse(converse(complement(composition(top,top)))),complement(zero)) != zero
| composition(complement(composition(top,top)),top) = zero ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(converse(complement(composition(top,top)))),complement(zero)),zero) ),[0],$fot(composition(complement(composition(top,top)),top))]]) ).
cnf(refute_1_1633,plain,
( composition(converse(converse(complement(composition(top,top)))),complement(zero)) != zero
| composition(complement(composition(top,top)),top) = zero ),
inference(resolve,[$cnf( $equal(composition(converse(converse(complement(composition(top,top)))),complement(zero)),composition(complement(composition(top,top)),top)) )],[refute_1_1631,refute_1_1632]) ).
cnf(refute_1_1634,plain,
composition(complement(composition(top,top)),top) = zero,
inference(resolve,[$cnf( $equal(composition(converse(converse(complement(composition(top,top)))),complement(zero)),zero) )],[refute_1_1554,refute_1_1633]) ).
cnf(refute_1_1635,plain,
( composition(complement(composition(top,top)),top) != zero
| composition(converse(top),composition(converse(complement(composition(top,top))),X_284)) != composition(converse(composition(complement(composition(top,top)),top)),X_284)
| composition(converse(top),composition(converse(complement(composition(top,top))),X_284)) = composition(converse(zero),X_284) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(top),composition(converse(complement(composition(top,top))),X_284)),composition(converse(composition(complement(composition(top,top)),top)),X_284)) ),[1,0,0],$fot(zero)]]) ).
cnf(refute_1_1636,plain,
( composition(converse(top),composition(converse(complement(composition(top,top))),X_284)) != composition(converse(composition(complement(composition(top,top)),top)),X_284)
| composition(converse(top),composition(converse(complement(composition(top,top))),X_284)) = composition(converse(zero),X_284) ),
inference(resolve,[$cnf( $equal(composition(complement(composition(top,top)),top),zero) )],[refute_1_1634,refute_1_1635]) ).
cnf(refute_1_1637,plain,
composition(converse(top),composition(converse(complement(composition(top,top))),X_284)) = composition(converse(zero),X_284),
inference(resolve,[$cnf( $equal(composition(converse(top),composition(converse(complement(composition(top,top))),X_284)),composition(converse(composition(complement(composition(top,top)),top)),X_284)) )],[refute_1_1531,refute_1_1636]) ).
cnf(refute_1_1638,plain,
composition(converse(top),composition(converse(X_282),X_284)) = composition(converse(composition(X_282,top)),X_284),
inference(subst,[],[refute_1_1530:[bind(X0,$fot(X_282)),bind(X1,$fot(top)),bind(X_124,$fot(X_284))]]) ).
cnf(refute_1_1639,plain,
( composition(converse(top),composition(converse(X_282),X_284)) != composition(converse(composition(X_282,top)),X_284)
| converse(top) != top
| composition(top,composition(converse(X_282),X_284)) = composition(converse(composition(X_282,top)),X_284) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(top),composition(converse(X_282),X_284)),composition(converse(composition(X_282,top)),X_284)) ),[0,0],$fot(top)]]) ).
cnf(refute_1_1640,plain,
( composition(converse(top),composition(converse(X_282),X_284)) != composition(converse(composition(X_282,top)),X_284)
| composition(top,composition(converse(X_282),X_284)) = composition(converse(composition(X_282,top)),X_284) ),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_1_191,refute_1_1639]) ).
cnf(refute_1_1641,plain,
composition(top,composition(converse(X_282),X_284)) = composition(converse(composition(X_282,top)),X_284),
inference(resolve,[$cnf( $equal(composition(converse(top),composition(converse(X_282),X_284)),composition(converse(composition(X_282,top)),X_284)) )],[refute_1_1638,refute_1_1640]) ).
cnf(refute_1_1642,plain,
( composition(top,composition(converse(X_282),X_284)) != composition(converse(composition(X_282,top)),X_284)
| composition(converse(composition(X_282,top)),X_284) = composition(top,composition(converse(X_282),X_284)) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(composition(top,composition(converse(X_282),X_284)))),bind(Y,$fot(composition(converse(composition(X_282,top)),X_284)))]]) ).
cnf(refute_1_1643,plain,
composition(converse(composition(X_282,top)),X_284) = composition(top,composition(converse(X_282),X_284)),
inference(resolve,[$cnf( $equal(composition(top,composition(converse(X_282),X_284)),composition(converse(composition(X_282,top)),X_284)) )],[refute_1_1641,refute_1_1642]) ).
cnf(refute_1_1644,plain,
composition(converse(composition(complement(composition(top,top)),top)),X_284) = composition(top,composition(converse(complement(composition(top,top))),X_284)),
inference(subst,[],[refute_1_1643:[bind(X_282,$fot(complement(composition(top,top))))]]) ).
cnf(refute_1_1645,plain,
( composition(converse(composition(complement(composition(top,top)),top)),X_284) != composition(top,composition(converse(complement(composition(top,top))),X_284))
| composition(converse(top),composition(converse(complement(composition(top,top))),X_284)) != composition(converse(composition(complement(composition(top,top)),top)),X_284)
| composition(converse(top),composition(converse(complement(composition(top,top))),X_284)) = composition(top,composition(converse(complement(composition(top,top))),X_284)) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(composition(converse(top),composition(converse(complement(composition(top,top))),X_284)))),bind(Y,$fot(composition(converse(composition(complement(composition(top,top)),top)),X_284))),bind(Z,$fot(composition(top,composition(converse(complement(composition(top,top))),X_284))))]]) ).
cnf(refute_1_1646,plain,
( composition(converse(composition(complement(composition(top,top)),top)),X_284) != composition(top,composition(converse(complement(composition(top,top))),X_284))
| composition(converse(top),composition(converse(complement(composition(top,top))),X_284)) = composition(top,composition(converse(complement(composition(top,top))),X_284)) ),
inference(resolve,[$cnf( $equal(composition(converse(top),composition(converse(complement(composition(top,top))),X_284)),composition(converse(composition(complement(composition(top,top)),top)),X_284)) )],[refute_1_1531,refute_1_1645]) ).
cnf(refute_1_1647,plain,
composition(converse(top),composition(converse(complement(composition(top,top))),X_284)) = composition(top,composition(converse(complement(composition(top,top))),X_284)),
inference(resolve,[$cnf( $equal(composition(converse(composition(complement(composition(top,top)),top)),X_284),composition(top,composition(converse(complement(composition(top,top))),X_284))) )],[refute_1_1644,refute_1_1646]) ).
cnf(refute_1_1648,plain,
( composition(converse(top),composition(converse(complement(composition(top,top))),X_284)) != composition(converse(zero),X_284)
| composition(converse(top),composition(converse(complement(composition(top,top))),X_284)) != composition(top,composition(converse(complement(composition(top,top))),X_284))
| composition(top,composition(converse(complement(composition(top,top))),X_284)) = composition(converse(zero),X_284) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(top),composition(converse(complement(composition(top,top))),X_284)),composition(converse(zero),X_284)) ),[0],$fot(composition(top,composition(converse(complement(composition(top,top))),X_284)))]]) ).
cnf(refute_1_1649,plain,
( composition(converse(top),composition(converse(complement(composition(top,top))),X_284)) != composition(converse(zero),X_284)
| composition(top,composition(converse(complement(composition(top,top))),X_284)) = composition(converse(zero),X_284) ),
inference(resolve,[$cnf( $equal(composition(converse(top),composition(converse(complement(composition(top,top))),X_284)),composition(top,composition(converse(complement(composition(top,top))),X_284))) )],[refute_1_1647,refute_1_1648]) ).
cnf(refute_1_1650,plain,
composition(converse(zero),X_284) = composition(converse(zero),X_284),
introduced(tautology,[refl,[$fot(composition(converse(zero),X_284))]]) ).
cnf(refute_1_1651,plain,
( composition(converse(zero),X_284) != composition(converse(zero),X_284)
| converse(zero) != zero
| composition(converse(zero),X_284) = composition(zero,X_284) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(zero),X_284),composition(converse(zero),X_284)) ),[1,0],$fot(zero)]]) ).
cnf(refute_1_1652,plain,
( converse(zero) != zero
| composition(converse(zero),X_284) = composition(zero,X_284) ),
inference(resolve,[$cnf( $equal(composition(converse(zero),X_284),composition(converse(zero),X_284)) )],[refute_1_1650,refute_1_1651]) ).
cnf(refute_1_1653,plain,
composition(converse(zero),X_284) = composition(zero,X_284),
inference(resolve,[$cnf( $equal(converse(zero),zero) )],[refute_1_659,refute_1_1652]) ).
cnf(refute_1_1654,plain,
( composition(converse(zero),X_284) != composition(zero,X_284)
| composition(top,composition(converse(complement(composition(top,top))),X_284)) != composition(converse(zero),X_284)
| composition(top,composition(converse(complement(composition(top,top))),X_284)) = composition(zero,X_284) ),
introduced(tautology,[equality,[$cnf( $equal(composition(top,composition(converse(complement(composition(top,top))),X_284)),composition(converse(zero),X_284)) ),[1],$fot(composition(zero,X_284))]]) ).
cnf(refute_1_1655,plain,
( composition(top,composition(converse(complement(composition(top,top))),X_284)) != composition(converse(zero),X_284)
| composition(top,composition(converse(complement(composition(top,top))),X_284)) = composition(zero,X_284) ),
inference(resolve,[$cnf( $equal(composition(converse(zero),X_284),composition(zero,X_284)) )],[refute_1_1653,refute_1_1654]) ).
cnf(refute_1_1656,plain,
( composition(converse(top),composition(converse(complement(composition(top,top))),X_284)) != composition(converse(zero),X_284)
| composition(top,composition(converse(complement(composition(top,top))),X_284)) = composition(zero,X_284) ),
inference(resolve,[$cnf( $equal(composition(top,composition(converse(complement(composition(top,top))),X_284)),composition(converse(zero),X_284)) )],[refute_1_1649,refute_1_1655]) ).
cnf(refute_1_1657,plain,
composition(top,composition(converse(complement(composition(top,top))),X_284)) = composition(zero,X_284),
inference(resolve,[$cnf( $equal(composition(converse(top),composition(converse(complement(composition(top,top))),X_284)),composition(converse(zero),X_284)) )],[refute_1_1637,refute_1_1656]) ).
cnf(refute_1_1658,plain,
composition(top,composition(converse(complement(composition(top,top))),complement(composition(complement(composition(top,top)),top)))) = composition(zero,complement(composition(complement(composition(top,top)),top))),
inference(subst,[],[refute_1_1657:[bind(X_284,$fot(complement(composition(complement(composition(top,top)),top))))]]) ).
cnf(refute_1_1659,plain,
composition(converse(complement(composition(top,top))),complement(composition(complement(composition(top,top)),top))) = zero,
inference(subst,[],[refute_1_675:[bind(X0,$fot(complement(composition(top,top))))]]) ).
cnf(refute_1_1660,plain,
( composition(converse(complement(composition(top,top))),complement(composition(complement(composition(top,top)),top))) != zero
| composition(top,composition(converse(complement(composition(top,top))),complement(composition(complement(composition(top,top)),top)))) != composition(zero,complement(composition(complement(composition(top,top)),top)))
| composition(top,zero) = composition(zero,complement(composition(complement(composition(top,top)),top))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(top,composition(converse(complement(composition(top,top))),complement(composition(complement(composition(top,top)),top)))),composition(zero,complement(composition(complement(composition(top,top)),top)))) ),[0,1],$fot(zero)]]) ).
cnf(refute_1_1661,plain,
( composition(top,composition(converse(complement(composition(top,top))),complement(composition(complement(composition(top,top)),top)))) != composition(zero,complement(composition(complement(composition(top,top)),top)))
| composition(top,zero) = composition(zero,complement(composition(complement(composition(top,top)),top))) ),
inference(resolve,[$cnf( $equal(composition(converse(complement(composition(top,top))),complement(composition(complement(composition(top,top)),top))),zero) )],[refute_1_1659,refute_1_1660]) ).
cnf(refute_1_1662,plain,
composition(top,zero) = composition(zero,complement(composition(complement(composition(top,top)),top))),
inference(resolve,[$cnf( $equal(composition(top,composition(converse(complement(composition(top,top))),complement(composition(complement(composition(top,top)),top)))),composition(zero,complement(composition(complement(composition(top,top)),top)))) )],[refute_1_1658,refute_1_1661]) ).
cnf(refute_1_1663,plain,
complement(composition(complement(composition(top,top)),top)) = complement(composition(complement(composition(top,top)),top)),
introduced(tautology,[refl,[$fot(complement(composition(complement(composition(top,top)),top)))]]) ).
cnf(refute_1_1664,plain,
( complement(composition(complement(composition(top,top)),top)) != complement(composition(complement(composition(top,top)),top))
| composition(complement(composition(top,top)),top) != zero
| complement(composition(complement(composition(top,top)),top)) = complement(zero) ),
introduced(tautology,[equality,[$cnf( $equal(complement(composition(complement(composition(top,top)),top)),complement(composition(complement(composition(top,top)),top))) ),[1,0],$fot(zero)]]) ).
cnf(refute_1_1665,plain,
( composition(complement(composition(top,top)),top) != zero
| complement(composition(complement(composition(top,top)),top)) = complement(zero) ),
inference(resolve,[$cnf( $equal(complement(composition(complement(composition(top,top)),top)),complement(composition(complement(composition(top,top)),top))) )],[refute_1_1663,refute_1_1664]) ).
cnf(refute_1_1666,plain,
complement(composition(complement(composition(top,top)),top)) = complement(zero),
inference(resolve,[$cnf( $equal(composition(complement(composition(top,top)),top),zero) )],[refute_1_1634,refute_1_1665]) ).
cnf(refute_1_1667,plain,
( complement(composition(complement(composition(top,top)),top)) != complement(zero)
| complement(zero) != top
| complement(composition(complement(composition(top,top)),top)) = top ),
inference(subst,[],[refute_1_37:[bind(X,$fot(complement(composition(complement(composition(top,top)),top)))),bind(Y,$fot(complement(zero))),bind(Z,$fot(top))]]) ).
cnf(refute_1_1668,plain,
( complement(zero) != top
| complement(composition(complement(composition(top,top)),top)) = top ),
inference(resolve,[$cnf( $equal(complement(composition(complement(composition(top,top)),top)),complement(zero)) )],[refute_1_1666,refute_1_1667]) ).
cnf(refute_1_1669,plain,
complement(composition(complement(composition(top,top)),top)) = top,
inference(resolve,[$cnf( $equal(complement(zero),top) )],[refute_1_1619,refute_1_1668]) ).
cnf(refute_1_1670,plain,
composition(zero,complement(composition(complement(composition(top,top)),top))) = composition(zero,complement(composition(complement(composition(top,top)),top))),
introduced(tautology,[refl,[$fot(composition(zero,complement(composition(complement(composition(top,top)),top))))]]) ).
cnf(refute_1_1671,plain,
( complement(composition(complement(composition(top,top)),top)) != top
| composition(zero,complement(composition(complement(composition(top,top)),top))) != composition(zero,complement(composition(complement(composition(top,top)),top)))
| composition(zero,complement(composition(complement(composition(top,top)),top))) = composition(zero,top) ),
introduced(tautology,[equality,[$cnf( $equal(composition(zero,complement(composition(complement(composition(top,top)),top))),composition(zero,complement(composition(complement(composition(top,top)),top)))) ),[1,1],$fot(top)]]) ).
cnf(refute_1_1672,plain,
( complement(composition(complement(composition(top,top)),top)) != top
| composition(zero,complement(composition(complement(composition(top,top)),top))) = composition(zero,top) ),
inference(resolve,[$cnf( $equal(composition(zero,complement(composition(complement(composition(top,top)),top))),composition(zero,complement(composition(complement(composition(top,top)),top)))) )],[refute_1_1670,refute_1_1671]) ).
cnf(refute_1_1673,plain,
composition(zero,complement(composition(complement(composition(top,top)),top))) = composition(zero,top),
inference(resolve,[$cnf( $equal(complement(composition(complement(composition(top,top)),top)),top) )],[refute_1_1669,refute_1_1672]) ).
cnf(refute_1_1674,plain,
( composition(top,zero) != composition(zero,complement(composition(complement(composition(top,top)),top)))
| composition(zero,complement(composition(complement(composition(top,top)),top))) != composition(zero,top)
| composition(top,zero) = composition(zero,top) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(top,zero),composition(zero,top)) ),[0],$fot(composition(zero,complement(composition(complement(composition(top,top)),top))))]]) ).
cnf(refute_1_1675,plain,
( composition(top,zero) != composition(zero,complement(composition(complement(composition(top,top)),top)))
| composition(top,zero) = composition(zero,top) ),
inference(resolve,[$cnf( $equal(composition(zero,complement(composition(complement(composition(top,top)),top))),composition(zero,top)) )],[refute_1_1673,refute_1_1674]) ).
cnf(refute_1_1676,plain,
composition(top,zero) = composition(zero,top),
inference(resolve,[$cnf( $equal(composition(top,zero),composition(zero,complement(composition(complement(composition(top,top)),top)))) )],[refute_1_1662,refute_1_1675]) ).
cnf(refute_1_1677,plain,
( composition(top,zero) != composition(zero,top)
| composition(zero,top) = composition(top,zero) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(composition(top,zero))),bind(Y,$fot(composition(zero,top)))]]) ).
cnf(refute_1_1678,plain,
composition(zero,top) = composition(top,zero),
inference(resolve,[$cnf( $equal(composition(top,zero),composition(zero,top)) )],[refute_1_1676,refute_1_1677]) ).
cnf(refute_1_1679,plain,
complement(composition(zero,top)) = complement(composition(zero,top)),
introduced(tautology,[refl,[$fot(complement(composition(zero,top)))]]) ).
cnf(refute_1_1680,plain,
( complement(composition(zero,top)) != complement(composition(zero,top))
| composition(zero,top) != composition(top,zero)
| complement(composition(zero,top)) = complement(composition(top,zero)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(composition(zero,top)),complement(composition(zero,top))) ),[1,0],$fot(composition(top,zero))]]) ).
cnf(refute_1_1681,plain,
( composition(zero,top) != composition(top,zero)
| complement(composition(zero,top)) = complement(composition(top,zero)) ),
inference(resolve,[$cnf( $equal(complement(composition(zero,top)),complement(composition(zero,top))) )],[refute_1_1679,refute_1_1680]) ).
cnf(refute_1_1682,plain,
complement(composition(zero,top)) = complement(composition(top,zero)),
inference(resolve,[$cnf( $equal(composition(zero,top),composition(top,zero)) )],[refute_1_1678,refute_1_1681]) ).
cnf(refute_1_1683,plain,
composition(complement(composition(zero,top)),top) = composition(complement(composition(zero,top)),top),
introduced(tautology,[refl,[$fot(composition(complement(composition(zero,top)),top))]]) ).
cnf(refute_1_1684,plain,
( complement(composition(zero,top)) != complement(composition(top,zero))
| composition(complement(composition(zero,top)),top) != composition(complement(composition(zero,top)),top)
| composition(complement(composition(zero,top)),top) = composition(complement(composition(top,zero)),top) ),
introduced(tautology,[equality,[$cnf( $equal(composition(complement(composition(zero,top)),top),composition(complement(composition(zero,top)),top)) ),[1,0],$fot(complement(composition(top,zero)))]]) ).
cnf(refute_1_1685,plain,
( complement(composition(zero,top)) != complement(composition(top,zero))
| composition(complement(composition(zero,top)),top) = composition(complement(composition(top,zero)),top) ),
inference(resolve,[$cnf( $equal(composition(complement(composition(zero,top)),top),composition(complement(composition(zero,top)),top)) )],[refute_1_1683,refute_1_1684]) ).
cnf(refute_1_1686,plain,
composition(complement(composition(zero,top)),top) = composition(complement(composition(top,zero)),top),
inference(resolve,[$cnf( $equal(complement(composition(zero,top)),complement(composition(top,zero))) )],[refute_1_1682,refute_1_1685]) ).
cnf(refute_1_1687,plain,
complement(composition(complement(composition(zero,top)),top)) = complement(composition(complement(composition(zero,top)),top)),
introduced(tautology,[refl,[$fot(complement(composition(complement(composition(zero,top)),top)))]]) ).
cnf(refute_1_1688,plain,
( complement(composition(complement(composition(zero,top)),top)) != complement(composition(complement(composition(zero,top)),top))
| composition(complement(composition(zero,top)),top) != composition(complement(composition(top,zero)),top)
| complement(composition(complement(composition(zero,top)),top)) = complement(composition(complement(composition(top,zero)),top)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(composition(complement(composition(zero,top)),top)),complement(composition(complement(composition(zero,top)),top))) ),[1,0],$fot(composition(complement(composition(top,zero)),top))]]) ).
cnf(refute_1_1689,plain,
( composition(complement(composition(zero,top)),top) != composition(complement(composition(top,zero)),top)
| complement(composition(complement(composition(zero,top)),top)) = complement(composition(complement(composition(top,zero)),top)) ),
inference(resolve,[$cnf( $equal(complement(composition(complement(composition(zero,top)),top)),complement(composition(complement(composition(zero,top)),top))) )],[refute_1_1687,refute_1_1688]) ).
cnf(refute_1_1690,plain,
complement(composition(complement(composition(zero,top)),top)) = complement(composition(complement(composition(top,zero)),top)),
inference(resolve,[$cnf( $equal(composition(complement(composition(zero,top)),top),composition(complement(composition(top,zero)),top)) )],[refute_1_1686,refute_1_1689]) ).
cnf(refute_1_1691,plain,
composition(complement(composition(top,zero)),complement(composition(complement(composition(zero,top)),top))) = composition(complement(composition(top,zero)),complement(composition(complement(composition(zero,top)),top))),
introduced(tautology,[refl,[$fot(composition(complement(composition(top,zero)),complement(composition(complement(composition(zero,top)),top))))]]) ).
cnf(refute_1_1692,plain,
( complement(composition(complement(composition(zero,top)),top)) != complement(composition(complement(composition(top,zero)),top))
| composition(complement(composition(top,zero)),complement(composition(complement(composition(zero,top)),top))) != composition(complement(composition(top,zero)),complement(composition(complement(composition(zero,top)),top)))
| composition(complement(composition(top,zero)),complement(composition(complement(composition(zero,top)),top))) = composition(complement(composition(top,zero)),complement(composition(complement(composition(top,zero)),top))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(complement(composition(top,zero)),complement(composition(complement(composition(zero,top)),top))),composition(complement(composition(top,zero)),complement(composition(complement(composition(zero,top)),top)))) ),[1,1],$fot(complement(composition(complement(composition(top,zero)),top)))]]) ).
cnf(refute_1_1693,plain,
( complement(composition(complement(composition(zero,top)),top)) != complement(composition(complement(composition(top,zero)),top))
| composition(complement(composition(top,zero)),complement(composition(complement(composition(zero,top)),top))) = composition(complement(composition(top,zero)),complement(composition(complement(composition(top,zero)),top))) ),
inference(resolve,[$cnf( $equal(composition(complement(composition(top,zero)),complement(composition(complement(composition(zero,top)),top))),composition(complement(composition(top,zero)),complement(composition(complement(composition(zero,top)),top)))) )],[refute_1_1691,refute_1_1692]) ).
cnf(refute_1_1694,plain,
composition(complement(composition(top,zero)),complement(composition(complement(composition(zero,top)),top))) = composition(complement(composition(top,zero)),complement(composition(complement(composition(top,zero)),top))),
inference(resolve,[$cnf( $equal(complement(composition(complement(composition(zero,top)),top)),complement(composition(complement(composition(top,zero)),top))) )],[refute_1_1690,refute_1_1693]) ).
cnf(refute_1_1695,plain,
( composition(complement(composition(top,zero)),complement(composition(complement(composition(zero,top)),top))) != composition(complement(composition(top,zero)),complement(composition(complement(composition(top,zero)),top)))
| composition(complement(composition(top,zero)),complement(composition(complement(composition(zero,top)),top))) != zero
| composition(complement(composition(top,zero)),complement(composition(complement(composition(top,zero)),top))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(composition(complement(composition(top,zero)),complement(composition(complement(composition(zero,top)),top))),zero) ),[0],$fot(composition(complement(composition(top,zero)),complement(composition(complement(composition(top,zero)),top))))]]) ).
cnf(refute_1_1696,plain,
( composition(complement(composition(top,zero)),complement(composition(complement(composition(zero,top)),top))) != zero
| composition(complement(composition(top,zero)),complement(composition(complement(composition(top,zero)),top))) = zero ),
inference(resolve,[$cnf( $equal(composition(complement(composition(top,zero)),complement(composition(complement(composition(zero,top)),top))),composition(complement(composition(top,zero)),complement(composition(complement(composition(top,zero)),top)))) )],[refute_1_1694,refute_1_1695]) ).
cnf(refute_1_1697,plain,
composition(complement(composition(top,zero)),complement(composition(complement(composition(top,zero)),top))) = zero,
inference(resolve,[$cnf( $equal(composition(complement(composition(top,zero)),complement(composition(complement(composition(zero,top)),top))),zero) )],[refute_1_1523,refute_1_1696]) ).
cnf(refute_1_1698,plain,
( composition(complement(composition(top,zero)),complement(composition(complement(composition(top,zero)),top))) != zero
| composition(join(X_316,complement(composition(top,zero))),complement(composition(complement(composition(top,zero)),top))) != join(composition(X_316,complement(composition(complement(composition(top,zero)),top))),composition(complement(composition(top,zero)),complement(composition(complement(composition(top,zero)),top))))
| composition(join(X_316,complement(composition(top,zero))),complement(composition(complement(composition(top,zero)),top))) = join(composition(X_316,complement(composition(complement(composition(top,zero)),top))),zero) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(X_316,complement(composition(top,zero))),complement(composition(complement(composition(top,zero)),top))),join(composition(X_316,complement(composition(complement(composition(top,zero)),top))),composition(complement(composition(top,zero)),complement(composition(complement(composition(top,zero)),top))))) ),[1,1],$fot(zero)]]) ).
cnf(refute_1_1699,plain,
( composition(join(X_316,complement(composition(top,zero))),complement(composition(complement(composition(top,zero)),top))) != join(composition(X_316,complement(composition(complement(composition(top,zero)),top))),composition(complement(composition(top,zero)),complement(composition(complement(composition(top,zero)),top))))
| composition(join(X_316,complement(composition(top,zero))),complement(composition(complement(composition(top,zero)),top))) = join(composition(X_316,complement(composition(complement(composition(top,zero)),top))),zero) ),
inference(resolve,[$cnf( $equal(composition(complement(composition(top,zero)),complement(composition(complement(composition(top,zero)),top))),zero) )],[refute_1_1697,refute_1_1698]) ).
cnf(refute_1_1700,plain,
composition(join(X_316,complement(composition(top,zero))),complement(composition(complement(composition(top,zero)),top))) = join(composition(X_316,complement(composition(complement(composition(top,zero)),top))),zero),
inference(resolve,[$cnf( $equal(composition(join(X_316,complement(composition(top,zero))),complement(composition(complement(composition(top,zero)),top))),join(composition(X_316,complement(composition(complement(composition(top,zero)),top))),composition(complement(composition(top,zero)),complement(composition(complement(composition(top,zero)),top))))) )],[refute_1_664,refute_1_1699]) ).
cnf(refute_1_1701,plain,
join(zero,composition(X_316,complement(composition(complement(composition(top,zero)),top)))) = composition(X_316,complement(composition(complement(composition(top,zero)),top))),
inference(subst,[],[refute_1_580:[bind(X_176,$fot(composition(X_316,complement(composition(complement(composition(top,zero)),top)))))]]) ).
cnf(refute_1_1702,plain,
join(composition(X_316,complement(composition(complement(composition(top,zero)),top))),zero) = join(zero,composition(X_316,complement(composition(complement(composition(top,zero)),top)))),
inference(subst,[],[refute_1_50:[bind(X0,$fot(composition(X_316,complement(composition(complement(composition(top,zero)),top))))),bind(X1,$fot(zero))]]) ).
cnf(refute_1_1703,plain,
( join(composition(X_316,complement(composition(complement(composition(top,zero)),top))),zero) != join(zero,composition(X_316,complement(composition(complement(composition(top,zero)),top))))
| join(zero,composition(X_316,complement(composition(complement(composition(top,zero)),top)))) != composition(X_316,complement(composition(complement(composition(top,zero)),top)))
| join(composition(X_316,complement(composition(complement(composition(top,zero)),top))),zero) = composition(X_316,complement(composition(complement(composition(top,zero)),top))) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(composition(X_316,complement(composition(complement(composition(top,zero)),top))),zero))),bind(Y,$fot(join(zero,composition(X_316,complement(composition(complement(composition(top,zero)),top)))))),bind(Z,$fot(composition(X_316,complement(composition(complement(composition(top,zero)),top)))))]]) ).
cnf(refute_1_1704,plain,
( join(zero,composition(X_316,complement(composition(complement(composition(top,zero)),top)))) != composition(X_316,complement(composition(complement(composition(top,zero)),top)))
| join(composition(X_316,complement(composition(complement(composition(top,zero)),top))),zero) = composition(X_316,complement(composition(complement(composition(top,zero)),top))) ),
inference(resolve,[$cnf( $equal(join(composition(X_316,complement(composition(complement(composition(top,zero)),top))),zero),join(zero,composition(X_316,complement(composition(complement(composition(top,zero)),top))))) )],[refute_1_1702,refute_1_1703]) ).
cnf(refute_1_1705,plain,
join(composition(X_316,complement(composition(complement(composition(top,zero)),top))),zero) = composition(X_316,complement(composition(complement(composition(top,zero)),top))),
inference(resolve,[$cnf( $equal(join(zero,composition(X_316,complement(composition(complement(composition(top,zero)),top)))),composition(X_316,complement(composition(complement(composition(top,zero)),top)))) )],[refute_1_1701,refute_1_1704]) ).
cnf(refute_1_1706,plain,
( composition(join(X_316,complement(composition(top,zero))),complement(composition(complement(composition(top,zero)),top))) != join(composition(X_316,complement(composition(complement(composition(top,zero)),top))),zero)
| join(composition(X_316,complement(composition(complement(composition(top,zero)),top))),zero) != composition(X_316,complement(composition(complement(composition(top,zero)),top)))
| composition(join(X_316,complement(composition(top,zero))),complement(composition(complement(composition(top,zero)),top))) = composition(X_316,complement(composition(complement(composition(top,zero)),top))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(join(X_316,complement(composition(top,zero))),complement(composition(complement(composition(top,zero)),top))),composition(X_316,complement(composition(complement(composition(top,zero)),top)))) ),[0],$fot(join(composition(X_316,complement(composition(complement(composition(top,zero)),top))),zero))]]) ).
cnf(refute_1_1707,plain,
( composition(join(X_316,complement(composition(top,zero))),complement(composition(complement(composition(top,zero)),top))) != join(composition(X_316,complement(composition(complement(composition(top,zero)),top))),zero)
| composition(join(X_316,complement(composition(top,zero))),complement(composition(complement(composition(top,zero)),top))) = composition(X_316,complement(composition(complement(composition(top,zero)),top))) ),
inference(resolve,[$cnf( $equal(join(composition(X_316,complement(composition(complement(composition(top,zero)),top))),zero),composition(X_316,complement(composition(complement(composition(top,zero)),top)))) )],[refute_1_1705,refute_1_1706]) ).
cnf(refute_1_1708,plain,
composition(join(X_316,complement(composition(top,zero))),complement(composition(complement(composition(top,zero)),top))) = composition(X_316,complement(composition(complement(composition(top,zero)),top))),
inference(resolve,[$cnf( $equal(composition(join(X_316,complement(composition(top,zero))),complement(composition(complement(composition(top,zero)),top))),join(composition(X_316,complement(composition(complement(composition(top,zero)),top))),zero)) )],[refute_1_1700,refute_1_1707]) ).
cnf(refute_1_1709,plain,
join(complement(converse(X0)),composition(converse(converse(X1)),complement(composition(converse(X1),converse(X0))))) = complement(converse(X0)),
inference(subst,[],[refute_1_112:[bind(X0,$fot(converse(X1))),bind(X1,$fot(converse(X0)))]]) ).
cnf(refute_1_1710,plain,
( composition(converse(X1),converse(X0)) != converse(composition(X0,X1))
| join(complement(converse(X0)),composition(converse(converse(X1)),complement(composition(converse(X1),converse(X0))))) != complement(converse(X0))
| join(complement(converse(X0)),composition(converse(converse(X1)),complement(converse(composition(X0,X1))))) = complement(converse(X0)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(converse(X0)),composition(converse(converse(X1)),complement(composition(converse(X1),converse(X0))))),complement(converse(X0))) ),[0,1,1,0],$fot(converse(composition(X0,X1)))]]) ).
cnf(refute_1_1711,plain,
( join(complement(converse(X0)),composition(converse(converse(X1)),complement(composition(converse(X1),converse(X0))))) != complement(converse(X0))
| join(complement(converse(X0)),composition(converse(converse(X1)),complement(converse(composition(X0,X1))))) = complement(converse(X0)) ),
inference(resolve,[$cnf( $equal(composition(converse(X1),converse(X0)),converse(composition(X0,X1))) )],[refute_1_1527,refute_1_1710]) ).
cnf(refute_1_1712,plain,
join(complement(converse(X0)),composition(converse(converse(X1)),complement(converse(composition(X0,X1))))) = complement(converse(X0)),
inference(resolve,[$cnf( $equal(join(complement(converse(X0)),composition(converse(converse(X1)),complement(composition(converse(X1),converse(X0))))),complement(converse(X0))) )],[refute_1_1709,refute_1_1711]) ).
cnf(refute_1_1713,plain,
converse(converse(X1)) = X1,
inference(subst,[],[refute_1_3:[bind(X0,$fot(X1))]]) ).
cnf(refute_1_1714,plain,
composition(converse(converse(X1)),complement(converse(composition(X0,X1)))) = composition(converse(converse(X1)),complement(converse(composition(X0,X1)))),
introduced(tautology,[refl,[$fot(composition(converse(converse(X1)),complement(converse(composition(X0,X1)))))]]) ).
cnf(refute_1_1715,plain,
( composition(converse(converse(X1)),complement(converse(composition(X0,X1)))) != composition(converse(converse(X1)),complement(converse(composition(X0,X1))))
| converse(converse(X1)) != X1
| composition(converse(converse(X1)),complement(converse(composition(X0,X1)))) = composition(X1,complement(converse(composition(X0,X1)))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(converse(X1)),complement(converse(composition(X0,X1)))),composition(converse(converse(X1)),complement(converse(composition(X0,X1))))) ),[1,0],$fot(X1)]]) ).
cnf(refute_1_1716,plain,
( converse(converse(X1)) != X1
| composition(converse(converse(X1)),complement(converse(composition(X0,X1)))) = composition(X1,complement(converse(composition(X0,X1)))) ),
inference(resolve,[$cnf( $equal(composition(converse(converse(X1)),complement(converse(composition(X0,X1)))),composition(converse(converse(X1)),complement(converse(composition(X0,X1))))) )],[refute_1_1714,refute_1_1715]) ).
cnf(refute_1_1717,plain,
composition(converse(converse(X1)),complement(converse(composition(X0,X1)))) = composition(X1,complement(converse(composition(X0,X1)))),
inference(resolve,[$cnf( $equal(converse(converse(X1)),X1) )],[refute_1_1713,refute_1_1716]) ).
cnf(refute_1_1718,plain,
join(complement(converse(X0)),composition(converse(converse(X1)),complement(converse(composition(X0,X1))))) = join(complement(converse(X0)),composition(converse(converse(X1)),complement(converse(composition(X0,X1))))),
introduced(tautology,[refl,[$fot(join(complement(converse(X0)),composition(converse(converse(X1)),complement(converse(composition(X0,X1))))))]]) ).
cnf(refute_1_1719,plain,
( composition(converse(converse(X1)),complement(converse(composition(X0,X1)))) != composition(X1,complement(converse(composition(X0,X1))))
| join(complement(converse(X0)),composition(converse(converse(X1)),complement(converse(composition(X0,X1))))) != join(complement(converse(X0)),composition(converse(converse(X1)),complement(converse(composition(X0,X1)))))
| join(complement(converse(X0)),composition(converse(converse(X1)),complement(converse(composition(X0,X1))))) = join(complement(converse(X0)),composition(X1,complement(converse(composition(X0,X1))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(converse(X0)),composition(converse(converse(X1)),complement(converse(composition(X0,X1))))),join(complement(converse(X0)),composition(converse(converse(X1)),complement(converse(composition(X0,X1)))))) ),[1,1],$fot(composition(X1,complement(converse(composition(X0,X1)))))]]) ).
cnf(refute_1_1720,plain,
( composition(converse(converse(X1)),complement(converse(composition(X0,X1)))) != composition(X1,complement(converse(composition(X0,X1))))
| join(complement(converse(X0)),composition(converse(converse(X1)),complement(converse(composition(X0,X1))))) = join(complement(converse(X0)),composition(X1,complement(converse(composition(X0,X1))))) ),
inference(resolve,[$cnf( $equal(join(complement(converse(X0)),composition(converse(converse(X1)),complement(converse(composition(X0,X1))))),join(complement(converse(X0)),composition(converse(converse(X1)),complement(converse(composition(X0,X1)))))) )],[refute_1_1718,refute_1_1719]) ).
cnf(refute_1_1721,plain,
join(complement(converse(X0)),composition(converse(converse(X1)),complement(converse(composition(X0,X1))))) = join(complement(converse(X0)),composition(X1,complement(converse(composition(X0,X1))))),
inference(resolve,[$cnf( $equal(composition(converse(converse(X1)),complement(converse(composition(X0,X1)))),composition(X1,complement(converse(composition(X0,X1))))) )],[refute_1_1717,refute_1_1720]) ).
cnf(refute_1_1722,plain,
( join(complement(converse(X0)),composition(converse(converse(X1)),complement(converse(composition(X0,X1))))) != complement(converse(X0))
| join(complement(converse(X0)),composition(converse(converse(X1)),complement(converse(composition(X0,X1))))) != join(complement(converse(X0)),composition(X1,complement(converse(composition(X0,X1)))))
| join(complement(converse(X0)),composition(X1,complement(converse(composition(X0,X1))))) = complement(converse(X0)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(converse(X0)),composition(converse(converse(X1)),complement(converse(composition(X0,X1))))),complement(converse(X0))) ),[0],$fot(join(complement(converse(X0)),composition(X1,complement(converse(composition(X0,X1))))))]]) ).
cnf(refute_1_1723,plain,
( join(complement(converse(X0)),composition(converse(converse(X1)),complement(converse(composition(X0,X1))))) != complement(converse(X0))
| join(complement(converse(X0)),composition(X1,complement(converse(composition(X0,X1))))) = complement(converse(X0)) ),
inference(resolve,[$cnf( $equal(join(complement(converse(X0)),composition(converse(converse(X1)),complement(converse(composition(X0,X1))))),join(complement(converse(X0)),composition(X1,complement(converse(composition(X0,X1)))))) )],[refute_1_1721,refute_1_1722]) ).
cnf(refute_1_1724,plain,
join(complement(converse(X0)),composition(X1,complement(converse(composition(X0,X1))))) = complement(converse(X0)),
inference(resolve,[$cnf( $equal(join(complement(converse(X0)),composition(converse(converse(X1)),complement(converse(composition(X0,X1))))),complement(converse(X0))) )],[refute_1_1712,refute_1_1723]) ).
cnf(refute_1_1725,plain,
join(complement(converse(top)),composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(composition(top,composition(zero,complement(composition(zero,composition(top,top))))))))) = complement(converse(top)),
inference(subst,[],[refute_1_1724:[bind(X0,$fot(top)),bind(X1,$fot(composition(zero,complement(composition(zero,composition(top,top))))))]]) ).
cnf(refute_1_1726,plain,
composition(converse(composition(zero,top)),complement(composition(composition(zero,top),top))) = zero,
inference(subst,[],[refute_1_675:[bind(X0,$fot(composition(zero,top)))]]) ).
cnf(refute_1_1727,plain,
( composition(converse(composition(zero,top)),complement(composition(composition(zero,top),top))) != zero
| converse(composition(zero,top)) != composition(top,zero)
| composition(composition(top,zero),complement(composition(composition(zero,top),top))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(composition(zero,top)),complement(composition(composition(zero,top),top))),zero) ),[0,0],$fot(composition(top,zero))]]) ).
cnf(refute_1_1728,plain,
( composition(converse(composition(zero,top)),complement(composition(composition(zero,top),top))) != zero
| composition(composition(top,zero),complement(composition(composition(zero,top),top))) = zero ),
inference(resolve,[$cnf( $equal(converse(composition(zero,top)),composition(top,zero)) )],[refute_1_1498,refute_1_1727]) ).
cnf(refute_1_1729,plain,
composition(composition(top,zero),complement(composition(composition(zero,top),top))) = zero,
inference(resolve,[$cnf( $equal(composition(converse(composition(zero,top)),complement(composition(composition(zero,top),top))),zero) )],[refute_1_1726,refute_1_1728]) ).
cnf(refute_1_1730,plain,
( composition(X0,composition(X1,X2)) != composition(composition(X0,X1),X2)
| composition(composition(X0,X1),X2) = composition(X0,composition(X1,X2)) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(composition(X0,composition(X1,X2)))),bind(Y,$fot(composition(composition(X0,X1),X2)))]]) ).
cnf(refute_1_1731,plain,
composition(composition(X0,X1),X2) = composition(X0,composition(X1,X2)),
inference(resolve,[$cnf( $equal(composition(X0,composition(X1,X2)),composition(composition(X0,X1),X2)) )],[refute_1_1524,refute_1_1730]) ).
cnf(refute_1_1732,plain,
composition(composition(zero,top),top) = composition(zero,composition(top,top)),
inference(subst,[],[refute_1_1731:[bind(X0,$fot(zero)),bind(X1,$fot(top)),bind(X2,$fot(top))]]) ).
cnf(refute_1_1733,plain,
complement(composition(composition(zero,top),top)) = complement(composition(composition(zero,top),top)),
introduced(tautology,[refl,[$fot(complement(composition(composition(zero,top),top)))]]) ).
cnf(refute_1_1734,plain,
( complement(composition(composition(zero,top),top)) != complement(composition(composition(zero,top),top))
| composition(composition(zero,top),top) != composition(zero,composition(top,top))
| complement(composition(composition(zero,top),top)) = complement(composition(zero,composition(top,top))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(composition(composition(zero,top),top)),complement(composition(composition(zero,top),top))) ),[1,0],$fot(composition(zero,composition(top,top)))]]) ).
cnf(refute_1_1735,plain,
( composition(composition(zero,top),top) != composition(zero,composition(top,top))
| complement(composition(composition(zero,top),top)) = complement(composition(zero,composition(top,top))) ),
inference(resolve,[$cnf( $equal(complement(composition(composition(zero,top),top)),complement(composition(composition(zero,top),top))) )],[refute_1_1733,refute_1_1734]) ).
cnf(refute_1_1736,plain,
complement(composition(composition(zero,top),top)) = complement(composition(zero,composition(top,top))),
inference(resolve,[$cnf( $equal(composition(composition(zero,top),top),composition(zero,composition(top,top))) )],[refute_1_1732,refute_1_1735]) ).
cnf(refute_1_1737,plain,
composition(zero,complement(composition(composition(zero,top),top))) = composition(zero,complement(composition(composition(zero,top),top))),
introduced(tautology,[refl,[$fot(composition(zero,complement(composition(composition(zero,top),top))))]]) ).
cnf(refute_1_1738,plain,
( complement(composition(composition(zero,top),top)) != complement(composition(zero,composition(top,top)))
| composition(zero,complement(composition(composition(zero,top),top))) != composition(zero,complement(composition(composition(zero,top),top)))
| composition(zero,complement(composition(composition(zero,top),top))) = composition(zero,complement(composition(zero,composition(top,top)))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(zero,complement(composition(composition(zero,top),top))),composition(zero,complement(composition(composition(zero,top),top)))) ),[1,1],$fot(complement(composition(zero,composition(top,top))))]]) ).
cnf(refute_1_1739,plain,
( complement(composition(composition(zero,top),top)) != complement(composition(zero,composition(top,top)))
| composition(zero,complement(composition(composition(zero,top),top))) = composition(zero,complement(composition(zero,composition(top,top)))) ),
inference(resolve,[$cnf( $equal(composition(zero,complement(composition(composition(zero,top),top))),composition(zero,complement(composition(composition(zero,top),top)))) )],[refute_1_1737,refute_1_1738]) ).
cnf(refute_1_1740,plain,
composition(zero,complement(composition(composition(zero,top),top))) = composition(zero,complement(composition(zero,composition(top,top)))),
inference(resolve,[$cnf( $equal(complement(composition(composition(zero,top),top)),complement(composition(zero,composition(top,top)))) )],[refute_1_1736,refute_1_1739]) ).
cnf(refute_1_1741,plain,
composition(top,composition(zero,complement(composition(composition(zero,top),top)))) = composition(top,composition(zero,complement(composition(composition(zero,top),top)))),
introduced(tautology,[refl,[$fot(composition(top,composition(zero,complement(composition(composition(zero,top),top)))))]]) ).
cnf(refute_1_1742,plain,
( composition(top,composition(zero,complement(composition(composition(zero,top),top)))) != composition(top,composition(zero,complement(composition(composition(zero,top),top))))
| composition(zero,complement(composition(composition(zero,top),top))) != composition(zero,complement(composition(zero,composition(top,top))))
| composition(top,composition(zero,complement(composition(composition(zero,top),top)))) = composition(top,composition(zero,complement(composition(zero,composition(top,top))))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(top,composition(zero,complement(composition(composition(zero,top),top)))),composition(top,composition(zero,complement(composition(composition(zero,top),top))))) ),[1,1],$fot(composition(zero,complement(composition(zero,composition(top,top)))))]]) ).
cnf(refute_1_1743,plain,
( composition(zero,complement(composition(composition(zero,top),top))) != composition(zero,complement(composition(zero,composition(top,top))))
| composition(top,composition(zero,complement(composition(composition(zero,top),top)))) = composition(top,composition(zero,complement(composition(zero,composition(top,top))))) ),
inference(resolve,[$cnf( $equal(composition(top,composition(zero,complement(composition(composition(zero,top),top)))),composition(top,composition(zero,complement(composition(composition(zero,top),top))))) )],[refute_1_1741,refute_1_1742]) ).
cnf(refute_1_1744,plain,
composition(top,composition(zero,complement(composition(composition(zero,top),top)))) = composition(top,composition(zero,complement(composition(zero,composition(top,top))))),
inference(resolve,[$cnf( $equal(composition(zero,complement(composition(composition(zero,top),top))),composition(zero,complement(composition(zero,composition(top,top))))) )],[refute_1_1740,refute_1_1743]) ).
cnf(refute_1_1745,plain,
composition(composition(top,zero),complement(composition(composition(zero,top),top))) = composition(top,composition(zero,complement(composition(composition(zero,top),top)))),
inference(subst,[],[refute_1_1731:[bind(X0,$fot(top)),bind(X1,$fot(zero)),bind(X2,$fot(complement(composition(composition(zero,top),top))))]]) ).
cnf(refute_1_1746,plain,
( composition(composition(top,zero),complement(composition(composition(zero,top),top))) != composition(top,composition(zero,complement(composition(composition(zero,top),top))))
| composition(top,composition(zero,complement(composition(composition(zero,top),top)))) != composition(top,composition(zero,complement(composition(zero,composition(top,top)))))
| composition(composition(top,zero),complement(composition(composition(zero,top),top))) = composition(top,composition(zero,complement(composition(zero,composition(top,top))))) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(composition(composition(top,zero),complement(composition(composition(zero,top),top))))),bind(Y,$fot(composition(top,composition(zero,complement(composition(composition(zero,top),top)))))),bind(Z,$fot(composition(top,composition(zero,complement(composition(zero,composition(top,top)))))))]]) ).
cnf(refute_1_1747,plain,
( composition(top,composition(zero,complement(composition(composition(zero,top),top)))) != composition(top,composition(zero,complement(composition(zero,composition(top,top)))))
| composition(composition(top,zero),complement(composition(composition(zero,top),top))) = composition(top,composition(zero,complement(composition(zero,composition(top,top))))) ),
inference(resolve,[$cnf( $equal(composition(composition(top,zero),complement(composition(composition(zero,top),top))),composition(top,composition(zero,complement(composition(composition(zero,top),top))))) )],[refute_1_1745,refute_1_1746]) ).
cnf(refute_1_1748,plain,
composition(composition(top,zero),complement(composition(composition(zero,top),top))) = composition(top,composition(zero,complement(composition(zero,composition(top,top))))),
inference(resolve,[$cnf( $equal(composition(top,composition(zero,complement(composition(composition(zero,top),top)))),composition(top,composition(zero,complement(composition(zero,composition(top,top)))))) )],[refute_1_1744,refute_1_1747]) ).
cnf(refute_1_1749,plain,
( composition(composition(top,zero),complement(composition(composition(zero,top),top))) != composition(top,composition(zero,complement(composition(zero,composition(top,top)))))
| composition(composition(top,zero),complement(composition(composition(zero,top),top))) != zero
| composition(top,composition(zero,complement(composition(zero,composition(top,top))))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(composition(composition(top,zero),complement(composition(composition(zero,top),top))),zero) ),[0],$fot(composition(top,composition(zero,complement(composition(zero,composition(top,top))))))]]) ).
cnf(refute_1_1750,plain,
( composition(composition(top,zero),complement(composition(composition(zero,top),top))) != zero
| composition(top,composition(zero,complement(composition(zero,composition(top,top))))) = zero ),
inference(resolve,[$cnf( $equal(composition(composition(top,zero),complement(composition(composition(zero,top),top))),composition(top,composition(zero,complement(composition(zero,composition(top,top)))))) )],[refute_1_1748,refute_1_1749]) ).
cnf(refute_1_1751,plain,
composition(top,composition(zero,complement(composition(zero,composition(top,top))))) = zero,
inference(resolve,[$cnf( $equal(composition(composition(top,zero),complement(composition(composition(zero,top),top))),zero) )],[refute_1_1729,refute_1_1750]) ).
cnf(refute_1_1752,plain,
( composition(top,composition(zero,complement(composition(zero,composition(top,top))))) != zero
| join(complement(converse(top)),composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(composition(top,composition(zero,complement(composition(zero,composition(top,top))))))))) != complement(converse(top))
| join(complement(converse(top)),composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero)))) = complement(converse(top)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(converse(top)),composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(composition(top,composition(zero,complement(composition(zero,composition(top,top))))))))),complement(converse(top))) ),[0,1,1,0,0],$fot(zero)]]) ).
cnf(refute_1_1753,plain,
( join(complement(converse(top)),composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(composition(top,composition(zero,complement(composition(zero,composition(top,top))))))))) != complement(converse(top))
| join(complement(converse(top)),composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero)))) = complement(converse(top)) ),
inference(resolve,[$cnf( $equal(composition(top,composition(zero,complement(composition(zero,composition(top,top))))),zero) )],[refute_1_1751,refute_1_1752]) ).
cnf(refute_1_1754,plain,
join(complement(converse(top)),composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero)))) = complement(converse(top)),
inference(resolve,[$cnf( $equal(join(complement(converse(top)),composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(composition(top,composition(zero,complement(composition(zero,composition(top,top))))))))),complement(converse(top))) )],[refute_1_1725,refute_1_1753]) ).
cnf(refute_1_1755,plain,
join(zero,composition(zero,composition(complement(composition(zero,composition(top,top))),top))) = composition(zero,composition(complement(composition(zero,composition(top,top))),top)),
inference(subst,[],[refute_1_580:[bind(X_176,$fot(composition(zero,composition(complement(composition(zero,composition(top,top))),top))))]]) ).
cnf(refute_1_1756,plain,
composition(complement(composition(zero,composition(top,top))),complement(converse(zero))) = composition(complement(composition(zero,composition(top,top))),complement(converse(zero))),
introduced(tautology,[refl,[$fot(composition(complement(composition(zero,composition(top,top))),complement(converse(zero))))]]) ).
cnf(refute_1_1757,plain,
( complement(converse(zero)) != top
| composition(complement(composition(zero,composition(top,top))),complement(converse(zero))) != composition(complement(composition(zero,composition(top,top))),complement(converse(zero)))
| composition(complement(composition(zero,composition(top,top))),complement(converse(zero))) = composition(complement(composition(zero,composition(top,top))),top) ),
introduced(tautology,[equality,[$cnf( $equal(composition(complement(composition(zero,composition(top,top))),complement(converse(zero))),composition(complement(composition(zero,composition(top,top))),complement(converse(zero)))) ),[1,1],$fot(top)]]) ).
cnf(refute_1_1758,plain,
( complement(converse(zero)) != top
| composition(complement(composition(zero,composition(top,top))),complement(converse(zero))) = composition(complement(composition(zero,composition(top,top))),top) ),
inference(resolve,[$cnf( $equal(composition(complement(composition(zero,composition(top,top))),complement(converse(zero))),composition(complement(composition(zero,composition(top,top))),complement(converse(zero)))) )],[refute_1_1756,refute_1_1757]) ).
cnf(refute_1_1759,plain,
composition(complement(composition(zero,composition(top,top))),complement(converse(zero))) = composition(complement(composition(zero,composition(top,top))),top),
inference(resolve,[$cnf( $equal(complement(converse(zero)),top) )],[refute_1_615,refute_1_1758]) ).
cnf(refute_1_1760,plain,
composition(zero,composition(complement(composition(zero,composition(top,top))),complement(converse(zero)))) = composition(zero,composition(complement(composition(zero,composition(top,top))),complement(converse(zero)))),
introduced(tautology,[refl,[$fot(composition(zero,composition(complement(composition(zero,composition(top,top))),complement(converse(zero)))))]]) ).
cnf(refute_1_1761,plain,
( composition(complement(composition(zero,composition(top,top))),complement(converse(zero))) != composition(complement(composition(zero,composition(top,top))),top)
| composition(zero,composition(complement(composition(zero,composition(top,top))),complement(converse(zero)))) != composition(zero,composition(complement(composition(zero,composition(top,top))),complement(converse(zero))))
| composition(zero,composition(complement(composition(zero,composition(top,top))),complement(converse(zero)))) = composition(zero,composition(complement(composition(zero,composition(top,top))),top)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(zero,composition(complement(composition(zero,composition(top,top))),complement(converse(zero)))),composition(zero,composition(complement(composition(zero,composition(top,top))),complement(converse(zero))))) ),[1,1],$fot(composition(complement(composition(zero,composition(top,top))),top))]]) ).
cnf(refute_1_1762,plain,
( composition(complement(composition(zero,composition(top,top))),complement(converse(zero))) != composition(complement(composition(zero,composition(top,top))),top)
| composition(zero,composition(complement(composition(zero,composition(top,top))),complement(converse(zero)))) = composition(zero,composition(complement(composition(zero,composition(top,top))),top)) ),
inference(resolve,[$cnf( $equal(composition(zero,composition(complement(composition(zero,composition(top,top))),complement(converse(zero)))),composition(zero,composition(complement(composition(zero,composition(top,top))),complement(converse(zero))))) )],[refute_1_1760,refute_1_1761]) ).
cnf(refute_1_1763,plain,
composition(zero,composition(complement(composition(zero,composition(top,top))),complement(converse(zero)))) = composition(zero,composition(complement(composition(zero,composition(top,top))),top)),
inference(resolve,[$cnf( $equal(composition(complement(composition(zero,composition(top,top))),complement(converse(zero))),composition(complement(composition(zero,composition(top,top))),top)) )],[refute_1_1759,refute_1_1762]) ).
cnf(refute_1_1764,plain,
composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero))) = composition(zero,composition(complement(composition(zero,composition(top,top))),complement(converse(zero)))),
inference(subst,[],[refute_1_1731:[bind(X0,$fot(zero)),bind(X1,$fot(complement(composition(zero,composition(top,top))))),bind(X2,$fot(complement(converse(zero))))]]) ).
cnf(refute_1_1765,plain,
( composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero))) != composition(zero,composition(complement(composition(zero,composition(top,top))),complement(converse(zero))))
| composition(zero,composition(complement(composition(zero,composition(top,top))),complement(converse(zero)))) != composition(zero,composition(complement(composition(zero,composition(top,top))),top))
| composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero))) = composition(zero,composition(complement(composition(zero,composition(top,top))),top)) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero))))),bind(Y,$fot(composition(zero,composition(complement(composition(zero,composition(top,top))),complement(converse(zero)))))),bind(Z,$fot(composition(zero,composition(complement(composition(zero,composition(top,top))),top))))]]) ).
cnf(refute_1_1766,plain,
( composition(zero,composition(complement(composition(zero,composition(top,top))),complement(converse(zero)))) != composition(zero,composition(complement(composition(zero,composition(top,top))),top))
| composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero))) = composition(zero,composition(complement(composition(zero,composition(top,top))),top)) ),
inference(resolve,[$cnf( $equal(composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero))),composition(zero,composition(complement(composition(zero,composition(top,top))),complement(converse(zero))))) )],[refute_1_1764,refute_1_1765]) ).
cnf(refute_1_1767,plain,
composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero))) = composition(zero,composition(complement(composition(zero,composition(top,top))),top)),
inference(resolve,[$cnf( $equal(composition(zero,composition(complement(composition(zero,composition(top,top))),complement(converse(zero)))),composition(zero,composition(complement(composition(zero,composition(top,top))),top))) )],[refute_1_1763,refute_1_1766]) ).
cnf(refute_1_1768,plain,
join(zero,composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero)))) = join(zero,composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero)))),
introduced(tautology,[refl,[$fot(join(zero,composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero)))))]]) ).
cnf(refute_1_1769,plain,
( composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero))) != composition(zero,composition(complement(composition(zero,composition(top,top))),top))
| join(zero,composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero)))) != join(zero,composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero))))
| join(zero,composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero)))) = join(zero,composition(zero,composition(complement(composition(zero,composition(top,top))),top))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero)))),join(zero,composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero))))) ),[1,1],$fot(composition(zero,composition(complement(composition(zero,composition(top,top))),top)))]]) ).
cnf(refute_1_1770,plain,
( composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero))) != composition(zero,composition(complement(composition(zero,composition(top,top))),top))
| join(zero,composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero)))) = join(zero,composition(zero,composition(complement(composition(zero,composition(top,top))),top))) ),
inference(resolve,[$cnf( $equal(join(zero,composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero)))),join(zero,composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero))))) )],[refute_1_1768,refute_1_1769]) ).
cnf(refute_1_1771,plain,
join(zero,composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero)))) = join(zero,composition(zero,composition(complement(composition(zero,composition(top,top))),top))),
inference(resolve,[$cnf( $equal(composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero))),composition(zero,composition(complement(composition(zero,composition(top,top))),top))) )],[refute_1_1767,refute_1_1770]) ).
cnf(refute_1_1772,plain,
complement(converse(top)) = complement(converse(top)),
introduced(tautology,[refl,[$fot(complement(converse(top)))]]) ).
cnf(refute_1_1773,plain,
( complement(converse(top)) != complement(converse(top))
| converse(top) != top
| complement(converse(top)) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(complement(converse(top)),complement(converse(top))) ),[1,0],$fot(top)]]) ).
cnf(refute_1_1774,plain,
( converse(top) != top
| complement(converse(top)) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(converse(top)),complement(converse(top))) )],[refute_1_1772,refute_1_1773]) ).
cnf(refute_1_1775,plain,
complement(converse(top)) = complement(top),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_1_191,refute_1_1774]) ).
cnf(refute_1_1776,plain,
( complement(converse(top)) != complement(top)
| complement(top) != zero
| complement(converse(top)) = zero ),
inference(subst,[],[refute_1_37:[bind(X,$fot(complement(converse(top)))),bind(Y,$fot(complement(top))),bind(Z,$fot(zero))]]) ).
cnf(refute_1_1777,plain,
( complement(top) != zero
| complement(converse(top)) = zero ),
inference(resolve,[$cnf( $equal(complement(converse(top)),complement(top)) )],[refute_1_1775,refute_1_1776]) ).
cnf(refute_1_1778,plain,
complement(converse(top)) = zero,
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_1_45,refute_1_1777]) ).
cnf(refute_1_1779,plain,
join(complement(converse(top)),composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero)))) = join(complement(converse(top)),composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero)))),
introduced(tautology,[refl,[$fot(join(complement(converse(top)),composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero)))))]]) ).
cnf(refute_1_1780,plain,
( complement(converse(top)) != zero
| join(complement(converse(top)),composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero)))) != join(complement(converse(top)),composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero))))
| join(complement(converse(top)),composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero)))) = join(zero,composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(converse(top)),composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero)))),join(complement(converse(top)),composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_1_1781,plain,
( complement(converse(top)) != zero
| join(complement(converse(top)),composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero)))) = join(zero,composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero)))) ),
inference(resolve,[$cnf( $equal(join(complement(converse(top)),composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero)))),join(complement(converse(top)),composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero))))) )],[refute_1_1779,refute_1_1780]) ).
cnf(refute_1_1782,plain,
join(complement(converse(top)),composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero)))) = join(zero,composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero)))),
inference(resolve,[$cnf( $equal(complement(converse(top)),zero) )],[refute_1_1778,refute_1_1781]) ).
cnf(refute_1_1783,plain,
( join(complement(converse(top)),composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero)))) != join(zero,composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero))))
| join(zero,composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero)))) != join(zero,composition(zero,composition(complement(composition(zero,composition(top,top))),top)))
| join(complement(converse(top)),composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero)))) = join(zero,composition(zero,composition(complement(composition(zero,composition(top,top))),top))) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(complement(converse(top)),composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero)))))),bind(Y,$fot(join(zero,composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero)))))),bind(Z,$fot(join(zero,composition(zero,composition(complement(composition(zero,composition(top,top))),top)))))]]) ).
cnf(refute_1_1784,plain,
( join(zero,composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero)))) != join(zero,composition(zero,composition(complement(composition(zero,composition(top,top))),top)))
| join(complement(converse(top)),composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero)))) = join(zero,composition(zero,composition(complement(composition(zero,composition(top,top))),top))) ),
inference(resolve,[$cnf( $equal(join(complement(converse(top)),composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero)))),join(zero,composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero))))) )],[refute_1_1782,refute_1_1783]) ).
cnf(refute_1_1785,plain,
join(complement(converse(top)),composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero)))) = join(zero,composition(zero,composition(complement(composition(zero,composition(top,top))),top))),
inference(resolve,[$cnf( $equal(join(zero,composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero)))),join(zero,composition(zero,composition(complement(composition(zero,composition(top,top))),top)))) )],[refute_1_1771,refute_1_1784]) ).
cnf(refute_1_1786,plain,
( join(complement(converse(top)),composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero)))) != join(zero,composition(zero,composition(complement(composition(zero,composition(top,top))),top)))
| join(zero,composition(zero,composition(complement(composition(zero,composition(top,top))),top))) != composition(zero,composition(complement(composition(zero,composition(top,top))),top))
| join(complement(converse(top)),composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero)))) = composition(zero,composition(complement(composition(zero,composition(top,top))),top)) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(complement(converse(top)),composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero)))))),bind(Y,$fot(join(zero,composition(zero,composition(complement(composition(zero,composition(top,top))),top))))),bind(Z,$fot(composition(zero,composition(complement(composition(zero,composition(top,top))),top))))]]) ).
cnf(refute_1_1787,plain,
( join(zero,composition(zero,composition(complement(composition(zero,composition(top,top))),top))) != composition(zero,composition(complement(composition(zero,composition(top,top))),top))
| join(complement(converse(top)),composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero)))) = composition(zero,composition(complement(composition(zero,composition(top,top))),top)) ),
inference(resolve,[$cnf( $equal(join(complement(converse(top)),composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero)))),join(zero,composition(zero,composition(complement(composition(zero,composition(top,top))),top)))) )],[refute_1_1785,refute_1_1786]) ).
cnf(refute_1_1788,plain,
join(complement(converse(top)),composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero)))) = composition(zero,composition(complement(composition(zero,composition(top,top))),top)),
inference(resolve,[$cnf( $equal(join(zero,composition(zero,composition(complement(composition(zero,composition(top,top))),top))),composition(zero,composition(complement(composition(zero,composition(top,top))),top))) )],[refute_1_1755,refute_1_1787]) ).
cnf(refute_1_1789,plain,
( join(complement(converse(top)),composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero)))) != complement(converse(top))
| join(complement(converse(top)),composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero)))) != composition(zero,composition(complement(composition(zero,composition(top,top))),top))
| composition(zero,composition(complement(composition(zero,composition(top,top))),top)) = complement(converse(top)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(converse(top)),composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero)))),complement(converse(top))) ),[0],$fot(composition(zero,composition(complement(composition(zero,composition(top,top))),top)))]]) ).
cnf(refute_1_1790,plain,
( join(complement(converse(top)),composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero)))) != complement(converse(top))
| composition(zero,composition(complement(composition(zero,composition(top,top))),top)) = complement(converse(top)) ),
inference(resolve,[$cnf( $equal(join(complement(converse(top)),composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero)))),composition(zero,composition(complement(composition(zero,composition(top,top))),top))) )],[refute_1_1788,refute_1_1789]) ).
cnf(refute_1_1791,plain,
( complement(converse(top)) != zero
| composition(zero,composition(complement(composition(zero,composition(top,top))),top)) != complement(converse(top))
| composition(zero,composition(complement(composition(zero,composition(top,top))),top)) = zero ),
introduced(tautology,[equality,[$cnf( $equal(composition(zero,composition(complement(composition(zero,composition(top,top))),top)),complement(converse(top))) ),[1],$fot(zero)]]) ).
cnf(refute_1_1792,plain,
( composition(zero,composition(complement(composition(zero,composition(top,top))),top)) != complement(converse(top))
| composition(zero,composition(complement(composition(zero,composition(top,top))),top)) = zero ),
inference(resolve,[$cnf( $equal(complement(converse(top)),zero) )],[refute_1_1778,refute_1_1791]) ).
cnf(refute_1_1793,plain,
( join(complement(converse(top)),composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero)))) != complement(converse(top))
| composition(zero,composition(complement(composition(zero,composition(top,top))),top)) = zero ),
inference(resolve,[$cnf( $equal(composition(zero,composition(complement(composition(zero,composition(top,top))),top)),complement(converse(top))) )],[refute_1_1790,refute_1_1792]) ).
cnf(refute_1_1794,plain,
composition(zero,composition(complement(composition(zero,composition(top,top))),top)) = zero,
inference(resolve,[$cnf( $equal(join(complement(converse(top)),composition(composition(zero,complement(composition(zero,composition(top,top)))),complement(converse(zero)))),complement(converse(top))) )],[refute_1_1754,refute_1_1793]) ).
cnf(refute_1_1795,plain,
composition(top,composition(zero,top)) = composition(top,composition(zero,top)),
introduced(tautology,[refl,[$fot(composition(top,composition(zero,top)))]]) ).
cnf(refute_1_1796,plain,
( composition(top,composition(zero,top)) != composition(top,composition(zero,top))
| composition(zero,top) != composition(top,zero)
| composition(top,composition(zero,top)) = composition(top,composition(top,zero)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(top,composition(zero,top)),composition(top,composition(zero,top))) ),[1,1],$fot(composition(top,zero))]]) ).
cnf(refute_1_1797,plain,
( composition(zero,top) != composition(top,zero)
| composition(top,composition(zero,top)) = composition(top,composition(top,zero)) ),
inference(resolve,[$cnf( $equal(composition(top,composition(zero,top)),composition(top,composition(zero,top))) )],[refute_1_1795,refute_1_1796]) ).
cnf(refute_1_1798,plain,
composition(top,composition(zero,top)) = composition(top,composition(top,zero)),
inference(resolve,[$cnf( $equal(composition(zero,top),composition(top,zero)) )],[refute_1_1678,refute_1_1797]) ).
cnf(refute_1_1799,plain,
converse(composition(converse(X0),composition(top,zero))) = composition(converse(composition(top,zero)),X0),
inference(subst,[],[refute_1_117:[bind(X_112,$fot(composition(top,zero)))]]) ).
cnf(refute_1_1800,plain,
( composition(zero,top) != composition(top,zero)
| converse(composition(top,zero)) != composition(zero,top)
| converse(composition(top,zero)) = composition(top,zero) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(top,zero)),composition(zero,top)) ),[1],$fot(composition(top,zero))]]) ).
cnf(refute_1_1801,plain,
( converse(composition(top,zero)) != composition(zero,top)
| converse(composition(top,zero)) = composition(top,zero) ),
inference(resolve,[$cnf( $equal(composition(zero,top),composition(top,zero)) )],[refute_1_1678,refute_1_1800]) ).
cnf(refute_1_1802,plain,
converse(composition(top,zero)) = composition(top,zero),
inference(resolve,[$cnf( $equal(converse(composition(top,zero)),composition(zero,top)) )],[refute_1_1374,refute_1_1801]) ).
cnf(refute_1_1803,plain,
( converse(composition(converse(X0),composition(top,zero))) != composition(converse(composition(top,zero)),X0)
| converse(composition(top,zero)) != composition(top,zero)
| converse(composition(converse(X0),composition(top,zero))) = composition(composition(top,zero),X0) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(X0),composition(top,zero))),composition(converse(composition(top,zero)),X0)) ),[1,0],$fot(composition(top,zero))]]) ).
cnf(refute_1_1804,plain,
( converse(composition(converse(X0),composition(top,zero))) != composition(converse(composition(top,zero)),X0)
| converse(composition(converse(X0),composition(top,zero))) = composition(composition(top,zero),X0) ),
inference(resolve,[$cnf( $equal(converse(composition(top,zero)),composition(top,zero)) )],[refute_1_1802,refute_1_1803]) ).
cnf(refute_1_1805,plain,
converse(composition(converse(X0),composition(top,zero))) = composition(composition(top,zero),X0),
inference(resolve,[$cnf( $equal(converse(composition(converse(X0),composition(top,zero))),composition(converse(composition(top,zero)),X0)) )],[refute_1_1799,refute_1_1804]) ).
cnf(refute_1_1806,plain,
composition(converse(zero),composition(top,X0)) = composition(converse(zero),composition(top,X0)),
introduced(tautology,[refl,[$fot(composition(converse(zero),composition(top,X0)))]]) ).
cnf(refute_1_1807,plain,
( composition(converse(zero),composition(top,X0)) != composition(converse(zero),composition(top,X0))
| converse(zero) != zero
| composition(converse(zero),composition(top,X0)) = composition(zero,composition(top,X0)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(zero),composition(top,X0)),composition(converse(zero),composition(top,X0))) ),[1,0],$fot(zero)]]) ).
cnf(refute_1_1808,plain,
( converse(zero) != zero
| composition(converse(zero),composition(top,X0)) = composition(zero,composition(top,X0)) ),
inference(resolve,[$cnf( $equal(composition(converse(zero),composition(top,X0)),composition(converse(zero),composition(top,X0))) )],[refute_1_1806,refute_1_1807]) ).
cnf(refute_1_1809,plain,
composition(converse(zero),composition(top,X0)) = composition(zero,composition(top,X0)),
inference(resolve,[$cnf( $equal(converse(zero),zero) )],[refute_1_659,refute_1_1808]) ).
cnf(refute_1_1810,plain,
composition(converse(X_283),composition(converse(top),X_284)) = composition(converse(composition(top,X_283)),X_284),
inference(subst,[],[refute_1_1530:[bind(X0,$fot(top)),bind(X1,$fot(X_283)),bind(X_124,$fot(X_284))]]) ).
cnf(refute_1_1811,plain,
( composition(converse(X_283),composition(converse(top),X_284)) != composition(converse(composition(top,X_283)),X_284)
| converse(top) != top
| composition(converse(X_283),composition(top,X_284)) = composition(converse(composition(top,X_283)),X_284) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(X_283),composition(converse(top),X_284)),composition(converse(composition(top,X_283)),X_284)) ),[0,1,0],$fot(top)]]) ).
cnf(refute_1_1812,plain,
( composition(converse(X_283),composition(converse(top),X_284)) != composition(converse(composition(top,X_283)),X_284)
| composition(converse(X_283),composition(top,X_284)) = composition(converse(composition(top,X_283)),X_284) ),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_1_191,refute_1_1811]) ).
cnf(refute_1_1813,plain,
composition(converse(X_283),composition(top,X_284)) = composition(converse(composition(top,X_283)),X_284),
inference(resolve,[$cnf( $equal(composition(converse(X_283),composition(converse(top),X_284)),composition(converse(composition(top,X_283)),X_284)) )],[refute_1_1810,refute_1_1812]) ).
cnf(refute_1_1814,plain,
( composition(converse(X_283),composition(top,X_284)) != composition(converse(composition(top,X_283)),X_284)
| composition(converse(composition(top,X_283)),X_284) = composition(converse(X_283),composition(top,X_284)) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(composition(converse(X_283),composition(top,X_284)))),bind(Y,$fot(composition(converse(composition(top,X_283)),X_284)))]]) ).
cnf(refute_1_1815,plain,
composition(converse(composition(top,X_283)),X_284) = composition(converse(X_283),composition(top,X_284)),
inference(resolve,[$cnf( $equal(composition(converse(X_283),composition(top,X_284)),composition(converse(composition(top,X_283)),X_284)) )],[refute_1_1813,refute_1_1814]) ).
cnf(refute_1_1816,plain,
composition(converse(composition(top,zero)),X0) = composition(converse(zero),composition(top,X0)),
inference(subst,[],[refute_1_1815:[bind(X_283,$fot(zero)),bind(X_284,$fot(X0))]]) ).
cnf(refute_1_1817,plain,
( composition(converse(composition(top,zero)),X0) != composition(converse(zero),composition(top,X0))
| converse(composition(converse(X0),composition(top,zero))) != composition(converse(composition(top,zero)),X0)
| converse(composition(converse(X0),composition(top,zero))) = composition(converse(zero),composition(top,X0)) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(converse(composition(converse(X0),composition(top,zero))))),bind(Y,$fot(composition(converse(composition(top,zero)),X0))),bind(Z,$fot(composition(converse(zero),composition(top,X0))))]]) ).
cnf(refute_1_1818,plain,
( composition(converse(composition(top,zero)),X0) != composition(converse(zero),composition(top,X0))
| converse(composition(converse(X0),composition(top,zero))) = composition(converse(zero),composition(top,X0)) ),
inference(resolve,[$cnf( $equal(converse(composition(converse(X0),composition(top,zero))),composition(converse(composition(top,zero)),X0)) )],[refute_1_1799,refute_1_1817]) ).
cnf(refute_1_1819,plain,
converse(composition(converse(X0),composition(top,zero))) = composition(converse(zero),composition(top,X0)),
inference(resolve,[$cnf( $equal(composition(converse(composition(top,zero)),X0),composition(converse(zero),composition(top,X0))) )],[refute_1_1816,refute_1_1818]) ).
cnf(refute_1_1820,plain,
( composition(converse(zero),composition(top,X0)) != composition(zero,composition(top,X0))
| converse(composition(converse(X0),composition(top,zero))) != composition(converse(zero),composition(top,X0))
| converse(composition(converse(X0),composition(top,zero))) = composition(zero,composition(top,X0)) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(converse(composition(converse(X0),composition(top,zero))))),bind(Y,$fot(composition(converse(zero),composition(top,X0)))),bind(Z,$fot(composition(zero,composition(top,X0))))]]) ).
cnf(refute_1_1821,plain,
( composition(converse(zero),composition(top,X0)) != composition(zero,composition(top,X0))
| converse(composition(converse(X0),composition(top,zero))) = composition(zero,composition(top,X0)) ),
inference(resolve,[$cnf( $equal(converse(composition(converse(X0),composition(top,zero))),composition(converse(zero),composition(top,X0))) )],[refute_1_1819,refute_1_1820]) ).
cnf(refute_1_1822,plain,
converse(composition(converse(X0),composition(top,zero))) = composition(zero,composition(top,X0)),
inference(resolve,[$cnf( $equal(composition(converse(zero),composition(top,X0)),composition(zero,composition(top,X0))) )],[refute_1_1809,refute_1_1821]) ).
cnf(refute_1_1823,plain,
( converse(composition(converse(X0),composition(top,zero))) != composition(composition(top,zero),X0)
| converse(composition(converse(X0),composition(top,zero))) != composition(zero,composition(top,X0))
| composition(zero,composition(top,X0)) = composition(composition(top,zero),X0) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(X0),composition(top,zero))),composition(composition(top,zero),X0)) ),[0],$fot(composition(zero,composition(top,X0)))]]) ).
cnf(refute_1_1824,plain,
( converse(composition(converse(X0),composition(top,zero))) != composition(composition(top,zero),X0)
| composition(zero,composition(top,X0)) = composition(composition(top,zero),X0) ),
inference(resolve,[$cnf( $equal(converse(composition(converse(X0),composition(top,zero))),composition(zero,composition(top,X0))) )],[refute_1_1822,refute_1_1823]) ).
cnf(refute_1_1825,plain,
composition(composition(top,zero),X0) = composition(top,composition(zero,X0)),
inference(subst,[],[refute_1_1731:[bind(X0,$fot(top)),bind(X1,$fot(zero)),bind(X2,$fot(X0))]]) ).
cnf(refute_1_1826,plain,
( composition(composition(top,zero),X0) != composition(top,composition(zero,X0))
| composition(zero,composition(top,X0)) != composition(composition(top,zero),X0)
| composition(zero,composition(top,X0)) = composition(top,composition(zero,X0)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(zero,composition(top,X0)),composition(composition(top,zero),X0)) ),[1],$fot(composition(top,composition(zero,X0)))]]) ).
cnf(refute_1_1827,plain,
( composition(zero,composition(top,X0)) != composition(composition(top,zero),X0)
| composition(zero,composition(top,X0)) = composition(top,composition(zero,X0)) ),
inference(resolve,[$cnf( $equal(composition(composition(top,zero),X0),composition(top,composition(zero,X0))) )],[refute_1_1825,refute_1_1826]) ).
cnf(refute_1_1828,plain,
( converse(composition(converse(X0),composition(top,zero))) != composition(composition(top,zero),X0)
| composition(zero,composition(top,X0)) = composition(top,composition(zero,X0)) ),
inference(resolve,[$cnf( $equal(composition(zero,composition(top,X0)),composition(composition(top,zero),X0)) )],[refute_1_1824,refute_1_1827]) ).
cnf(refute_1_1829,plain,
composition(zero,composition(top,X0)) = composition(top,composition(zero,X0)),
inference(resolve,[$cnf( $equal(converse(composition(converse(X0),composition(top,zero))),composition(composition(top,zero),X0)) )],[refute_1_1805,refute_1_1828]) ).
cnf(refute_1_1830,plain,
composition(zero,composition(top,top)) = composition(top,composition(zero,top)),
inference(subst,[],[refute_1_1829:[bind(X0,$fot(top))]]) ).
cnf(refute_1_1831,plain,
( composition(top,composition(zero,top)) != composition(top,composition(top,zero))
| composition(zero,composition(top,top)) != composition(top,composition(zero,top))
| composition(zero,composition(top,top)) = composition(top,composition(top,zero)) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(composition(zero,composition(top,top)))),bind(Y,$fot(composition(top,composition(zero,top)))),bind(Z,$fot(composition(top,composition(top,zero))))]]) ).
cnf(refute_1_1832,plain,
( composition(top,composition(zero,top)) != composition(top,composition(top,zero))
| composition(zero,composition(top,top)) = composition(top,composition(top,zero)) ),
inference(resolve,[$cnf( $equal(composition(zero,composition(top,top)),composition(top,composition(zero,top))) )],[refute_1_1830,refute_1_1831]) ).
cnf(refute_1_1833,plain,
composition(zero,composition(top,top)) = composition(top,composition(top,zero)),
inference(resolve,[$cnf( $equal(composition(top,composition(zero,top)),composition(top,composition(top,zero))) )],[refute_1_1798,refute_1_1832]) ).
cnf(refute_1_1834,plain,
complement(composition(zero,composition(top,top))) = complement(composition(zero,composition(top,top))),
introduced(tautology,[refl,[$fot(complement(composition(zero,composition(top,top))))]]) ).
cnf(refute_1_1835,plain,
( complement(composition(zero,composition(top,top))) != complement(composition(zero,composition(top,top)))
| composition(zero,composition(top,top)) != composition(top,composition(top,zero))
| complement(composition(zero,composition(top,top))) = complement(composition(top,composition(top,zero))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(composition(zero,composition(top,top))),complement(composition(zero,composition(top,top)))) ),[1,0],$fot(composition(top,composition(top,zero)))]]) ).
cnf(refute_1_1836,plain,
( composition(zero,composition(top,top)) != composition(top,composition(top,zero))
| complement(composition(zero,composition(top,top))) = complement(composition(top,composition(top,zero))) ),
inference(resolve,[$cnf( $equal(complement(composition(zero,composition(top,top))),complement(composition(zero,composition(top,top)))) )],[refute_1_1834,refute_1_1835]) ).
cnf(refute_1_1837,plain,
complement(composition(zero,composition(top,top))) = complement(composition(top,composition(top,zero))),
inference(resolve,[$cnf( $equal(composition(zero,composition(top,top)),composition(top,composition(top,zero))) )],[refute_1_1833,refute_1_1836]) ).
cnf(refute_1_1838,plain,
composition(complement(composition(zero,composition(top,top))),top) = composition(complement(composition(zero,composition(top,top))),top),
introduced(tautology,[refl,[$fot(composition(complement(composition(zero,composition(top,top))),top))]]) ).
cnf(refute_1_1839,plain,
( complement(composition(zero,composition(top,top))) != complement(composition(top,composition(top,zero)))
| composition(complement(composition(zero,composition(top,top))),top) != composition(complement(composition(zero,composition(top,top))),top)
| composition(complement(composition(zero,composition(top,top))),top) = composition(complement(composition(top,composition(top,zero))),top) ),
introduced(tautology,[equality,[$cnf( $equal(composition(complement(composition(zero,composition(top,top))),top),composition(complement(composition(zero,composition(top,top))),top)) ),[1,0],$fot(complement(composition(top,composition(top,zero))))]]) ).
cnf(refute_1_1840,plain,
( complement(composition(zero,composition(top,top))) != complement(composition(top,composition(top,zero)))
| composition(complement(composition(zero,composition(top,top))),top) = composition(complement(composition(top,composition(top,zero))),top) ),
inference(resolve,[$cnf( $equal(composition(complement(composition(zero,composition(top,top))),top),composition(complement(composition(zero,composition(top,top))),top)) )],[refute_1_1838,refute_1_1839]) ).
cnf(refute_1_1841,plain,
composition(complement(composition(zero,composition(top,top))),top) = composition(complement(composition(top,composition(top,zero))),top),
inference(resolve,[$cnf( $equal(complement(composition(zero,composition(top,top))),complement(composition(top,composition(top,zero)))) )],[refute_1_1837,refute_1_1840]) ).
cnf(refute_1_1842,plain,
composition(zero,composition(complement(composition(zero,composition(top,top))),top)) = composition(zero,composition(complement(composition(zero,composition(top,top))),top)),
introduced(tautology,[refl,[$fot(composition(zero,composition(complement(composition(zero,composition(top,top))),top)))]]) ).
cnf(refute_1_1843,plain,
( composition(complement(composition(zero,composition(top,top))),top) != composition(complement(composition(top,composition(top,zero))),top)
| composition(zero,composition(complement(composition(zero,composition(top,top))),top)) != composition(zero,composition(complement(composition(zero,composition(top,top))),top))
| composition(zero,composition(complement(composition(zero,composition(top,top))),top)) = composition(zero,composition(complement(composition(top,composition(top,zero))),top)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(zero,composition(complement(composition(zero,composition(top,top))),top)),composition(zero,composition(complement(composition(zero,composition(top,top))),top))) ),[1,1],$fot(composition(complement(composition(top,composition(top,zero))),top))]]) ).
cnf(refute_1_1844,plain,
( composition(complement(composition(zero,composition(top,top))),top) != composition(complement(composition(top,composition(top,zero))),top)
| composition(zero,composition(complement(composition(zero,composition(top,top))),top)) = composition(zero,composition(complement(composition(top,composition(top,zero))),top)) ),
inference(resolve,[$cnf( $equal(composition(zero,composition(complement(composition(zero,composition(top,top))),top)),composition(zero,composition(complement(composition(zero,composition(top,top))),top))) )],[refute_1_1842,refute_1_1843]) ).
cnf(refute_1_1845,plain,
composition(zero,composition(complement(composition(zero,composition(top,top))),top)) = composition(zero,composition(complement(composition(top,composition(top,zero))),top)),
inference(resolve,[$cnf( $equal(composition(complement(composition(zero,composition(top,top))),top),composition(complement(composition(top,composition(top,zero))),top)) )],[refute_1_1841,refute_1_1844]) ).
cnf(refute_1_1846,plain,
( composition(zero,composition(complement(composition(zero,composition(top,top))),top)) != composition(zero,composition(complement(composition(top,composition(top,zero))),top))
| composition(zero,composition(complement(composition(zero,composition(top,top))),top)) != zero
| composition(zero,composition(complement(composition(top,composition(top,zero))),top)) = zero ),
introduced(tautology,[equality,[$cnf( $equal(composition(zero,composition(complement(composition(zero,composition(top,top))),top)),zero) ),[0],$fot(composition(zero,composition(complement(composition(top,composition(top,zero))),top)))]]) ).
cnf(refute_1_1847,plain,
( composition(zero,composition(complement(composition(zero,composition(top,top))),top)) != zero
| composition(zero,composition(complement(composition(top,composition(top,zero))),top)) = zero ),
inference(resolve,[$cnf( $equal(composition(zero,composition(complement(composition(zero,composition(top,top))),top)),composition(zero,composition(complement(composition(top,composition(top,zero))),top))) )],[refute_1_1845,refute_1_1846]) ).
cnf(refute_1_1848,plain,
composition(zero,composition(complement(composition(top,composition(top,zero))),top)) = zero,
inference(resolve,[$cnf( $equal(composition(zero,composition(complement(composition(zero,composition(top,top))),top)),zero) )],[refute_1_1794,refute_1_1847]) ).
cnf(refute_1_1849,plain,
composition(zero,composition(composition(top,complement(composition(top,composition(zero,top)))),X2)) = composition(composition(zero,composition(top,complement(composition(top,composition(zero,top))))),X2),
inference(subst,[],[refute_1_1524:[bind(X0,$fot(zero)),bind(X1,$fot(composition(top,complement(composition(top,composition(zero,top))))))]]) ).
cnf(refute_1_1850,plain,
composition(converse(composition(top,zero)),complement(composition(composition(top,zero),top))) = zero,
inference(subst,[],[refute_1_675:[bind(X0,$fot(composition(top,zero)))]]) ).
cnf(refute_1_1851,plain,
( composition(converse(composition(top,zero)),complement(composition(composition(top,zero),top))) != zero
| converse(composition(top,zero)) != composition(zero,top)
| composition(composition(zero,top),complement(composition(composition(top,zero),top))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(composition(top,zero)),complement(composition(composition(top,zero),top))),zero) ),[0,0],$fot(composition(zero,top))]]) ).
cnf(refute_1_1852,plain,
( composition(converse(composition(top,zero)),complement(composition(composition(top,zero),top))) != zero
| composition(composition(zero,top),complement(composition(composition(top,zero),top))) = zero ),
inference(resolve,[$cnf( $equal(converse(composition(top,zero)),composition(zero,top)) )],[refute_1_1374,refute_1_1851]) ).
cnf(refute_1_1853,plain,
composition(composition(zero,top),complement(composition(composition(top,zero),top))) = zero,
inference(resolve,[$cnf( $equal(composition(converse(composition(top,zero)),complement(composition(composition(top,zero),top))),zero) )],[refute_1_1850,refute_1_1852]) ).
cnf(refute_1_1854,plain,
composition(composition(top,zero),top) = composition(top,composition(zero,top)),
inference(subst,[],[refute_1_1731:[bind(X0,$fot(top)),bind(X1,$fot(zero)),bind(X2,$fot(top))]]) ).
cnf(refute_1_1855,plain,
complement(composition(composition(top,zero),top)) = complement(composition(composition(top,zero),top)),
introduced(tautology,[refl,[$fot(complement(composition(composition(top,zero),top)))]]) ).
cnf(refute_1_1856,plain,
( complement(composition(composition(top,zero),top)) != complement(composition(composition(top,zero),top))
| composition(composition(top,zero),top) != composition(top,composition(zero,top))
| complement(composition(composition(top,zero),top)) = complement(composition(top,composition(zero,top))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(composition(composition(top,zero),top)),complement(composition(composition(top,zero),top))) ),[1,0],$fot(composition(top,composition(zero,top)))]]) ).
cnf(refute_1_1857,plain,
( composition(composition(top,zero),top) != composition(top,composition(zero,top))
| complement(composition(composition(top,zero),top)) = complement(composition(top,composition(zero,top))) ),
inference(resolve,[$cnf( $equal(complement(composition(composition(top,zero),top)),complement(composition(composition(top,zero),top))) )],[refute_1_1855,refute_1_1856]) ).
cnf(refute_1_1858,plain,
complement(composition(composition(top,zero),top)) = complement(composition(top,composition(zero,top))),
inference(resolve,[$cnf( $equal(composition(composition(top,zero),top),composition(top,composition(zero,top))) )],[refute_1_1854,refute_1_1857]) ).
cnf(refute_1_1859,plain,
composition(top,complement(composition(composition(top,zero),top))) = composition(top,complement(composition(composition(top,zero),top))),
introduced(tautology,[refl,[$fot(composition(top,complement(composition(composition(top,zero),top))))]]) ).
cnf(refute_1_1860,plain,
( complement(composition(composition(top,zero),top)) != complement(composition(top,composition(zero,top)))
| composition(top,complement(composition(composition(top,zero),top))) != composition(top,complement(composition(composition(top,zero),top)))
| composition(top,complement(composition(composition(top,zero),top))) = composition(top,complement(composition(top,composition(zero,top)))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(top,complement(composition(composition(top,zero),top))),composition(top,complement(composition(composition(top,zero),top)))) ),[1,1],$fot(complement(composition(top,composition(zero,top))))]]) ).
cnf(refute_1_1861,plain,
( complement(composition(composition(top,zero),top)) != complement(composition(top,composition(zero,top)))
| composition(top,complement(composition(composition(top,zero),top))) = composition(top,complement(composition(top,composition(zero,top)))) ),
inference(resolve,[$cnf( $equal(composition(top,complement(composition(composition(top,zero),top))),composition(top,complement(composition(composition(top,zero),top)))) )],[refute_1_1859,refute_1_1860]) ).
cnf(refute_1_1862,plain,
composition(top,complement(composition(composition(top,zero),top))) = composition(top,complement(composition(top,composition(zero,top)))),
inference(resolve,[$cnf( $equal(complement(composition(composition(top,zero),top)),complement(composition(top,composition(zero,top)))) )],[refute_1_1858,refute_1_1861]) ).
cnf(refute_1_1863,plain,
composition(zero,composition(top,complement(composition(composition(top,zero),top)))) = composition(zero,composition(top,complement(composition(composition(top,zero),top)))),
introduced(tautology,[refl,[$fot(composition(zero,composition(top,complement(composition(composition(top,zero),top)))))]]) ).
cnf(refute_1_1864,plain,
( composition(top,complement(composition(composition(top,zero),top))) != composition(top,complement(composition(top,composition(zero,top))))
| composition(zero,composition(top,complement(composition(composition(top,zero),top)))) != composition(zero,composition(top,complement(composition(composition(top,zero),top))))
| composition(zero,composition(top,complement(composition(composition(top,zero),top)))) = composition(zero,composition(top,complement(composition(top,composition(zero,top))))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(zero,composition(top,complement(composition(composition(top,zero),top)))),composition(zero,composition(top,complement(composition(composition(top,zero),top))))) ),[1,1],$fot(composition(top,complement(composition(top,composition(zero,top)))))]]) ).
cnf(refute_1_1865,plain,
( composition(top,complement(composition(composition(top,zero),top))) != composition(top,complement(composition(top,composition(zero,top))))
| composition(zero,composition(top,complement(composition(composition(top,zero),top)))) = composition(zero,composition(top,complement(composition(top,composition(zero,top))))) ),
inference(resolve,[$cnf( $equal(composition(zero,composition(top,complement(composition(composition(top,zero),top)))),composition(zero,composition(top,complement(composition(composition(top,zero),top))))) )],[refute_1_1863,refute_1_1864]) ).
cnf(refute_1_1866,plain,
composition(zero,composition(top,complement(composition(composition(top,zero),top)))) = composition(zero,composition(top,complement(composition(top,composition(zero,top))))),
inference(resolve,[$cnf( $equal(composition(top,complement(composition(composition(top,zero),top))),composition(top,complement(composition(top,composition(zero,top))))) )],[refute_1_1862,refute_1_1865]) ).
cnf(refute_1_1867,plain,
composition(composition(zero,top),complement(composition(composition(top,zero),top))) = composition(zero,composition(top,complement(composition(composition(top,zero),top)))),
inference(subst,[],[refute_1_1731:[bind(X0,$fot(zero)),bind(X1,$fot(top)),bind(X2,$fot(complement(composition(composition(top,zero),top))))]]) ).
cnf(refute_1_1868,plain,
( composition(composition(zero,top),complement(composition(composition(top,zero),top))) != composition(zero,composition(top,complement(composition(composition(top,zero),top))))
| composition(zero,composition(top,complement(composition(composition(top,zero),top)))) != composition(zero,composition(top,complement(composition(top,composition(zero,top)))))
| composition(composition(zero,top),complement(composition(composition(top,zero),top))) = composition(zero,composition(top,complement(composition(top,composition(zero,top))))) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(composition(composition(zero,top),complement(composition(composition(top,zero),top))))),bind(Y,$fot(composition(zero,composition(top,complement(composition(composition(top,zero),top)))))),bind(Z,$fot(composition(zero,composition(top,complement(composition(top,composition(zero,top)))))))]]) ).
cnf(refute_1_1869,plain,
( composition(zero,composition(top,complement(composition(composition(top,zero),top)))) != composition(zero,composition(top,complement(composition(top,composition(zero,top)))))
| composition(composition(zero,top),complement(composition(composition(top,zero),top))) = composition(zero,composition(top,complement(composition(top,composition(zero,top))))) ),
inference(resolve,[$cnf( $equal(composition(composition(zero,top),complement(composition(composition(top,zero),top))),composition(zero,composition(top,complement(composition(composition(top,zero),top))))) )],[refute_1_1867,refute_1_1868]) ).
cnf(refute_1_1870,plain,
composition(composition(zero,top),complement(composition(composition(top,zero),top))) = composition(zero,composition(top,complement(composition(top,composition(zero,top))))),
inference(resolve,[$cnf( $equal(composition(zero,composition(top,complement(composition(composition(top,zero),top)))),composition(zero,composition(top,complement(composition(top,composition(zero,top)))))) )],[refute_1_1866,refute_1_1869]) ).
cnf(refute_1_1871,plain,
( composition(composition(zero,top),complement(composition(composition(top,zero),top))) != composition(zero,composition(top,complement(composition(top,composition(zero,top)))))
| composition(composition(zero,top),complement(composition(composition(top,zero),top))) != zero
| composition(zero,composition(top,complement(composition(top,composition(zero,top))))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(composition(composition(zero,top),complement(composition(composition(top,zero),top))),zero) ),[0],$fot(composition(zero,composition(top,complement(composition(top,composition(zero,top))))))]]) ).
cnf(refute_1_1872,plain,
( composition(composition(zero,top),complement(composition(composition(top,zero),top))) != zero
| composition(zero,composition(top,complement(composition(top,composition(zero,top))))) = zero ),
inference(resolve,[$cnf( $equal(composition(composition(zero,top),complement(composition(composition(top,zero),top))),composition(zero,composition(top,complement(composition(top,composition(zero,top)))))) )],[refute_1_1870,refute_1_1871]) ).
cnf(refute_1_1873,plain,
composition(zero,composition(top,complement(composition(top,composition(zero,top))))) = zero,
inference(resolve,[$cnf( $equal(composition(composition(zero,top),complement(composition(composition(top,zero),top))),zero) )],[refute_1_1853,refute_1_1872]) ).
cnf(refute_1_1874,plain,
( composition(zero,composition(composition(top,complement(composition(top,composition(zero,top)))),X2)) != composition(composition(zero,composition(top,complement(composition(top,composition(zero,top))))),X2)
| composition(zero,composition(top,complement(composition(top,composition(zero,top))))) != zero
| composition(zero,composition(composition(top,complement(composition(top,composition(zero,top)))),X2)) = composition(zero,X2) ),
introduced(tautology,[equality,[$cnf( $equal(composition(zero,composition(composition(top,complement(composition(top,composition(zero,top)))),X2)),composition(composition(zero,composition(top,complement(composition(top,composition(zero,top))))),X2)) ),[1,0],$fot(zero)]]) ).
cnf(refute_1_1875,plain,
( composition(zero,composition(composition(top,complement(composition(top,composition(zero,top)))),X2)) != composition(composition(zero,composition(top,complement(composition(top,composition(zero,top))))),X2)
| composition(zero,composition(composition(top,complement(composition(top,composition(zero,top)))),X2)) = composition(zero,X2) ),
inference(resolve,[$cnf( $equal(composition(zero,composition(top,complement(composition(top,composition(zero,top))))),zero) )],[refute_1_1873,refute_1_1874]) ).
cnf(refute_1_1876,plain,
composition(zero,composition(composition(top,complement(composition(top,composition(zero,top)))),X2)) = composition(zero,X2),
inference(resolve,[$cnf( $equal(composition(zero,composition(composition(top,complement(composition(top,composition(zero,top)))),X2)),composition(composition(zero,composition(top,complement(composition(top,composition(zero,top))))),X2)) )],[refute_1_1849,refute_1_1875]) ).
cnf(refute_1_1877,plain,
composition(composition(top,complement(composition(top,composition(zero,top)))),X2) = composition(top,composition(complement(composition(top,composition(zero,top))),X2)),
inference(subst,[],[refute_1_1731:[bind(X0,$fot(top)),bind(X1,$fot(complement(composition(top,composition(zero,top)))))]]) ).
cnf(refute_1_1878,plain,
composition(zero,composition(composition(top,complement(composition(top,composition(zero,top)))),X2)) = composition(zero,composition(composition(top,complement(composition(top,composition(zero,top)))),X2)),
introduced(tautology,[refl,[$fot(composition(zero,composition(composition(top,complement(composition(top,composition(zero,top)))),X2)))]]) ).
cnf(refute_1_1879,plain,
( composition(composition(top,complement(composition(top,composition(zero,top)))),X2) != composition(top,composition(complement(composition(top,composition(zero,top))),X2))
| composition(zero,composition(composition(top,complement(composition(top,composition(zero,top)))),X2)) != composition(zero,composition(composition(top,complement(composition(top,composition(zero,top)))),X2))
| composition(zero,composition(composition(top,complement(composition(top,composition(zero,top)))),X2)) = composition(zero,composition(top,composition(complement(composition(top,composition(zero,top))),X2))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(zero,composition(composition(top,complement(composition(top,composition(zero,top)))),X2)),composition(zero,composition(composition(top,complement(composition(top,composition(zero,top)))),X2))) ),[1,1],$fot(composition(top,composition(complement(composition(top,composition(zero,top))),X2)))]]) ).
cnf(refute_1_1880,plain,
( composition(composition(top,complement(composition(top,composition(zero,top)))),X2) != composition(top,composition(complement(composition(top,composition(zero,top))),X2))
| composition(zero,composition(composition(top,complement(composition(top,composition(zero,top)))),X2)) = composition(zero,composition(top,composition(complement(composition(top,composition(zero,top))),X2))) ),
inference(resolve,[$cnf( $equal(composition(zero,composition(composition(top,complement(composition(top,composition(zero,top)))),X2)),composition(zero,composition(composition(top,complement(composition(top,composition(zero,top)))),X2))) )],[refute_1_1878,refute_1_1879]) ).
cnf(refute_1_1881,plain,
composition(zero,composition(composition(top,complement(composition(top,composition(zero,top)))),X2)) = composition(zero,composition(top,composition(complement(composition(top,composition(zero,top))),X2))),
inference(resolve,[$cnf( $equal(composition(composition(top,complement(composition(top,composition(zero,top)))),X2),composition(top,composition(complement(composition(top,composition(zero,top))),X2))) )],[refute_1_1877,refute_1_1880]) ).
cnf(refute_1_1882,plain,
( composition(zero,composition(composition(top,complement(composition(top,composition(zero,top)))),X2)) != composition(zero,X2)
| composition(zero,composition(composition(top,complement(composition(top,composition(zero,top)))),X2)) != composition(zero,composition(top,composition(complement(composition(top,composition(zero,top))),X2)))
| composition(zero,composition(top,composition(complement(composition(top,composition(zero,top))),X2))) = composition(zero,X2) ),
introduced(tautology,[equality,[$cnf( $equal(composition(zero,composition(composition(top,complement(composition(top,composition(zero,top)))),X2)),composition(zero,X2)) ),[0],$fot(composition(zero,composition(top,composition(complement(composition(top,composition(zero,top))),X2))))]]) ).
cnf(refute_1_1883,plain,
( composition(zero,composition(composition(top,complement(composition(top,composition(zero,top)))),X2)) != composition(zero,X2)
| composition(zero,composition(top,composition(complement(composition(top,composition(zero,top))),X2))) = composition(zero,X2) ),
inference(resolve,[$cnf( $equal(composition(zero,composition(composition(top,complement(composition(top,composition(zero,top)))),X2)),composition(zero,composition(top,composition(complement(composition(top,composition(zero,top))),X2)))) )],[refute_1_1881,refute_1_1882]) ).
cnf(refute_1_1884,plain,
composition(zero,composition(top,composition(complement(composition(top,composition(zero,top))),X2))) = composition(zero,X2),
inference(resolve,[$cnf( $equal(composition(zero,composition(composition(top,complement(composition(top,composition(zero,top)))),X2)),composition(zero,X2)) )],[refute_1_1876,refute_1_1883]) ).
cnf(refute_1_1885,plain,
complement(composition(top,composition(zero,top))) = complement(composition(top,composition(zero,top))),
introduced(tautology,[refl,[$fot(complement(composition(top,composition(zero,top))))]]) ).
cnf(refute_1_1886,plain,
( complement(composition(top,composition(zero,top))) != complement(composition(top,composition(zero,top)))
| composition(top,composition(zero,top)) != composition(top,composition(top,zero))
| complement(composition(top,composition(zero,top))) = complement(composition(top,composition(top,zero))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(composition(top,composition(zero,top))),complement(composition(top,composition(zero,top)))) ),[1,0],$fot(composition(top,composition(top,zero)))]]) ).
cnf(refute_1_1887,plain,
( composition(top,composition(zero,top)) != composition(top,composition(top,zero))
| complement(composition(top,composition(zero,top))) = complement(composition(top,composition(top,zero))) ),
inference(resolve,[$cnf( $equal(complement(composition(top,composition(zero,top))),complement(composition(top,composition(zero,top)))) )],[refute_1_1885,refute_1_1886]) ).
cnf(refute_1_1888,plain,
complement(composition(top,composition(zero,top))) = complement(composition(top,composition(top,zero))),
inference(resolve,[$cnf( $equal(composition(top,composition(zero,top)),composition(top,composition(top,zero))) )],[refute_1_1798,refute_1_1887]) ).
cnf(refute_1_1889,plain,
composition(complement(composition(top,composition(zero,top))),X2) = composition(complement(composition(top,composition(zero,top))),X2),
introduced(tautology,[refl,[$fot(composition(complement(composition(top,composition(zero,top))),X2))]]) ).
cnf(refute_1_1890,plain,
( complement(composition(top,composition(zero,top))) != complement(composition(top,composition(top,zero)))
| composition(complement(composition(top,composition(zero,top))),X2) != composition(complement(composition(top,composition(zero,top))),X2)
| composition(complement(composition(top,composition(zero,top))),X2) = composition(complement(composition(top,composition(top,zero))),X2) ),
introduced(tautology,[equality,[$cnf( $equal(composition(complement(composition(top,composition(zero,top))),X2),composition(complement(composition(top,composition(zero,top))),X2)) ),[1,0],$fot(complement(composition(top,composition(top,zero))))]]) ).
cnf(refute_1_1891,plain,
( complement(composition(top,composition(zero,top))) != complement(composition(top,composition(top,zero)))
| composition(complement(composition(top,composition(zero,top))),X2) = composition(complement(composition(top,composition(top,zero))),X2) ),
inference(resolve,[$cnf( $equal(composition(complement(composition(top,composition(zero,top))),X2),composition(complement(composition(top,composition(zero,top))),X2)) )],[refute_1_1889,refute_1_1890]) ).
cnf(refute_1_1892,plain,
composition(complement(composition(top,composition(zero,top))),X2) = composition(complement(composition(top,composition(top,zero))),X2),
inference(resolve,[$cnf( $equal(complement(composition(top,composition(zero,top))),complement(composition(top,composition(top,zero)))) )],[refute_1_1888,refute_1_1891]) ).
cnf(refute_1_1893,plain,
composition(top,composition(complement(composition(top,composition(zero,top))),X2)) = composition(top,composition(complement(composition(top,composition(zero,top))),X2)),
introduced(tautology,[refl,[$fot(composition(top,composition(complement(composition(top,composition(zero,top))),X2)))]]) ).
cnf(refute_1_1894,plain,
( composition(complement(composition(top,composition(zero,top))),X2) != composition(complement(composition(top,composition(top,zero))),X2)
| composition(top,composition(complement(composition(top,composition(zero,top))),X2)) != composition(top,composition(complement(composition(top,composition(zero,top))),X2))
| composition(top,composition(complement(composition(top,composition(zero,top))),X2)) = composition(top,composition(complement(composition(top,composition(top,zero))),X2)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(top,composition(complement(composition(top,composition(zero,top))),X2)),composition(top,composition(complement(composition(top,composition(zero,top))),X2))) ),[1,1],$fot(composition(complement(composition(top,composition(top,zero))),X2))]]) ).
cnf(refute_1_1895,plain,
( composition(complement(composition(top,composition(zero,top))),X2) != composition(complement(composition(top,composition(top,zero))),X2)
| composition(top,composition(complement(composition(top,composition(zero,top))),X2)) = composition(top,composition(complement(composition(top,composition(top,zero))),X2)) ),
inference(resolve,[$cnf( $equal(composition(top,composition(complement(composition(top,composition(zero,top))),X2)),composition(top,composition(complement(composition(top,composition(zero,top))),X2))) )],[refute_1_1893,refute_1_1894]) ).
cnf(refute_1_1896,plain,
composition(top,composition(complement(composition(top,composition(zero,top))),X2)) = composition(top,composition(complement(composition(top,composition(top,zero))),X2)),
inference(resolve,[$cnf( $equal(composition(complement(composition(top,composition(zero,top))),X2),composition(complement(composition(top,composition(top,zero))),X2)) )],[refute_1_1892,refute_1_1895]) ).
cnf(refute_1_1897,plain,
composition(zero,composition(top,composition(complement(composition(top,composition(zero,top))),X2))) = composition(zero,composition(top,composition(complement(composition(top,composition(zero,top))),X2))),
introduced(tautology,[refl,[$fot(composition(zero,composition(top,composition(complement(composition(top,composition(zero,top))),X2))))]]) ).
cnf(refute_1_1898,plain,
( composition(top,composition(complement(composition(top,composition(zero,top))),X2)) != composition(top,composition(complement(composition(top,composition(top,zero))),X2))
| composition(zero,composition(top,composition(complement(composition(top,composition(zero,top))),X2))) != composition(zero,composition(top,composition(complement(composition(top,composition(zero,top))),X2)))
| composition(zero,composition(top,composition(complement(composition(top,composition(zero,top))),X2))) = composition(zero,composition(top,composition(complement(composition(top,composition(top,zero))),X2))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(zero,composition(top,composition(complement(composition(top,composition(zero,top))),X2))),composition(zero,composition(top,composition(complement(composition(top,composition(zero,top))),X2)))) ),[1,1],$fot(composition(top,composition(complement(composition(top,composition(top,zero))),X2)))]]) ).
cnf(refute_1_1899,plain,
( composition(top,composition(complement(composition(top,composition(zero,top))),X2)) != composition(top,composition(complement(composition(top,composition(top,zero))),X2))
| composition(zero,composition(top,composition(complement(composition(top,composition(zero,top))),X2))) = composition(zero,composition(top,composition(complement(composition(top,composition(top,zero))),X2))) ),
inference(resolve,[$cnf( $equal(composition(zero,composition(top,composition(complement(composition(top,composition(zero,top))),X2))),composition(zero,composition(top,composition(complement(composition(top,composition(zero,top))),X2)))) )],[refute_1_1897,refute_1_1898]) ).
cnf(refute_1_1900,plain,
composition(zero,composition(top,composition(complement(composition(top,composition(zero,top))),X2))) = composition(zero,composition(top,composition(complement(composition(top,composition(top,zero))),X2))),
inference(resolve,[$cnf( $equal(composition(top,composition(complement(composition(top,composition(zero,top))),X2)),composition(top,composition(complement(composition(top,composition(top,zero))),X2))) )],[refute_1_1896,refute_1_1899]) ).
cnf(refute_1_1901,plain,
( composition(zero,composition(top,composition(complement(composition(top,composition(zero,top))),X2))) != composition(zero,X2)
| composition(zero,composition(top,composition(complement(composition(top,composition(zero,top))),X2))) != composition(zero,composition(top,composition(complement(composition(top,composition(top,zero))),X2)))
| composition(zero,composition(top,composition(complement(composition(top,composition(top,zero))),X2))) = composition(zero,X2) ),
introduced(tautology,[equality,[$cnf( $equal(composition(zero,composition(top,composition(complement(composition(top,composition(zero,top))),X2))),composition(zero,X2)) ),[0],$fot(composition(zero,composition(top,composition(complement(composition(top,composition(top,zero))),X2))))]]) ).
cnf(refute_1_1902,plain,
( composition(zero,composition(top,composition(complement(composition(top,composition(zero,top))),X2))) != composition(zero,X2)
| composition(zero,composition(top,composition(complement(composition(top,composition(top,zero))),X2))) = composition(zero,X2) ),
inference(resolve,[$cnf( $equal(composition(zero,composition(top,composition(complement(composition(top,composition(zero,top))),X2))),composition(zero,composition(top,composition(complement(composition(top,composition(top,zero))),X2)))) )],[refute_1_1900,refute_1_1901]) ).
cnf(refute_1_1903,plain,
composition(zero,composition(top,composition(complement(composition(top,composition(top,zero))),X2))) = composition(zero,X2),
inference(resolve,[$cnf( $equal(composition(zero,composition(top,composition(complement(composition(top,composition(zero,top))),X2))),composition(zero,X2)) )],[refute_1_1884,refute_1_1902]) ).
cnf(refute_1_1904,plain,
composition(zero,composition(top,composition(complement(composition(top,composition(top,zero))),X2))) = composition(top,composition(zero,composition(complement(composition(top,composition(top,zero))),X2))),
inference(subst,[],[refute_1_1829:[bind(X0,$fot(composition(complement(composition(top,composition(top,zero))),X2)))]]) ).
cnf(refute_1_1905,plain,
( composition(zero,composition(top,composition(complement(composition(top,composition(top,zero))),X2))) != composition(top,composition(zero,composition(complement(composition(top,composition(top,zero))),X2)))
| composition(zero,composition(top,composition(complement(composition(top,composition(top,zero))),X2))) != composition(zero,X2)
| composition(top,composition(zero,composition(complement(composition(top,composition(top,zero))),X2))) = composition(zero,X2) ),
introduced(tautology,[equality,[$cnf( $equal(composition(zero,composition(top,composition(complement(composition(top,composition(top,zero))),X2))),composition(zero,X2)) ),[0],$fot(composition(top,composition(zero,composition(complement(composition(top,composition(top,zero))),X2))))]]) ).
cnf(refute_1_1906,plain,
( composition(zero,composition(top,composition(complement(composition(top,composition(top,zero))),X2))) != composition(zero,X2)
| composition(top,composition(zero,composition(complement(composition(top,composition(top,zero))),X2))) = composition(zero,X2) ),
inference(resolve,[$cnf( $equal(composition(zero,composition(top,composition(complement(composition(top,composition(top,zero))),X2))),composition(top,composition(zero,composition(complement(composition(top,composition(top,zero))),X2)))) )],[refute_1_1904,refute_1_1905]) ).
cnf(refute_1_1907,plain,
composition(top,composition(zero,composition(complement(composition(top,composition(top,zero))),X2))) = composition(zero,X2),
inference(resolve,[$cnf( $equal(composition(zero,composition(top,composition(complement(composition(top,composition(top,zero))),X2))),composition(zero,X2)) )],[refute_1_1903,refute_1_1906]) ).
cnf(refute_1_1908,plain,
composition(converse(zero),composition(converse(skolemFOFtoCNF_X0_1),X_284)) = composition(converse(composition(skolemFOFtoCNF_X0_1,zero)),X_284),
inference(subst,[],[refute_1_1530:[bind(X0,$fot(skolemFOFtoCNF_X0_1)),bind(X1,$fot(zero)),bind(X_124,$fot(X_284))]]) ).
cnf(refute_1_1909,plain,
( composition(converse(zero),composition(converse(skolemFOFtoCNF_X0_1),X_284)) != composition(converse(composition(skolemFOFtoCNF_X0_1,zero)),X_284)
| composition(skolemFOFtoCNF_X0_1,zero) != zero
| composition(converse(zero),composition(converse(skolemFOFtoCNF_X0_1),X_284)) = composition(converse(zero),X_284) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(zero),composition(converse(skolemFOFtoCNF_X0_1),X_284)),composition(converse(composition(skolemFOFtoCNF_X0_1,zero)),X_284)) ),[1,0,0],$fot(zero)]]) ).
cnf(refute_1_1910,plain,
( composition(converse(zero),composition(converse(skolemFOFtoCNF_X0_1),X_284)) != composition(converse(composition(skolemFOFtoCNF_X0_1,zero)),X_284)
| composition(converse(zero),composition(converse(skolemFOFtoCNF_X0_1),X_284)) = composition(converse(zero),X_284) ),
inference(resolve,[$cnf( $equal(composition(skolemFOFtoCNF_X0_1,zero),zero) )],[refute_1_1558,refute_1_1909]) ).
cnf(refute_1_1911,plain,
composition(converse(zero),composition(converse(skolemFOFtoCNF_X0_1),X_284)) = composition(converse(zero),X_284),
inference(resolve,[$cnf( $equal(composition(converse(zero),composition(converse(skolemFOFtoCNF_X0_1),X_284)),composition(converse(composition(skolemFOFtoCNF_X0_1,zero)),X_284)) )],[refute_1_1908,refute_1_1910]) ).
cnf(refute_1_1912,plain,
composition(zero,composition(converse(X_264),X2)) = composition(composition(zero,converse(X_264)),X2),
inference(subst,[],[refute_1_1524:[bind(X0,$fot(zero)),bind(X1,$fot(converse(X_264)))]]) ).
cnf(refute_1_1913,plain,
converse(composition(X_264,zero)) = composition(zero,converse(X_264)),
inference(subst,[],[refute_1_662:[bind(X_111,$fot(X_264))]]) ).
cnf(refute_1_1914,plain,
( converse(composition(X_264,zero)) != composition(zero,converse(X_264))
| composition(zero,converse(X_264)) = converse(composition(X_264,zero)) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(converse(composition(X_264,zero)))),bind(Y,$fot(composition(zero,converse(X_264))))]]) ).
cnf(refute_1_1915,plain,
composition(zero,converse(X_264)) = converse(composition(X_264,zero)),
inference(resolve,[$cnf( $equal(converse(composition(X_264,zero)),composition(zero,converse(X_264))) )],[refute_1_1913,refute_1_1914]) ).
cnf(refute_1_1916,plain,
( composition(zero,composition(converse(X_264),X2)) != composition(composition(zero,converse(X_264)),X2)
| composition(zero,converse(X_264)) != converse(composition(X_264,zero))
| composition(zero,composition(converse(X_264),X2)) = composition(converse(composition(X_264,zero)),X2) ),
introduced(tautology,[equality,[$cnf( $equal(composition(zero,composition(converse(X_264),X2)),composition(composition(zero,converse(X_264)),X2)) ),[1,0],$fot(converse(composition(X_264,zero)))]]) ).
cnf(refute_1_1917,plain,
( composition(zero,composition(converse(X_264),X2)) != composition(composition(zero,converse(X_264)),X2)
| composition(zero,composition(converse(X_264),X2)) = composition(converse(composition(X_264,zero)),X2) ),
inference(resolve,[$cnf( $equal(composition(zero,converse(X_264)),converse(composition(X_264,zero))) )],[refute_1_1915,refute_1_1916]) ).
cnf(refute_1_1918,plain,
composition(zero,composition(converse(X_264),X2)) = composition(converse(composition(X_264,zero)),X2),
inference(resolve,[$cnf( $equal(composition(zero,composition(converse(X_264),X2)),composition(composition(zero,converse(X_264)),X2)) )],[refute_1_1912,refute_1_1917]) ).
cnf(refute_1_1919,plain,
( composition(zero,composition(converse(X_264),X2)) != composition(converse(composition(X_264,zero)),X2)
| composition(converse(composition(X_264,zero)),X2) = composition(zero,composition(converse(X_264),X2)) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(composition(zero,composition(converse(X_264),X2)))),bind(Y,$fot(composition(converse(composition(X_264,zero)),X2)))]]) ).
cnf(refute_1_1920,plain,
composition(converse(composition(X_264,zero)),X2) = composition(zero,composition(converse(X_264),X2)),
inference(resolve,[$cnf( $equal(composition(zero,composition(converse(X_264),X2)),composition(converse(composition(X_264,zero)),X2)) )],[refute_1_1918,refute_1_1919]) ).
cnf(refute_1_1921,plain,
composition(converse(composition(skolemFOFtoCNF_X0_1,zero)),X_284) = composition(zero,composition(converse(skolemFOFtoCNF_X0_1),X_284)),
inference(subst,[],[refute_1_1920:[bind(X2,$fot(X_284)),bind(X_264,$fot(skolemFOFtoCNF_X0_1))]]) ).
cnf(refute_1_1922,plain,
( composition(converse(composition(skolemFOFtoCNF_X0_1,zero)),X_284) != composition(zero,composition(converse(skolemFOFtoCNF_X0_1),X_284))
| composition(converse(zero),composition(converse(skolemFOFtoCNF_X0_1),X_284)) != composition(converse(composition(skolemFOFtoCNF_X0_1,zero)),X_284)
| composition(converse(zero),composition(converse(skolemFOFtoCNF_X0_1),X_284)) = composition(zero,composition(converse(skolemFOFtoCNF_X0_1),X_284)) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(composition(converse(zero),composition(converse(skolemFOFtoCNF_X0_1),X_284)))),bind(Y,$fot(composition(converse(composition(skolemFOFtoCNF_X0_1,zero)),X_284))),bind(Z,$fot(composition(zero,composition(converse(skolemFOFtoCNF_X0_1),X_284))))]]) ).
cnf(refute_1_1923,plain,
( composition(converse(composition(skolemFOFtoCNF_X0_1,zero)),X_284) != composition(zero,composition(converse(skolemFOFtoCNF_X0_1),X_284))
| composition(converse(zero),composition(converse(skolemFOFtoCNF_X0_1),X_284)) = composition(zero,composition(converse(skolemFOFtoCNF_X0_1),X_284)) ),
inference(resolve,[$cnf( $equal(composition(converse(zero),composition(converse(skolemFOFtoCNF_X0_1),X_284)),composition(converse(composition(skolemFOFtoCNF_X0_1,zero)),X_284)) )],[refute_1_1908,refute_1_1922]) ).
cnf(refute_1_1924,plain,
composition(converse(zero),composition(converse(skolemFOFtoCNF_X0_1),X_284)) = composition(zero,composition(converse(skolemFOFtoCNF_X0_1),X_284)),
inference(resolve,[$cnf( $equal(composition(converse(composition(skolemFOFtoCNF_X0_1,zero)),X_284),composition(zero,composition(converse(skolemFOFtoCNF_X0_1),X_284))) )],[refute_1_1921,refute_1_1923]) ).
cnf(refute_1_1925,plain,
( composition(converse(zero),composition(converse(skolemFOFtoCNF_X0_1),X_284)) != composition(converse(zero),X_284)
| composition(converse(zero),composition(converse(skolemFOFtoCNF_X0_1),X_284)) != composition(zero,composition(converse(skolemFOFtoCNF_X0_1),X_284))
| composition(zero,composition(converse(skolemFOFtoCNF_X0_1),X_284)) = composition(converse(zero),X_284) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(zero),composition(converse(skolemFOFtoCNF_X0_1),X_284)),composition(converse(zero),X_284)) ),[0],$fot(composition(zero,composition(converse(skolemFOFtoCNF_X0_1),X_284)))]]) ).
cnf(refute_1_1926,plain,
( composition(converse(zero),composition(converse(skolemFOFtoCNF_X0_1),X_284)) != composition(converse(zero),X_284)
| composition(zero,composition(converse(skolemFOFtoCNF_X0_1),X_284)) = composition(converse(zero),X_284) ),
inference(resolve,[$cnf( $equal(composition(converse(zero),composition(converse(skolemFOFtoCNF_X0_1),X_284)),composition(zero,composition(converse(skolemFOFtoCNF_X0_1),X_284))) )],[refute_1_1924,refute_1_1925]) ).
cnf(refute_1_1927,plain,
( composition(converse(zero),X_284) != composition(zero,X_284)
| composition(zero,composition(converse(skolemFOFtoCNF_X0_1),X_284)) != composition(converse(zero),X_284)
| composition(zero,composition(converse(skolemFOFtoCNF_X0_1),X_284)) = composition(zero,X_284) ),
introduced(tautology,[equality,[$cnf( $equal(composition(zero,composition(converse(skolemFOFtoCNF_X0_1),X_284)),composition(converse(zero),X_284)) ),[1],$fot(composition(zero,X_284))]]) ).
cnf(refute_1_1928,plain,
( composition(zero,composition(converse(skolemFOFtoCNF_X0_1),X_284)) != composition(converse(zero),X_284)
| composition(zero,composition(converse(skolemFOFtoCNF_X0_1),X_284)) = composition(zero,X_284) ),
inference(resolve,[$cnf( $equal(composition(converse(zero),X_284),composition(zero,X_284)) )],[refute_1_1653,refute_1_1927]) ).
cnf(refute_1_1929,plain,
( composition(converse(zero),composition(converse(skolemFOFtoCNF_X0_1),X_284)) != composition(converse(zero),X_284)
| composition(zero,composition(converse(skolemFOFtoCNF_X0_1),X_284)) = composition(zero,X_284) ),
inference(resolve,[$cnf( $equal(composition(zero,composition(converse(skolemFOFtoCNF_X0_1),X_284)),composition(converse(zero),X_284)) )],[refute_1_1926,refute_1_1928]) ).
cnf(refute_1_1930,plain,
composition(zero,composition(converse(skolemFOFtoCNF_X0_1),X_284)) = composition(zero,X_284),
inference(resolve,[$cnf( $equal(composition(converse(zero),composition(converse(skolemFOFtoCNF_X0_1),X_284)),composition(converse(zero),X_284)) )],[refute_1_1911,refute_1_1929]) ).
cnf(refute_1_1931,plain,
composition(top,composition(converse(complement(composition(top,top))),composition(converse(X0),X_124))) = composition(zero,composition(converse(X0),X_124)),
inference(subst,[],[refute_1_1657:[bind(X_284,$fot(composition(converse(X0),X_124)))]]) ).
cnf(refute_1_1932,plain,
composition(converse(complement(composition(top,top))),composition(converse(X0),X_124)) = composition(converse(composition(X0,complement(composition(top,top)))),X_124),
inference(subst,[],[refute_1_1530:[bind(X1,$fot(complement(composition(top,top))))]]) ).
cnf(refute_1_1933,plain,
( composition(converse(complement(composition(top,top))),composition(converse(X0),X_124)) != composition(converse(composition(X0,complement(composition(top,top)))),X_124)
| composition(top,composition(converse(complement(composition(top,top))),composition(converse(X0),X_124))) != composition(zero,composition(converse(X0),X_124))
| composition(top,composition(converse(composition(X0,complement(composition(top,top)))),X_124)) = composition(zero,composition(converse(X0),X_124)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(top,composition(converse(complement(composition(top,top))),composition(converse(X0),X_124))),composition(zero,composition(converse(X0),X_124))) ),[0,1],$fot(composition(converse(composition(X0,complement(composition(top,top)))),X_124))]]) ).
cnf(refute_1_1934,plain,
( composition(top,composition(converse(complement(composition(top,top))),composition(converse(X0),X_124))) != composition(zero,composition(converse(X0),X_124))
| composition(top,composition(converse(composition(X0,complement(composition(top,top)))),X_124)) = composition(zero,composition(converse(X0),X_124)) ),
inference(resolve,[$cnf( $equal(composition(converse(complement(composition(top,top))),composition(converse(X0),X_124)),composition(converse(composition(X0,complement(composition(top,top)))),X_124)) )],[refute_1_1932,refute_1_1933]) ).
cnf(refute_1_1935,plain,
composition(top,composition(converse(composition(X0,complement(composition(top,top)))),X_124)) = composition(zero,composition(converse(X0),X_124)),
inference(resolve,[$cnf( $equal(composition(top,composition(converse(complement(composition(top,top))),composition(converse(X0),X_124))),composition(zero,composition(converse(X0),X_124))) )],[refute_1_1931,refute_1_1934]) ).
cnf(refute_1_1936,plain,
composition(join(X_316,top),complement(composition(top,top))) = join(composition(X_316,complement(composition(top,top))),composition(top,complement(composition(top,top)))),
inference(subst,[],[refute_1_663:[bind(X0,$fot(X_316)),bind(X1,$fot(top)),bind(X2,$fot(complement(composition(top,top))))]]) ).
cnf(refute_1_1937,plain,
join(zero,composition(converse(top),complement(composition(top,top)))) = zero,
inference(subst,[],[refute_1_671:[bind(X0,$fot(top))]]) ).
cnf(refute_1_1938,plain,
( converse(top) != top
| join(zero,composition(converse(top),complement(composition(top,top)))) != zero
| join(zero,composition(top,complement(composition(top,top)))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,composition(converse(top),complement(composition(top,top)))),zero) ),[0,1,0],$fot(top)]]) ).
cnf(refute_1_1939,plain,
( join(zero,composition(converse(top),complement(composition(top,top)))) != zero
| join(zero,composition(top,complement(composition(top,top)))) = zero ),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_1_191,refute_1_1938]) ).
cnf(refute_1_1940,plain,
join(zero,composition(top,complement(composition(top,top)))) = zero,
inference(resolve,[$cnf( $equal(join(zero,composition(converse(top),complement(composition(top,top)))),zero) )],[refute_1_1937,refute_1_1939]) ).
cnf(refute_1_1941,plain,
join(zero,composition(top,complement(composition(top,top)))) = composition(top,complement(composition(top,top))),
inference(subst,[],[refute_1_580:[bind(X_176,$fot(composition(top,complement(composition(top,top)))))]]) ).
cnf(refute_1_1942,plain,
( join(zero,composition(top,complement(composition(top,top)))) != composition(top,complement(composition(top,top)))
| join(zero,composition(top,complement(composition(top,top)))) != zero
| composition(top,complement(composition(top,top))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,composition(top,complement(composition(top,top)))),zero) ),[0],$fot(composition(top,complement(composition(top,top))))]]) ).
cnf(refute_1_1943,plain,
( join(zero,composition(top,complement(composition(top,top)))) != zero
| composition(top,complement(composition(top,top))) = zero ),
inference(resolve,[$cnf( $equal(join(zero,composition(top,complement(composition(top,top)))),composition(top,complement(composition(top,top)))) )],[refute_1_1941,refute_1_1942]) ).
cnf(refute_1_1944,plain,
composition(top,complement(composition(top,top))) = zero,
inference(resolve,[$cnf( $equal(join(zero,composition(top,complement(composition(top,top)))),zero) )],[refute_1_1940,refute_1_1943]) ).
cnf(refute_1_1945,plain,
( composition(join(X_316,top),complement(composition(top,top))) != join(composition(X_316,complement(composition(top,top))),composition(top,complement(composition(top,top))))
| composition(top,complement(composition(top,top))) != zero
| composition(join(X_316,top),complement(composition(top,top))) = join(composition(X_316,complement(composition(top,top))),zero) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(X_316,top),complement(composition(top,top))),join(composition(X_316,complement(composition(top,top))),composition(top,complement(composition(top,top))))) ),[1,1],$fot(zero)]]) ).
cnf(refute_1_1946,plain,
( composition(join(X_316,top),complement(composition(top,top))) != join(composition(X_316,complement(composition(top,top))),composition(top,complement(composition(top,top))))
| composition(join(X_316,top),complement(composition(top,top))) = join(composition(X_316,complement(composition(top,top))),zero) ),
inference(resolve,[$cnf( $equal(composition(top,complement(composition(top,top))),zero) )],[refute_1_1944,refute_1_1945]) ).
cnf(refute_1_1947,plain,
composition(join(X_316,top),complement(composition(top,top))) = join(composition(X_316,complement(composition(top,top))),zero),
inference(resolve,[$cnf( $equal(composition(join(X_316,top),complement(composition(top,top))),join(composition(X_316,complement(composition(top,top))),composition(top,complement(composition(top,top))))) )],[refute_1_1936,refute_1_1946]) ).
cnf(refute_1_1948,plain,
join(X_316,top) = top,
inference(subst,[],[refute_1_813:[bind(X_169,$fot(X_316))]]) ).
cnf(refute_1_1949,plain,
composition(join(X_316,top),complement(composition(top,top))) = composition(join(X_316,top),complement(composition(top,top))),
introduced(tautology,[refl,[$fot(composition(join(X_316,top),complement(composition(top,top))))]]) ).
cnf(refute_1_1950,plain,
( composition(join(X_316,top),complement(composition(top,top))) != composition(join(X_316,top),complement(composition(top,top)))
| join(X_316,top) != top
| composition(join(X_316,top),complement(composition(top,top))) = composition(top,complement(composition(top,top))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(X_316,top),complement(composition(top,top))),composition(join(X_316,top),complement(composition(top,top)))) ),[1,0],$fot(top)]]) ).
cnf(refute_1_1951,plain,
( join(X_316,top) != top
| composition(join(X_316,top),complement(composition(top,top))) = composition(top,complement(composition(top,top))) ),
inference(resolve,[$cnf( $equal(composition(join(X_316,top),complement(composition(top,top))),composition(join(X_316,top),complement(composition(top,top)))) )],[refute_1_1949,refute_1_1950]) ).
cnf(refute_1_1952,plain,
composition(join(X_316,top),complement(composition(top,top))) = composition(top,complement(composition(top,top))),
inference(resolve,[$cnf( $equal(join(X_316,top),top) )],[refute_1_1948,refute_1_1951]) ).
cnf(refute_1_1953,plain,
( composition(join(X_316,top),complement(composition(top,top))) != composition(top,complement(composition(top,top)))
| composition(top,complement(composition(top,top))) != zero
| composition(join(X_316,top),complement(composition(top,top))) = zero ),
inference(subst,[],[refute_1_37:[bind(X,$fot(composition(join(X_316,top),complement(composition(top,top))))),bind(Y,$fot(composition(top,complement(composition(top,top))))),bind(Z,$fot(zero))]]) ).
cnf(refute_1_1954,plain,
( composition(top,complement(composition(top,top))) != zero
| composition(join(X_316,top),complement(composition(top,top))) = zero ),
inference(resolve,[$cnf( $equal(composition(join(X_316,top),complement(composition(top,top))),composition(top,complement(composition(top,top)))) )],[refute_1_1952,refute_1_1953]) ).
cnf(refute_1_1955,plain,
composition(join(X_316,top),complement(composition(top,top))) = zero,
inference(resolve,[$cnf( $equal(composition(top,complement(composition(top,top))),zero) )],[refute_1_1944,refute_1_1954]) ).
cnf(refute_1_1956,plain,
( composition(join(X_316,top),complement(composition(top,top))) != join(composition(X_316,complement(composition(top,top))),zero)
| composition(join(X_316,top),complement(composition(top,top))) != zero
| zero = join(composition(X_316,complement(composition(top,top))),zero) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(X_316,top),complement(composition(top,top))),join(composition(X_316,complement(composition(top,top))),zero)) ),[0],$fot(zero)]]) ).
cnf(refute_1_1957,plain,
( composition(join(X_316,top),complement(composition(top,top))) != join(composition(X_316,complement(composition(top,top))),zero)
| zero = join(composition(X_316,complement(composition(top,top))),zero) ),
inference(resolve,[$cnf( $equal(composition(join(X_316,top),complement(composition(top,top))),zero) )],[refute_1_1955,refute_1_1956]) ).
cnf(refute_1_1958,plain,
join(zero,composition(X_316,complement(composition(top,top)))) = composition(X_316,complement(composition(top,top))),
inference(subst,[],[refute_1_580:[bind(X_176,$fot(composition(X_316,complement(composition(top,top)))))]]) ).
cnf(refute_1_1959,plain,
join(composition(X_316,complement(composition(top,top))),zero) = join(zero,composition(X_316,complement(composition(top,top)))),
inference(subst,[],[refute_1_50:[bind(X0,$fot(composition(X_316,complement(composition(top,top))))),bind(X1,$fot(zero))]]) ).
cnf(refute_1_1960,plain,
( join(composition(X_316,complement(composition(top,top))),zero) != join(zero,composition(X_316,complement(composition(top,top))))
| join(zero,composition(X_316,complement(composition(top,top)))) != composition(X_316,complement(composition(top,top)))
| join(composition(X_316,complement(composition(top,top))),zero) = composition(X_316,complement(composition(top,top))) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(composition(X_316,complement(composition(top,top))),zero))),bind(Y,$fot(join(zero,composition(X_316,complement(composition(top,top)))))),bind(Z,$fot(composition(X_316,complement(composition(top,top)))))]]) ).
cnf(refute_1_1961,plain,
( join(zero,composition(X_316,complement(composition(top,top)))) != composition(X_316,complement(composition(top,top)))
| join(composition(X_316,complement(composition(top,top))),zero) = composition(X_316,complement(composition(top,top))) ),
inference(resolve,[$cnf( $equal(join(composition(X_316,complement(composition(top,top))),zero),join(zero,composition(X_316,complement(composition(top,top))))) )],[refute_1_1959,refute_1_1960]) ).
cnf(refute_1_1962,plain,
join(composition(X_316,complement(composition(top,top))),zero) = composition(X_316,complement(composition(top,top))),
inference(resolve,[$cnf( $equal(join(zero,composition(X_316,complement(composition(top,top)))),composition(X_316,complement(composition(top,top)))) )],[refute_1_1958,refute_1_1961]) ).
cnf(refute_1_1963,plain,
( join(composition(X_316,complement(composition(top,top))),zero) != composition(X_316,complement(composition(top,top)))
| zero != join(composition(X_316,complement(composition(top,top))),zero)
| zero = composition(X_316,complement(composition(top,top))) ),
introduced(tautology,[equality,[$cnf( $equal(zero,join(composition(X_316,complement(composition(top,top))),zero)) ),[1],$fot(composition(X_316,complement(composition(top,top))))]]) ).
cnf(refute_1_1964,plain,
( zero != join(composition(X_316,complement(composition(top,top))),zero)
| zero = composition(X_316,complement(composition(top,top))) ),
inference(resolve,[$cnf( $equal(join(composition(X_316,complement(composition(top,top))),zero),composition(X_316,complement(composition(top,top)))) )],[refute_1_1962,refute_1_1963]) ).
cnf(refute_1_1965,plain,
( composition(join(X_316,top),complement(composition(top,top))) != join(composition(X_316,complement(composition(top,top))),zero)
| zero = composition(X_316,complement(composition(top,top))) ),
inference(resolve,[$cnf( $equal(zero,join(composition(X_316,complement(composition(top,top))),zero)) )],[refute_1_1957,refute_1_1964]) ).
cnf(refute_1_1966,plain,
zero = composition(X_316,complement(composition(top,top))),
inference(resolve,[$cnf( $equal(composition(join(X_316,top),complement(composition(top,top))),join(composition(X_316,complement(composition(top,top))),zero)) )],[refute_1_1947,refute_1_1965]) ).
cnf(refute_1_1967,plain,
( zero != composition(X_316,complement(composition(top,top)))
| composition(X_316,complement(composition(top,top))) = zero ),
inference(subst,[],[refute_1_17:[bind(X,$fot(zero)),bind(Y,$fot(composition(X_316,complement(composition(top,top)))))]]) ).
cnf(refute_1_1968,plain,
composition(X_316,complement(composition(top,top))) = zero,
inference(resolve,[$cnf( $equal(zero,composition(X_316,complement(composition(top,top)))) )],[refute_1_1966,refute_1_1967]) ).
cnf(refute_1_1969,plain,
composition(X0,complement(composition(top,top))) = zero,
inference(subst,[],[refute_1_1968:[bind(X_316,$fot(X0))]]) ).
cnf(refute_1_1970,plain,
converse(composition(X0,complement(composition(top,top)))) = converse(composition(X0,complement(composition(top,top)))),
introduced(tautology,[refl,[$fot(converse(composition(X0,complement(composition(top,top)))))]]) ).
cnf(refute_1_1971,plain,
( composition(X0,complement(composition(top,top))) != zero
| converse(composition(X0,complement(composition(top,top)))) != converse(composition(X0,complement(composition(top,top))))
| converse(composition(X0,complement(composition(top,top)))) = converse(zero) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(X0,complement(composition(top,top)))),converse(composition(X0,complement(composition(top,top))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_1_1972,plain,
( composition(X0,complement(composition(top,top))) != zero
| converse(composition(X0,complement(composition(top,top)))) = converse(zero) ),
inference(resolve,[$cnf( $equal(converse(composition(X0,complement(composition(top,top)))),converse(composition(X0,complement(composition(top,top))))) )],[refute_1_1970,refute_1_1971]) ).
cnf(refute_1_1973,plain,
converse(composition(X0,complement(composition(top,top)))) = converse(zero),
inference(resolve,[$cnf( $equal(composition(X0,complement(composition(top,top))),zero) )],[refute_1_1969,refute_1_1972]) ).
cnf(refute_1_1974,plain,
( converse(composition(X0,complement(composition(top,top)))) != converse(zero)
| converse(zero) != zero
| converse(composition(X0,complement(composition(top,top)))) = zero ),
inference(subst,[],[refute_1_37:[bind(X,$fot(converse(composition(X0,complement(composition(top,top)))))),bind(Y,$fot(converse(zero))),bind(Z,$fot(zero))]]) ).
cnf(refute_1_1975,plain,
( converse(zero) != zero
| converse(composition(X0,complement(composition(top,top)))) = zero ),
inference(resolve,[$cnf( $equal(converse(composition(X0,complement(composition(top,top)))),converse(zero)) )],[refute_1_1973,refute_1_1974]) ).
cnf(refute_1_1976,plain,
converse(composition(X0,complement(composition(top,top)))) = zero,
inference(resolve,[$cnf( $equal(converse(zero),zero) )],[refute_1_659,refute_1_1975]) ).
cnf(refute_1_1977,plain,
composition(converse(composition(X0,complement(composition(top,top)))),X_124) = composition(converse(composition(X0,complement(composition(top,top)))),X_124),
introduced(tautology,[refl,[$fot(composition(converse(composition(X0,complement(composition(top,top)))),X_124))]]) ).
cnf(refute_1_1978,plain,
( composition(converse(composition(X0,complement(composition(top,top)))),X_124) != composition(converse(composition(X0,complement(composition(top,top)))),X_124)
| converse(composition(X0,complement(composition(top,top)))) != zero
| composition(converse(composition(X0,complement(composition(top,top)))),X_124) = composition(zero,X_124) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(composition(X0,complement(composition(top,top)))),X_124),composition(converse(composition(X0,complement(composition(top,top)))),X_124)) ),[1,0],$fot(zero)]]) ).
cnf(refute_1_1979,plain,
( converse(composition(X0,complement(composition(top,top)))) != zero
| composition(converse(composition(X0,complement(composition(top,top)))),X_124) = composition(zero,X_124) ),
inference(resolve,[$cnf( $equal(composition(converse(composition(X0,complement(composition(top,top)))),X_124),composition(converse(composition(X0,complement(composition(top,top)))),X_124)) )],[refute_1_1977,refute_1_1978]) ).
cnf(refute_1_1980,plain,
composition(converse(composition(X0,complement(composition(top,top)))),X_124) = composition(zero,X_124),
inference(resolve,[$cnf( $equal(converse(composition(X0,complement(composition(top,top)))),zero) )],[refute_1_1976,refute_1_1979]) ).
cnf(refute_1_1981,plain,
composition(top,composition(converse(composition(X0,complement(composition(top,top)))),X_124)) = composition(top,composition(converse(composition(X0,complement(composition(top,top)))),X_124)),
introduced(tautology,[refl,[$fot(composition(top,composition(converse(composition(X0,complement(composition(top,top)))),X_124)))]]) ).
cnf(refute_1_1982,plain,
( composition(converse(composition(X0,complement(composition(top,top)))),X_124) != composition(zero,X_124)
| composition(top,composition(converse(composition(X0,complement(composition(top,top)))),X_124)) != composition(top,composition(converse(composition(X0,complement(composition(top,top)))),X_124))
| composition(top,composition(converse(composition(X0,complement(composition(top,top)))),X_124)) = composition(top,composition(zero,X_124)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(top,composition(converse(composition(X0,complement(composition(top,top)))),X_124)),composition(top,composition(converse(composition(X0,complement(composition(top,top)))),X_124))) ),[1,1],$fot(composition(zero,X_124))]]) ).
cnf(refute_1_1983,plain,
( composition(converse(composition(X0,complement(composition(top,top)))),X_124) != composition(zero,X_124)
| composition(top,composition(converse(composition(X0,complement(composition(top,top)))),X_124)) = composition(top,composition(zero,X_124)) ),
inference(resolve,[$cnf( $equal(composition(top,composition(converse(composition(X0,complement(composition(top,top)))),X_124)),composition(top,composition(converse(composition(X0,complement(composition(top,top)))),X_124))) )],[refute_1_1981,refute_1_1982]) ).
cnf(refute_1_1984,plain,
composition(top,composition(converse(composition(X0,complement(composition(top,top)))),X_124)) = composition(top,composition(zero,X_124)),
inference(resolve,[$cnf( $equal(composition(converse(composition(X0,complement(composition(top,top)))),X_124),composition(zero,X_124)) )],[refute_1_1980,refute_1_1983]) ).
cnf(refute_1_1985,plain,
( composition(top,composition(converse(composition(X0,complement(composition(top,top)))),X_124)) != composition(top,composition(zero,X_124))
| composition(top,composition(converse(composition(X0,complement(composition(top,top)))),X_124)) != composition(zero,composition(converse(X0),X_124))
| composition(top,composition(zero,X_124)) = composition(zero,composition(converse(X0),X_124)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(top,composition(converse(composition(X0,complement(composition(top,top)))),X_124)),composition(zero,composition(converse(X0),X_124))) ),[0],$fot(composition(top,composition(zero,X_124)))]]) ).
cnf(refute_1_1986,plain,
( composition(top,composition(converse(composition(X0,complement(composition(top,top)))),X_124)) != composition(zero,composition(converse(X0),X_124))
| composition(top,composition(zero,X_124)) = composition(zero,composition(converse(X0),X_124)) ),
inference(resolve,[$cnf( $equal(composition(top,composition(converse(composition(X0,complement(composition(top,top)))),X_124)),composition(top,composition(zero,X_124))) )],[refute_1_1984,refute_1_1985]) ).
cnf(refute_1_1987,plain,
composition(top,composition(zero,X_124)) = composition(zero,composition(converse(X0),X_124)),
inference(resolve,[$cnf( $equal(composition(top,composition(converse(composition(X0,complement(composition(top,top)))),X_124)),composition(zero,composition(converse(X0),X_124))) )],[refute_1_1935,refute_1_1986]) ).
cnf(refute_1_1988,plain,
( composition(top,composition(zero,X_124)) != composition(zero,composition(converse(X0),X_124))
| composition(zero,composition(converse(X0),X_124)) = composition(top,composition(zero,X_124)) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(composition(top,composition(zero,X_124)))),bind(Y,$fot(composition(zero,composition(converse(X0),X_124))))]]) ).
cnf(refute_1_1989,plain,
composition(zero,composition(converse(X0),X_124)) = composition(top,composition(zero,X_124)),
inference(resolve,[$cnf( $equal(composition(top,composition(zero,X_124)),composition(zero,composition(converse(X0),X_124))) )],[refute_1_1987,refute_1_1988]) ).
cnf(refute_1_1990,plain,
composition(zero,composition(converse(skolemFOFtoCNF_X0_1),X_284)) = composition(top,composition(zero,X_284)),
inference(subst,[],[refute_1_1989:[bind(X0,$fot(skolemFOFtoCNF_X0_1)),bind(X_124,$fot(X_284))]]) ).
cnf(refute_1_1991,plain,
( composition(zero,composition(converse(skolemFOFtoCNF_X0_1),X_284)) != composition(top,composition(zero,X_284))
| composition(zero,composition(converse(skolemFOFtoCNF_X0_1),X_284)) != composition(zero,X_284)
| composition(top,composition(zero,X_284)) = composition(zero,X_284) ),
introduced(tautology,[equality,[$cnf( $equal(composition(zero,composition(converse(skolemFOFtoCNF_X0_1),X_284)),composition(zero,X_284)) ),[0],$fot(composition(top,composition(zero,X_284)))]]) ).
cnf(refute_1_1992,plain,
( composition(zero,composition(converse(skolemFOFtoCNF_X0_1),X_284)) != composition(zero,X_284)
| composition(top,composition(zero,X_284)) = composition(zero,X_284) ),
inference(resolve,[$cnf( $equal(composition(zero,composition(converse(skolemFOFtoCNF_X0_1),X_284)),composition(top,composition(zero,X_284))) )],[refute_1_1990,refute_1_1991]) ).
cnf(refute_1_1993,plain,
composition(top,composition(zero,X_284)) = composition(zero,X_284),
inference(resolve,[$cnf( $equal(composition(zero,composition(converse(skolemFOFtoCNF_X0_1),X_284)),composition(zero,X_284)) )],[refute_1_1930,refute_1_1992]) ).
cnf(refute_1_1994,plain,
composition(top,composition(zero,composition(complement(composition(top,composition(top,zero))),X2))) = composition(zero,composition(complement(composition(top,composition(top,zero))),X2)),
inference(subst,[],[refute_1_1993:[bind(X_284,$fot(composition(complement(composition(top,composition(top,zero))),X2)))]]) ).
cnf(refute_1_1995,plain,
( composition(top,composition(zero,composition(complement(composition(top,composition(top,zero))),X2))) != composition(zero,X2)
| composition(top,composition(zero,composition(complement(composition(top,composition(top,zero))),X2))) != composition(zero,composition(complement(composition(top,composition(top,zero))),X2))
| composition(zero,composition(complement(composition(top,composition(top,zero))),X2)) = composition(zero,X2) ),
introduced(tautology,[equality,[$cnf( $equal(composition(top,composition(zero,composition(complement(composition(top,composition(top,zero))),X2))),composition(zero,X2)) ),[0],$fot(composition(zero,composition(complement(composition(top,composition(top,zero))),X2)))]]) ).
cnf(refute_1_1996,plain,
( composition(top,composition(zero,composition(complement(composition(top,composition(top,zero))),X2))) != composition(zero,X2)
| composition(zero,composition(complement(composition(top,composition(top,zero))),X2)) = composition(zero,X2) ),
inference(resolve,[$cnf( $equal(composition(top,composition(zero,composition(complement(composition(top,composition(top,zero))),X2))),composition(zero,composition(complement(composition(top,composition(top,zero))),X2))) )],[refute_1_1994,refute_1_1995]) ).
cnf(refute_1_1997,plain,
composition(zero,composition(complement(composition(top,composition(top,zero))),X2)) = composition(zero,X2),
inference(resolve,[$cnf( $equal(composition(top,composition(zero,composition(complement(composition(top,composition(top,zero))),X2))),composition(zero,X2)) )],[refute_1_1907,refute_1_1996]) ).
cnf(refute_1_1998,plain,
composition(zero,composition(complement(composition(top,composition(top,zero))),top)) = composition(zero,top),
inference(subst,[],[refute_1_1997:[bind(X2,$fot(top))]]) ).
cnf(refute_1_1999,plain,
( composition(zero,composition(complement(composition(top,composition(top,zero))),top)) != composition(zero,top)
| composition(zero,top) != composition(top,zero)
| composition(zero,composition(complement(composition(top,composition(top,zero))),top)) = composition(top,zero) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(composition(zero,composition(complement(composition(top,composition(top,zero))),top)))),bind(Y,$fot(composition(zero,top))),bind(Z,$fot(composition(top,zero)))]]) ).
cnf(refute_1_2000,plain,
( composition(zero,top) != composition(top,zero)
| composition(zero,composition(complement(composition(top,composition(top,zero))),top)) = composition(top,zero) ),
inference(resolve,[$cnf( $equal(composition(zero,composition(complement(composition(top,composition(top,zero))),top)),composition(zero,top)) )],[refute_1_1998,refute_1_1999]) ).
cnf(refute_1_2001,plain,
composition(zero,composition(complement(composition(top,composition(top,zero))),top)) = composition(top,zero),
inference(resolve,[$cnf( $equal(composition(zero,top),composition(top,zero)) )],[refute_1_1678,refute_1_2000]) ).
cnf(refute_1_2002,plain,
( composition(zero,composition(complement(composition(top,composition(top,zero))),top)) != composition(top,zero)
| composition(zero,composition(complement(composition(top,composition(top,zero))),top)) != zero
| composition(top,zero) = zero ),
introduced(tautology,[equality,[$cnf( $equal(composition(zero,composition(complement(composition(top,composition(top,zero))),top)),zero) ),[0],$fot(composition(top,zero))]]) ).
cnf(refute_1_2003,plain,
( composition(zero,composition(complement(composition(top,composition(top,zero))),top)) != zero
| composition(top,zero) = zero ),
inference(resolve,[$cnf( $equal(composition(zero,composition(complement(composition(top,composition(top,zero))),top)),composition(top,zero)) )],[refute_1_2001,refute_1_2002]) ).
cnf(refute_1_2004,plain,
composition(top,zero) = zero,
inference(resolve,[$cnf( $equal(composition(zero,composition(complement(composition(top,composition(top,zero))),top)),zero) )],[refute_1_1848,refute_1_2003]) ).
cnf(refute_1_2005,plain,
join(complement(composition(zero,complement(composition(zero,composition(top,top))))),composition(converse(top),complement(composition(top,composition(zero,complement(composition(zero,composition(top,top)))))))) = complement(composition(zero,complement(composition(zero,composition(top,top))))),
inference(subst,[],[refute_1_112:[bind(X0,$fot(top)),bind(X1,$fot(composition(zero,complement(composition(zero,composition(top,top))))))]]) ).
cnf(refute_1_2006,plain,
( composition(top,composition(zero,complement(composition(zero,composition(top,top))))) != zero
| join(complement(composition(zero,complement(composition(zero,composition(top,top))))),composition(converse(top),complement(composition(top,composition(zero,complement(composition(zero,composition(top,top)))))))) != complement(composition(zero,complement(composition(zero,composition(top,top)))))
| join(complement(composition(zero,complement(composition(zero,composition(top,top))))),composition(converse(top),complement(zero))) = complement(composition(zero,complement(composition(zero,composition(top,top))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(composition(zero,complement(composition(zero,composition(top,top))))),composition(converse(top),complement(composition(top,composition(zero,complement(composition(zero,composition(top,top)))))))),complement(composition(zero,complement(composition(zero,composition(top,top)))))) ),[0,1,1,0],$fot(zero)]]) ).
cnf(refute_1_2007,plain,
( join(complement(composition(zero,complement(composition(zero,composition(top,top))))),composition(converse(top),complement(composition(top,composition(zero,complement(composition(zero,composition(top,top)))))))) != complement(composition(zero,complement(composition(zero,composition(top,top)))))
| join(complement(composition(zero,complement(composition(zero,composition(top,top))))),composition(converse(top),complement(zero))) = complement(composition(zero,complement(composition(zero,composition(top,top))))) ),
inference(resolve,[$cnf( $equal(composition(top,composition(zero,complement(composition(zero,composition(top,top))))),zero) )],[refute_1_1751,refute_1_2006]) ).
cnf(refute_1_2008,plain,
join(complement(composition(zero,complement(composition(zero,composition(top,top))))),composition(converse(top),complement(zero))) = complement(composition(zero,complement(composition(zero,composition(top,top))))),
inference(resolve,[$cnf( $equal(join(complement(composition(zero,complement(composition(zero,composition(top,top))))),composition(converse(top),complement(composition(top,composition(zero,complement(composition(zero,composition(top,top)))))))),complement(composition(zero,complement(composition(zero,composition(top,top)))))) )],[refute_1_2005,refute_1_2007]) ).
cnf(refute_1_2009,plain,
composition(top,complement(zero)) = composition(top,complement(zero)),
introduced(tautology,[refl,[$fot(composition(top,complement(zero)))]]) ).
cnf(refute_1_2010,plain,
( complement(zero) != top
| composition(top,complement(zero)) != composition(top,complement(zero))
| composition(top,complement(zero)) = composition(top,top) ),
introduced(tautology,[equality,[$cnf( $equal(composition(top,complement(zero)),composition(top,complement(zero))) ),[1,1],$fot(top)]]) ).
cnf(refute_1_2011,plain,
( complement(zero) != top
| composition(top,complement(zero)) = composition(top,top) ),
inference(resolve,[$cnf( $equal(composition(top,complement(zero)),composition(top,complement(zero))) )],[refute_1_2009,refute_1_2010]) ).
cnf(refute_1_2012,plain,
composition(top,complement(zero)) = composition(top,top),
inference(resolve,[$cnf( $equal(complement(zero),top) )],[refute_1_1619,refute_1_2011]) ).
cnf(refute_1_2013,plain,
composition(converse(top),complement(zero)) = composition(converse(top),complement(zero)),
introduced(tautology,[refl,[$fot(composition(converse(top),complement(zero)))]]) ).
cnf(refute_1_2014,plain,
( composition(converse(top),complement(zero)) != composition(converse(top),complement(zero))
| converse(top) != top
| composition(converse(top),complement(zero)) = composition(top,complement(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(top),complement(zero)),composition(converse(top),complement(zero))) ),[1,0],$fot(top)]]) ).
cnf(refute_1_2015,plain,
( converse(top) != top
| composition(converse(top),complement(zero)) = composition(top,complement(zero)) ),
inference(resolve,[$cnf( $equal(composition(converse(top),complement(zero)),composition(converse(top),complement(zero))) )],[refute_1_2013,refute_1_2014]) ).
cnf(refute_1_2016,plain,
composition(converse(top),complement(zero)) = composition(top,complement(zero)),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_1_191,refute_1_2015]) ).
cnf(refute_1_2017,plain,
( composition(converse(top),complement(zero)) != composition(top,complement(zero))
| composition(top,complement(zero)) != composition(top,top)
| composition(converse(top),complement(zero)) = composition(top,top) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(composition(converse(top),complement(zero)))),bind(Y,$fot(composition(top,complement(zero)))),bind(Z,$fot(composition(top,top)))]]) ).
cnf(refute_1_2018,plain,
( composition(top,complement(zero)) != composition(top,top)
| composition(converse(top),complement(zero)) = composition(top,top) ),
inference(resolve,[$cnf( $equal(composition(converse(top),complement(zero)),composition(top,complement(zero))) )],[refute_1_2016,refute_1_2017]) ).
cnf(refute_1_2019,plain,
composition(converse(top),complement(zero)) = composition(top,top),
inference(resolve,[$cnf( $equal(composition(top,complement(zero)),composition(top,top)) )],[refute_1_2012,refute_1_2018]) ).
cnf(refute_1_2020,plain,
join(composition(converse(top),complement(zero)),complement(composition(zero,complement(composition(zero,composition(top,top)))))) = join(composition(converse(top),complement(zero)),complement(composition(zero,complement(composition(zero,composition(top,top)))))),
introduced(tautology,[refl,[$fot(join(composition(converse(top),complement(zero)),complement(composition(zero,complement(composition(zero,composition(top,top)))))))]]) ).
cnf(refute_1_2021,plain,
( composition(converse(top),complement(zero)) != composition(top,top)
| join(composition(converse(top),complement(zero)),complement(composition(zero,complement(composition(zero,composition(top,top)))))) != join(composition(converse(top),complement(zero)),complement(composition(zero,complement(composition(zero,composition(top,top))))))
| join(composition(converse(top),complement(zero)),complement(composition(zero,complement(composition(zero,composition(top,top)))))) = join(composition(top,top),complement(composition(zero,complement(composition(zero,composition(top,top)))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(composition(converse(top),complement(zero)),complement(composition(zero,complement(composition(zero,composition(top,top)))))),join(composition(converse(top),complement(zero)),complement(composition(zero,complement(composition(zero,composition(top,top))))))) ),[1,0],$fot(composition(top,top))]]) ).
cnf(refute_1_2022,plain,
( composition(converse(top),complement(zero)) != composition(top,top)
| join(composition(converse(top),complement(zero)),complement(composition(zero,complement(composition(zero,composition(top,top)))))) = join(composition(top,top),complement(composition(zero,complement(composition(zero,composition(top,top)))))) ),
inference(resolve,[$cnf( $equal(join(composition(converse(top),complement(zero)),complement(composition(zero,complement(composition(zero,composition(top,top)))))),join(composition(converse(top),complement(zero)),complement(composition(zero,complement(composition(zero,composition(top,top))))))) )],[refute_1_2020,refute_1_2021]) ).
cnf(refute_1_2023,plain,
join(composition(converse(top),complement(zero)),complement(composition(zero,complement(composition(zero,composition(top,top)))))) = join(composition(top,top),complement(composition(zero,complement(composition(zero,composition(top,top)))))),
inference(resolve,[$cnf( $equal(composition(converse(top),complement(zero)),composition(top,top)) )],[refute_1_2019,refute_1_2022]) ).
cnf(refute_1_2024,plain,
join(complement(composition(zero,complement(composition(zero,composition(top,top))))),composition(converse(top),complement(zero))) = join(composition(converse(top),complement(zero)),complement(composition(zero,complement(composition(zero,composition(top,top)))))),
inference(subst,[],[refute_1_52:[bind(X0,$fot(composition(converse(top),complement(zero)))),bind(X1,$fot(complement(composition(zero,complement(composition(zero,composition(top,top)))))))]]) ).
cnf(refute_1_2025,plain,
( join(complement(composition(zero,complement(composition(zero,composition(top,top))))),composition(converse(top),complement(zero))) != join(composition(converse(top),complement(zero)),complement(composition(zero,complement(composition(zero,composition(top,top))))))
| join(composition(converse(top),complement(zero)),complement(composition(zero,complement(composition(zero,composition(top,top)))))) != join(composition(top,top),complement(composition(zero,complement(composition(zero,composition(top,top))))))
| join(complement(composition(zero,complement(composition(zero,composition(top,top))))),composition(converse(top),complement(zero))) = join(composition(top,top),complement(composition(zero,complement(composition(zero,composition(top,top)))))) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(complement(composition(zero,complement(composition(zero,composition(top,top))))),composition(converse(top),complement(zero))))),bind(Y,$fot(join(composition(converse(top),complement(zero)),complement(composition(zero,complement(composition(zero,composition(top,top)))))))),bind(Z,$fot(join(composition(top,top),complement(composition(zero,complement(composition(zero,composition(top,top))))))))]]) ).
cnf(refute_1_2026,plain,
( join(composition(converse(top),complement(zero)),complement(composition(zero,complement(composition(zero,composition(top,top)))))) != join(composition(top,top),complement(composition(zero,complement(composition(zero,composition(top,top))))))
| join(complement(composition(zero,complement(composition(zero,composition(top,top))))),composition(converse(top),complement(zero))) = join(composition(top,top),complement(composition(zero,complement(composition(zero,composition(top,top)))))) ),
inference(resolve,[$cnf( $equal(join(complement(composition(zero,complement(composition(zero,composition(top,top))))),composition(converse(top),complement(zero))),join(composition(converse(top),complement(zero)),complement(composition(zero,complement(composition(zero,composition(top,top))))))) )],[refute_1_2024,refute_1_2025]) ).
cnf(refute_1_2027,plain,
join(complement(composition(zero,complement(composition(zero,composition(top,top))))),composition(converse(top),complement(zero))) = join(composition(top,top),complement(composition(zero,complement(composition(zero,composition(top,top)))))),
inference(resolve,[$cnf( $equal(join(composition(converse(top),complement(zero)),complement(composition(zero,complement(composition(zero,composition(top,top)))))),join(composition(top,top),complement(composition(zero,complement(composition(zero,composition(top,top))))))) )],[refute_1_2023,refute_1_2026]) ).
cnf(refute_1_2028,plain,
( join(complement(composition(zero,complement(composition(zero,composition(top,top))))),composition(converse(top),complement(zero))) != complement(composition(zero,complement(composition(zero,composition(top,top)))))
| join(complement(composition(zero,complement(composition(zero,composition(top,top))))),composition(converse(top),complement(zero))) != join(composition(top,top),complement(composition(zero,complement(composition(zero,composition(top,top))))))
| join(composition(top,top),complement(composition(zero,complement(composition(zero,composition(top,top)))))) = complement(composition(zero,complement(composition(zero,composition(top,top))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(composition(zero,complement(composition(zero,composition(top,top))))),composition(converse(top),complement(zero))),complement(composition(zero,complement(composition(zero,composition(top,top)))))) ),[0],$fot(join(composition(top,top),complement(composition(zero,complement(composition(zero,composition(top,top)))))))]]) ).
cnf(refute_1_2029,plain,
( join(complement(composition(zero,complement(composition(zero,composition(top,top))))),composition(converse(top),complement(zero))) != complement(composition(zero,complement(composition(zero,composition(top,top)))))
| join(composition(top,top),complement(composition(zero,complement(composition(zero,composition(top,top)))))) = complement(composition(zero,complement(composition(zero,composition(top,top))))) ),
inference(resolve,[$cnf( $equal(join(complement(composition(zero,complement(composition(zero,composition(top,top))))),composition(converse(top),complement(zero))),join(composition(top,top),complement(composition(zero,complement(composition(zero,composition(top,top))))))) )],[refute_1_2027,refute_1_2028]) ).
cnf(refute_1_2030,plain,
join(composition(top,top),complement(composition(zero,complement(composition(zero,composition(top,top)))))) = complement(composition(zero,complement(composition(zero,composition(top,top))))),
inference(resolve,[$cnf( $equal(join(complement(composition(zero,complement(composition(zero,composition(top,top))))),composition(converse(top),complement(zero))),complement(composition(zero,complement(composition(zero,composition(top,top)))))) )],[refute_1_2008,refute_1_2029]) ).
cnf(refute_1_2031,plain,
composition(zero,complement(composition(zero,composition(top,top)))) = composition(zero,complement(composition(zero,composition(top,top)))),
introduced(tautology,[refl,[$fot(composition(zero,complement(composition(zero,composition(top,top)))))]]) ).
cnf(refute_1_2032,plain,
( complement(composition(zero,composition(top,top))) != complement(composition(top,composition(top,zero)))
| composition(zero,complement(composition(zero,composition(top,top)))) != composition(zero,complement(composition(zero,composition(top,top))))
| composition(zero,complement(composition(zero,composition(top,top)))) = composition(zero,complement(composition(top,composition(top,zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(zero,complement(composition(zero,composition(top,top)))),composition(zero,complement(composition(zero,composition(top,top))))) ),[1,1],$fot(complement(composition(top,composition(top,zero))))]]) ).
cnf(refute_1_2033,plain,
( complement(composition(zero,composition(top,top))) != complement(composition(top,composition(top,zero)))
| composition(zero,complement(composition(zero,composition(top,top)))) = composition(zero,complement(composition(top,composition(top,zero)))) ),
inference(resolve,[$cnf( $equal(composition(zero,complement(composition(zero,composition(top,top)))),composition(zero,complement(composition(zero,composition(top,top))))) )],[refute_1_2031,refute_1_2032]) ).
cnf(refute_1_2034,plain,
composition(zero,complement(composition(zero,composition(top,top)))) = composition(zero,complement(composition(top,composition(top,zero)))),
inference(resolve,[$cnf( $equal(complement(composition(zero,composition(top,top))),complement(composition(top,composition(top,zero)))) )],[refute_1_1837,refute_1_2033]) ).
cnf(refute_1_2035,plain,
complement(composition(zero,complement(composition(zero,composition(top,top))))) = complement(composition(zero,complement(composition(zero,composition(top,top))))),
introduced(tautology,[refl,[$fot(complement(composition(zero,complement(composition(zero,composition(top,top))))))]]) ).
cnf(refute_1_2036,plain,
( complement(composition(zero,complement(composition(zero,composition(top,top))))) != complement(composition(zero,complement(composition(zero,composition(top,top)))))
| composition(zero,complement(composition(zero,composition(top,top)))) != composition(zero,complement(composition(top,composition(top,zero))))
| complement(composition(zero,complement(composition(zero,composition(top,top))))) = complement(composition(zero,complement(composition(top,composition(top,zero))))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(composition(zero,complement(composition(zero,composition(top,top))))),complement(composition(zero,complement(composition(zero,composition(top,top)))))) ),[1,0],$fot(composition(zero,complement(composition(top,composition(top,zero)))))]]) ).
cnf(refute_1_2037,plain,
( composition(zero,complement(composition(zero,composition(top,top)))) != composition(zero,complement(composition(top,composition(top,zero))))
| complement(composition(zero,complement(composition(zero,composition(top,top))))) = complement(composition(zero,complement(composition(top,composition(top,zero))))) ),
inference(resolve,[$cnf( $equal(complement(composition(zero,complement(composition(zero,composition(top,top))))),complement(composition(zero,complement(composition(zero,composition(top,top)))))) )],[refute_1_2035,refute_1_2036]) ).
cnf(refute_1_2038,plain,
complement(composition(zero,complement(composition(zero,composition(top,top))))) = complement(composition(zero,complement(composition(top,composition(top,zero))))),
inference(resolve,[$cnf( $equal(composition(zero,complement(composition(zero,composition(top,top)))),composition(zero,complement(composition(top,composition(top,zero))))) )],[refute_1_2034,refute_1_2037]) ).
cnf(refute_1_2039,plain,
join(composition(top,top),complement(composition(zero,complement(composition(zero,composition(top,top)))))) = join(composition(top,top),complement(composition(zero,complement(composition(zero,composition(top,top)))))),
introduced(tautology,[refl,[$fot(join(composition(top,top),complement(composition(zero,complement(composition(zero,composition(top,top)))))))]]) ).
cnf(refute_1_2040,plain,
( complement(composition(zero,complement(composition(zero,composition(top,top))))) != complement(composition(zero,complement(composition(top,composition(top,zero)))))
| join(composition(top,top),complement(composition(zero,complement(composition(zero,composition(top,top)))))) != join(composition(top,top),complement(composition(zero,complement(composition(zero,composition(top,top))))))
| join(composition(top,top),complement(composition(zero,complement(composition(zero,composition(top,top)))))) = join(composition(top,top),complement(composition(zero,complement(composition(top,composition(top,zero)))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(composition(top,top),complement(composition(zero,complement(composition(zero,composition(top,top)))))),join(composition(top,top),complement(composition(zero,complement(composition(zero,composition(top,top))))))) ),[1,1],$fot(complement(composition(zero,complement(composition(top,composition(top,zero))))))]]) ).
cnf(refute_1_2041,plain,
( complement(composition(zero,complement(composition(zero,composition(top,top))))) != complement(composition(zero,complement(composition(top,composition(top,zero)))))
| join(composition(top,top),complement(composition(zero,complement(composition(zero,composition(top,top)))))) = join(composition(top,top),complement(composition(zero,complement(composition(top,composition(top,zero)))))) ),
inference(resolve,[$cnf( $equal(join(composition(top,top),complement(composition(zero,complement(composition(zero,composition(top,top)))))),join(composition(top,top),complement(composition(zero,complement(composition(zero,composition(top,top))))))) )],[refute_1_2039,refute_1_2040]) ).
cnf(refute_1_2042,plain,
join(composition(top,top),complement(composition(zero,complement(composition(zero,composition(top,top)))))) = join(composition(top,top),complement(composition(zero,complement(composition(top,composition(top,zero)))))),
inference(resolve,[$cnf( $equal(complement(composition(zero,complement(composition(zero,composition(top,top))))),complement(composition(zero,complement(composition(top,composition(top,zero)))))) )],[refute_1_2038,refute_1_2041]) ).
cnf(refute_1_2043,plain,
( join(composition(top,top),complement(composition(zero,complement(composition(zero,composition(top,top)))))) != complement(composition(zero,complement(composition(zero,composition(top,top)))))
| join(composition(top,top),complement(composition(zero,complement(composition(zero,composition(top,top)))))) != join(composition(top,top),complement(composition(zero,complement(composition(top,composition(top,zero))))))
| join(composition(top,top),complement(composition(zero,complement(composition(top,composition(top,zero)))))) = complement(composition(zero,complement(composition(zero,composition(top,top))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(composition(top,top),complement(composition(zero,complement(composition(zero,composition(top,top)))))),complement(composition(zero,complement(composition(zero,composition(top,top)))))) ),[0],$fot(join(composition(top,top),complement(composition(zero,complement(composition(top,composition(top,zero)))))))]]) ).
cnf(refute_1_2044,plain,
( join(composition(top,top),complement(composition(zero,complement(composition(zero,composition(top,top)))))) != complement(composition(zero,complement(composition(zero,composition(top,top)))))
| join(composition(top,top),complement(composition(zero,complement(composition(top,composition(top,zero)))))) = complement(composition(zero,complement(composition(zero,composition(top,top))))) ),
inference(resolve,[$cnf( $equal(join(composition(top,top),complement(composition(zero,complement(composition(zero,composition(top,top)))))),join(composition(top,top),complement(composition(zero,complement(composition(top,composition(top,zero))))))) )],[refute_1_2042,refute_1_2043]) ).
cnf(refute_1_2045,plain,
( complement(composition(zero,complement(composition(zero,composition(top,top))))) != complement(composition(zero,complement(composition(top,composition(top,zero)))))
| join(composition(top,top),complement(composition(zero,complement(composition(top,composition(top,zero)))))) != complement(composition(zero,complement(composition(zero,composition(top,top)))))
| join(composition(top,top),complement(composition(zero,complement(composition(top,composition(top,zero)))))) = complement(composition(zero,complement(composition(top,composition(top,zero))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(composition(top,top),complement(composition(zero,complement(composition(top,composition(top,zero)))))),complement(composition(zero,complement(composition(zero,composition(top,top)))))) ),[1],$fot(complement(composition(zero,complement(composition(top,composition(top,zero))))))]]) ).
cnf(refute_1_2046,plain,
( join(composition(top,top),complement(composition(zero,complement(composition(top,composition(top,zero)))))) != complement(composition(zero,complement(composition(zero,composition(top,top)))))
| join(composition(top,top),complement(composition(zero,complement(composition(top,composition(top,zero)))))) = complement(composition(zero,complement(composition(top,composition(top,zero))))) ),
inference(resolve,[$cnf( $equal(complement(composition(zero,complement(composition(zero,composition(top,top))))),complement(composition(zero,complement(composition(top,composition(top,zero)))))) )],[refute_1_2038,refute_1_2045]) ).
cnf(refute_1_2047,plain,
( join(composition(top,top),complement(composition(zero,complement(composition(zero,composition(top,top)))))) != complement(composition(zero,complement(composition(zero,composition(top,top)))))
| join(composition(top,top),complement(composition(zero,complement(composition(top,composition(top,zero)))))) = complement(composition(zero,complement(composition(top,composition(top,zero))))) ),
inference(resolve,[$cnf( $equal(join(composition(top,top),complement(composition(zero,complement(composition(top,composition(top,zero)))))),complement(composition(zero,complement(composition(zero,composition(top,top)))))) )],[refute_1_2044,refute_1_2046]) ).
cnf(refute_1_2048,plain,
join(composition(top,top),complement(composition(zero,complement(composition(top,composition(top,zero)))))) = complement(composition(zero,complement(composition(top,composition(top,zero))))),
inference(resolve,[$cnf( $equal(join(composition(top,top),complement(composition(zero,complement(composition(zero,composition(top,top)))))),complement(composition(zero,complement(composition(zero,composition(top,top)))))) )],[refute_1_2030,refute_1_2047]) ).
cnf(refute_1_2049,plain,
join(one,top) = top,
inference(subst,[],[refute_1_813:[bind(X_169,$fot(one))]]) ).
cnf(refute_1_2050,plain,
composition(join(one,top),top) = composition(join(one,top),top),
introduced(tautology,[refl,[$fot(composition(join(one,top),top))]]) ).
cnf(refute_1_2051,plain,
( composition(join(one,top),top) != composition(join(one,top),top)
| join(one,top) != top
| composition(join(one,top),top) = composition(top,top) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,top),top),composition(join(one,top),top)) ),[1,0],$fot(top)]]) ).
cnf(refute_1_2052,plain,
( join(one,top) != top
| composition(join(one,top),top) = composition(top,top) ),
inference(resolve,[$cnf( $equal(composition(join(one,top),top),composition(join(one,top),top)) )],[refute_1_2050,refute_1_2051]) ).
cnf(refute_1_2053,plain,
composition(join(one,top),top) = composition(top,top),
inference(resolve,[$cnf( $equal(join(one,top),top) )],[refute_1_2049,refute_1_2052]) ).
cnf(refute_1_2054,plain,
join(composition(X_317,X_318),composition(X_316,X_318)) = join(composition(X_316,X_318),composition(X_317,X_318)),
inference(subst,[],[refute_1_50:[bind(X0,$fot(composition(X_317,X_318))),bind(X1,$fot(composition(X_316,X_318)))]]) ).
cnf(refute_1_2055,plain,
composition(join(X_316,X_317),X_318) = join(composition(X_316,X_318),composition(X_317,X_318)),
inference(subst,[],[refute_1_663:[bind(X0,$fot(X_316)),bind(X1,$fot(X_317)),bind(X2,$fot(X_318))]]) ).
cnf(refute_1_2056,plain,
( composition(join(X_316,X_317),X_318) != join(composition(X_316,X_318),composition(X_317,X_318))
| join(composition(X_316,X_318),composition(X_317,X_318)) = composition(join(X_316,X_317),X_318) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(composition(join(X_316,X_317),X_318))),bind(Y,$fot(join(composition(X_316,X_318),composition(X_317,X_318))))]]) ).
cnf(refute_1_2057,plain,
join(composition(X_316,X_318),composition(X_317,X_318)) = composition(join(X_316,X_317),X_318),
inference(resolve,[$cnf( $equal(composition(join(X_316,X_317),X_318),join(composition(X_316,X_318),composition(X_317,X_318))) )],[refute_1_2055,refute_1_2056]) ).
cnf(refute_1_2058,plain,
( join(composition(X_316,X_318),composition(X_317,X_318)) != composition(join(X_316,X_317),X_318)
| join(composition(X_317,X_318),composition(X_316,X_318)) != join(composition(X_316,X_318),composition(X_317,X_318))
| join(composition(X_317,X_318),composition(X_316,X_318)) = composition(join(X_316,X_317),X_318) ),
introduced(tautology,[equality,[$cnf( $equal(join(composition(X_317,X_318),composition(X_316,X_318)),join(composition(X_316,X_318),composition(X_317,X_318))) ),[1],$fot(composition(join(X_316,X_317),X_318))]]) ).
cnf(refute_1_2059,plain,
( join(composition(X_317,X_318),composition(X_316,X_318)) != join(composition(X_316,X_318),composition(X_317,X_318))
| join(composition(X_317,X_318),composition(X_316,X_318)) = composition(join(X_316,X_317),X_318) ),
inference(resolve,[$cnf( $equal(join(composition(X_316,X_318),composition(X_317,X_318)),composition(join(X_316,X_317),X_318)) )],[refute_1_2057,refute_1_2058]) ).
cnf(refute_1_2060,plain,
join(composition(X_317,X_318),composition(X_316,X_318)) = composition(join(X_316,X_317),X_318),
inference(resolve,[$cnf( $equal(join(composition(X_317,X_318),composition(X_316,X_318)),join(composition(X_316,X_318),composition(X_317,X_318))) )],[refute_1_2054,refute_1_2059]) ).
cnf(refute_1_2061,plain,
( composition(join(X0,X1),X2) != join(composition(X0,X2),composition(X1,X2))
| join(composition(X0,X2),composition(X1,X2)) = composition(join(X0,X1),X2) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(composition(join(X0,X1),X2))),bind(Y,$fot(join(composition(X0,X2),composition(X1,X2))))]]) ).
cnf(refute_1_2062,plain,
join(composition(X0,X2),composition(X1,X2)) = composition(join(X0,X1),X2),
inference(resolve,[$cnf( $equal(composition(join(X0,X1),X2),join(composition(X0,X2),composition(X1,X2))) )],[refute_1_663,refute_1_2061]) ).
cnf(refute_1_2063,plain,
join(composition(X_317,X_318),composition(X_316,X_318)) = composition(join(X_317,X_316),X_318),
inference(subst,[],[refute_1_2062:[bind(X0,$fot(X_317)),bind(X1,$fot(X_316)),bind(X2,$fot(X_318))]]) ).
cnf(refute_1_2064,plain,
( join(composition(X_317,X_318),composition(X_316,X_318)) != composition(join(X_316,X_317),X_318)
| join(composition(X_317,X_318),composition(X_316,X_318)) != composition(join(X_317,X_316),X_318)
| composition(join(X_317,X_316),X_318) = composition(join(X_316,X_317),X_318) ),
introduced(tautology,[equality,[$cnf( $equal(join(composition(X_317,X_318),composition(X_316,X_318)),composition(join(X_316,X_317),X_318)) ),[0],$fot(composition(join(X_317,X_316),X_318))]]) ).
cnf(refute_1_2065,plain,
( join(composition(X_317,X_318),composition(X_316,X_318)) != composition(join(X_316,X_317),X_318)
| composition(join(X_317,X_316),X_318) = composition(join(X_316,X_317),X_318) ),
inference(resolve,[$cnf( $equal(join(composition(X_317,X_318),composition(X_316,X_318)),composition(join(X_317,X_316),X_318)) )],[refute_1_2063,refute_1_2064]) ).
cnf(refute_1_2066,plain,
composition(join(X_317,X_316),X_318) = composition(join(X_316,X_317),X_318),
inference(resolve,[$cnf( $equal(join(composition(X_317,X_318),composition(X_316,X_318)),composition(join(X_316,X_317),X_318)) )],[refute_1_2060,refute_1_2065]) ).
cnf(refute_1_2067,plain,
( composition(join(X_317,X_316),X_318) != composition(join(X_316,X_317),X_318)
| composition(join(X_316,X_317),X_318) = composition(join(X_317,X_316),X_318) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(composition(join(X_317,X_316),X_318))),bind(Y,$fot(composition(join(X_316,X_317),X_318)))]]) ).
cnf(refute_1_2068,plain,
composition(join(X_316,X_317),X_318) = composition(join(X_317,X_316),X_318),
inference(resolve,[$cnf( $equal(composition(join(X_317,X_316),X_318),composition(join(X_316,X_317),X_318)) )],[refute_1_2066,refute_1_2067]) ).
cnf(refute_1_2069,plain,
composition(join(top,one),top) = composition(join(one,top),top),
inference(subst,[],[refute_1_2068:[bind(X_316,$fot(top)),bind(X_317,$fot(one)),bind(X_318,$fot(top))]]) ).
cnf(refute_1_2070,plain,
composition(join(X_316,one),X_318) = join(composition(X_316,X_318),composition(one,X_318)),
inference(subst,[],[refute_1_663:[bind(X0,$fot(X_316)),bind(X1,$fot(one)),bind(X2,$fot(X_318))]]) ).
cnf(refute_1_2071,plain,
X_318 = composition(one,X_318),
inference(subst,[],[refute_1_143:[bind(X_126,$fot(X_318))]]) ).
cnf(refute_1_2072,plain,
( X_318 != composition(one,X_318)
| composition(one,X_318) = X_318 ),
inference(subst,[],[refute_1_17:[bind(X,$fot(X_318)),bind(Y,$fot(composition(one,X_318)))]]) ).
cnf(refute_1_2073,plain,
composition(one,X_318) = X_318,
inference(resolve,[$cnf( $equal(X_318,composition(one,X_318)) )],[refute_1_2071,refute_1_2072]) ).
cnf(refute_1_2074,plain,
( composition(join(X_316,one),X_318) != join(composition(X_316,X_318),composition(one,X_318))
| composition(one,X_318) != X_318
| composition(join(X_316,one),X_318) = join(composition(X_316,X_318),X_318) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(X_316,one),X_318),join(composition(X_316,X_318),composition(one,X_318))) ),[1,1],$fot(X_318)]]) ).
cnf(refute_1_2075,plain,
( composition(join(X_316,one),X_318) != join(composition(X_316,X_318),composition(one,X_318))
| composition(join(X_316,one),X_318) = join(composition(X_316,X_318),X_318) ),
inference(resolve,[$cnf( $equal(composition(one,X_318),X_318) )],[refute_1_2073,refute_1_2074]) ).
cnf(refute_1_2076,plain,
composition(join(X_316,one),X_318) = join(composition(X_316,X_318),X_318),
inference(resolve,[$cnf( $equal(composition(join(X_316,one),X_318),join(composition(X_316,X_318),composition(one,X_318))) )],[refute_1_2070,refute_1_2075]) ).
cnf(refute_1_2077,plain,
join(composition(X_316,X_318),X_318) = join(X_318,composition(X_316,X_318)),
inference(subst,[],[refute_1_50:[bind(X0,$fot(composition(X_316,X_318))),bind(X1,$fot(X_318))]]) ).
cnf(refute_1_2078,plain,
( composition(join(X_316,one),X_318) != join(composition(X_316,X_318),X_318)
| join(composition(X_316,X_318),X_318) != join(X_318,composition(X_316,X_318))
| composition(join(X_316,one),X_318) = join(X_318,composition(X_316,X_318)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(join(X_316,one),X_318),join(X_318,composition(X_316,X_318))) ),[0],$fot(join(composition(X_316,X_318),X_318))]]) ).
cnf(refute_1_2079,plain,
( composition(join(X_316,one),X_318) != join(composition(X_316,X_318),X_318)
| composition(join(X_316,one),X_318) = join(X_318,composition(X_316,X_318)) ),
inference(resolve,[$cnf( $equal(join(composition(X_316,X_318),X_318),join(X_318,composition(X_316,X_318))) )],[refute_1_2077,refute_1_2078]) ).
cnf(refute_1_2080,plain,
composition(join(X_316,one),X_318) = join(X_318,composition(X_316,X_318)),
inference(resolve,[$cnf( $equal(composition(join(X_316,one),X_318),join(composition(X_316,X_318),X_318)) )],[refute_1_2076,refute_1_2079]) ).
cnf(refute_1_2081,plain,
( composition(join(X_316,one),X_318) != join(X_318,composition(X_316,X_318))
| join(X_318,composition(X_316,X_318)) = composition(join(X_316,one),X_318) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(composition(join(X_316,one),X_318))),bind(Y,$fot(join(X_318,composition(X_316,X_318))))]]) ).
cnf(refute_1_2082,plain,
join(X_318,composition(X_316,X_318)) = composition(join(X_316,one),X_318),
inference(resolve,[$cnf( $equal(composition(join(X_316,one),X_318),join(X_318,composition(X_316,X_318))) )],[refute_1_2080,refute_1_2081]) ).
cnf(refute_1_2083,plain,
join(top,composition(top,top)) = composition(join(top,one),top),
inference(subst,[],[refute_1_2082:[bind(X_316,$fot(top)),bind(X_318,$fot(top))]]) ).
cnf(refute_1_2084,plain,
( composition(join(top,one),top) != composition(join(one,top),top)
| join(top,composition(top,top)) != composition(join(top,one),top)
| join(top,composition(top,top)) = composition(join(one,top),top) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(top,composition(top,top)))),bind(Y,$fot(composition(join(top,one),top))),bind(Z,$fot(composition(join(one,top),top)))]]) ).
cnf(refute_1_2085,plain,
( composition(join(top,one),top) != composition(join(one,top),top)
| join(top,composition(top,top)) = composition(join(one,top),top) ),
inference(resolve,[$cnf( $equal(join(top,composition(top,top)),composition(join(top,one),top)) )],[refute_1_2083,refute_1_2084]) ).
cnf(refute_1_2086,plain,
join(top,composition(top,top)) = composition(join(one,top),top),
inference(resolve,[$cnf( $equal(composition(join(top,one),top),composition(join(one,top),top)) )],[refute_1_2069,refute_1_2085]) ).
cnf(refute_1_2087,plain,
( composition(join(one,top),top) != composition(top,top)
| join(top,composition(top,top)) != composition(join(one,top),top)
| join(top,composition(top,top)) = composition(top,top) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(top,composition(top,top)))),bind(Y,$fot(composition(join(one,top),top))),bind(Z,$fot(composition(top,top)))]]) ).
cnf(refute_1_2088,plain,
( composition(join(one,top),top) != composition(top,top)
| join(top,composition(top,top)) = composition(top,top) ),
inference(resolve,[$cnf( $equal(join(top,composition(top,top)),composition(join(one,top),top)) )],[refute_1_2086,refute_1_2087]) ).
cnf(refute_1_2089,plain,
join(top,composition(top,top)) = composition(top,top),
inference(resolve,[$cnf( $equal(composition(join(one,top),top),composition(top,top)) )],[refute_1_2053,refute_1_2088]) ).
cnf(refute_1_2090,plain,
join(composition(top,top),top) = join(top,composition(top,top)),
inference(subst,[],[refute_1_50:[bind(X0,$fot(composition(top,top))),bind(X1,$fot(top))]]) ).
cnf(refute_1_2091,plain,
( join(composition(top,top),top) != join(top,composition(top,top))
| join(top,composition(top,top)) != composition(top,top)
| join(composition(top,top),top) = composition(top,top) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(composition(top,top),top))),bind(Y,$fot(join(top,composition(top,top)))),bind(Z,$fot(composition(top,top)))]]) ).
cnf(refute_1_2092,plain,
( join(top,composition(top,top)) != composition(top,top)
| join(composition(top,top),top) = composition(top,top) ),
inference(resolve,[$cnf( $equal(join(composition(top,top),top),join(top,composition(top,top))) )],[refute_1_2090,refute_1_2091]) ).
cnf(refute_1_2093,plain,
join(composition(top,top),top) = composition(top,top),
inference(resolve,[$cnf( $equal(join(top,composition(top,top)),composition(top,top)) )],[refute_1_2089,refute_1_2092]) ).
cnf(refute_1_2094,plain,
( composition(top,zero) != zero
| composition(zero,top) != composition(top,zero)
| composition(zero,top) = zero ),
inference(subst,[],[refute_1_37:[bind(X,$fot(composition(zero,top))),bind(Y,$fot(composition(top,zero))),bind(Z,$fot(zero))]]) ).
cnf(refute_1_2095,plain,
( composition(top,zero) != zero
| composition(zero,top) = zero ),
inference(resolve,[$cnf( $equal(composition(zero,top),composition(top,zero)) )],[refute_1_1678,refute_1_2094]) ).
cnf(refute_1_2096,plain,
composition(zero,top) = zero,
inference(resolve,[$cnf( $equal(composition(top,zero),zero) )],[refute_1_2004,refute_1_2095]) ).
cnf(refute_1_2097,plain,
composition(top,composition(top,zero)) = composition(top,composition(top,zero)),
introduced(tautology,[refl,[$fot(composition(top,composition(top,zero)))]]) ).
cnf(refute_1_2098,plain,
( composition(top,composition(top,zero)) != composition(top,composition(top,zero))
| composition(top,zero) != zero
| composition(top,composition(top,zero)) = composition(top,zero) ),
introduced(tautology,[equality,[$cnf( $equal(composition(top,composition(top,zero)),composition(top,composition(top,zero))) ),[1,1],$fot(zero)]]) ).
cnf(refute_1_2099,plain,
( composition(top,zero) != zero
| composition(top,composition(top,zero)) = composition(top,zero) ),
inference(resolve,[$cnf( $equal(composition(top,composition(top,zero)),composition(top,composition(top,zero))) )],[refute_1_2097,refute_1_2098]) ).
cnf(refute_1_2100,plain,
composition(top,composition(top,zero)) = composition(top,zero),
inference(resolve,[$cnf( $equal(composition(top,zero),zero) )],[refute_1_2004,refute_1_2099]) ).
cnf(refute_1_2101,plain,
( composition(top,composition(top,zero)) != composition(top,zero)
| composition(top,zero) != zero
| composition(top,composition(top,zero)) = zero ),
inference(subst,[],[refute_1_37:[bind(X,$fot(composition(top,composition(top,zero)))),bind(Y,$fot(composition(top,zero))),bind(Z,$fot(zero))]]) ).
cnf(refute_1_2102,plain,
( composition(top,zero) != zero
| composition(top,composition(top,zero)) = zero ),
inference(resolve,[$cnf( $equal(composition(top,composition(top,zero)),composition(top,zero)) )],[refute_1_2100,refute_1_2101]) ).
cnf(refute_1_2103,plain,
composition(top,composition(top,zero)) = zero,
inference(resolve,[$cnf( $equal(composition(top,zero),zero) )],[refute_1_2004,refute_1_2102]) ).
cnf(refute_1_2104,plain,
complement(composition(top,composition(top,zero))) = complement(composition(top,composition(top,zero))),
introduced(tautology,[refl,[$fot(complement(composition(top,composition(top,zero))))]]) ).
cnf(refute_1_2105,plain,
( complement(composition(top,composition(top,zero))) != complement(composition(top,composition(top,zero)))
| composition(top,composition(top,zero)) != zero
| complement(composition(top,composition(top,zero))) = complement(zero) ),
introduced(tautology,[equality,[$cnf( $equal(complement(composition(top,composition(top,zero))),complement(composition(top,composition(top,zero)))) ),[1,0],$fot(zero)]]) ).
cnf(refute_1_2106,plain,
( composition(top,composition(top,zero)) != zero
| complement(composition(top,composition(top,zero))) = complement(zero) ),
inference(resolve,[$cnf( $equal(complement(composition(top,composition(top,zero))),complement(composition(top,composition(top,zero)))) )],[refute_1_2104,refute_1_2105]) ).
cnf(refute_1_2107,plain,
complement(composition(top,composition(top,zero))) = complement(zero),
inference(resolve,[$cnf( $equal(composition(top,composition(top,zero)),zero) )],[refute_1_2103,refute_1_2106]) ).
cnf(refute_1_2108,plain,
( complement(composition(top,composition(top,zero))) != complement(zero)
| complement(zero) != top
| complement(composition(top,composition(top,zero))) = top ),
inference(subst,[],[refute_1_37:[bind(X,$fot(complement(composition(top,composition(top,zero))))),bind(Y,$fot(complement(zero))),bind(Z,$fot(top))]]) ).
cnf(refute_1_2109,plain,
( complement(zero) != top
| complement(composition(top,composition(top,zero))) = top ),
inference(resolve,[$cnf( $equal(complement(composition(top,composition(top,zero))),complement(zero)) )],[refute_1_2107,refute_1_2108]) ).
cnf(refute_1_2110,plain,
complement(composition(top,composition(top,zero))) = top,
inference(resolve,[$cnf( $equal(complement(zero),top) )],[refute_1_1619,refute_1_2109]) ).
cnf(refute_1_2111,plain,
composition(zero,complement(composition(top,composition(top,zero)))) = composition(zero,complement(composition(top,composition(top,zero)))),
introduced(tautology,[refl,[$fot(composition(zero,complement(composition(top,composition(top,zero)))))]]) ).
cnf(refute_1_2112,plain,
( complement(composition(top,composition(top,zero))) != top
| composition(zero,complement(composition(top,composition(top,zero)))) != composition(zero,complement(composition(top,composition(top,zero))))
| composition(zero,complement(composition(top,composition(top,zero)))) = composition(zero,top) ),
introduced(tautology,[equality,[$cnf( $equal(composition(zero,complement(composition(top,composition(top,zero)))),composition(zero,complement(composition(top,composition(top,zero))))) ),[1,1],$fot(top)]]) ).
cnf(refute_1_2113,plain,
( complement(composition(top,composition(top,zero))) != top
| composition(zero,complement(composition(top,composition(top,zero)))) = composition(zero,top) ),
inference(resolve,[$cnf( $equal(composition(zero,complement(composition(top,composition(top,zero)))),composition(zero,complement(composition(top,composition(top,zero))))) )],[refute_1_2111,refute_1_2112]) ).
cnf(refute_1_2114,plain,
composition(zero,complement(composition(top,composition(top,zero)))) = composition(zero,top),
inference(resolve,[$cnf( $equal(complement(composition(top,composition(top,zero))),top) )],[refute_1_2110,refute_1_2113]) ).
cnf(refute_1_2115,plain,
( composition(zero,complement(composition(top,composition(top,zero)))) != composition(zero,top)
| composition(zero,top) != zero
| composition(zero,complement(composition(top,composition(top,zero)))) = zero ),
inference(subst,[],[refute_1_37:[bind(X,$fot(composition(zero,complement(composition(top,composition(top,zero)))))),bind(Y,$fot(composition(zero,top))),bind(Z,$fot(zero))]]) ).
cnf(refute_1_2116,plain,
( composition(zero,top) != zero
| composition(zero,complement(composition(top,composition(top,zero)))) = zero ),
inference(resolve,[$cnf( $equal(composition(zero,complement(composition(top,composition(top,zero)))),composition(zero,top)) )],[refute_1_2114,refute_1_2115]) ).
cnf(refute_1_2117,plain,
composition(zero,complement(composition(top,composition(top,zero)))) = zero,
inference(resolve,[$cnf( $equal(composition(zero,top),zero) )],[refute_1_2096,refute_1_2116]) ).
cnf(refute_1_2118,plain,
complement(composition(zero,complement(composition(top,composition(top,zero))))) = complement(composition(zero,complement(composition(top,composition(top,zero))))),
introduced(tautology,[refl,[$fot(complement(composition(zero,complement(composition(top,composition(top,zero))))))]]) ).
cnf(refute_1_2119,plain,
( complement(composition(zero,complement(composition(top,composition(top,zero))))) != complement(composition(zero,complement(composition(top,composition(top,zero)))))
| composition(zero,complement(composition(top,composition(top,zero)))) != zero
| complement(composition(zero,complement(composition(top,composition(top,zero))))) = complement(zero) ),
introduced(tautology,[equality,[$cnf( $equal(complement(composition(zero,complement(composition(top,composition(top,zero))))),complement(composition(zero,complement(composition(top,composition(top,zero)))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_1_2120,plain,
( composition(zero,complement(composition(top,composition(top,zero)))) != zero
| complement(composition(zero,complement(composition(top,composition(top,zero))))) = complement(zero) ),
inference(resolve,[$cnf( $equal(complement(composition(zero,complement(composition(top,composition(top,zero))))),complement(composition(zero,complement(composition(top,composition(top,zero)))))) )],[refute_1_2118,refute_1_2119]) ).
cnf(refute_1_2121,plain,
complement(composition(zero,complement(composition(top,composition(top,zero))))) = complement(zero),
inference(resolve,[$cnf( $equal(composition(zero,complement(composition(top,composition(top,zero)))),zero) )],[refute_1_2117,refute_1_2120]) ).
cnf(refute_1_2122,plain,
( complement(composition(zero,complement(composition(top,composition(top,zero))))) != complement(zero)
| complement(zero) != top
| complement(composition(zero,complement(composition(top,composition(top,zero))))) = top ),
inference(subst,[],[refute_1_37:[bind(X,$fot(complement(composition(zero,complement(composition(top,composition(top,zero))))))),bind(Y,$fot(complement(zero))),bind(Z,$fot(top))]]) ).
cnf(refute_1_2123,plain,
( complement(zero) != top
| complement(composition(zero,complement(composition(top,composition(top,zero))))) = top ),
inference(resolve,[$cnf( $equal(complement(composition(zero,complement(composition(top,composition(top,zero))))),complement(zero)) )],[refute_1_2121,refute_1_2122]) ).
cnf(refute_1_2124,plain,
complement(composition(zero,complement(composition(top,composition(top,zero))))) = top,
inference(resolve,[$cnf( $equal(complement(zero),top) )],[refute_1_1619,refute_1_2123]) ).
cnf(refute_1_2125,plain,
join(composition(top,top),complement(composition(zero,complement(composition(top,composition(top,zero)))))) = join(composition(top,top),complement(composition(zero,complement(composition(top,composition(top,zero)))))),
introduced(tautology,[refl,[$fot(join(composition(top,top),complement(composition(zero,complement(composition(top,composition(top,zero)))))))]]) ).
cnf(refute_1_2126,plain,
( complement(composition(zero,complement(composition(top,composition(top,zero))))) != top
| join(composition(top,top),complement(composition(zero,complement(composition(top,composition(top,zero)))))) != join(composition(top,top),complement(composition(zero,complement(composition(top,composition(top,zero))))))
| join(composition(top,top),complement(composition(zero,complement(composition(top,composition(top,zero)))))) = join(composition(top,top),top) ),
introduced(tautology,[equality,[$cnf( $equal(join(composition(top,top),complement(composition(zero,complement(composition(top,composition(top,zero)))))),join(composition(top,top),complement(composition(zero,complement(composition(top,composition(top,zero))))))) ),[1,1],$fot(top)]]) ).
cnf(refute_1_2127,plain,
( complement(composition(zero,complement(composition(top,composition(top,zero))))) != top
| join(composition(top,top),complement(composition(zero,complement(composition(top,composition(top,zero)))))) = join(composition(top,top),top) ),
inference(resolve,[$cnf( $equal(join(composition(top,top),complement(composition(zero,complement(composition(top,composition(top,zero)))))),join(composition(top,top),complement(composition(zero,complement(composition(top,composition(top,zero))))))) )],[refute_1_2125,refute_1_2126]) ).
cnf(refute_1_2128,plain,
join(composition(top,top),complement(composition(zero,complement(composition(top,composition(top,zero)))))) = join(composition(top,top),top),
inference(resolve,[$cnf( $equal(complement(composition(zero,complement(composition(top,composition(top,zero))))),top) )],[refute_1_2124,refute_1_2127]) ).
cnf(refute_1_2129,plain,
( join(composition(top,top),complement(composition(zero,complement(composition(top,composition(top,zero)))))) != join(composition(top,top),top)
| join(composition(top,top),top) != composition(top,top)
| join(composition(top,top),complement(composition(zero,complement(composition(top,composition(top,zero)))))) = composition(top,top) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(composition(top,top),complement(composition(zero,complement(composition(top,composition(top,zero)))))))),bind(Y,$fot(join(composition(top,top),top))),bind(Z,$fot(composition(top,top)))]]) ).
cnf(refute_1_2130,plain,
( join(composition(top,top),top) != composition(top,top)
| join(composition(top,top),complement(composition(zero,complement(composition(top,composition(top,zero)))))) = composition(top,top) ),
inference(resolve,[$cnf( $equal(join(composition(top,top),complement(composition(zero,complement(composition(top,composition(top,zero)))))),join(composition(top,top),top)) )],[refute_1_2128,refute_1_2129]) ).
cnf(refute_1_2131,plain,
join(composition(top,top),complement(composition(zero,complement(composition(top,composition(top,zero)))))) = composition(top,top),
inference(resolve,[$cnf( $equal(join(composition(top,top),top),composition(top,top)) )],[refute_1_2093,refute_1_2130]) ).
cnf(refute_1_2132,plain,
( join(composition(top,top),complement(composition(zero,complement(composition(top,composition(top,zero)))))) != complement(composition(zero,complement(composition(top,composition(top,zero)))))
| join(composition(top,top),complement(composition(zero,complement(composition(top,composition(top,zero)))))) != composition(top,top)
| composition(top,top) = complement(composition(zero,complement(composition(top,composition(top,zero))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(composition(top,top),complement(composition(zero,complement(composition(top,composition(top,zero)))))),complement(composition(zero,complement(composition(top,composition(top,zero)))))) ),[0],$fot(composition(top,top))]]) ).
cnf(refute_1_2133,plain,
( join(composition(top,top),complement(composition(zero,complement(composition(top,composition(top,zero)))))) != complement(composition(zero,complement(composition(top,composition(top,zero)))))
| composition(top,top) = complement(composition(zero,complement(composition(top,composition(top,zero))))) ),
inference(resolve,[$cnf( $equal(join(composition(top,top),complement(composition(zero,complement(composition(top,composition(top,zero)))))),composition(top,top)) )],[refute_1_2131,refute_1_2132]) ).
cnf(refute_1_2134,plain,
( complement(composition(zero,complement(composition(top,composition(top,zero))))) != top
| composition(top,top) != complement(composition(zero,complement(composition(top,composition(top,zero)))))
| composition(top,top) = top ),
introduced(tautology,[equality,[$cnf( $equal(composition(top,top),complement(composition(zero,complement(composition(top,composition(top,zero)))))) ),[1],$fot(top)]]) ).
cnf(refute_1_2135,plain,
( composition(top,top) != complement(composition(zero,complement(composition(top,composition(top,zero)))))
| composition(top,top) = top ),
inference(resolve,[$cnf( $equal(complement(composition(zero,complement(composition(top,composition(top,zero))))),top) )],[refute_1_2124,refute_1_2134]) ).
cnf(refute_1_2136,plain,
( join(composition(top,top),complement(composition(zero,complement(composition(top,composition(top,zero)))))) != complement(composition(zero,complement(composition(top,composition(top,zero)))))
| composition(top,top) = top ),
inference(resolve,[$cnf( $equal(composition(top,top),complement(composition(zero,complement(composition(top,composition(top,zero)))))) )],[refute_1_2133,refute_1_2135]) ).
cnf(refute_1_2137,plain,
composition(top,top) = top,
inference(resolve,[$cnf( $equal(join(composition(top,top),complement(composition(zero,complement(composition(top,composition(top,zero)))))),complement(composition(zero,complement(composition(top,composition(top,zero)))))) )],[refute_1_2048,refute_1_2136]) ).
cnf(refute_1_2138,plain,
complement(composition(top,zero)) = complement(composition(top,zero)),
introduced(tautology,[refl,[$fot(complement(composition(top,zero)))]]) ).
cnf(refute_1_2139,plain,
( complement(composition(top,zero)) != complement(composition(top,zero))
| composition(top,zero) != zero
| complement(composition(top,zero)) = complement(zero) ),
introduced(tautology,[equality,[$cnf( $equal(complement(composition(top,zero)),complement(composition(top,zero))) ),[1,0],$fot(zero)]]) ).
cnf(refute_1_2140,plain,
( composition(top,zero) != zero
| complement(composition(top,zero)) = complement(zero) ),
inference(resolve,[$cnf( $equal(complement(composition(top,zero)),complement(composition(top,zero))) )],[refute_1_2138,refute_1_2139]) ).
cnf(refute_1_2141,plain,
complement(composition(top,zero)) = complement(zero),
inference(resolve,[$cnf( $equal(composition(top,zero),zero) )],[refute_1_2004,refute_1_2140]) ).
cnf(refute_1_2142,plain,
( complement(composition(top,zero)) != complement(zero)
| complement(zero) != top
| complement(composition(top,zero)) = top ),
inference(subst,[],[refute_1_37:[bind(X,$fot(complement(composition(top,zero)))),bind(Y,$fot(complement(zero))),bind(Z,$fot(top))]]) ).
cnf(refute_1_2143,plain,
( complement(zero) != top
| complement(composition(top,zero)) = top ),
inference(resolve,[$cnf( $equal(complement(composition(top,zero)),complement(zero)) )],[refute_1_2141,refute_1_2142]) ).
cnf(refute_1_2144,plain,
complement(composition(top,zero)) = top,
inference(resolve,[$cnf( $equal(complement(zero),top) )],[refute_1_1619,refute_1_2143]) ).
cnf(refute_1_2145,plain,
composition(complement(composition(top,zero)),top) = composition(complement(composition(top,zero)),top),
introduced(tautology,[refl,[$fot(composition(complement(composition(top,zero)),top))]]) ).
cnf(refute_1_2146,plain,
( complement(composition(top,zero)) != top
| composition(complement(composition(top,zero)),top) != composition(complement(composition(top,zero)),top)
| composition(complement(composition(top,zero)),top) = composition(top,top) ),
introduced(tautology,[equality,[$cnf( $equal(composition(complement(composition(top,zero)),top),composition(complement(composition(top,zero)),top)) ),[1,0],$fot(top)]]) ).
cnf(refute_1_2147,plain,
( complement(composition(top,zero)) != top
| composition(complement(composition(top,zero)),top) = composition(top,top) ),
inference(resolve,[$cnf( $equal(composition(complement(composition(top,zero)),top),composition(complement(composition(top,zero)),top)) )],[refute_1_2145,refute_1_2146]) ).
cnf(refute_1_2148,plain,
composition(complement(composition(top,zero)),top) = composition(top,top),
inference(resolve,[$cnf( $equal(complement(composition(top,zero)),top) )],[refute_1_2144,refute_1_2147]) ).
cnf(refute_1_2149,plain,
( composition(complement(composition(top,zero)),top) != composition(top,top)
| composition(top,top) != top
| composition(complement(composition(top,zero)),top) = top ),
inference(subst,[],[refute_1_37:[bind(X,$fot(composition(complement(composition(top,zero)),top))),bind(Y,$fot(composition(top,top))),bind(Z,$fot(top))]]) ).
cnf(refute_1_2150,plain,
( composition(top,top) != top
| composition(complement(composition(top,zero)),top) = top ),
inference(resolve,[$cnf( $equal(composition(complement(composition(top,zero)),top),composition(top,top)) )],[refute_1_2148,refute_1_2149]) ).
cnf(refute_1_2151,plain,
composition(complement(composition(top,zero)),top) = top,
inference(resolve,[$cnf( $equal(composition(top,top),top) )],[refute_1_2137,refute_1_2150]) ).
cnf(refute_1_2152,plain,
complement(composition(complement(composition(top,zero)),top)) = complement(composition(complement(composition(top,zero)),top)),
introduced(tautology,[refl,[$fot(complement(composition(complement(composition(top,zero)),top)))]]) ).
cnf(refute_1_2153,plain,
( complement(composition(complement(composition(top,zero)),top)) != complement(composition(complement(composition(top,zero)),top))
| composition(complement(composition(top,zero)),top) != top
| complement(composition(complement(composition(top,zero)),top)) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(complement(composition(complement(composition(top,zero)),top)),complement(composition(complement(composition(top,zero)),top))) ),[1,0],$fot(top)]]) ).
cnf(refute_1_2154,plain,
( composition(complement(composition(top,zero)),top) != top
| complement(composition(complement(composition(top,zero)),top)) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(composition(complement(composition(top,zero)),top)),complement(composition(complement(composition(top,zero)),top))) )],[refute_1_2152,refute_1_2153]) ).
cnf(refute_1_2155,plain,
complement(composition(complement(composition(top,zero)),top)) = complement(top),
inference(resolve,[$cnf( $equal(composition(complement(composition(top,zero)),top),top) )],[refute_1_2151,refute_1_2154]) ).
cnf(refute_1_2156,plain,
( complement(composition(complement(composition(top,zero)),top)) != complement(top)
| complement(top) != zero
| complement(composition(complement(composition(top,zero)),top)) = zero ),
inference(subst,[],[refute_1_37:[bind(X,$fot(complement(composition(complement(composition(top,zero)),top)))),bind(Y,$fot(complement(top))),bind(Z,$fot(zero))]]) ).
cnf(refute_1_2157,plain,
( complement(top) != zero
| complement(composition(complement(composition(top,zero)),top)) = zero ),
inference(resolve,[$cnf( $equal(complement(composition(complement(composition(top,zero)),top)),complement(top)) )],[refute_1_2155,refute_1_2156]) ).
cnf(refute_1_2158,plain,
complement(composition(complement(composition(top,zero)),top)) = zero,
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_1_45,refute_1_2157]) ).
cnf(refute_1_2159,plain,
composition(top,complement(composition(complement(composition(top,zero)),top))) = composition(top,complement(composition(complement(composition(top,zero)),top))),
introduced(tautology,[refl,[$fot(composition(top,complement(composition(complement(composition(top,zero)),top))))]]) ).
cnf(refute_1_2160,plain,
( complement(composition(complement(composition(top,zero)),top)) != zero
| composition(top,complement(composition(complement(composition(top,zero)),top))) != composition(top,complement(composition(complement(composition(top,zero)),top)))
| composition(top,complement(composition(complement(composition(top,zero)),top))) = composition(top,zero) ),
introduced(tautology,[equality,[$cnf( $equal(composition(top,complement(composition(complement(composition(top,zero)),top))),composition(top,complement(composition(complement(composition(top,zero)),top)))) ),[1,1],$fot(zero)]]) ).
cnf(refute_1_2161,plain,
( complement(composition(complement(composition(top,zero)),top)) != zero
| composition(top,complement(composition(complement(composition(top,zero)),top))) = composition(top,zero) ),
inference(resolve,[$cnf( $equal(composition(top,complement(composition(complement(composition(top,zero)),top))),composition(top,complement(composition(complement(composition(top,zero)),top)))) )],[refute_1_2159,refute_1_2160]) ).
cnf(refute_1_2162,plain,
composition(top,complement(composition(complement(composition(top,zero)),top))) = composition(top,zero),
inference(resolve,[$cnf( $equal(complement(composition(complement(composition(top,zero)),top)),zero) )],[refute_1_2158,refute_1_2161]) ).
cnf(refute_1_2163,plain,
join(X_316,complement(composition(top,zero))) = join(X_316,complement(composition(top,zero))),
introduced(tautology,[refl,[$fot(join(X_316,complement(composition(top,zero))))]]) ).
cnf(refute_1_2164,plain,
( complement(composition(top,zero)) != top
| join(X_316,complement(composition(top,zero))) != join(X_316,complement(composition(top,zero)))
| join(X_316,complement(composition(top,zero))) = join(X_316,top) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_316,complement(composition(top,zero))),join(X_316,complement(composition(top,zero)))) ),[1,1],$fot(top)]]) ).
cnf(refute_1_2165,plain,
( complement(composition(top,zero)) != top
| join(X_316,complement(composition(top,zero))) = join(X_316,top) ),
inference(resolve,[$cnf( $equal(join(X_316,complement(composition(top,zero))),join(X_316,complement(composition(top,zero)))) )],[refute_1_2163,refute_1_2164]) ).
cnf(refute_1_2166,plain,
join(X_316,complement(composition(top,zero))) = join(X_316,top),
inference(resolve,[$cnf( $equal(complement(composition(top,zero)),top) )],[refute_1_2144,refute_1_2165]) ).
cnf(refute_1_2167,plain,
( join(X_316,complement(composition(top,zero))) != join(X_316,top)
| join(X_316,top) != top
| join(X_316,complement(composition(top,zero))) = top ),
inference(subst,[],[refute_1_37:[bind(X,$fot(join(X_316,complement(composition(top,zero))))),bind(Y,$fot(join(X_316,top))),bind(Z,$fot(top))]]) ).
cnf(refute_1_2168,plain,
( join(X_316,top) != top
| join(X_316,complement(composition(top,zero))) = top ),
inference(resolve,[$cnf( $equal(join(X_316,complement(composition(top,zero))),join(X_316,top)) )],[refute_1_2166,refute_1_2167]) ).
cnf(refute_1_2169,plain,
join(X_316,complement(composition(top,zero))) = top,
inference(resolve,[$cnf( $equal(join(X_316,top),top) )],[refute_1_1948,refute_1_2168]) ).
cnf(refute_1_2170,plain,
composition(join(X_316,complement(composition(top,zero))),complement(composition(complement(composition(top,zero)),top))) = composition(join(X_316,complement(composition(top,zero))),complement(composition(complement(composition(top,zero)),top))),
introduced(tautology,[refl,[$fot(composition(join(X_316,complement(composition(top,zero))),complement(composition(complement(composition(top,zero)),top))))]]) ).
cnf(refute_1_2171,plain,
( composition(join(X_316,complement(composition(top,zero))),complement(composition(complement(composition(top,zero)),top))) != composition(join(X_316,complement(composition(top,zero))),complement(composition(complement(composition(top,zero)),top)))
| join(X_316,complement(composition(top,zero))) != top
| composition(join(X_316,complement(composition(top,zero))),complement(composition(complement(composition(top,zero)),top))) = composition(top,complement(composition(complement(composition(top,zero)),top))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(X_316,complement(composition(top,zero))),complement(composition(complement(composition(top,zero)),top))),composition(join(X_316,complement(composition(top,zero))),complement(composition(complement(composition(top,zero)),top)))) ),[1,0],$fot(top)]]) ).
cnf(refute_1_2172,plain,
( join(X_316,complement(composition(top,zero))) != top
| composition(join(X_316,complement(composition(top,zero))),complement(composition(complement(composition(top,zero)),top))) = composition(top,complement(composition(complement(composition(top,zero)),top))) ),
inference(resolve,[$cnf( $equal(composition(join(X_316,complement(composition(top,zero))),complement(composition(complement(composition(top,zero)),top))),composition(join(X_316,complement(composition(top,zero))),complement(composition(complement(composition(top,zero)),top)))) )],[refute_1_2170,refute_1_2171]) ).
cnf(refute_1_2173,plain,
composition(join(X_316,complement(composition(top,zero))),complement(composition(complement(composition(top,zero)),top))) = composition(top,complement(composition(complement(composition(top,zero)),top))),
inference(resolve,[$cnf( $equal(join(X_316,complement(composition(top,zero))),top) )],[refute_1_2169,refute_1_2172]) ).
cnf(refute_1_2174,plain,
( composition(join(X_316,complement(composition(top,zero))),complement(composition(complement(composition(top,zero)),top))) != composition(top,complement(composition(complement(composition(top,zero)),top)))
| composition(top,complement(composition(complement(composition(top,zero)),top))) != composition(top,zero)
| composition(join(X_316,complement(composition(top,zero))),complement(composition(complement(composition(top,zero)),top))) = composition(top,zero) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(composition(join(X_316,complement(composition(top,zero))),complement(composition(complement(composition(top,zero)),top))))),bind(Y,$fot(composition(top,complement(composition(complement(composition(top,zero)),top))))),bind(Z,$fot(composition(top,zero)))]]) ).
cnf(refute_1_2175,plain,
( composition(top,complement(composition(complement(composition(top,zero)),top))) != composition(top,zero)
| composition(join(X_316,complement(composition(top,zero))),complement(composition(complement(composition(top,zero)),top))) = composition(top,zero) ),
inference(resolve,[$cnf( $equal(composition(join(X_316,complement(composition(top,zero))),complement(composition(complement(composition(top,zero)),top))),composition(top,complement(composition(complement(composition(top,zero)),top)))) )],[refute_1_2173,refute_1_2174]) ).
cnf(refute_1_2176,plain,
composition(join(X_316,complement(composition(top,zero))),complement(composition(complement(composition(top,zero)),top))) = composition(top,zero),
inference(resolve,[$cnf( $equal(composition(top,complement(composition(complement(composition(top,zero)),top))),composition(top,zero)) )],[refute_1_2162,refute_1_2175]) ).
cnf(refute_1_2177,plain,
( composition(join(X_316,complement(composition(top,zero))),complement(composition(complement(composition(top,zero)),top))) != composition(top,zero)
| composition(top,zero) != zero
| composition(join(X_316,complement(composition(top,zero))),complement(composition(complement(composition(top,zero)),top))) = zero ),
inference(subst,[],[refute_1_37:[bind(X,$fot(composition(join(X_316,complement(composition(top,zero))),complement(composition(complement(composition(top,zero)),top))))),bind(Y,$fot(composition(top,zero))),bind(Z,$fot(zero))]]) ).
cnf(refute_1_2178,plain,
( composition(top,zero) != zero
| composition(join(X_316,complement(composition(top,zero))),complement(composition(complement(composition(top,zero)),top))) = zero ),
inference(resolve,[$cnf( $equal(composition(join(X_316,complement(composition(top,zero))),complement(composition(complement(composition(top,zero)),top))),composition(top,zero)) )],[refute_1_2176,refute_1_2177]) ).
cnf(refute_1_2179,plain,
composition(join(X_316,complement(composition(top,zero))),complement(composition(complement(composition(top,zero)),top))) = zero,
inference(resolve,[$cnf( $equal(composition(top,zero),zero) )],[refute_1_2004,refute_1_2178]) ).
cnf(refute_1_2180,plain,
( composition(join(X_316,complement(composition(top,zero))),complement(composition(complement(composition(top,zero)),top))) != composition(X_316,complement(composition(complement(composition(top,zero)),top)))
| composition(join(X_316,complement(composition(top,zero))),complement(composition(complement(composition(top,zero)),top))) != zero
| zero = composition(X_316,complement(composition(complement(composition(top,zero)),top))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(X_316,complement(composition(top,zero))),complement(composition(complement(composition(top,zero)),top))),composition(X_316,complement(composition(complement(composition(top,zero)),top)))) ),[0],$fot(zero)]]) ).
cnf(refute_1_2181,plain,
( composition(join(X_316,complement(composition(top,zero))),complement(composition(complement(composition(top,zero)),top))) != composition(X_316,complement(composition(complement(composition(top,zero)),top)))
| zero = composition(X_316,complement(composition(complement(composition(top,zero)),top))) ),
inference(resolve,[$cnf( $equal(composition(join(X_316,complement(composition(top,zero))),complement(composition(complement(composition(top,zero)),top))),zero) )],[refute_1_2179,refute_1_2180]) ).
cnf(refute_1_2182,plain,
composition(X_316,complement(composition(complement(composition(top,zero)),top))) = composition(X_316,complement(composition(complement(composition(top,zero)),top))),
introduced(tautology,[refl,[$fot(composition(X_316,complement(composition(complement(composition(top,zero)),top))))]]) ).
cnf(refute_1_2183,plain,
( complement(composition(complement(composition(top,zero)),top)) != zero
| composition(X_316,complement(composition(complement(composition(top,zero)),top))) != composition(X_316,complement(composition(complement(composition(top,zero)),top)))
| composition(X_316,complement(composition(complement(composition(top,zero)),top))) = composition(X_316,zero) ),
introduced(tautology,[equality,[$cnf( $equal(composition(X_316,complement(composition(complement(composition(top,zero)),top))),composition(X_316,complement(composition(complement(composition(top,zero)),top)))) ),[1,1],$fot(zero)]]) ).
cnf(refute_1_2184,plain,
( complement(composition(complement(composition(top,zero)),top)) != zero
| composition(X_316,complement(composition(complement(composition(top,zero)),top))) = composition(X_316,zero) ),
inference(resolve,[$cnf( $equal(composition(X_316,complement(composition(complement(composition(top,zero)),top))),composition(X_316,complement(composition(complement(composition(top,zero)),top)))) )],[refute_1_2182,refute_1_2183]) ).
cnf(refute_1_2185,plain,
composition(X_316,complement(composition(complement(composition(top,zero)),top))) = composition(X_316,zero),
inference(resolve,[$cnf( $equal(complement(composition(complement(composition(top,zero)),top)),zero) )],[refute_1_2158,refute_1_2184]) ).
cnf(refute_1_2186,plain,
( composition(X_316,complement(composition(complement(composition(top,zero)),top))) != composition(X_316,zero)
| zero != composition(X_316,complement(composition(complement(composition(top,zero)),top)))
| zero = composition(X_316,zero) ),
introduced(tautology,[equality,[$cnf( $equal(zero,composition(X_316,complement(composition(complement(composition(top,zero)),top)))) ),[1],$fot(composition(X_316,zero))]]) ).
cnf(refute_1_2187,plain,
( zero != composition(X_316,complement(composition(complement(composition(top,zero)),top)))
| zero = composition(X_316,zero) ),
inference(resolve,[$cnf( $equal(composition(X_316,complement(composition(complement(composition(top,zero)),top))),composition(X_316,zero)) )],[refute_1_2185,refute_1_2186]) ).
cnf(refute_1_2188,plain,
( composition(join(X_316,complement(composition(top,zero))),complement(composition(complement(composition(top,zero)),top))) != composition(X_316,complement(composition(complement(composition(top,zero)),top)))
| zero = composition(X_316,zero) ),
inference(resolve,[$cnf( $equal(zero,composition(X_316,complement(composition(complement(composition(top,zero)),top)))) )],[refute_1_2181,refute_1_2187]) ).
cnf(refute_1_2189,plain,
zero = composition(X_316,zero),
inference(resolve,[$cnf( $equal(composition(join(X_316,complement(composition(top,zero))),complement(composition(complement(composition(top,zero)),top))),composition(X_316,complement(composition(complement(composition(top,zero)),top)))) )],[refute_1_1708,refute_1_2188]) ).
cnf(refute_1_2190,plain,
( zero != composition(X_316,zero)
| composition(X_316,zero) = zero ),
inference(subst,[],[refute_1_17:[bind(X,$fot(zero)),bind(Y,$fot(composition(X_316,zero)))]]) ).
cnf(refute_1_2191,plain,
composition(X_316,zero) = zero,
inference(resolve,[$cnf( $equal(zero,composition(X_316,zero)) )],[refute_1_2189,refute_1_2190]) ).
cnf(refute_1_2192,plain,
composition(X_111,zero) = zero,
inference(subst,[],[refute_1_2191:[bind(X_316,$fot(X_111))]]) ).
cnf(refute_1_2193,plain,
converse(composition(X_111,zero)) = converse(composition(X_111,zero)),
introduced(tautology,[refl,[$fot(converse(composition(X_111,zero)))]]) ).
cnf(refute_1_2194,plain,
( composition(X_111,zero) != zero
| converse(composition(X_111,zero)) != converse(composition(X_111,zero))
| converse(composition(X_111,zero)) = converse(zero) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(X_111,zero)),converse(composition(X_111,zero))) ),[1,0],$fot(zero)]]) ).
cnf(refute_1_2195,plain,
( composition(X_111,zero) != zero
| converse(composition(X_111,zero)) = converse(zero) ),
inference(resolve,[$cnf( $equal(converse(composition(X_111,zero)),converse(composition(X_111,zero))) )],[refute_1_2193,refute_1_2194]) ).
cnf(refute_1_2196,plain,
converse(composition(X_111,zero)) = converse(zero),
inference(resolve,[$cnf( $equal(composition(X_111,zero),zero) )],[refute_1_2192,refute_1_2195]) ).
cnf(refute_1_2197,plain,
( converse(composition(X_111,zero)) != converse(zero)
| converse(zero) != zero
| converse(composition(X_111,zero)) = zero ),
inference(subst,[],[refute_1_37:[bind(X,$fot(converse(composition(X_111,zero)))),bind(Y,$fot(converse(zero))),bind(Z,$fot(zero))]]) ).
cnf(refute_1_2198,plain,
( converse(zero) != zero
| converse(composition(X_111,zero)) = zero ),
inference(resolve,[$cnf( $equal(converse(composition(X_111,zero)),converse(zero)) )],[refute_1_2196,refute_1_2197]) ).
cnf(refute_1_2199,plain,
converse(composition(X_111,zero)) = zero,
inference(resolve,[$cnf( $equal(converse(zero),zero) )],[refute_1_659,refute_1_2198]) ).
cnf(refute_1_2200,plain,
( converse(composition(X_111,zero)) != composition(zero,converse(X_111))
| converse(composition(X_111,zero)) != zero
| zero = composition(zero,converse(X_111)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(X_111,zero)),composition(zero,converse(X_111))) ),[0],$fot(zero)]]) ).
cnf(refute_1_2201,plain,
( converse(composition(X_111,zero)) != composition(zero,converse(X_111))
| zero = composition(zero,converse(X_111)) ),
inference(resolve,[$cnf( $equal(converse(composition(X_111,zero)),zero) )],[refute_1_2199,refute_1_2200]) ).
cnf(refute_1_2202,plain,
zero = composition(zero,converse(X_111)),
inference(resolve,[$cnf( $equal(converse(composition(X_111,zero)),composition(zero,converse(X_111))) )],[refute_1_662,refute_1_2201]) ).
cnf(refute_1_2203,plain,
zero = composition(zero,converse(composition(converse(X0),X_112))),
inference(subst,[],[refute_1_2202:[bind(X_111,$fot(composition(converse(X0),X_112)))]]) ).
cnf(refute_1_2204,plain,
( converse(composition(converse(X0),X_112)) != composition(converse(X_112),X0)
| zero != composition(zero,converse(composition(converse(X0),X_112)))
| zero = composition(zero,composition(converse(X_112),X0)) ),
introduced(tautology,[equality,[$cnf( $equal(zero,composition(zero,converse(composition(converse(X0),X_112)))) ),[1,1],$fot(composition(converse(X_112),X0))]]) ).
cnf(refute_1_2205,plain,
( zero != composition(zero,converse(composition(converse(X0),X_112)))
| zero = composition(zero,composition(converse(X_112),X0)) ),
inference(resolve,[$cnf( $equal(converse(composition(converse(X0),X_112)),composition(converse(X_112),X0)) )],[refute_1_117,refute_1_2204]) ).
cnf(refute_1_2206,plain,
zero = composition(zero,composition(converse(X_112),X0)),
inference(resolve,[$cnf( $equal(zero,composition(zero,converse(composition(converse(X0),X_112)))) )],[refute_1_2203,refute_1_2205]) ).
cnf(refute_1_2207,plain,
composition(top,composition(zero,X_124)) = composition(zero,X_124),
inference(subst,[],[refute_1_1993:[bind(X_284,$fot(X_124))]]) ).
cnf(refute_1_2208,plain,
( composition(top,composition(zero,X_124)) != composition(zero,X_124)
| composition(top,composition(zero,X_124)) != composition(zero,composition(converse(X0),X_124))
| composition(zero,X_124) = composition(zero,composition(converse(X0),X_124)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(top,composition(zero,X_124)),composition(zero,composition(converse(X0),X_124))) ),[0],$fot(composition(zero,X_124))]]) ).
cnf(refute_1_2209,plain,
( composition(top,composition(zero,X_124)) != composition(zero,composition(converse(X0),X_124))
| composition(zero,X_124) = composition(zero,composition(converse(X0),X_124)) ),
inference(resolve,[$cnf( $equal(composition(top,composition(zero,X_124)),composition(zero,X_124)) )],[refute_1_2207,refute_1_2208]) ).
cnf(refute_1_2210,plain,
composition(zero,X_124) = composition(zero,composition(converse(X0),X_124)),
inference(resolve,[$cnf( $equal(composition(top,composition(zero,X_124)),composition(zero,composition(converse(X0),X_124))) )],[refute_1_1987,refute_1_2209]) ).
cnf(refute_1_2211,plain,
( composition(zero,X_124) != composition(zero,composition(converse(X0),X_124))
| composition(zero,composition(converse(X0),X_124)) = composition(zero,X_124) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(composition(zero,X_124))),bind(Y,$fot(composition(zero,composition(converse(X0),X_124))))]]) ).
cnf(refute_1_2212,plain,
composition(zero,composition(converse(X0),X_124)) = composition(zero,X_124),
inference(resolve,[$cnf( $equal(composition(zero,X_124),composition(zero,composition(converse(X0),X_124))) )],[refute_1_2210,refute_1_2211]) ).
cnf(refute_1_2213,plain,
composition(zero,composition(converse(X_112),X0)) = composition(zero,X0),
inference(subst,[],[refute_1_2212:[bind(X0,$fot(X_112)),bind(X_124,$fot(X0))]]) ).
cnf(refute_1_2214,plain,
( composition(zero,composition(converse(X_112),X0)) != composition(zero,X0)
| zero != composition(zero,composition(converse(X_112),X0))
| zero = composition(zero,X0) ),
introduced(tautology,[equality,[$cnf( $equal(zero,composition(zero,composition(converse(X_112),X0))) ),[1],$fot(composition(zero,X0))]]) ).
cnf(refute_1_2215,plain,
( zero != composition(zero,composition(converse(X_112),X0))
| zero = composition(zero,X0) ),
inference(resolve,[$cnf( $equal(composition(zero,composition(converse(X_112),X0)),composition(zero,X0)) )],[refute_1_2213,refute_1_2214]) ).
cnf(refute_1_2216,plain,
zero = composition(zero,X0),
inference(resolve,[$cnf( $equal(zero,composition(zero,composition(converse(X_112),X0))) )],[refute_1_2206,refute_1_2215]) ).
cnf(refute_1_2217,plain,
( zero != composition(zero,X0)
| composition(zero,X0) = zero ),
inference(subst,[],[refute_1_17:[bind(X,$fot(zero)),bind(Y,$fot(composition(zero,X0)))]]) ).
cnf(refute_1_2218,plain,
composition(zero,X0) = zero,
inference(resolve,[$cnf( $equal(zero,composition(zero,X0)) )],[refute_1_2216,refute_1_2217]) ).
cnf(refute_1_2219,plain,
composition(zero,skolemFOFtoCNF_X0_1) = zero,
inference(subst,[],[refute_1_2218:[bind(X0,$fot(skolemFOFtoCNF_X0_1))]]) ).
cnf(refute_1_2220,plain,
( composition(zero,skolemFOFtoCNF_X0_1) != zero
| zero != zero
| composition(zero,skolemFOFtoCNF_X0_1) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(zero,skolemFOFtoCNF_X0_1),zero) ),[0],$fot(zero)]]) ).
cnf(refute_1_2221,plain,
( zero != zero
| composition(zero,skolemFOFtoCNF_X0_1) = zero ),
inference(resolve,[$cnf( $equal(composition(zero,skolemFOFtoCNF_X0_1),zero) )],[refute_1_2219,refute_1_2220]) ).
cnf(refute_1_2222,plain,
zero != zero,
inference(resolve,[$cnf( $equal(composition(zero,skolemFOFtoCNF_X0_1),zero) )],[refute_1_2221,refute_1_0]) ).
cnf(refute_1_2223,plain,
zero = zero,
introduced(tautology,[refl,[$fot(zero)]]) ).
cnf(refute_1_2224,plain,
$false,
inference(resolve,[$cnf( $equal(zero,zero) )],[refute_1_2223,refute_1_2222]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : REL013+1 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.35 % Computer : n015.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Fri Jul 8 12:28:06 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.95/2.13 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.95/2.13
% 1.95/2.13 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.25/2.45
%------------------------------------------------------------------------------