TSTP Solution File: REL015+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : REL015+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n026.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 19:43:27 EDT 2022
% Result : Theorem 0.74s 0.91s
% Output : CNFRefutation 0.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 70
% Number of leaves : 142
% Syntax : Number of formulae : 641 ( 344 unt; 0 def)
% Number of atoms : 1067 (1066 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 855 ( 429 ~; 426 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 632 ( 19 sgn 66 !; 0 ?)
% 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_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,
composition(top,top) = top ).
fof(subgoal_0,plain,
composition(top,top) = top,
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
composition(top,top) != top,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,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_1,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(canonicalize,[],[maddux1_join_commutativity]) ).
fof(normalize_0_3,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(canonicalize,[],[maddux4_definiton_of_meet]) ).
fof(normalize_0_5,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(canonicalize,[],[converse_additivity]) ).
fof(normalize_0_7,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X0] : converse(converse(X0)) = X0,
inference(canonicalize,[],[converse_idempotence]) ).
fof(normalize_0_9,plain,
! [X0] : converse(converse(X0)) = X0,
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X0] : top = join(X0,complement(X0)),
inference(canonicalize,[],[def_top]) ).
fof(normalize_0_11,plain,
! [X0] : top = join(X0,complement(X0)),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(canonicalize,[],[maddux2_join_associativity]) ).
fof(normalize_0_13,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(canonicalize,[],[def_zero]) ).
fof(normalize_0_15,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(canonicalize,[],[converse_cancellativity]) ).
fof(normalize_0_17,plain,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(specialize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(canonicalize,[],[converse_multiplicativity]) ).
fof(normalize_0_19,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(specialize,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [X0] : composition(X0,one) = X0,
inference(canonicalize,[],[composition_identity]) ).
fof(normalize_0_21,plain,
! [X0] : composition(X0,one) = X0,
inference(specialize,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(canonicalize,[],[composition_distributivity]) ).
fof(normalize_0_23,plain,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(specialize,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
composition(top,top) != top,
inference(canonicalize,[],[negate_0_0]) ).
cnf(refute_0_0,plain,
X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
join(X0,X1) = join(X1,X0),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_3,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_4,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( join(X0,X1) != join(X1,X0)
| join(X1,X0) = join(X0,X1) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(join(X0,X1))),bind(Y,$fot(join(X1,X0)))]]) ).
cnf(refute_0_6,plain,
join(X1,X0) = join(X0,X1),
inference(resolve,[$cnf( $equal(join(X0,X1),join(X1,X0)) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),
inference(subst,[],[refute_0_6:[bind(X0,$fot(complement(join(complement(X0),X1)))),bind(X1,$fot(complement(join(complement(X0),complement(X1)))))]]) ).
cnf(refute_0_8,plain,
( X0 != join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1)))
| join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) != join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))
| X0 = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) ),
introduced(tautology,[equality,[$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_9,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( $equal(join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
X0 = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),
inference(resolve,[$cnf( $equal(X0,join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1)))) )],[refute_0_0,refute_0_9]) ).
cnf(refute_0_11,plain,
join(complement(join(complement(X0),X1)),meet(X0,X1)) = join(meet(X0,X1),complement(join(complement(X0),X1))),
inference(subst,[],[refute_0_6:[bind(X0,$fot(meet(X0,X1))),bind(X1,$fot(complement(join(complement(X0),X1))))]]) ).
cnf(refute_0_12,plain,
meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_13,plain,
( meet(X0,X1) != complement(join(complement(X0),complement(X1)))
| complement(join(complement(X0),complement(X1))) = meet(X0,X1) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(meet(X0,X1))),bind(Y,$fot(complement(join(complement(X0),complement(X1)))))]]) ).
cnf(refute_0_14,plain,
complement(join(complement(X0),complement(X1))) = meet(X0,X1),
inference(resolve,[$cnf( $equal(meet(X0,X1),complement(join(complement(X0),complement(X1)))) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),
introduced(tautology,[refl,[$fot(join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))))]]) ).
cnf(refute_0_16,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_17,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( $equal(join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(complement(join(complement(X0),X1)),meet(X0,X1)),
inference(resolve,[$cnf( $equal(complement(join(complement(X0),complement(X1))),meet(X0,X1)) )],[refute_0_14,refute_0_17]) ).
cnf(refute_0_19,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_20,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_4,refute_0_19]) ).
cnf(refute_0_21,plain,
( join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) != join(complement(join(complement(X0),X1)),meet(X0,X1))
| join(complement(join(complement(X0),X1)),meet(X0,X1)) != join(meet(X0,X1),complement(join(complement(X0),X1)))
| join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(meet(X0,X1),complement(join(complement(X0),X1))) ),
inference(subst,[],[refute_0_20:[bind(X,$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_22,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( $equal(join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),join(complement(join(complement(X0),X1)),meet(X0,X1))) )],[refute_0_18,refute_0_21]) ).
cnf(refute_0_23,plain,
join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(meet(X0,X1),complement(join(complement(X0),X1))),
inference(resolve,[$cnf( $equal(join(complement(join(complement(X0),X1)),meet(X0,X1)),join(meet(X0,X1),complement(join(complement(X0),X1)))) )],[refute_0_11,refute_0_22]) ).
cnf(refute_0_24,plain,
( X0 != join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))
| join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) != join(meet(X0,X1),complement(join(complement(X0),X1)))
| X0 = join(meet(X0,X1),complement(join(complement(X0),X1))) ),
introduced(tautology,[equality,[$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_25,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( $equal(join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),join(meet(X0,X1),complement(join(complement(X0),X1)))) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
X0 = join(meet(X0,X1),complement(join(complement(X0),X1))),
inference(resolve,[$cnf( $equal(X0,join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))) )],[refute_0_10,refute_0_25]) ).
cnf(refute_0_27,plain,
X_66 = join(meet(X_66,complement(X1)),complement(join(complement(X_66),complement(X1)))),
inference(subst,[],[refute_0_26:[bind(X0,$fot(X_66)),bind(X1,$fot(complement(X1)))]]) ).
cnf(refute_0_28,plain,
meet(X_66,X1) = complement(join(complement(X_66),complement(X1))),
inference(subst,[],[refute_0_12:[bind(X0,$fot(X_66))]]) ).
cnf(refute_0_29,plain,
( meet(X_66,X1) != complement(join(complement(X_66),complement(X1)))
| complement(join(complement(X_66),complement(X1))) = meet(X_66,X1) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(meet(X_66,X1))),bind(Y,$fot(complement(join(complement(X_66),complement(X1)))))]]) ).
cnf(refute_0_30,plain,
complement(join(complement(X_66),complement(X1))) = meet(X_66,X1),
inference(resolve,[$cnf( $equal(meet(X_66,X1),complement(join(complement(X_66),complement(X1)))) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
( X_66 != join(meet(X_66,complement(X1)),complement(join(complement(X_66),complement(X1))))
| complement(join(complement(X_66),complement(X1))) != meet(X_66,X1)
| X_66 = join(meet(X_66,complement(X1)),meet(X_66,X1)) ),
introduced(tautology,[equality,[$cnf( $equal(X_66,join(meet(X_66,complement(X1)),complement(join(complement(X_66),complement(X1))))) ),[1,1],$fot(meet(X_66,X1))]]) ).
cnf(refute_0_32,plain,
( X_66 != join(meet(X_66,complement(X1)),complement(join(complement(X_66),complement(X1))))
| X_66 = join(meet(X_66,complement(X1)),meet(X_66,X1)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_66),complement(X1))),meet(X_66,X1)) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
X_66 = join(meet(X_66,complement(X1)),meet(X_66,X1)),
inference(resolve,[$cnf( $equal(X_66,join(meet(X_66,complement(X1)),complement(join(complement(X_66),complement(X1))))) )],[refute_0_27,refute_0_32]) ).
cnf(refute_0_34,plain,
join(meet(X_66,complement(X1)),meet(X_66,X1)) = join(meet(X_66,X1),meet(X_66,complement(X1))),
inference(subst,[],[refute_0_6:[bind(X0,$fot(meet(X_66,X1))),bind(X1,$fot(meet(X_66,complement(X1))))]]) ).
cnf(refute_0_35,plain,
( X_66 != join(meet(X_66,complement(X1)),meet(X_66,X1))
| join(meet(X_66,complement(X1)),meet(X_66,X1)) != join(meet(X_66,X1),meet(X_66,complement(X1)))
| X_66 = join(meet(X_66,X1),meet(X_66,complement(X1))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_66,join(meet(X_66,X1),meet(X_66,complement(X1)))) ),[0],$fot(join(meet(X_66,complement(X1)),meet(X_66,X1)))]]) ).
cnf(refute_0_36,plain,
( X_66 != join(meet(X_66,complement(X1)),meet(X_66,X1))
| X_66 = join(meet(X_66,X1),meet(X_66,complement(X1))) ),
inference(resolve,[$cnf( $equal(join(meet(X_66,complement(X1)),meet(X_66,X1)),join(meet(X_66,X1),meet(X_66,complement(X1)))) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
X_66 = join(meet(X_66,X1),meet(X_66,complement(X1))),
inference(resolve,[$cnf( $equal(X_66,join(meet(X_66,complement(X1)),meet(X_66,X1))) )],[refute_0_33,refute_0_36]) ).
cnf(refute_0_38,plain,
X_78 = join(meet(X_78,converse(complement(converse(complement(X_78))))),meet(X_78,complement(converse(complement(converse(complement(X_78))))))),
inference(subst,[],[refute_0_37:[bind(X1,$fot(converse(complement(converse(complement(X_78)))))),bind(X_66,$fot(X_78))]]) ).
cnf(refute_0_39,plain,
X_66 = join(meet(X_66,converse(complement(converse(complement(X_66))))),complement(join(complement(X_66),converse(complement(converse(complement(X_66))))))),
inference(subst,[],[refute_0_26:[bind(X0,$fot(X_66)),bind(X1,$fot(converse(complement(converse(complement(X_66))))))]]) ).
cnf(refute_0_40,plain,
converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_41,plain,
converse(join(converse(X0),X_13)) = join(converse(converse(X0)),converse(X_13)),
inference(subst,[],[refute_0_40:[bind(X0,$fot(converse(X0))),bind(X1,$fot(X_13))]]) ).
cnf(refute_0_42,plain,
converse(converse(X0)) = X0,
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_43,plain,
( converse(converse(X0)) != X0
| converse(join(converse(X0),X_13)) != join(converse(converse(X0)),converse(X_13))
| converse(join(converse(X0),X_13)) = join(X0,converse(X_13)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(X0),X_13)),join(converse(converse(X0)),converse(X_13))) ),[1,0],$fot(X0)]]) ).
cnf(refute_0_44,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( $equal(converse(converse(X0)),X0) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
converse(join(converse(X0),X_13)) = join(X0,converse(X_13)),
inference(resolve,[$cnf( $equal(converse(join(converse(X0),X_13)),join(converse(converse(X0)),converse(X_13))) )],[refute_0_41,refute_0_44]) ).
cnf(refute_0_46,plain,
converse(join(converse(X_16),complement(converse(X_16)))) = join(X_16,converse(complement(converse(X_16)))),
inference(subst,[],[refute_0_45:[bind(X0,$fot(X_16)),bind(X_13,$fot(complement(converse(X_16))))]]) ).
cnf(refute_0_47,plain,
top = join(X0,complement(X0)),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_48,plain,
top = join(converse(X_16),complement(converse(X_16))),
inference(subst,[],[refute_0_47:[bind(X0,$fot(converse(X_16)))]]) ).
cnf(refute_0_49,plain,
( top != join(converse(X_16),complement(converse(X_16)))
| join(converse(X_16),complement(converse(X_16))) = top ),
inference(subst,[],[refute_0_4:[bind(X,$fot(top)),bind(Y,$fot(join(converse(X_16),complement(converse(X_16)))))]]) ).
cnf(refute_0_50,plain,
join(converse(X_16),complement(converse(X_16))) = top,
inference(resolve,[$cnf( $equal(top,join(converse(X_16),complement(converse(X_16)))) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
( converse(join(converse(X_16),complement(converse(X_16)))) != join(X_16,converse(complement(converse(X_16))))
| join(converse(X_16),complement(converse(X_16))) != top
| converse(top) = join(X_16,converse(complement(converse(X_16)))) ),
introduced(tautology,[equality,[$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_52,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( $equal(join(converse(X_16),complement(converse(X_16))),top) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
converse(top) = join(X_16,converse(complement(converse(X_16)))),
inference(resolve,[$cnf( $equal(converse(join(converse(X_16),complement(converse(X_16)))),join(X_16,converse(complement(converse(X_16))))) )],[refute_0_46,refute_0_52]) ).
cnf(refute_0_54,plain,
converse(join(converse(top),complement(converse(zero)))) = join(converse(converse(top)),converse(complement(converse(zero)))),
inference(subst,[],[refute_0_40:[bind(X0,$fot(converse(top))),bind(X1,$fot(complement(converse(zero))))]]) ).
cnf(refute_0_55,plain,
converse(join(top,converse(complement(converse(zero))))) = join(converse(top),converse(converse(complement(converse(zero))))),
inference(subst,[],[refute_0_40:[bind(X0,$fot(top)),bind(X1,$fot(converse(complement(converse(zero)))))]]) ).
cnf(refute_0_56,plain,
join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_57,plain,
join(top,join(zero,X_29)) = join(join(top,zero),X_29),
inference(subst,[],[refute_0_56:[bind(X0,$fot(top)),bind(X1,$fot(zero)),bind(X2,$fot(X_29))]]) ).
cnf(refute_0_58,plain,
top = join(top,complement(top)),
inference(subst,[],[refute_0_47:[bind(X0,$fot(top))]]) ).
cnf(refute_0_59,plain,
zero = meet(X0,complement(X0)),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_60,plain,
zero = meet(join(complement(X_6),complement(X_7)),complement(join(complement(X_6),complement(X_7)))),
inference(subst,[],[refute_0_59:[bind(X0,$fot(join(complement(X_6),complement(X_7))))]]) ).
cnf(refute_0_61,plain,
meet(X_6,X_7) = complement(join(complement(X_6),complement(X_7))),
inference(subst,[],[refute_0_12:[bind(X0,$fot(X_6)),bind(X1,$fot(X_7))]]) ).
cnf(refute_0_62,plain,
( meet(X_6,X_7) != complement(join(complement(X_6),complement(X_7)))
| complement(join(complement(X_6),complement(X_7))) = meet(X_6,X_7) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(meet(X_6,X_7))),bind(Y,$fot(complement(join(complement(X_6),complement(X_7)))))]]) ).
cnf(refute_0_63,plain,
complement(join(complement(X_6),complement(X_7))) = meet(X_6,X_7),
inference(resolve,[$cnf( $equal(meet(X_6,X_7),complement(join(complement(X_6),complement(X_7)))) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
( complement(join(complement(X_6),complement(X_7))) != meet(X_6,X_7)
| zero != meet(join(complement(X_6),complement(X_7)),complement(join(complement(X_6),complement(X_7))))
| zero = meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(join(complement(X_6),complement(X_7)),complement(join(complement(X_6),complement(X_7))))) ),[1,1],$fot(meet(X_6,X_7))]]) ).
cnf(refute_0_65,plain,
( zero != meet(join(complement(X_6),complement(X_7)),complement(join(complement(X_6),complement(X_7))))
| zero = meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_6),complement(X_7))),meet(X_6,X_7)) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
zero = meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)),
inference(resolve,[$cnf( $equal(zero,meet(join(complement(X_6),complement(X_7)),complement(join(complement(X_6),complement(X_7))))) )],[refute_0_60,refute_0_65]) ).
cnf(refute_0_67,plain,
( top != join(X0,complement(X0))
| join(X0,complement(X0)) = top ),
inference(subst,[],[refute_0_4:[bind(X,$fot(top)),bind(Y,$fot(join(X0,complement(X0))))]]) ).
cnf(refute_0_68,plain,
join(X0,complement(X0)) = top,
inference(resolve,[$cnf( $equal(top,join(X0,complement(X0))) )],[refute_0_47,refute_0_67]) ).
cnf(refute_0_69,plain,
join(meet(X_6,X_7),complement(meet(X_6,X_7))) = top,
inference(subst,[],[refute_0_68:[bind(X0,$fot(meet(X_6,X_7)))]]) ).
cnf(refute_0_70,plain,
complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))) = complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))),
introduced(tautology,[refl,[$fot(complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))))]]) ).
cnf(refute_0_71,plain,
( complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))) != complement(join(meet(X_6,X_7),complement(meet(X_6,X_7))))
| join(meet(X_6,X_7),complement(meet(X_6,X_7))) != top
| complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))),complement(join(meet(X_6,X_7),complement(meet(X_6,X_7))))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_72,plain,
( join(meet(X_6,X_7),complement(meet(X_6,X_7))) != top
| complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))),complement(join(meet(X_6,X_7),complement(meet(X_6,X_7))))) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))) = complement(top),
inference(resolve,[$cnf( $equal(join(meet(X_6,X_7),complement(meet(X_6,X_7))),top) )],[refute_0_69,refute_0_72]) ).
cnf(refute_0_74,plain,
meet(join(complement(X_6),complement(X_7)),X1) = complement(join(complement(join(complement(X_6),complement(X_7))),complement(X1))),
inference(subst,[],[refute_0_12:[bind(X0,$fot(join(complement(X_6),complement(X_7))))]]) ).
cnf(refute_0_75,plain,
( complement(join(complement(X_6),complement(X_7))) != meet(X_6,X_7)
| meet(join(complement(X_6),complement(X_7)),X1) != complement(join(complement(join(complement(X_6),complement(X_7))),complement(X1)))
| meet(join(complement(X_6),complement(X_7)),X1) = complement(join(meet(X_6,X_7),complement(X1))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(complement(X_6),complement(X_7)),X1),complement(join(complement(join(complement(X_6),complement(X_7))),complement(X1)))) ),[1,0,0],$fot(meet(X_6,X_7))]]) ).
cnf(refute_0_76,plain,
( meet(join(complement(X_6),complement(X_7)),X1) != complement(join(complement(join(complement(X_6),complement(X_7))),complement(X1)))
| meet(join(complement(X_6),complement(X_7)),X1) = complement(join(meet(X_6,X_7),complement(X1))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_6),complement(X_7))),meet(X_6,X_7)) )],[refute_0_63,refute_0_75]) ).
cnf(refute_0_77,plain,
meet(join(complement(X_6),complement(X_7)),X1) = complement(join(meet(X_6,X_7),complement(X1))),
inference(resolve,[$cnf( $equal(meet(join(complement(X_6),complement(X_7)),X1),complement(join(complement(join(complement(X_6),complement(X_7))),complement(X1)))) )],[refute_0_74,refute_0_76]) ).
cnf(refute_0_78,plain,
meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)) = complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))),
inference(subst,[],[refute_0_77:[bind(X1,$fot(meet(X_6,X_7)))]]) ).
cnf(refute_0_79,plain,
( complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))) != complement(top)
| meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)) != complement(join(meet(X_6,X_7),complement(meet(X_6,X_7))))
| meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)) = complement(top) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)))),bind(Y,$fot(complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))))),bind(Z,$fot(complement(top)))]]) ).
cnf(refute_0_80,plain,
( complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))) != complement(top)
| meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)) = complement(top) ),
inference(resolve,[$cnf( $equal(meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)),complement(join(meet(X_6,X_7),complement(meet(X_6,X_7))))) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)) = complement(top),
inference(resolve,[$cnf( $equal(complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))),complement(top)) )],[refute_0_73,refute_0_80]) ).
cnf(refute_0_82,plain,
( meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)) != complement(top)
| zero != meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7))
| zero = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7))) ),[1],$fot(complement(top))]]) ).
cnf(refute_0_83,plain,
( zero != meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7))
| zero = complement(top) ),
inference(resolve,[$cnf( $equal(meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)),complement(top)) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
zero = complement(top),
inference(resolve,[$cnf( $equal(zero,meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7))) )],[refute_0_66,refute_0_83]) ).
cnf(refute_0_85,plain,
( zero != complement(top)
| complement(top) = zero ),
inference(subst,[],[refute_0_4:[bind(X,$fot(zero)),bind(Y,$fot(complement(top)))]]) ).
cnf(refute_0_86,plain,
complement(top) = zero,
inference(resolve,[$cnf( $equal(zero,complement(top)) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
( complement(top) != zero
| top != join(top,complement(top))
| top = join(top,zero) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(top,complement(top))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_88,plain,
( top != join(top,complement(top))
| top = join(top,zero) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
top = join(top,zero),
inference(resolve,[$cnf( $equal(top,join(top,complement(top))) )],[refute_0_58,refute_0_88]) ).
cnf(refute_0_90,plain,
( top != join(top,zero)
| join(top,zero) = top ),
inference(subst,[],[refute_0_4:[bind(X,$fot(top)),bind(Y,$fot(join(top,zero)))]]) ).
cnf(refute_0_91,plain,
join(top,zero) = top,
inference(resolve,[$cnf( $equal(top,join(top,zero)) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
( join(top,join(zero,X_29)) != join(join(top,zero),X_29)
| join(top,zero) != top
| join(top,join(zero,X_29)) = join(top,X_29) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,join(zero,X_29)),join(join(top,zero),X_29)) ),[1,0],$fot(top)]]) ).
cnf(refute_0_93,plain,
( join(top,join(zero,X_29)) != join(join(top,zero),X_29)
| join(top,join(zero,X_29)) = join(top,X_29) ),
inference(resolve,[$cnf( $equal(join(top,zero),top) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
join(top,join(zero,X_29)) = join(top,X_29),
inference(resolve,[$cnf( $equal(join(top,join(zero,X_29)),join(join(top,zero),X_29)) )],[refute_0_57,refute_0_93]) ).
cnf(refute_0_95,plain,
join(top,join(zero,converse(complement(converse(zero))))) = join(top,converse(complement(converse(zero)))),
inference(subst,[],[refute_0_94:[bind(X_29,$fot(converse(complement(converse(zero)))))]]) ).
cnf(refute_0_96,plain,
converse(top) = join(zero,converse(complement(converse(zero)))),
inference(subst,[],[refute_0_53:[bind(X_16,$fot(zero))]]) ).
cnf(refute_0_97,plain,
( converse(top) != join(zero,converse(complement(converse(zero))))
| join(zero,converse(complement(converse(zero)))) = converse(top) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(converse(top))),bind(Y,$fot(join(zero,converse(complement(converse(zero))))))]]) ).
cnf(refute_0_98,plain,
join(zero,converse(complement(converse(zero)))) = converse(top),
inference(resolve,[$cnf( $equal(converse(top),join(zero,converse(complement(converse(zero))))) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
( join(top,join(zero,converse(complement(converse(zero))))) != join(top,converse(complement(converse(zero))))
| join(zero,converse(complement(converse(zero)))) != converse(top)
| join(top,converse(top)) = join(top,converse(complement(converse(zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,join(zero,converse(complement(converse(zero))))),join(top,converse(complement(converse(zero))))) ),[0,1],$fot(converse(top))]]) ).
cnf(refute_0_100,plain,
( join(top,join(zero,converse(complement(converse(zero))))) != join(top,converse(complement(converse(zero))))
| join(top,converse(top)) = join(top,converse(complement(converse(zero)))) ),
inference(resolve,[$cnf( $equal(join(zero,converse(complement(converse(zero)))),converse(top)) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
join(top,converse(top)) = join(top,converse(complement(converse(zero)))),
inference(resolve,[$cnf( $equal(join(top,join(zero,converse(complement(converse(zero))))),join(top,converse(complement(converse(zero))))) )],[refute_0_95,refute_0_100]) ).
cnf(refute_0_102,plain,
( join(top,converse(top)) != join(top,converse(complement(converse(zero))))
| join(top,converse(complement(converse(zero)))) = join(top,converse(top)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(join(top,converse(top)))),bind(Y,$fot(join(top,converse(complement(converse(zero))))))]]) ).
cnf(refute_0_103,plain,
join(top,converse(complement(converse(zero)))) = join(top,converse(top)),
inference(resolve,[$cnf( $equal(join(top,converse(top)),join(top,converse(complement(converse(zero))))) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
( converse(join(top,converse(complement(converse(zero))))) != join(converse(top),converse(converse(complement(converse(zero)))))
| join(top,converse(complement(converse(zero)))) != join(top,converse(top))
| converse(join(top,converse(top))) = join(converse(top),converse(converse(complement(converse(zero))))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(top,converse(complement(converse(zero))))),join(converse(top),converse(converse(complement(converse(zero)))))) ),[0,0],$fot(join(top,converse(top)))]]) ).
cnf(refute_0_105,plain,
( converse(join(top,converse(complement(converse(zero))))) != join(converse(top),converse(converse(complement(converse(zero)))))
| converse(join(top,converse(top))) = join(converse(top),converse(converse(complement(converse(zero))))) ),
inference(resolve,[$cnf( $equal(join(top,converse(complement(converse(zero)))),join(top,converse(top))) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
converse(join(top,converse(top))) = join(converse(top),converse(converse(complement(converse(zero))))),
inference(resolve,[$cnf( $equal(converse(join(top,converse(complement(converse(zero))))),join(converse(top),converse(converse(complement(converse(zero)))))) )],[refute_0_55,refute_0_105]) ).
cnf(refute_0_107,plain,
join(converse(top),top) = join(top,converse(top)),
inference(subst,[],[refute_0_6:[bind(X0,$fot(top)),bind(X1,$fot(converse(top)))]]) ).
cnf(refute_0_108,plain,
converse(join(X_12,converse(X0))) = join(converse(X_12),converse(converse(X0))),
inference(subst,[],[refute_0_40:[bind(X0,$fot(X_12)),bind(X1,$fot(converse(X0)))]]) ).
cnf(refute_0_109,plain,
( converse(converse(X0)) != X0
| converse(join(X_12,converse(X0))) != join(converse(X_12),converse(converse(X0)))
| converse(join(X_12,converse(X0))) = join(converse(X_12),X0) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(X_12,converse(X0))),join(converse(X_12),converse(converse(X0)))) ),[1,1],$fot(X0)]]) ).
cnf(refute_0_110,plain,
( converse(join(X_12,converse(X0))) != join(converse(X_12),converse(converse(X0)))
| converse(join(X_12,converse(X0))) = join(converse(X_12),X0) ),
inference(resolve,[$cnf( $equal(converse(converse(X0)),X0) )],[refute_0_42,refute_0_109]) ).
cnf(refute_0_111,plain,
converse(join(X_12,converse(X0))) = join(converse(X_12),X0),
inference(resolve,[$cnf( $equal(converse(join(X_12,converse(X0))),join(converse(X_12),converse(converse(X0)))) )],[refute_0_108,refute_0_110]) ).
cnf(refute_0_112,plain,
converse(join(top,converse(top))) = join(converse(top),top),
inference(subst,[],[refute_0_111:[bind(X0,$fot(top)),bind(X_12,$fot(top))]]) ).
cnf(refute_0_113,plain,
( converse(join(top,converse(top))) != join(converse(top),top)
| join(converse(top),top) != join(top,converse(top))
| converse(join(top,converse(top))) = join(top,converse(top)) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(converse(join(top,converse(top))))),bind(Y,$fot(join(converse(top),top))),bind(Z,$fot(join(top,converse(top))))]]) ).
cnf(refute_0_114,plain,
( join(converse(top),top) != join(top,converse(top))
| converse(join(top,converse(top))) = join(top,converse(top)) ),
inference(resolve,[$cnf( $equal(converse(join(top,converse(top))),join(converse(top),top)) )],[refute_0_112,refute_0_113]) ).
cnf(refute_0_115,plain,
converse(join(top,converse(top))) = join(top,converse(top)),
inference(resolve,[$cnf( $equal(join(converse(top),top),join(top,converse(top))) )],[refute_0_107,refute_0_114]) ).
cnf(refute_0_116,plain,
( converse(join(top,converse(top))) != join(converse(top),converse(converse(complement(converse(zero)))))
| converse(join(top,converse(top))) != join(top,converse(top))
| join(top,converse(top)) = join(converse(top),converse(converse(complement(converse(zero))))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(top,converse(top))),join(converse(top),converse(converse(complement(converse(zero)))))) ),[0],$fot(join(top,converse(top)))]]) ).
cnf(refute_0_117,plain,
( converse(join(top,converse(top))) != join(converse(top),converse(converse(complement(converse(zero)))))
| join(top,converse(top)) = join(converse(top),converse(converse(complement(converse(zero))))) ),
inference(resolve,[$cnf( $equal(converse(join(top,converse(top))),join(top,converse(top))) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
converse(join(top,converse(complement(converse(zero))))) = join(converse(top),complement(converse(zero))),
inference(subst,[],[refute_0_111:[bind(X0,$fot(complement(converse(zero)))),bind(X_12,$fot(top))]]) ).
cnf(refute_0_119,plain,
( converse(join(X0,X1)) != join(converse(X0),converse(X1))
| join(converse(X0),converse(X1)) = converse(join(X0,X1)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(converse(join(X0,X1)))),bind(Y,$fot(join(converse(X0),converse(X1))))]]) ).
cnf(refute_0_120,plain,
join(converse(X0),converse(X1)) = converse(join(X0,X1)),
inference(resolve,[$cnf( $equal(converse(join(X0,X1)),join(converse(X0),converse(X1))) )],[refute_0_40,refute_0_119]) ).
cnf(refute_0_121,plain,
join(converse(top),converse(converse(complement(converse(zero))))) = converse(join(top,converse(complement(converse(zero))))),
inference(subst,[],[refute_0_120:[bind(X0,$fot(top)),bind(X1,$fot(converse(complement(converse(zero)))))]]) ).
cnf(refute_0_122,plain,
( converse(join(top,converse(complement(converse(zero))))) != join(converse(top),complement(converse(zero)))
| join(converse(top),converse(converse(complement(converse(zero))))) != converse(join(top,converse(complement(converse(zero)))))
| join(converse(top),converse(converse(complement(converse(zero))))) = join(converse(top),complement(converse(zero))) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(join(converse(top),converse(converse(complement(converse(zero))))))),bind(Y,$fot(converse(join(top,converse(complement(converse(zero))))))),bind(Z,$fot(join(converse(top),complement(converse(zero)))))]]) ).
cnf(refute_0_123,plain,
( converse(join(top,converse(complement(converse(zero))))) != join(converse(top),complement(converse(zero)))
| join(converse(top),converse(converse(complement(converse(zero))))) = join(converse(top),complement(converse(zero))) ),
inference(resolve,[$cnf( $equal(join(converse(top),converse(converse(complement(converse(zero))))),converse(join(top,converse(complement(converse(zero)))))) )],[refute_0_121,refute_0_122]) ).
cnf(refute_0_124,plain,
join(converse(top),converse(converse(complement(converse(zero))))) = join(converse(top),complement(converse(zero))),
inference(resolve,[$cnf( $equal(converse(join(top,converse(complement(converse(zero))))),join(converse(top),complement(converse(zero)))) )],[refute_0_118,refute_0_123]) ).
cnf(refute_0_125,plain,
( join(converse(top),converse(converse(complement(converse(zero))))) != join(converse(top),complement(converse(zero)))
| join(top,converse(top)) != join(converse(top),converse(converse(complement(converse(zero)))))
| join(top,converse(top)) = join(converse(top),complement(converse(zero))) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,converse(top)),join(converse(top),converse(converse(complement(converse(zero)))))) ),[1],$fot(join(converse(top),complement(converse(zero))))]]) ).
cnf(refute_0_126,plain,
( join(top,converse(top)) != join(converse(top),converse(converse(complement(converse(zero)))))
| join(top,converse(top)) = join(converse(top),complement(converse(zero))) ),
inference(resolve,[$cnf( $equal(join(converse(top),converse(converse(complement(converse(zero))))),join(converse(top),complement(converse(zero)))) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
( converse(join(top,converse(top))) != join(converse(top),converse(converse(complement(converse(zero)))))
| join(top,converse(top)) = join(converse(top),complement(converse(zero))) ),
inference(resolve,[$cnf( $equal(join(top,converse(top)),join(converse(top),converse(converse(complement(converse(zero)))))) )],[refute_0_117,refute_0_126]) ).
cnf(refute_0_128,plain,
join(top,converse(top)) = join(converse(top),complement(converse(zero))),
inference(resolve,[$cnf( $equal(converse(join(top,converse(top))),join(converse(top),converse(converse(complement(converse(zero)))))) )],[refute_0_106,refute_0_127]) ).
cnf(refute_0_129,plain,
join(X_27,join(zero,join(zero,meet(top,top)))) = join(join(X_27,zero),join(zero,meet(top,top))),
inference(subst,[],[refute_0_56:[bind(X0,$fot(X_27)),bind(X1,$fot(zero)),bind(X2,$fot(join(zero,meet(top,top))))]]) ).
cnf(refute_0_130,plain,
top = join(join(zero,zero),complement(join(zero,zero))),
inference(subst,[],[refute_0_47:[bind(X0,$fot(join(zero,zero)))]]) ).
cnf(refute_0_131,plain,
meet(top,X1) = complement(join(complement(top),complement(X1))),
inference(subst,[],[refute_0_12:[bind(X0,$fot(top))]]) ).
cnf(refute_0_132,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_133,plain,
( meet(top,X1) != complement(join(complement(top),complement(X1)))
| meet(top,X1) = complement(join(zero,complement(X1))) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_86,refute_0_132]) ).
cnf(refute_0_134,plain,
meet(top,X1) = complement(join(zero,complement(X1))),
inference(resolve,[$cnf( $equal(meet(top,X1),complement(join(complement(top),complement(X1)))) )],[refute_0_131,refute_0_133]) ).
cnf(refute_0_135,plain,
meet(top,top) = complement(join(zero,complement(top))),
inference(subst,[],[refute_0_134:[bind(X1,$fot(top))]]) ).
cnf(refute_0_136,plain,
( complement(top) != zero
| meet(top,top) != complement(join(zero,complement(top)))
| meet(top,top) = complement(join(zero,zero)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,top),complement(join(zero,complement(top)))) ),[1,0,1],$fot(zero)]]) ).
cnf(refute_0_137,plain,
( meet(top,top) != complement(join(zero,complement(top)))
| meet(top,top) = complement(join(zero,zero)) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_86,refute_0_136]) ).
cnf(refute_0_138,plain,
meet(top,top) = complement(join(zero,zero)),
inference(resolve,[$cnf( $equal(meet(top,top),complement(join(zero,complement(top)))) )],[refute_0_135,refute_0_137]) ).
cnf(refute_0_139,plain,
( meet(top,top) != complement(join(zero,zero))
| complement(join(zero,zero)) = meet(top,top) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(meet(top,top))),bind(Y,$fot(complement(join(zero,zero))))]]) ).
cnf(refute_0_140,plain,
complement(join(zero,zero)) = meet(top,top),
inference(resolve,[$cnf( $equal(meet(top,top),complement(join(zero,zero))) )],[refute_0_138,refute_0_139]) ).
cnf(refute_0_141,plain,
( complement(join(zero,zero)) != meet(top,top)
| top != join(join(zero,zero),complement(join(zero,zero)))
| top = join(join(zero,zero),meet(top,top)) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(join(zero,zero),complement(join(zero,zero)))) ),[1,1],$fot(meet(top,top))]]) ).
cnf(refute_0_142,plain,
( top != join(join(zero,zero),complement(join(zero,zero)))
| top = join(join(zero,zero),meet(top,top)) ),
inference(resolve,[$cnf( $equal(complement(join(zero,zero)),meet(top,top)) )],[refute_0_140,refute_0_141]) ).
cnf(refute_0_143,plain,
top = join(join(zero,zero),meet(top,top)),
inference(resolve,[$cnf( $equal(top,join(join(zero,zero),complement(join(zero,zero)))) )],[refute_0_130,refute_0_142]) ).
cnf(refute_0_144,plain,
( join(X0,join(X1,X2)) != join(join(X0,X1),X2)
| join(join(X0,X1),X2) = join(X0,join(X1,X2)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(join(X0,join(X1,X2)))),bind(Y,$fot(join(join(X0,X1),X2)))]]) ).
cnf(refute_0_145,plain,
join(join(X0,X1),X2) = join(X0,join(X1,X2)),
inference(resolve,[$cnf( $equal(join(X0,join(X1,X2)),join(join(X0,X1),X2)) )],[refute_0_56,refute_0_144]) ).
cnf(refute_0_146,plain,
join(join(zero,zero),meet(top,top)) = join(zero,join(zero,meet(top,top))),
inference(subst,[],[refute_0_145:[bind(X0,$fot(zero)),bind(X1,$fot(zero)),bind(X2,$fot(meet(top,top)))]]) ).
cnf(refute_0_147,plain,
( join(join(zero,zero),meet(top,top)) != join(zero,join(zero,meet(top,top)))
| top != join(join(zero,zero),meet(top,top))
| top = join(zero,join(zero,meet(top,top))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(join(zero,zero),meet(top,top))) ),[1],$fot(join(zero,join(zero,meet(top,top))))]]) ).
cnf(refute_0_148,plain,
( top != join(join(zero,zero),meet(top,top))
| top = join(zero,join(zero,meet(top,top))) ),
inference(resolve,[$cnf( $equal(join(join(zero,zero),meet(top,top)),join(zero,join(zero,meet(top,top)))) )],[refute_0_146,refute_0_147]) ).
cnf(refute_0_149,plain,
top = join(zero,join(zero,meet(top,top))),
inference(resolve,[$cnf( $equal(top,join(join(zero,zero),meet(top,top))) )],[refute_0_143,refute_0_148]) ).
cnf(refute_0_150,plain,
( top != join(zero,join(zero,meet(top,top)))
| join(zero,join(zero,meet(top,top))) = top ),
inference(subst,[],[refute_0_4:[bind(X,$fot(top)),bind(Y,$fot(join(zero,join(zero,meet(top,top)))))]]) ).
cnf(refute_0_151,plain,
join(zero,join(zero,meet(top,top))) = top,
inference(resolve,[$cnf( $equal(top,join(zero,join(zero,meet(top,top)))) )],[refute_0_149,refute_0_150]) ).
cnf(refute_0_152,plain,
( join(X_27,join(zero,join(zero,meet(top,top)))) != join(join(X_27,zero),join(zero,meet(top,top)))
| join(zero,join(zero,meet(top,top))) != top
| join(X_27,top) = join(join(X_27,zero),join(zero,meet(top,top))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_27,join(zero,join(zero,meet(top,top)))),join(join(X_27,zero),join(zero,meet(top,top)))) ),[0,1],$fot(top)]]) ).
cnf(refute_0_153,plain,
( join(X_27,join(zero,join(zero,meet(top,top)))) != join(join(X_27,zero),join(zero,meet(top,top)))
| join(X_27,top) = join(join(X_27,zero),join(zero,meet(top,top))) ),
inference(resolve,[$cnf( $equal(join(zero,join(zero,meet(top,top))),top) )],[refute_0_151,refute_0_152]) ).
cnf(refute_0_154,plain,
join(X_27,top) = join(join(X_27,zero),join(zero,meet(top,top))),
inference(resolve,[$cnf( $equal(join(X_27,join(zero,join(zero,meet(top,top)))),join(join(X_27,zero),join(zero,meet(top,top)))) )],[refute_0_129,refute_0_153]) ).
cnf(refute_0_155,plain,
join(X0,join(X_27,X_28)) = join(join(X_27,X_28),X0),
inference(subst,[],[refute_0_1:[bind(X1,$fot(join(X_27,X_28)))]]) ).
cnf(refute_0_156,plain,
join(X_27,join(X_28,X0)) = join(join(X_27,X_28),X0),
inference(subst,[],[refute_0_56:[bind(X0,$fot(X_27)),bind(X1,$fot(X_28)),bind(X2,$fot(X0))]]) ).
cnf(refute_0_157,plain,
( join(X_27,join(X_28,X0)) != join(join(X_27,X_28),X0)
| join(join(X_27,X_28),X0) = join(X_27,join(X_28,X0)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(join(X_27,join(X_28,X0)))),bind(Y,$fot(join(join(X_27,X_28),X0)))]]) ).
cnf(refute_0_158,plain,
join(join(X_27,X_28),X0) = join(X_27,join(X_28,X0)),
inference(resolve,[$cnf( $equal(join(X_27,join(X_28,X0)),join(join(X_27,X_28),X0)) )],[refute_0_156,refute_0_157]) ).
cnf(refute_0_159,plain,
( join(X0,join(X_27,X_28)) != join(join(X_27,X_28),X0)
| join(join(X_27,X_28),X0) != join(X_27,join(X_28,X0))
| join(X0,join(X_27,X_28)) = join(X_27,join(X_28,X0)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X0,join(X_27,X_28)),join(X_27,join(X_28,X0))) ),[0],$fot(join(join(X_27,X_28),X0))]]) ).
cnf(refute_0_160,plain,
( join(X0,join(X_27,X_28)) != join(join(X_27,X_28),X0)
| join(X0,join(X_27,X_28)) = join(X_27,join(X_28,X0)) ),
inference(resolve,[$cnf( $equal(join(join(X_27,X_28),X0),join(X_27,join(X_28,X0))) )],[refute_0_158,refute_0_159]) ).
cnf(refute_0_161,plain,
join(X0,join(X_27,X_28)) = join(X_27,join(X_28,X0)),
inference(resolve,[$cnf( $equal(join(X0,join(X_27,X_28)),join(join(X_27,X_28),X0)) )],[refute_0_155,refute_0_160]) ).
cnf(refute_0_162,plain,
( join(X0,join(X_27,X_28)) != join(X_27,join(X_28,X0))
| join(X_27,join(X_28,X0)) = join(X0,join(X_27,X_28)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(join(X0,join(X_27,X_28)))),bind(Y,$fot(join(X_27,join(X_28,X0))))]]) ).
cnf(refute_0_163,plain,
join(X_27,join(X_28,X0)) = join(X0,join(X_27,X_28)),
inference(resolve,[$cnf( $equal(join(X0,join(X_27,X_28)),join(X_27,join(X_28,X0))) )],[refute_0_161,refute_0_162]) ).
cnf(refute_0_164,plain,
join(meet(top,top),join(X_27,zero)) = join(zero,join(meet(top,top),X_27)),
inference(subst,[],[refute_0_163:[bind(X0,$fot(zero)),bind(X_27,$fot(meet(top,top))),bind(X_28,$fot(X_27))]]) ).
cnf(refute_0_165,plain,
join(zero,join(meet(top,top),join(X_27,zero))) = join(zero,join(meet(top,top),join(X_27,zero))),
introduced(tautology,[refl,[$fot(join(zero,join(meet(top,top),join(X_27,zero))))]]) ).
cnf(refute_0_166,plain,
( join(meet(top,top),join(X_27,zero)) != join(zero,join(meet(top,top),X_27))
| join(zero,join(meet(top,top),join(X_27,zero))) != join(zero,join(meet(top,top),join(X_27,zero)))
| join(zero,join(meet(top,top),join(X_27,zero))) = join(zero,join(zero,join(meet(top,top),X_27))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(meet(top,top),join(X_27,zero))),join(zero,join(meet(top,top),join(X_27,zero)))) ),[1,1],$fot(join(zero,join(meet(top,top),X_27)))]]) ).
cnf(refute_0_167,plain,
( join(meet(top,top),join(X_27,zero)) != join(zero,join(meet(top,top),X_27))
| join(zero,join(meet(top,top),join(X_27,zero))) = join(zero,join(zero,join(meet(top,top),X_27))) ),
inference(resolve,[$cnf( $equal(join(zero,join(meet(top,top),join(X_27,zero))),join(zero,join(meet(top,top),join(X_27,zero)))) )],[refute_0_165,refute_0_166]) ).
cnf(refute_0_168,plain,
join(zero,join(meet(top,top),join(X_27,zero))) = join(zero,join(zero,join(meet(top,top),X_27))),
inference(resolve,[$cnf( $equal(join(meet(top,top),join(X_27,zero)),join(zero,join(meet(top,top),X_27))) )],[refute_0_164,refute_0_167]) ).
cnf(refute_0_169,plain,
join(join(X_27,zero),join(zero,meet(top,top))) = join(zero,join(meet(top,top),join(X_27,zero))),
inference(subst,[],[refute_0_161:[bind(X0,$fot(join(X_27,zero))),bind(X_27,$fot(zero)),bind(X_28,$fot(meet(top,top)))]]) ).
cnf(refute_0_170,plain,
( join(join(X_27,zero),join(zero,meet(top,top))) != join(zero,join(meet(top,top),join(X_27,zero)))
| join(zero,join(meet(top,top),join(X_27,zero))) != join(zero,join(zero,join(meet(top,top),X_27)))
| join(join(X_27,zero),join(zero,meet(top,top))) = join(zero,join(zero,join(meet(top,top),X_27))) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(join(join(X_27,zero),join(zero,meet(top,top))))),bind(Y,$fot(join(zero,join(meet(top,top),join(X_27,zero))))),bind(Z,$fot(join(zero,join(zero,join(meet(top,top),X_27)))))]]) ).
cnf(refute_0_171,plain,
( join(zero,join(meet(top,top),join(X_27,zero))) != join(zero,join(zero,join(meet(top,top),X_27)))
| join(join(X_27,zero),join(zero,meet(top,top))) = join(zero,join(zero,join(meet(top,top),X_27))) ),
inference(resolve,[$cnf( $equal(join(join(X_27,zero),join(zero,meet(top,top))),join(zero,join(meet(top,top),join(X_27,zero)))) )],[refute_0_169,refute_0_170]) ).
cnf(refute_0_172,plain,
join(join(X_27,zero),join(zero,meet(top,top))) = join(zero,join(zero,join(meet(top,top),X_27))),
inference(resolve,[$cnf( $equal(join(zero,join(meet(top,top),join(X_27,zero))),join(zero,join(zero,join(meet(top,top),X_27)))) )],[refute_0_168,refute_0_171]) ).
cnf(refute_0_173,plain,
( join(X_27,top) != join(join(X_27,zero),join(zero,meet(top,top)))
| join(join(X_27,zero),join(zero,meet(top,top))) != join(zero,join(zero,join(meet(top,top),X_27)))
| join(X_27,top) = join(zero,join(zero,join(meet(top,top),X_27))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_27,top),join(zero,join(zero,join(meet(top,top),X_27)))) ),[0],$fot(join(join(X_27,zero),join(zero,meet(top,top))))]]) ).
cnf(refute_0_174,plain,
( join(X_27,top) != join(join(X_27,zero),join(zero,meet(top,top)))
| join(X_27,top) = join(zero,join(zero,join(meet(top,top),X_27))) ),
inference(resolve,[$cnf( $equal(join(join(X_27,zero),join(zero,meet(top,top))),join(zero,join(zero,join(meet(top,top),X_27)))) )],[refute_0_172,refute_0_173]) ).
cnf(refute_0_175,plain,
join(X_27,top) = join(zero,join(zero,join(meet(top,top),X_27))),
inference(resolve,[$cnf( $equal(join(X_27,top),join(join(X_27,zero),join(zero,meet(top,top)))) )],[refute_0_154,refute_0_174]) ).
cnf(refute_0_176,plain,
join(X_27,join(complement(X_27),X_29)) = join(join(X_27,complement(X_27)),X_29),
inference(subst,[],[refute_0_56:[bind(X0,$fot(X_27)),bind(X1,$fot(complement(X_27))),bind(X2,$fot(X_29))]]) ).
cnf(refute_0_177,plain,
top = join(X_27,complement(X_27)),
inference(subst,[],[refute_0_47:[bind(X0,$fot(X_27))]]) ).
cnf(refute_0_178,plain,
( top != join(X_27,complement(X_27))
| join(X_27,complement(X_27)) = top ),
inference(subst,[],[refute_0_4:[bind(X,$fot(top)),bind(Y,$fot(join(X_27,complement(X_27))))]]) ).
cnf(refute_0_179,plain,
join(X_27,complement(X_27)) = top,
inference(resolve,[$cnf( $equal(top,join(X_27,complement(X_27))) )],[refute_0_177,refute_0_178]) ).
cnf(refute_0_180,plain,
( join(X_27,complement(X_27)) != top
| join(X_27,join(complement(X_27),X_29)) != join(join(X_27,complement(X_27)),X_29)
| join(X_27,join(complement(X_27),X_29)) = join(top,X_29) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_27,join(complement(X_27),X_29)),join(join(X_27,complement(X_27)),X_29)) ),[1,0],$fot(top)]]) ).
cnf(refute_0_181,plain,
( join(X_27,join(complement(X_27),X_29)) != join(join(X_27,complement(X_27)),X_29)
| join(X_27,join(complement(X_27),X_29)) = join(top,X_29) ),
inference(resolve,[$cnf( $equal(join(X_27,complement(X_27)),top) )],[refute_0_179,refute_0_180]) ).
cnf(refute_0_182,plain,
join(X_27,join(complement(X_27),X_29)) = join(top,X_29),
inference(resolve,[$cnf( $equal(join(X_27,join(complement(X_27),X_29)),join(join(X_27,complement(X_27)),X_29)) )],[refute_0_176,refute_0_181]) ).
cnf(refute_0_183,plain,
join(X_36,join(complement(X_36),complement(complement(X_36)))) = join(top,complement(complement(X_36))),
inference(subst,[],[refute_0_182:[bind(X_27,$fot(X_36)),bind(X_29,$fot(complement(complement(X_36))))]]) ).
cnf(refute_0_184,plain,
top = join(complement(X_36),complement(complement(X_36))),
inference(subst,[],[refute_0_47:[bind(X0,$fot(complement(X_36)))]]) ).
cnf(refute_0_185,plain,
( top != join(complement(X_36),complement(complement(X_36)))
| join(complement(X_36),complement(complement(X_36))) = top ),
inference(subst,[],[refute_0_4:[bind(X,$fot(top)),bind(Y,$fot(join(complement(X_36),complement(complement(X_36)))))]]) ).
cnf(refute_0_186,plain,
join(complement(X_36),complement(complement(X_36))) = top,
inference(resolve,[$cnf( $equal(top,join(complement(X_36),complement(complement(X_36)))) )],[refute_0_184,refute_0_185]) ).
cnf(refute_0_187,plain,
( join(X_36,join(complement(X_36),complement(complement(X_36)))) != join(top,complement(complement(X_36)))
| join(complement(X_36),complement(complement(X_36))) != top
| join(X_36,top) = join(top,complement(complement(X_36))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_36,join(complement(X_36),complement(complement(X_36)))),join(top,complement(complement(X_36)))) ),[0,1],$fot(top)]]) ).
cnf(refute_0_188,plain,
( join(X_36,join(complement(X_36),complement(complement(X_36)))) != join(top,complement(complement(X_36)))
| join(X_36,top) = join(top,complement(complement(X_36))) ),
inference(resolve,[$cnf( $equal(join(complement(X_36),complement(complement(X_36))),top) )],[refute_0_186,refute_0_187]) ).
cnf(refute_0_189,plain,
join(X_36,top) = join(top,complement(complement(X_36))),
inference(resolve,[$cnf( $equal(join(X_36,join(complement(X_36),complement(complement(X_36)))),join(top,complement(complement(X_36)))) )],[refute_0_183,refute_0_188]) ).
cnf(refute_0_190,plain,
join(X_27,join(complement(X_27),complement(X_27))) = join(top,complement(X_27)),
inference(subst,[],[refute_0_182:[bind(X_29,$fot(complement(X_27)))]]) ).
cnf(refute_0_191,plain,
join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_192,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_6:[bind(X0,$fot(complement(X1))),bind(X1,$fot(composition(converse(X0),complement(composition(X0,X1)))))]]) ).
cnf(refute_0_193,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_194,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( $equal(join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),join(complement(X1),composition(converse(X0),complement(composition(X0,X1))))) )],[refute_0_192,refute_0_193]) ).
cnf(refute_0_195,plain,
join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))) = complement(X1),
inference(resolve,[$cnf( $equal(join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),complement(X1)) )],[refute_0_191,refute_0_194]) ).
cnf(refute_0_196,plain,
join(complement(X_39),composition(converse(one),complement(composition(one,X_39)))) = complement(X_39),
inference(subst,[],[refute_0_195:[bind(X0,$fot(one)),bind(X1,$fot(X_39))]]) ).
cnf(refute_0_197,plain,
converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_198,plain,
converse(composition(converse(X0),X_20)) = composition(converse(X_20),converse(converse(X0))),
inference(subst,[],[refute_0_197:[bind(X0,$fot(converse(X0))),bind(X1,$fot(X_20))]]) ).
cnf(refute_0_199,plain,
( converse(composition(converse(X0),X_20)) != composition(converse(X_20),converse(converse(X0)))
| converse(converse(X0)) != X0
| converse(composition(converse(X0),X_20)) = composition(converse(X_20),X0) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(X0),X_20)),composition(converse(X_20),converse(converse(X0)))) ),[1,1],$fot(X0)]]) ).
cnf(refute_0_200,plain,
( converse(composition(converse(X0),X_20)) != composition(converse(X_20),converse(converse(X0)))
| converse(composition(converse(X0),X_20)) = composition(converse(X_20),X0) ),
inference(resolve,[$cnf( $equal(converse(converse(X0)),X0) )],[refute_0_42,refute_0_199]) ).
cnf(refute_0_201,plain,
converse(composition(converse(X0),X_20)) = composition(converse(X_20),X0),
inference(resolve,[$cnf( $equal(converse(composition(converse(X0),X_20)),composition(converse(X_20),converse(converse(X0)))) )],[refute_0_198,refute_0_200]) ).
cnf(refute_0_202,plain,
converse(composition(converse(X_21),one)) = composition(converse(one),X_21),
inference(subst,[],[refute_0_201:[bind(X0,$fot(X_21)),bind(X_20,$fot(one))]]) ).
cnf(refute_0_203,plain,
composition(X0,one) = X0,
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_204,plain,
composition(converse(X_21),one) = converse(X_21),
inference(subst,[],[refute_0_203:[bind(X0,$fot(converse(X_21)))]]) ).
cnf(refute_0_205,plain,
( composition(converse(X_21),one) != converse(X_21)
| converse(composition(converse(X_21),one)) != composition(converse(one),X_21)
| converse(converse(X_21)) = composition(converse(one),X_21) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(X_21),one)),composition(converse(one),X_21)) ),[0,0],$fot(converse(X_21))]]) ).
cnf(refute_0_206,plain,
( converse(composition(converse(X_21),one)) != composition(converse(one),X_21)
| converse(converse(X_21)) = composition(converse(one),X_21) ),
inference(resolve,[$cnf( $equal(composition(converse(X_21),one),converse(X_21)) )],[refute_0_204,refute_0_205]) ).
cnf(refute_0_207,plain,
converse(converse(X_21)) = composition(converse(one),X_21),
inference(resolve,[$cnf( $equal(converse(composition(converse(X_21),one)),composition(converse(one),X_21)) )],[refute_0_202,refute_0_206]) ).
cnf(refute_0_208,plain,
converse(converse(X_21)) = X_21,
inference(subst,[],[refute_0_42:[bind(X0,$fot(X_21))]]) ).
cnf(refute_0_209,plain,
( converse(converse(X_21)) != X_21
| converse(converse(X_21)) != composition(converse(one),X_21)
| X_21 = composition(converse(one),X_21) ),
introduced(tautology,[equality,[$cnf( $equal(converse(converse(X_21)),composition(converse(one),X_21)) ),[0],$fot(X_21)]]) ).
cnf(refute_0_210,plain,
( converse(converse(X_21)) != composition(converse(one),X_21)
| X_21 = composition(converse(one),X_21) ),
inference(resolve,[$cnf( $equal(converse(converse(X_21)),X_21) )],[refute_0_208,refute_0_209]) ).
cnf(refute_0_211,plain,
X_21 = composition(converse(one),X_21),
inference(resolve,[$cnf( $equal(converse(converse(X_21)),composition(converse(one),X_21)) )],[refute_0_207,refute_0_210]) ).
cnf(refute_0_212,plain,
composition(converse(one),one) = converse(one),
inference(subst,[],[refute_0_203:[bind(X0,$fot(converse(one)))]]) ).
cnf(refute_0_213,plain,
one = composition(converse(one),one),
inference(subst,[],[refute_0_211:[bind(X_21,$fot(one))]]) ).
cnf(refute_0_214,plain,
( one != composition(converse(one),one)
| composition(converse(one),one) = one ),
inference(subst,[],[refute_0_4:[bind(X,$fot(one)),bind(Y,$fot(composition(converse(one),one)))]]) ).
cnf(refute_0_215,plain,
composition(converse(one),one) = one,
inference(resolve,[$cnf( $equal(one,composition(converse(one),one)) )],[refute_0_213,refute_0_214]) ).
cnf(refute_0_216,plain,
( composition(converse(one),one) != converse(one)
| composition(converse(one),one) != one
| one = converse(one) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(one),one),converse(one)) ),[0],$fot(one)]]) ).
cnf(refute_0_217,plain,
( composition(converse(one),one) != converse(one)
| one = converse(one) ),
inference(resolve,[$cnf( $equal(composition(converse(one),one),one) )],[refute_0_215,refute_0_216]) ).
cnf(refute_0_218,plain,
one = converse(one),
inference(resolve,[$cnf( $equal(composition(converse(one),one),converse(one)) )],[refute_0_212,refute_0_217]) ).
cnf(refute_0_219,plain,
( one != converse(one)
| converse(one) = one ),
inference(subst,[],[refute_0_4:[bind(X,$fot(one)),bind(Y,$fot(converse(one)))]]) ).
cnf(refute_0_220,plain,
converse(one) = one,
inference(resolve,[$cnf( $equal(one,converse(one)) )],[refute_0_218,refute_0_219]) ).
cnf(refute_0_221,plain,
composition(converse(one),X_21) = composition(converse(one),X_21),
introduced(tautology,[refl,[$fot(composition(converse(one),X_21))]]) ).
cnf(refute_0_222,plain,
( composition(converse(one),X_21) != composition(converse(one),X_21)
| converse(one) != one
| composition(converse(one),X_21) = composition(one,X_21) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(one),X_21),composition(converse(one),X_21)) ),[1,0],$fot(one)]]) ).
cnf(refute_0_223,plain,
( converse(one) != one
| composition(converse(one),X_21) = composition(one,X_21) ),
inference(resolve,[$cnf( $equal(composition(converse(one),X_21),composition(converse(one),X_21)) )],[refute_0_221,refute_0_222]) ).
cnf(refute_0_224,plain,
composition(converse(one),X_21) = composition(one,X_21),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_220,refute_0_223]) ).
cnf(refute_0_225,plain,
( X_21 != composition(converse(one),X_21)
| composition(converse(one),X_21) != composition(one,X_21)
| X_21 = composition(one,X_21) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_21,composition(one,X_21)) ),[0],$fot(composition(converse(one),X_21))]]) ).
cnf(refute_0_226,plain,
( X_21 != composition(converse(one),X_21)
| X_21 = composition(one,X_21) ),
inference(resolve,[$cnf( $equal(composition(converse(one),X_21),composition(one,X_21)) )],[refute_0_224,refute_0_225]) ).
cnf(refute_0_227,plain,
X_21 = composition(one,X_21),
inference(resolve,[$cnf( $equal(X_21,composition(converse(one),X_21)) )],[refute_0_211,refute_0_226]) ).
cnf(refute_0_228,plain,
X_39 = composition(one,X_39),
inference(subst,[],[refute_0_227:[bind(X_21,$fot(X_39))]]) ).
cnf(refute_0_229,plain,
( X_39 != composition(one,X_39)
| composition(one,X_39) = X_39 ),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_39)),bind(Y,$fot(composition(one,X_39)))]]) ).
cnf(refute_0_230,plain,
composition(one,X_39) = X_39,
inference(resolve,[$cnf( $equal(X_39,composition(one,X_39)) )],[refute_0_228,refute_0_229]) ).
cnf(refute_0_231,plain,
( composition(one,X_39) != X_39
| join(complement(X_39),composition(converse(one),complement(composition(one,X_39)))) != complement(X_39)
| join(complement(X_39),composition(converse(one),complement(X_39))) = complement(X_39) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_39),composition(converse(one),complement(composition(one,X_39)))),complement(X_39)) ),[0,1,1,0],$fot(X_39)]]) ).
cnf(refute_0_232,plain,
( join(complement(X_39),composition(converse(one),complement(composition(one,X_39)))) != complement(X_39)
| join(complement(X_39),composition(converse(one),complement(X_39))) = complement(X_39) ),
inference(resolve,[$cnf( $equal(composition(one,X_39),X_39) )],[refute_0_230,refute_0_231]) ).
cnf(refute_0_233,plain,
join(complement(X_39),composition(converse(one),complement(X_39))) = complement(X_39),
inference(resolve,[$cnf( $equal(join(complement(X_39),composition(converse(one),complement(composition(one,X_39)))),complement(X_39)) )],[refute_0_196,refute_0_232]) ).
cnf(refute_0_234,plain,
( X_21 != composition(one,X_21)
| composition(one,X_21) = X_21 ),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_21)),bind(Y,$fot(composition(one,X_21)))]]) ).
cnf(refute_0_235,plain,
composition(one,X_21) = X_21,
inference(resolve,[$cnf( $equal(X_21,composition(one,X_21)) )],[refute_0_227,refute_0_234]) ).
cnf(refute_0_236,plain,
composition(one,complement(X_39)) = complement(X_39),
inference(subst,[],[refute_0_235:[bind(X_21,$fot(complement(X_39)))]]) ).
cnf(refute_0_237,plain,
composition(converse(one),complement(X_39)) = composition(converse(one),complement(X_39)),
introduced(tautology,[refl,[$fot(composition(converse(one),complement(X_39)))]]) ).
cnf(refute_0_238,plain,
( composition(converse(one),complement(X_39)) != composition(converse(one),complement(X_39))
| converse(one) != one
| composition(converse(one),complement(X_39)) = composition(one,complement(X_39)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(one),complement(X_39)),composition(converse(one),complement(X_39))) ),[1,0],$fot(one)]]) ).
cnf(refute_0_239,plain,
( converse(one) != one
| composition(converse(one),complement(X_39)) = composition(one,complement(X_39)) ),
inference(resolve,[$cnf( $equal(composition(converse(one),complement(X_39)),composition(converse(one),complement(X_39))) )],[refute_0_237,refute_0_238]) ).
cnf(refute_0_240,plain,
composition(converse(one),complement(X_39)) = composition(one,complement(X_39)),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_220,refute_0_239]) ).
cnf(refute_0_241,plain,
( composition(converse(one),complement(X_39)) != composition(one,complement(X_39))
| composition(one,complement(X_39)) != complement(X_39)
| composition(converse(one),complement(X_39)) = complement(X_39) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(composition(converse(one),complement(X_39)))),bind(Y,$fot(composition(one,complement(X_39)))),bind(Z,$fot(complement(X_39)))]]) ).
cnf(refute_0_242,plain,
( composition(one,complement(X_39)) != complement(X_39)
| composition(converse(one),complement(X_39)) = complement(X_39) ),
inference(resolve,[$cnf( $equal(composition(converse(one),complement(X_39)),composition(one,complement(X_39))) )],[refute_0_240,refute_0_241]) ).
cnf(refute_0_243,plain,
composition(converse(one),complement(X_39)) = complement(X_39),
inference(resolve,[$cnf( $equal(composition(one,complement(X_39)),complement(X_39)) )],[refute_0_236,refute_0_242]) ).
cnf(refute_0_244,plain,
join(complement(X_39),composition(converse(one),complement(X_39))) = join(complement(X_39),composition(converse(one),complement(X_39))),
introduced(tautology,[refl,[$fot(join(complement(X_39),composition(converse(one),complement(X_39))))]]) ).
cnf(refute_0_245,plain,
( composition(converse(one),complement(X_39)) != complement(X_39)
| join(complement(X_39),composition(converse(one),complement(X_39))) != join(complement(X_39),composition(converse(one),complement(X_39)))
| join(complement(X_39),composition(converse(one),complement(X_39))) = join(complement(X_39),complement(X_39)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_39),composition(converse(one),complement(X_39))),join(complement(X_39),composition(converse(one),complement(X_39)))) ),[1,1],$fot(complement(X_39))]]) ).
cnf(refute_0_246,plain,
( composition(converse(one),complement(X_39)) != complement(X_39)
| join(complement(X_39),composition(converse(one),complement(X_39))) = join(complement(X_39),complement(X_39)) ),
inference(resolve,[$cnf( $equal(join(complement(X_39),composition(converse(one),complement(X_39))),join(complement(X_39),composition(converse(one),complement(X_39)))) )],[refute_0_244,refute_0_245]) ).
cnf(refute_0_247,plain,
join(complement(X_39),composition(converse(one),complement(X_39))) = join(complement(X_39),complement(X_39)),
inference(resolve,[$cnf( $equal(composition(converse(one),complement(X_39)),complement(X_39)) )],[refute_0_243,refute_0_246]) ).
cnf(refute_0_248,plain,
( join(complement(X_39),composition(converse(one),complement(X_39))) != complement(X_39)
| join(complement(X_39),composition(converse(one),complement(X_39))) != join(complement(X_39),complement(X_39))
| join(complement(X_39),complement(X_39)) = complement(X_39) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_39),composition(converse(one),complement(X_39))),complement(X_39)) ),[0],$fot(join(complement(X_39),complement(X_39)))]]) ).
cnf(refute_0_249,plain,
( join(complement(X_39),composition(converse(one),complement(X_39))) != complement(X_39)
| join(complement(X_39),complement(X_39)) = complement(X_39) ),
inference(resolve,[$cnf( $equal(join(complement(X_39),composition(converse(one),complement(X_39))),join(complement(X_39),complement(X_39))) )],[refute_0_247,refute_0_248]) ).
cnf(refute_0_250,plain,
join(complement(X_39),complement(X_39)) = complement(X_39),
inference(resolve,[$cnf( $equal(join(complement(X_39),composition(converse(one),complement(X_39))),complement(X_39)) )],[refute_0_233,refute_0_249]) ).
cnf(refute_0_251,plain,
join(complement(X_27),complement(X_27)) = complement(X_27),
inference(subst,[],[refute_0_250:[bind(X_39,$fot(X_27))]]) ).
cnf(refute_0_252,plain,
( join(X_27,join(complement(X_27),complement(X_27))) != join(top,complement(X_27))
| join(complement(X_27),complement(X_27)) != complement(X_27)
| join(X_27,complement(X_27)) = join(top,complement(X_27)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_27,join(complement(X_27),complement(X_27))),join(top,complement(X_27))) ),[0,1],$fot(complement(X_27))]]) ).
cnf(refute_0_253,plain,
( join(X_27,join(complement(X_27),complement(X_27))) != join(top,complement(X_27))
| join(X_27,complement(X_27)) = join(top,complement(X_27)) ),
inference(resolve,[$cnf( $equal(join(complement(X_27),complement(X_27)),complement(X_27)) )],[refute_0_251,refute_0_252]) ).
cnf(refute_0_254,plain,
join(X_27,complement(X_27)) = join(top,complement(X_27)),
inference(resolve,[$cnf( $equal(join(X_27,join(complement(X_27),complement(X_27))),join(top,complement(X_27))) )],[refute_0_190,refute_0_253]) ).
cnf(refute_0_255,plain,
( join(X_27,complement(X_27)) != join(top,complement(X_27))
| join(X_27,complement(X_27)) != top
| top = join(top,complement(X_27)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_27,complement(X_27)),join(top,complement(X_27))) ),[0],$fot(top)]]) ).
cnf(refute_0_256,plain,
( join(X_27,complement(X_27)) != join(top,complement(X_27))
| top = join(top,complement(X_27)) ),
inference(resolve,[$cnf( $equal(join(X_27,complement(X_27)),top) )],[refute_0_179,refute_0_255]) ).
cnf(refute_0_257,plain,
top = join(top,complement(X_27)),
inference(resolve,[$cnf( $equal(join(X_27,complement(X_27)),join(top,complement(X_27))) )],[refute_0_254,refute_0_256]) ).
cnf(refute_0_258,plain,
( top != join(top,complement(X_27))
| join(top,complement(X_27)) = top ),
inference(subst,[],[refute_0_4:[bind(X,$fot(top)),bind(Y,$fot(join(top,complement(X_27))))]]) ).
cnf(refute_0_259,plain,
join(top,complement(X_27)) = top,
inference(resolve,[$cnf( $equal(top,join(top,complement(X_27))) )],[refute_0_257,refute_0_258]) ).
cnf(refute_0_260,plain,
join(top,complement(complement(X_36))) = top,
inference(subst,[],[refute_0_259:[bind(X_27,$fot(complement(X_36)))]]) ).
cnf(refute_0_261,plain,
( join(X_36,top) != join(top,complement(complement(X_36)))
| join(top,complement(complement(X_36))) != top
| join(X_36,top) = top ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_36,top),top) ),[0],$fot(join(top,complement(complement(X_36))))]]) ).
cnf(refute_0_262,plain,
( join(X_36,top) != join(top,complement(complement(X_36)))
| join(X_36,top) = top ),
inference(resolve,[$cnf( $equal(join(top,complement(complement(X_36))),top) )],[refute_0_260,refute_0_261]) ).
cnf(refute_0_263,plain,
join(X_36,top) = top,
inference(resolve,[$cnf( $equal(join(X_36,top),join(top,complement(complement(X_36)))) )],[refute_0_189,refute_0_262]) ).
cnf(refute_0_264,plain,
join(X_27,top) = top,
inference(subst,[],[refute_0_263:[bind(X_36,$fot(X_27))]]) ).
cnf(refute_0_265,plain,
( join(X_27,top) != join(zero,join(zero,join(meet(top,top),X_27)))
| join(X_27,top) != top
| top = join(zero,join(zero,join(meet(top,top),X_27))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_27,top),join(zero,join(zero,join(meet(top,top),X_27)))) ),[0],$fot(top)]]) ).
cnf(refute_0_266,plain,
( join(X_27,top) != join(zero,join(zero,join(meet(top,top),X_27)))
| top = join(zero,join(zero,join(meet(top,top),X_27))) ),
inference(resolve,[$cnf( $equal(join(X_27,top),top) )],[refute_0_264,refute_0_265]) ).
cnf(refute_0_267,plain,
join(top,join(zero,X_27)) = join(top,X_27),
inference(subst,[],[refute_0_94:[bind(X_29,$fot(X_27))]]) ).
cnf(refute_0_268,plain,
join(X_27,join(X_28,X_29)) = join(join(X_27,X_28),X_29),
inference(subst,[],[refute_0_56:[bind(X0,$fot(X_27)),bind(X1,$fot(X_28)),bind(X2,$fot(X_29))]]) ).
cnf(refute_0_269,plain,
join(X_28,X_27) = join(X_27,X_28),
inference(subst,[],[refute_0_1:[bind(X0,$fot(X_28)),bind(X1,$fot(X_27))]]) ).
cnf(refute_0_270,plain,
( join(X_28,X_27) != join(X_27,X_28)
| join(X_27,X_28) = join(X_28,X_27) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(join(X_28,X_27))),bind(Y,$fot(join(X_27,X_28)))]]) ).
cnf(refute_0_271,plain,
join(X_27,X_28) = join(X_28,X_27),
inference(resolve,[$cnf( $equal(join(X_28,X_27),join(X_27,X_28)) )],[refute_0_269,refute_0_270]) ).
cnf(refute_0_272,plain,
( join(X_27,X_28) != join(X_28,X_27)
| join(X_27,join(X_28,X_29)) != join(join(X_27,X_28),X_29)
| join(X_27,join(X_28,X_29)) = join(join(X_28,X_27),X_29) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_27,join(X_28,X_29)),join(join(X_27,X_28),X_29)) ),[1,0],$fot(join(X_28,X_27))]]) ).
cnf(refute_0_273,plain,
( join(X_27,join(X_28,X_29)) != join(join(X_27,X_28),X_29)
| join(X_27,join(X_28,X_29)) = join(join(X_28,X_27),X_29) ),
inference(resolve,[$cnf( $equal(join(X_27,X_28),join(X_28,X_27)) )],[refute_0_271,refute_0_272]) ).
cnf(refute_0_274,plain,
join(X_27,join(X_28,X_29)) = join(join(X_28,X_27),X_29),
inference(resolve,[$cnf( $equal(join(X_27,join(X_28,X_29)),join(join(X_27,X_28),X_29)) )],[refute_0_268,refute_0_273]) ).
cnf(refute_0_275,plain,
join(join(X_28,X_27),X_29) = join(X_28,join(X_27,X_29)),
inference(subst,[],[refute_0_145:[bind(X0,$fot(X_28)),bind(X1,$fot(X_27)),bind(X2,$fot(X_29))]]) ).
cnf(refute_0_276,plain,
( join(X_27,join(X_28,X_29)) != join(join(X_28,X_27),X_29)
| join(join(X_28,X_27),X_29) != join(X_28,join(X_27,X_29))
| join(X_27,join(X_28,X_29)) = join(X_28,join(X_27,X_29)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_27,join(X_28,X_29)),join(X_28,join(X_27,X_29))) ),[0],$fot(join(join(X_28,X_27),X_29))]]) ).
cnf(refute_0_277,plain,
( join(X_27,join(X_28,X_29)) != join(join(X_28,X_27),X_29)
| join(X_27,join(X_28,X_29)) = join(X_28,join(X_27,X_29)) ),
inference(resolve,[$cnf( $equal(join(join(X_28,X_27),X_29),join(X_28,join(X_27,X_29))) )],[refute_0_275,refute_0_276]) ).
cnf(refute_0_278,plain,
join(X_27,join(X_28,X_29)) = join(X_28,join(X_27,X_29)),
inference(resolve,[$cnf( $equal(join(X_27,join(X_28,X_29)),join(join(X_28,X_27),X_29)) )],[refute_0_274,refute_0_277]) ).
cnf(refute_0_279,plain,
( join(X_27,join(X_28,X_29)) != join(X_28,join(X_27,X_29))
| join(X_28,join(X_27,X_29)) = join(X_27,join(X_28,X_29)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(join(X_27,join(X_28,X_29)))),bind(Y,$fot(join(X_28,join(X_27,X_29))))]]) ).
cnf(refute_0_280,plain,
join(X_28,join(X_27,X_29)) = join(X_27,join(X_28,X_29)),
inference(resolve,[$cnf( $equal(join(X_27,join(X_28,X_29)),join(X_28,join(X_27,X_29))) )],[refute_0_278,refute_0_279]) ).
cnf(refute_0_281,plain,
join(zero,join(top,X_27)) = join(top,join(zero,X_27)),
inference(subst,[],[refute_0_280:[bind(X_27,$fot(top)),bind(X_28,$fot(zero)),bind(X_29,$fot(X_27))]]) ).
cnf(refute_0_282,plain,
( join(top,join(zero,X_27)) != join(top,X_27)
| join(zero,join(top,X_27)) != join(top,join(zero,X_27))
| join(zero,join(top,X_27)) = join(top,X_27) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(join(zero,join(top,X_27)))),bind(Y,$fot(join(top,join(zero,X_27)))),bind(Z,$fot(join(top,X_27)))]]) ).
cnf(refute_0_283,plain,
( join(top,join(zero,X_27)) != join(top,X_27)
| join(zero,join(top,X_27)) = join(top,X_27) ),
inference(resolve,[$cnf( $equal(join(zero,join(top,X_27)),join(top,join(zero,X_27))) )],[refute_0_281,refute_0_282]) ).
cnf(refute_0_284,plain,
join(zero,join(top,X_27)) = join(top,X_27),
inference(resolve,[$cnf( $equal(join(top,join(zero,X_27)),join(top,X_27)) )],[refute_0_267,refute_0_283]) ).
cnf(refute_0_285,plain,
join(zero,join(complement(zero),X_27)) = join(top,X_27),
inference(subst,[],[refute_0_182:[bind(X_27,$fot(zero)),bind(X_29,$fot(X_27))]]) ).
cnf(refute_0_286,plain,
complement(complement(top)) = complement(complement(top)),
introduced(tautology,[refl,[$fot(complement(complement(top)))]]) ).
cnf(refute_0_287,plain,
( complement(complement(top)) != complement(complement(top))
| complement(top) != zero
| complement(complement(top)) = complement(zero) ),
introduced(tautology,[equality,[$cnf( $equal(complement(complement(top)),complement(complement(top))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_288,plain,
( complement(top) != zero
| complement(complement(top)) = complement(zero) ),
inference(resolve,[$cnf( $equal(complement(complement(top)),complement(complement(top))) )],[refute_0_286,refute_0_287]) ).
cnf(refute_0_289,plain,
complement(complement(top)) = complement(zero),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_86,refute_0_288]) ).
cnf(refute_0_290,plain,
meet(X1,X1) = complement(join(complement(X1),complement(X1))),
inference(subst,[],[refute_0_12:[bind(X0,$fot(X1))]]) ).
cnf(refute_0_291,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(subst,[],[refute_0_250:[bind(X_39,$fot(X1))]]) ).
cnf(refute_0_292,plain,
( join(complement(X1),complement(X1)) != complement(X1)
| meet(X1,X1) != complement(join(complement(X1),complement(X1)))
| meet(X1,X1) = complement(complement(X1)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X1,X1),complement(join(complement(X1),complement(X1)))) ),[1,0],$fot(complement(X1))]]) ).
cnf(refute_0_293,plain,
( meet(X1,X1) != complement(join(complement(X1),complement(X1)))
| meet(X1,X1) = complement(complement(X1)) ),
inference(resolve,[$cnf( $equal(join(complement(X1),complement(X1)),complement(X1)) )],[refute_0_291,refute_0_292]) ).
cnf(refute_0_294,plain,
meet(X1,X1) = complement(complement(X1)),
inference(resolve,[$cnf( $equal(meet(X1,X1),complement(join(complement(X1),complement(X1)))) )],[refute_0_290,refute_0_293]) ).
cnf(refute_0_295,plain,
meet(top,top) = complement(complement(top)),
inference(subst,[],[refute_0_294:[bind(X1,$fot(top))]]) ).
cnf(refute_0_296,plain,
( complement(complement(top)) != complement(zero)
| meet(top,top) != complement(complement(top))
| meet(top,top) = complement(zero) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(meet(top,top))),bind(Y,$fot(complement(complement(top)))),bind(Z,$fot(complement(zero)))]]) ).
cnf(refute_0_297,plain,
( complement(complement(top)) != complement(zero)
| meet(top,top) = complement(zero) ),
inference(resolve,[$cnf( $equal(meet(top,top),complement(complement(top))) )],[refute_0_295,refute_0_296]) ).
cnf(refute_0_298,plain,
meet(top,top) = complement(zero),
inference(resolve,[$cnf( $equal(complement(complement(top)),complement(zero)) )],[refute_0_289,refute_0_297]) ).
cnf(refute_0_299,plain,
join(meet(top,top),X_27) = join(meet(top,top),X_27),
introduced(tautology,[refl,[$fot(join(meet(top,top),X_27))]]) ).
cnf(refute_0_300,plain,
( join(meet(top,top),X_27) != join(meet(top,top),X_27)
| meet(top,top) != complement(zero)
| join(meet(top,top),X_27) = join(complement(zero),X_27) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(top,top),X_27),join(meet(top,top),X_27)) ),[1,0],$fot(complement(zero))]]) ).
cnf(refute_0_301,plain,
( meet(top,top) != complement(zero)
| join(meet(top,top),X_27) = join(complement(zero),X_27) ),
inference(resolve,[$cnf( $equal(join(meet(top,top),X_27),join(meet(top,top),X_27)) )],[refute_0_299,refute_0_300]) ).
cnf(refute_0_302,plain,
join(meet(top,top),X_27) = join(complement(zero),X_27),
inference(resolve,[$cnf( $equal(meet(top,top),complement(zero)) )],[refute_0_298,refute_0_301]) ).
cnf(refute_0_303,plain,
join(zero,join(meet(top,top),X_27)) = join(zero,join(meet(top,top),X_27)),
introduced(tautology,[refl,[$fot(join(zero,join(meet(top,top),X_27)))]]) ).
cnf(refute_0_304,plain,
( join(meet(top,top),X_27) != join(complement(zero),X_27)
| join(zero,join(meet(top,top),X_27)) != join(zero,join(meet(top,top),X_27))
| join(zero,join(meet(top,top),X_27)) = join(zero,join(complement(zero),X_27)) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(meet(top,top),X_27)),join(zero,join(meet(top,top),X_27))) ),[1,1],$fot(join(complement(zero),X_27))]]) ).
cnf(refute_0_305,plain,
( join(meet(top,top),X_27) != join(complement(zero),X_27)
| join(zero,join(meet(top,top),X_27)) = join(zero,join(complement(zero),X_27)) ),
inference(resolve,[$cnf( $equal(join(zero,join(meet(top,top),X_27)),join(zero,join(meet(top,top),X_27))) )],[refute_0_303,refute_0_304]) ).
cnf(refute_0_306,plain,
join(zero,join(meet(top,top),X_27)) = join(zero,join(complement(zero),X_27)),
inference(resolve,[$cnf( $equal(join(meet(top,top),X_27),join(complement(zero),X_27)) )],[refute_0_302,refute_0_305]) ).
cnf(refute_0_307,plain,
( join(zero,join(complement(zero),X_27)) != join(top,X_27)
| join(zero,join(meet(top,top),X_27)) != join(zero,join(complement(zero),X_27))
| join(zero,join(meet(top,top),X_27)) = join(top,X_27) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(join(zero,join(meet(top,top),X_27)))),bind(Y,$fot(join(zero,join(complement(zero),X_27)))),bind(Z,$fot(join(top,X_27)))]]) ).
cnf(refute_0_308,plain,
( join(zero,join(complement(zero),X_27)) != join(top,X_27)
| join(zero,join(meet(top,top),X_27)) = join(top,X_27) ),
inference(resolve,[$cnf( $equal(join(zero,join(meet(top,top),X_27)),join(zero,join(complement(zero),X_27))) )],[refute_0_306,refute_0_307]) ).
cnf(refute_0_309,plain,
join(zero,join(meet(top,top),X_27)) = join(top,X_27),
inference(resolve,[$cnf( $equal(join(zero,join(complement(zero),X_27)),join(top,X_27)) )],[refute_0_285,refute_0_308]) ).
cnf(refute_0_310,plain,
join(zero,join(zero,join(meet(top,top),X_27))) = join(zero,join(zero,join(meet(top,top),X_27))),
introduced(tautology,[refl,[$fot(join(zero,join(zero,join(meet(top,top),X_27))))]]) ).
cnf(refute_0_311,plain,
( join(zero,join(meet(top,top),X_27)) != join(top,X_27)
| join(zero,join(zero,join(meet(top,top),X_27))) != join(zero,join(zero,join(meet(top,top),X_27)))
| join(zero,join(zero,join(meet(top,top),X_27))) = join(zero,join(top,X_27)) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(zero,join(meet(top,top),X_27))),join(zero,join(zero,join(meet(top,top),X_27)))) ),[1,1],$fot(join(top,X_27))]]) ).
cnf(refute_0_312,plain,
( join(zero,join(meet(top,top),X_27)) != join(top,X_27)
| join(zero,join(zero,join(meet(top,top),X_27))) = join(zero,join(top,X_27)) ),
inference(resolve,[$cnf( $equal(join(zero,join(zero,join(meet(top,top),X_27))),join(zero,join(zero,join(meet(top,top),X_27)))) )],[refute_0_310,refute_0_311]) ).
cnf(refute_0_313,plain,
join(zero,join(zero,join(meet(top,top),X_27))) = join(zero,join(top,X_27)),
inference(resolve,[$cnf( $equal(join(zero,join(meet(top,top),X_27)),join(top,X_27)) )],[refute_0_309,refute_0_312]) ).
cnf(refute_0_314,plain,
( join(zero,join(top,X_27)) != join(top,X_27)
| join(zero,join(zero,join(meet(top,top),X_27))) != join(zero,join(top,X_27))
| join(zero,join(zero,join(meet(top,top),X_27))) = join(top,X_27) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(join(zero,join(zero,join(meet(top,top),X_27))))),bind(Y,$fot(join(zero,join(top,X_27)))),bind(Z,$fot(join(top,X_27)))]]) ).
cnf(refute_0_315,plain,
( join(zero,join(top,X_27)) != join(top,X_27)
| join(zero,join(zero,join(meet(top,top),X_27))) = join(top,X_27) ),
inference(resolve,[$cnf( $equal(join(zero,join(zero,join(meet(top,top),X_27))),join(zero,join(top,X_27))) )],[refute_0_313,refute_0_314]) ).
cnf(refute_0_316,plain,
join(zero,join(zero,join(meet(top,top),X_27))) = join(top,X_27),
inference(resolve,[$cnf( $equal(join(zero,join(top,X_27)),join(top,X_27)) )],[refute_0_284,refute_0_315]) ).
cnf(refute_0_317,plain,
( join(zero,join(zero,join(meet(top,top),X_27))) != join(top,X_27)
| top != join(zero,join(zero,join(meet(top,top),X_27)))
| top = join(top,X_27) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(zero,join(zero,join(meet(top,top),X_27)))) ),[1],$fot(join(top,X_27))]]) ).
cnf(refute_0_318,plain,
( top != join(zero,join(zero,join(meet(top,top),X_27)))
| top = join(top,X_27) ),
inference(resolve,[$cnf( $equal(join(zero,join(zero,join(meet(top,top),X_27))),join(top,X_27)) )],[refute_0_316,refute_0_317]) ).
cnf(refute_0_319,plain,
( join(X_27,top) != join(zero,join(zero,join(meet(top,top),X_27)))
| top = join(top,X_27) ),
inference(resolve,[$cnf( $equal(top,join(zero,join(zero,join(meet(top,top),X_27)))) )],[refute_0_266,refute_0_318]) ).
cnf(refute_0_320,plain,
top = join(top,X_27),
inference(resolve,[$cnf( $equal(join(X_27,top),join(zero,join(zero,join(meet(top,top),X_27)))) )],[refute_0_175,refute_0_319]) ).
cnf(refute_0_321,plain,
( top != join(top,X_27)
| join(top,X_27) = top ),
inference(subst,[],[refute_0_4:[bind(X,$fot(top)),bind(Y,$fot(join(top,X_27)))]]) ).
cnf(refute_0_322,plain,
join(top,X_27) = top,
inference(resolve,[$cnf( $equal(top,join(top,X_27)) )],[refute_0_320,refute_0_321]) ).
cnf(refute_0_323,plain,
join(top,converse(top)) = top,
inference(subst,[],[refute_0_322:[bind(X_27,$fot(converse(top)))]]) ).
cnf(refute_0_324,plain,
( join(top,converse(top)) != join(converse(top),complement(converse(zero)))
| join(top,converse(top)) != top
| top = join(converse(top),complement(converse(zero))) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,converse(top)),join(converse(top),complement(converse(zero)))) ),[0],$fot(top)]]) ).
cnf(refute_0_325,plain,
( join(top,converse(top)) != join(converse(top),complement(converse(zero)))
| top = join(converse(top),complement(converse(zero))) ),
inference(resolve,[$cnf( $equal(join(top,converse(top)),top) )],[refute_0_323,refute_0_324]) ).
cnf(refute_0_326,plain,
top = join(converse(top),complement(converse(zero))),
inference(resolve,[$cnf( $equal(join(top,converse(top)),join(converse(top),complement(converse(zero)))) )],[refute_0_128,refute_0_325]) ).
cnf(refute_0_327,plain,
( top != join(converse(top),complement(converse(zero)))
| join(converse(top),complement(converse(zero))) = top ),
inference(subst,[],[refute_0_4:[bind(X,$fot(top)),bind(Y,$fot(join(converse(top),complement(converse(zero)))))]]) ).
cnf(refute_0_328,plain,
join(converse(top),complement(converse(zero))) = top,
inference(resolve,[$cnf( $equal(top,join(converse(top),complement(converse(zero)))) )],[refute_0_326,refute_0_327]) ).
cnf(refute_0_329,plain,
( converse(join(converse(top),complement(converse(zero)))) != join(converse(converse(top)),converse(complement(converse(zero))))
| join(converse(top),complement(converse(zero))) != top
| converse(top) = join(converse(converse(top)),converse(complement(converse(zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(top),complement(converse(zero)))),join(converse(converse(top)),converse(complement(converse(zero))))) ),[0,0],$fot(top)]]) ).
cnf(refute_0_330,plain,
( converse(join(converse(top),complement(converse(zero)))) != join(converse(converse(top)),converse(complement(converse(zero))))
| converse(top) = join(converse(converse(top)),converse(complement(converse(zero)))) ),
inference(resolve,[$cnf( $equal(join(converse(top),complement(converse(zero))),top) )],[refute_0_328,refute_0_329]) ).
cnf(refute_0_331,plain,
converse(top) = join(converse(converse(top)),converse(complement(converse(zero)))),
inference(resolve,[$cnf( $equal(converse(join(converse(top),complement(converse(zero)))),join(converse(converse(top)),converse(complement(converse(zero))))) )],[refute_0_54,refute_0_330]) ).
cnf(refute_0_332,plain,
join(top,converse(complement(converse(zero)))) = top,
inference(subst,[],[refute_0_322:[bind(X_27,$fot(converse(complement(converse(zero)))))]]) ).
cnf(refute_0_333,plain,
converse(join(converse(top),complement(converse(zero)))) = join(top,converse(complement(converse(zero)))),
inference(subst,[],[refute_0_45:[bind(X0,$fot(top)),bind(X_13,$fot(complement(converse(zero))))]]) ).
cnf(refute_0_334,plain,
( converse(join(converse(top),complement(converse(zero)))) != join(top,converse(complement(converse(zero))))
| join(top,converse(complement(converse(zero)))) != top
| converse(join(converse(top),complement(converse(zero)))) = top ),
inference(subst,[],[refute_0_20:[bind(X,$fot(converse(join(converse(top),complement(converse(zero)))))),bind(Y,$fot(join(top,converse(complement(converse(zero)))))),bind(Z,$fot(top))]]) ).
cnf(refute_0_335,plain,
( join(top,converse(complement(converse(zero)))) != top
| converse(join(converse(top),complement(converse(zero)))) = top ),
inference(resolve,[$cnf( $equal(converse(join(converse(top),complement(converse(zero)))),join(top,converse(complement(converse(zero))))) )],[refute_0_333,refute_0_334]) ).
cnf(refute_0_336,plain,
converse(join(converse(top),complement(converse(zero)))) = top,
inference(resolve,[$cnf( $equal(join(top,converse(complement(converse(zero)))),top) )],[refute_0_332,refute_0_335]) ).
cnf(refute_0_337,plain,
join(converse(converse(top)),converse(complement(converse(zero)))) = converse(join(converse(top),complement(converse(zero)))),
inference(subst,[],[refute_0_120:[bind(X0,$fot(converse(top))),bind(X1,$fot(complement(converse(zero))))]]) ).
cnf(refute_0_338,plain,
( converse(join(converse(top),complement(converse(zero)))) != top
| join(converse(converse(top)),converse(complement(converse(zero)))) != converse(join(converse(top),complement(converse(zero))))
| join(converse(converse(top)),converse(complement(converse(zero)))) = top ),
inference(subst,[],[refute_0_20:[bind(X,$fot(join(converse(converse(top)),converse(complement(converse(zero)))))),bind(Y,$fot(converse(join(converse(top),complement(converse(zero)))))),bind(Z,$fot(top))]]) ).
cnf(refute_0_339,plain,
( converse(join(converse(top),complement(converse(zero)))) != top
| join(converse(converse(top)),converse(complement(converse(zero)))) = top ),
inference(resolve,[$cnf( $equal(join(converse(converse(top)),converse(complement(converse(zero)))),converse(join(converse(top),complement(converse(zero))))) )],[refute_0_337,refute_0_338]) ).
cnf(refute_0_340,plain,
join(converse(converse(top)),converse(complement(converse(zero)))) = top,
inference(resolve,[$cnf( $equal(converse(join(converse(top),complement(converse(zero)))),top) )],[refute_0_336,refute_0_339]) ).
cnf(refute_0_341,plain,
( converse(top) != join(converse(converse(top)),converse(complement(converse(zero))))
| join(converse(converse(top)),converse(complement(converse(zero)))) != top
| converse(top) = top ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(top),top) ),[0],$fot(join(converse(converse(top)),converse(complement(converse(zero)))))]]) ).
cnf(refute_0_342,plain,
( converse(top) != join(converse(converse(top)),converse(complement(converse(zero))))
| converse(top) = top ),
inference(resolve,[$cnf( $equal(join(converse(converse(top)),converse(complement(converse(zero)))),top) )],[refute_0_340,refute_0_341]) ).
cnf(refute_0_343,plain,
converse(top) = top,
inference(resolve,[$cnf( $equal(converse(top),join(converse(converse(top)),converse(complement(converse(zero))))) )],[refute_0_331,refute_0_342]) ).
cnf(refute_0_344,plain,
( converse(top) != join(X_16,converse(complement(converse(X_16))))
| converse(top) != top
| top = join(X_16,converse(complement(converse(X_16)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(top),join(X_16,converse(complement(converse(X_16))))) ),[0],$fot(top)]]) ).
cnf(refute_0_345,plain,
( converse(top) != join(X_16,converse(complement(converse(X_16))))
| top = join(X_16,converse(complement(converse(X_16)))) ),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_0_343,refute_0_344]) ).
cnf(refute_0_346,plain,
top = join(X_16,converse(complement(converse(X_16)))),
inference(resolve,[$cnf( $equal(converse(top),join(X_16,converse(complement(converse(X_16))))) )],[refute_0_53,refute_0_345]) ).
cnf(refute_0_347,plain,
top = join(complement(X_66),converse(complement(converse(complement(X_66))))),
inference(subst,[],[refute_0_346:[bind(X_16,$fot(complement(X_66)))]]) ).
cnf(refute_0_348,plain,
( top != join(complement(X_66),converse(complement(converse(complement(X_66)))))
| join(complement(X_66),converse(complement(converse(complement(X_66))))) = top ),
inference(subst,[],[refute_0_4:[bind(X,$fot(top)),bind(Y,$fot(join(complement(X_66),converse(complement(converse(complement(X_66)))))))]]) ).
cnf(refute_0_349,plain,
join(complement(X_66),converse(complement(converse(complement(X_66))))) = top,
inference(resolve,[$cnf( $equal(top,join(complement(X_66),converse(complement(converse(complement(X_66)))))) )],[refute_0_347,refute_0_348]) ).
cnf(refute_0_350,plain,
( X_66 != join(meet(X_66,converse(complement(converse(complement(X_66))))),complement(join(complement(X_66),converse(complement(converse(complement(X_66)))))))
| join(complement(X_66),converse(complement(converse(complement(X_66))))) != top
| X_66 = join(meet(X_66,converse(complement(converse(complement(X_66))))),complement(top)) ),
introduced(tautology,[equality,[$cnf( $equal(X_66,join(meet(X_66,converse(complement(converse(complement(X_66))))),complement(join(complement(X_66),converse(complement(converse(complement(X_66)))))))) ),[1,1,0],$fot(top)]]) ).
cnf(refute_0_351,plain,
( X_66 != join(meet(X_66,converse(complement(converse(complement(X_66))))),complement(join(complement(X_66),converse(complement(converse(complement(X_66)))))))
| X_66 = join(meet(X_66,converse(complement(converse(complement(X_66))))),complement(top)) ),
inference(resolve,[$cnf( $equal(join(complement(X_66),converse(complement(converse(complement(X_66))))),top) )],[refute_0_349,refute_0_350]) ).
cnf(refute_0_352,plain,
X_66 = join(meet(X_66,converse(complement(converse(complement(X_66))))),complement(top)),
inference(resolve,[$cnf( $equal(X_66,join(meet(X_66,converse(complement(converse(complement(X_66))))),complement(join(complement(X_66),converse(complement(converse(complement(X_66)))))))) )],[refute_0_39,refute_0_351]) ).
cnf(refute_0_353,plain,
join(complement(top),meet(X_66,converse(complement(converse(complement(X_66)))))) = join(complement(top),meet(X_66,converse(complement(converse(complement(X_66)))))),
introduced(tautology,[refl,[$fot(join(complement(top),meet(X_66,converse(complement(converse(complement(X_66)))))))]]) ).
cnf(refute_0_354,plain,
( complement(top) != zero
| join(complement(top),meet(X_66,converse(complement(converse(complement(X_66)))))) != join(complement(top),meet(X_66,converse(complement(converse(complement(X_66))))))
| join(complement(top),meet(X_66,converse(complement(converse(complement(X_66)))))) = join(zero,meet(X_66,converse(complement(converse(complement(X_66)))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(X_66,converse(complement(converse(complement(X_66)))))),join(complement(top),meet(X_66,converse(complement(converse(complement(X_66))))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_355,plain,
( complement(top) != zero
| join(complement(top),meet(X_66,converse(complement(converse(complement(X_66)))))) = join(zero,meet(X_66,converse(complement(converse(complement(X_66)))))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_66,converse(complement(converse(complement(X_66)))))),join(complement(top),meet(X_66,converse(complement(converse(complement(X_66))))))) )],[refute_0_353,refute_0_354]) ).
cnf(refute_0_356,plain,
join(complement(top),meet(X_66,converse(complement(converse(complement(X_66)))))) = join(zero,meet(X_66,converse(complement(converse(complement(X_66)))))),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_86,refute_0_355]) ).
cnf(refute_0_357,plain,
join(meet(X_66,converse(complement(converse(complement(X_66))))),complement(top)) = join(complement(top),meet(X_66,converse(complement(converse(complement(X_66)))))),
inference(subst,[],[refute_0_6:[bind(X0,$fot(complement(top))),bind(X1,$fot(meet(X_66,converse(complement(converse(complement(X_66)))))))]]) ).
cnf(refute_0_358,plain,
( join(complement(top),meet(X_66,converse(complement(converse(complement(X_66)))))) != join(zero,meet(X_66,converse(complement(converse(complement(X_66))))))
| join(meet(X_66,converse(complement(converse(complement(X_66))))),complement(top)) != join(complement(top),meet(X_66,converse(complement(converse(complement(X_66))))))
| join(meet(X_66,converse(complement(converse(complement(X_66))))),complement(top)) = join(zero,meet(X_66,converse(complement(converse(complement(X_66)))))) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(join(meet(X_66,converse(complement(converse(complement(X_66))))),complement(top)))),bind(Y,$fot(join(complement(top),meet(X_66,converse(complement(converse(complement(X_66)))))))),bind(Z,$fot(join(zero,meet(X_66,converse(complement(converse(complement(X_66))))))))]]) ).
cnf(refute_0_359,plain,
( join(complement(top),meet(X_66,converse(complement(converse(complement(X_66)))))) != join(zero,meet(X_66,converse(complement(converse(complement(X_66))))))
| join(meet(X_66,converse(complement(converse(complement(X_66))))),complement(top)) = join(zero,meet(X_66,converse(complement(converse(complement(X_66)))))) ),
inference(resolve,[$cnf( $equal(join(meet(X_66,converse(complement(converse(complement(X_66))))),complement(top)),join(complement(top),meet(X_66,converse(complement(converse(complement(X_66))))))) )],[refute_0_357,refute_0_358]) ).
cnf(refute_0_360,plain,
join(meet(X_66,converse(complement(converse(complement(X_66))))),complement(top)) = join(zero,meet(X_66,converse(complement(converse(complement(X_66)))))),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_66,converse(complement(converse(complement(X_66)))))),join(zero,meet(X_66,converse(complement(converse(complement(X_66))))))) )],[refute_0_356,refute_0_359]) ).
cnf(refute_0_361,plain,
( X_66 != join(meet(X_66,converse(complement(converse(complement(X_66))))),complement(top))
| join(meet(X_66,converse(complement(converse(complement(X_66))))),complement(top)) != join(zero,meet(X_66,converse(complement(converse(complement(X_66))))))
| X_66 = join(zero,meet(X_66,converse(complement(converse(complement(X_66)))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_66,join(zero,meet(X_66,converse(complement(converse(complement(X_66))))))) ),[0],$fot(join(meet(X_66,converse(complement(converse(complement(X_66))))),complement(top)))]]) ).
cnf(refute_0_362,plain,
( X_66 != join(meet(X_66,converse(complement(converse(complement(X_66))))),complement(top))
| X_66 = join(zero,meet(X_66,converse(complement(converse(complement(X_66)))))) ),
inference(resolve,[$cnf( $equal(join(meet(X_66,converse(complement(converse(complement(X_66))))),complement(top)),join(zero,meet(X_66,converse(complement(converse(complement(X_66))))))) )],[refute_0_360,refute_0_361]) ).
cnf(refute_0_363,plain,
X_66 = join(zero,meet(X_66,converse(complement(converse(complement(X_66)))))),
inference(resolve,[$cnf( $equal(X_66,join(meet(X_66,converse(complement(converse(complement(X_66))))),complement(top))) )],[refute_0_352,refute_0_362]) ).
cnf(refute_0_364,plain,
join(zero,join(zero,X2)) = join(join(zero,zero),X2),
inference(subst,[],[refute_0_56:[bind(X0,$fot(zero)),bind(X1,$fot(zero))]]) ).
cnf(refute_0_365,plain,
join(complement(top),complement(top)) = complement(top),
inference(subst,[],[refute_0_250:[bind(X_39,$fot(top))]]) ).
cnf(refute_0_366,plain,
( complement(top) != zero
| join(complement(top),complement(top)) != complement(top)
| join(complement(top),zero) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),complement(top)),complement(top)) ),[0,1],$fot(zero)]]) ).
cnf(refute_0_367,plain,
( join(complement(top),complement(top)) != complement(top)
| join(complement(top),zero) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_86,refute_0_366]) ).
cnf(refute_0_368,plain,
join(complement(top),zero) = complement(top),
inference(resolve,[$cnf( $equal(join(complement(top),complement(top)),complement(top)) )],[refute_0_365,refute_0_367]) ).
cnf(refute_0_369,plain,
join(zero,complement(top)) = join(zero,complement(top)),
introduced(tautology,[refl,[$fot(join(zero,complement(top)))]]) ).
cnf(refute_0_370,plain,
( complement(top) != zero
| join(zero,complement(top)) != join(zero,complement(top))
| join(zero,complement(top)) = join(zero,zero) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(top)),join(zero,complement(top))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_371,plain,
( complement(top) != zero
| join(zero,complement(top)) = join(zero,zero) ),
inference(resolve,[$cnf( $equal(join(zero,complement(top)),join(zero,complement(top))) )],[refute_0_369,refute_0_370]) ).
cnf(refute_0_372,plain,
join(zero,complement(top)) = join(zero,zero),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_86,refute_0_371]) ).
cnf(refute_0_373,plain,
join(complement(top),zero) = join(zero,complement(top)),
inference(subst,[],[refute_0_6:[bind(X0,$fot(zero)),bind(X1,$fot(complement(top)))]]) ).
cnf(refute_0_374,plain,
( join(complement(top),zero) != join(zero,complement(top))
| join(zero,complement(top)) != join(zero,zero)
| join(complement(top),zero) = join(zero,zero) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(join(complement(top),zero))),bind(Y,$fot(join(zero,complement(top)))),bind(Z,$fot(join(zero,zero)))]]) ).
cnf(refute_0_375,plain,
( join(zero,complement(top)) != join(zero,zero)
| join(complement(top),zero) = join(zero,zero) ),
inference(resolve,[$cnf( $equal(join(complement(top),zero),join(zero,complement(top))) )],[refute_0_373,refute_0_374]) ).
cnf(refute_0_376,plain,
join(complement(top),zero) = join(zero,zero),
inference(resolve,[$cnf( $equal(join(zero,complement(top)),join(zero,zero)) )],[refute_0_372,refute_0_375]) ).
cnf(refute_0_377,plain,
( join(complement(top),zero) != complement(top)
| join(complement(top),zero) != join(zero,zero)
| join(zero,zero) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),zero),complement(top)) ),[0],$fot(join(zero,zero))]]) ).
cnf(refute_0_378,plain,
( join(complement(top),zero) != complement(top)
| join(zero,zero) = complement(top) ),
inference(resolve,[$cnf( $equal(join(complement(top),zero),join(zero,zero)) )],[refute_0_376,refute_0_377]) ).
cnf(refute_0_379,plain,
( complement(top) != zero
| join(zero,zero) != complement(top)
| join(zero,zero) = zero ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,zero),complement(top)) ),[1],$fot(zero)]]) ).
cnf(refute_0_380,plain,
( join(zero,zero) != complement(top)
| join(zero,zero) = zero ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_86,refute_0_379]) ).
cnf(refute_0_381,plain,
( join(complement(top),zero) != complement(top)
| join(zero,zero) = zero ),
inference(resolve,[$cnf( $equal(join(zero,zero),complement(top)) )],[refute_0_378,refute_0_380]) ).
cnf(refute_0_382,plain,
join(zero,zero) = zero,
inference(resolve,[$cnf( $equal(join(complement(top),zero),complement(top)) )],[refute_0_368,refute_0_381]) ).
cnf(refute_0_383,plain,
( join(zero,join(zero,X2)) != join(join(zero,zero),X2)
| join(zero,zero) != zero
| join(zero,join(zero,X2)) = join(zero,X2) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(zero,X2)),join(join(zero,zero),X2)) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_384,plain,
( join(zero,join(zero,X2)) != join(join(zero,zero),X2)
| join(zero,join(zero,X2)) = join(zero,X2) ),
inference(resolve,[$cnf( $equal(join(zero,zero),zero) )],[refute_0_382,refute_0_383]) ).
cnf(refute_0_385,plain,
join(zero,join(zero,X2)) = join(zero,X2),
inference(resolve,[$cnf( $equal(join(zero,join(zero,X2)),join(join(zero,zero),X2)) )],[refute_0_364,refute_0_384]) ).
cnf(refute_0_386,plain,
join(zero,join(zero,meet(X_68,top))) = join(zero,meet(X_68,top)),
inference(subst,[],[refute_0_385:[bind(X2,$fot(meet(X_68,top)))]]) ).
cnf(refute_0_387,plain,
X_66 = join(meet(X_66,top),complement(join(complement(X_66),top))),
inference(subst,[],[refute_0_26:[bind(X0,$fot(X_66)),bind(X1,$fot(top))]]) ).
cnf(refute_0_388,plain,
join(complement(X_66),top) = top,
inference(subst,[],[refute_0_263:[bind(X_36,$fot(complement(X_66)))]]) ).
cnf(refute_0_389,plain,
( X_66 != join(meet(X_66,top),complement(join(complement(X_66),top)))
| join(complement(X_66),top) != top
| X_66 = join(meet(X_66,top),complement(top)) ),
introduced(tautology,[equality,[$cnf( $equal(X_66,join(meet(X_66,top),complement(join(complement(X_66),top)))) ),[1,1,0],$fot(top)]]) ).
cnf(refute_0_390,plain,
( X_66 != join(meet(X_66,top),complement(join(complement(X_66),top)))
| X_66 = join(meet(X_66,top),complement(top)) ),
inference(resolve,[$cnf( $equal(join(complement(X_66),top),top) )],[refute_0_388,refute_0_389]) ).
cnf(refute_0_391,plain,
X_66 = join(meet(X_66,top),complement(top)),
inference(resolve,[$cnf( $equal(X_66,join(meet(X_66,top),complement(join(complement(X_66),top)))) )],[refute_0_387,refute_0_390]) ).
cnf(refute_0_392,plain,
join(complement(top),meet(X_66,top)) = join(complement(top),meet(X_66,top)),
introduced(tautology,[refl,[$fot(join(complement(top),meet(X_66,top)))]]) ).
cnf(refute_0_393,plain,
( complement(top) != zero
| join(complement(top),meet(X_66,top)) != join(complement(top),meet(X_66,top))
| join(complement(top),meet(X_66,top)) = join(zero,meet(X_66,top)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(X_66,top)),join(complement(top),meet(X_66,top))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_394,plain,
( complement(top) != zero
| join(complement(top),meet(X_66,top)) = join(zero,meet(X_66,top)) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_66,top)),join(complement(top),meet(X_66,top))) )],[refute_0_392,refute_0_393]) ).
cnf(refute_0_395,plain,
join(complement(top),meet(X_66,top)) = join(zero,meet(X_66,top)),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_86,refute_0_394]) ).
cnf(refute_0_396,plain,
join(meet(X_66,top),complement(top)) = join(complement(top),meet(X_66,top)),
inference(subst,[],[refute_0_6:[bind(X0,$fot(complement(top))),bind(X1,$fot(meet(X_66,top)))]]) ).
cnf(refute_0_397,plain,
( join(complement(top),meet(X_66,top)) != join(zero,meet(X_66,top))
| join(meet(X_66,top),complement(top)) != join(complement(top),meet(X_66,top))
| join(meet(X_66,top),complement(top)) = join(zero,meet(X_66,top)) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(join(meet(X_66,top),complement(top)))),bind(Y,$fot(join(complement(top),meet(X_66,top)))),bind(Z,$fot(join(zero,meet(X_66,top))))]]) ).
cnf(refute_0_398,plain,
( join(complement(top),meet(X_66,top)) != join(zero,meet(X_66,top))
| join(meet(X_66,top),complement(top)) = join(zero,meet(X_66,top)) ),
inference(resolve,[$cnf( $equal(join(meet(X_66,top),complement(top)),join(complement(top),meet(X_66,top))) )],[refute_0_396,refute_0_397]) ).
cnf(refute_0_399,plain,
join(meet(X_66,top),complement(top)) = join(zero,meet(X_66,top)),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_66,top)),join(zero,meet(X_66,top))) )],[refute_0_395,refute_0_398]) ).
cnf(refute_0_400,plain,
( X_66 != join(meet(X_66,top),complement(top))
| join(meet(X_66,top),complement(top)) != join(zero,meet(X_66,top))
| X_66 = join(zero,meet(X_66,top)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_66,join(zero,meet(X_66,top))) ),[0],$fot(join(meet(X_66,top),complement(top)))]]) ).
cnf(refute_0_401,plain,
( X_66 != join(meet(X_66,top),complement(top))
| X_66 = join(zero,meet(X_66,top)) ),
inference(resolve,[$cnf( $equal(join(meet(X_66,top),complement(top)),join(zero,meet(X_66,top))) )],[refute_0_399,refute_0_400]) ).
cnf(refute_0_402,plain,
X_66 = join(zero,meet(X_66,top)),
inference(resolve,[$cnf( $equal(X_66,join(meet(X_66,top),complement(top))) )],[refute_0_391,refute_0_401]) ).
cnf(refute_0_403,plain,
X_68 = join(zero,meet(X_68,top)),
inference(subst,[],[refute_0_402:[bind(X_66,$fot(X_68))]]) ).
cnf(refute_0_404,plain,
( X_68 != join(zero,meet(X_68,top))
| join(zero,meet(X_68,top)) = X_68 ),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_68)),bind(Y,$fot(join(zero,meet(X_68,top))))]]) ).
cnf(refute_0_405,plain,
join(zero,meet(X_68,top)) = X_68,
inference(resolve,[$cnf( $equal(X_68,join(zero,meet(X_68,top))) )],[refute_0_403,refute_0_404]) ).
cnf(refute_0_406,plain,
( join(zero,join(zero,meet(X_68,top))) != join(zero,meet(X_68,top))
| join(zero,meet(X_68,top)) != X_68
| join(zero,X_68) = join(zero,meet(X_68,top)) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(zero,meet(X_68,top))),join(zero,meet(X_68,top))) ),[0,1],$fot(X_68)]]) ).
cnf(refute_0_407,plain,
( join(zero,join(zero,meet(X_68,top))) != join(zero,meet(X_68,top))
| join(zero,X_68) = join(zero,meet(X_68,top)) ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_68,top)),X_68) )],[refute_0_405,refute_0_406]) ).
cnf(refute_0_408,plain,
join(zero,X_68) = join(zero,meet(X_68,top)),
inference(resolve,[$cnf( $equal(join(zero,join(zero,meet(X_68,top))),join(zero,meet(X_68,top))) )],[refute_0_386,refute_0_407]) ).
cnf(refute_0_409,plain,
( join(zero,X_68) != join(zero,meet(X_68,top))
| join(zero,meet(X_68,top)) != X_68
| join(zero,X_68) = X_68 ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(zero,X_68),X_68) ),[0],$fot(join(zero,meet(X_68,top)))]]) ).
cnf(refute_0_410,plain,
( join(zero,X_68) != join(zero,meet(X_68,top))
| join(zero,X_68) = X_68 ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_68,top)),X_68) )],[refute_0_405,refute_0_409]) ).
cnf(refute_0_411,plain,
join(zero,X_68) = X_68,
inference(resolve,[$cnf( $equal(join(zero,X_68),join(zero,meet(X_68,top))) )],[refute_0_408,refute_0_410]) ).
cnf(refute_0_412,plain,
join(zero,meet(X_66,converse(complement(converse(complement(X_66)))))) = meet(X_66,converse(complement(converse(complement(X_66))))),
inference(subst,[],[refute_0_411:[bind(X_68,$fot(meet(X_66,converse(complement(converse(complement(X_66)))))))]]) ).
cnf(refute_0_413,plain,
( X_66 != join(zero,meet(X_66,converse(complement(converse(complement(X_66))))))
| join(zero,meet(X_66,converse(complement(converse(complement(X_66)))))) != meet(X_66,converse(complement(converse(complement(X_66)))))
| X_66 = meet(X_66,converse(complement(converse(complement(X_66))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_66,meet(X_66,converse(complement(converse(complement(X_66)))))) ),[0],$fot(join(zero,meet(X_66,converse(complement(converse(complement(X_66)))))))]]) ).
cnf(refute_0_414,plain,
( X_66 != join(zero,meet(X_66,converse(complement(converse(complement(X_66))))))
| X_66 = meet(X_66,converse(complement(converse(complement(X_66))))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_66,converse(complement(converse(complement(X_66)))))),meet(X_66,converse(complement(converse(complement(X_66)))))) )],[refute_0_412,refute_0_413]) ).
cnf(refute_0_415,plain,
X_66 = meet(X_66,converse(complement(converse(complement(X_66))))),
inference(resolve,[$cnf( $equal(X_66,join(zero,meet(X_66,converse(complement(converse(complement(X_66))))))) )],[refute_0_363,refute_0_414]) ).
cnf(refute_0_416,plain,
X_78 = meet(X_78,converse(complement(converse(complement(X_78))))),
inference(subst,[],[refute_0_415:[bind(X_66,$fot(X_78))]]) ).
cnf(refute_0_417,plain,
( X_78 != meet(X_78,converse(complement(converse(complement(X_78)))))
| meet(X_78,converse(complement(converse(complement(X_78))))) = X_78 ),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_78)),bind(Y,$fot(meet(X_78,converse(complement(converse(complement(X_78)))))))]]) ).
cnf(refute_0_418,plain,
meet(X_78,converse(complement(converse(complement(X_78))))) = X_78,
inference(resolve,[$cnf( $equal(X_78,meet(X_78,converse(complement(converse(complement(X_78)))))) )],[refute_0_416,refute_0_417]) ).
cnf(refute_0_419,plain,
( X_78 != join(meet(X_78,converse(complement(converse(complement(X_78))))),meet(X_78,complement(converse(complement(converse(complement(X_78)))))))
| meet(X_78,converse(complement(converse(complement(X_78))))) != X_78
| X_78 = join(X_78,meet(X_78,complement(converse(complement(converse(complement(X_78))))))) ),
introduced(tautology,[equality,[$cnf( $equal(X_78,join(meet(X_78,converse(complement(converse(complement(X_78))))),meet(X_78,complement(converse(complement(converse(complement(X_78)))))))) ),[1,0],$fot(X_78)]]) ).
cnf(refute_0_420,plain,
( X_78 != join(meet(X_78,converse(complement(converse(complement(X_78))))),meet(X_78,complement(converse(complement(converse(complement(X_78)))))))
| X_78 = join(X_78,meet(X_78,complement(converse(complement(converse(complement(X_78))))))) ),
inference(resolve,[$cnf( $equal(meet(X_78,converse(complement(converse(complement(X_78))))),X_78) )],[refute_0_418,refute_0_419]) ).
cnf(refute_0_421,plain,
X_78 = join(X_78,meet(X_78,complement(converse(complement(converse(complement(X_78))))))),
inference(resolve,[$cnf( $equal(X_78,join(meet(X_78,converse(complement(converse(complement(X_78))))),meet(X_78,complement(converse(complement(converse(complement(X_78)))))))) )],[refute_0_38,refute_0_420]) ).
cnf(refute_0_422,plain,
composition(top,top) = join(composition(top,top),meet(composition(top,top),complement(converse(complement(converse(complement(composition(top,top)))))))),
inference(subst,[],[refute_0_421:[bind(X_78,$fot(composition(top,top)))]]) ).
cnf(refute_0_423,plain,
complement(composition(top,top)) = composition(one,complement(composition(top,top))),
inference(subst,[],[refute_0_227:[bind(X_21,$fot(complement(composition(top,top))))]]) ).
cnf(refute_0_424,plain,
composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_425,plain,
composition(join(X_122,top),complement(composition(top,top))) = join(composition(X_122,complement(composition(top,top))),composition(top,complement(composition(top,top)))),
inference(subst,[],[refute_0_424:[bind(X0,$fot(X_122)),bind(X1,$fot(top)),bind(X2,$fot(complement(composition(top,top))))]]) ).
cnf(refute_0_426,plain,
join(complement(top),composition(converse(X_38),complement(composition(X_38,top)))) = complement(top),
inference(subst,[],[refute_0_195:[bind(X0,$fot(X_38)),bind(X1,$fot(top))]]) ).
cnf(refute_0_427,plain,
( complement(top) != zero
| join(complement(top),composition(converse(X_38),complement(composition(X_38,top)))) != complement(top)
| join(zero,composition(converse(X_38),complement(composition(X_38,top)))) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),composition(converse(X_38),complement(composition(X_38,top)))),complement(top)) ),[0,0],$fot(zero)]]) ).
cnf(refute_0_428,plain,
( join(complement(top),composition(converse(X_38),complement(composition(X_38,top)))) != complement(top)
| join(zero,composition(converse(X_38),complement(composition(X_38,top)))) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_86,refute_0_427]) ).
cnf(refute_0_429,plain,
join(zero,composition(converse(X_38),complement(composition(X_38,top)))) = complement(top),
inference(resolve,[$cnf( $equal(join(complement(top),composition(converse(X_38),complement(composition(X_38,top)))),complement(top)) )],[refute_0_426,refute_0_428]) ).
cnf(refute_0_430,plain,
( complement(top) != zero
| join(zero,composition(converse(X_38),complement(composition(X_38,top)))) != complement(top)
| join(zero,composition(converse(X_38),complement(composition(X_38,top)))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,composition(converse(X_38),complement(composition(X_38,top)))),complement(top)) ),[1],$fot(zero)]]) ).
cnf(refute_0_431,plain,
( join(zero,composition(converse(X_38),complement(composition(X_38,top)))) != complement(top)
| join(zero,composition(converse(X_38),complement(composition(X_38,top)))) = zero ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_86,refute_0_430]) ).
cnf(refute_0_432,plain,
join(zero,composition(converse(X_38),complement(composition(X_38,top)))) = zero,
inference(resolve,[$cnf( $equal(join(zero,composition(converse(X_38),complement(composition(X_38,top)))),complement(top)) )],[refute_0_429,refute_0_431]) ).
cnf(refute_0_433,plain,
join(zero,composition(converse(top),complement(composition(top,top)))) = zero,
inference(subst,[],[refute_0_432:[bind(X_38,$fot(top))]]) ).
cnf(refute_0_434,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_0_435,plain,
( join(zero,composition(converse(top),complement(composition(top,top)))) != zero
| join(zero,composition(top,complement(composition(top,top)))) = zero ),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_0_343,refute_0_434]) ).
cnf(refute_0_436,plain,
join(zero,composition(top,complement(composition(top,top)))) = zero,
inference(resolve,[$cnf( $equal(join(zero,composition(converse(top),complement(composition(top,top)))),zero) )],[refute_0_433,refute_0_435]) ).
cnf(refute_0_437,plain,
join(zero,composition(top,complement(composition(top,top)))) = composition(top,complement(composition(top,top))),
inference(subst,[],[refute_0_411:[bind(X_68,$fot(composition(top,complement(composition(top,top)))))]]) ).
cnf(refute_0_438,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_0_439,plain,
( join(zero,composition(top,complement(composition(top,top)))) != zero
| composition(top,complement(composition(top,top))) = zero ),
inference(resolve,[$cnf( $equal(join(zero,composition(top,complement(composition(top,top)))),composition(top,complement(composition(top,top)))) )],[refute_0_437,refute_0_438]) ).
cnf(refute_0_440,plain,
composition(top,complement(composition(top,top))) = zero,
inference(resolve,[$cnf( $equal(join(zero,composition(top,complement(composition(top,top)))),zero) )],[refute_0_436,refute_0_439]) ).
cnf(refute_0_441,plain,
( composition(join(X_122,top),complement(composition(top,top))) != join(composition(X_122,complement(composition(top,top))),composition(top,complement(composition(top,top))))
| composition(top,complement(composition(top,top))) != zero
| composition(join(X_122,top),complement(composition(top,top))) = join(composition(X_122,complement(composition(top,top))),zero) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(X_122,top),complement(composition(top,top))),join(composition(X_122,complement(composition(top,top))),composition(top,complement(composition(top,top))))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_442,plain,
( composition(join(X_122,top),complement(composition(top,top))) != join(composition(X_122,complement(composition(top,top))),composition(top,complement(composition(top,top))))
| composition(join(X_122,top),complement(composition(top,top))) = join(composition(X_122,complement(composition(top,top))),zero) ),
inference(resolve,[$cnf( $equal(composition(top,complement(composition(top,top))),zero) )],[refute_0_440,refute_0_441]) ).
cnf(refute_0_443,plain,
composition(join(X_122,top),complement(composition(top,top))) = join(composition(X_122,complement(composition(top,top))),zero),
inference(resolve,[$cnf( $equal(composition(join(X_122,top),complement(composition(top,top))),join(composition(X_122,complement(composition(top,top))),composition(top,complement(composition(top,top))))) )],[refute_0_425,refute_0_442]) ).
cnf(refute_0_444,plain,
join(X_122,top) = top,
inference(subst,[],[refute_0_263:[bind(X_36,$fot(X_122))]]) ).
cnf(refute_0_445,plain,
composition(join(X_122,top),complement(composition(top,top))) = composition(join(X_122,top),complement(composition(top,top))),
introduced(tautology,[refl,[$fot(composition(join(X_122,top),complement(composition(top,top))))]]) ).
cnf(refute_0_446,plain,
( composition(join(X_122,top),complement(composition(top,top))) != composition(join(X_122,top),complement(composition(top,top)))
| join(X_122,top) != top
| composition(join(X_122,top),complement(composition(top,top))) = composition(top,complement(composition(top,top))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(X_122,top),complement(composition(top,top))),composition(join(X_122,top),complement(composition(top,top)))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_447,plain,
( join(X_122,top) != top
| composition(join(X_122,top),complement(composition(top,top))) = composition(top,complement(composition(top,top))) ),
inference(resolve,[$cnf( $equal(composition(join(X_122,top),complement(composition(top,top))),composition(join(X_122,top),complement(composition(top,top)))) )],[refute_0_445,refute_0_446]) ).
cnf(refute_0_448,plain,
composition(join(X_122,top),complement(composition(top,top))) = composition(top,complement(composition(top,top))),
inference(resolve,[$cnf( $equal(join(X_122,top),top) )],[refute_0_444,refute_0_447]) ).
cnf(refute_0_449,plain,
( composition(join(X_122,top),complement(composition(top,top))) != composition(top,complement(composition(top,top)))
| composition(top,complement(composition(top,top))) != zero
| composition(join(X_122,top),complement(composition(top,top))) = zero ),
inference(subst,[],[refute_0_20:[bind(X,$fot(composition(join(X_122,top),complement(composition(top,top))))),bind(Y,$fot(composition(top,complement(composition(top,top))))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_450,plain,
( composition(top,complement(composition(top,top))) != zero
| composition(join(X_122,top),complement(composition(top,top))) = zero ),
inference(resolve,[$cnf( $equal(composition(join(X_122,top),complement(composition(top,top))),composition(top,complement(composition(top,top)))) )],[refute_0_448,refute_0_449]) ).
cnf(refute_0_451,plain,
composition(join(X_122,top),complement(composition(top,top))) = zero,
inference(resolve,[$cnf( $equal(composition(top,complement(composition(top,top))),zero) )],[refute_0_440,refute_0_450]) ).
cnf(refute_0_452,plain,
( composition(join(X_122,top),complement(composition(top,top))) != join(composition(X_122,complement(composition(top,top))),zero)
| composition(join(X_122,top),complement(composition(top,top))) != zero
| zero = join(composition(X_122,complement(composition(top,top))),zero) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(X_122,top),complement(composition(top,top))),join(composition(X_122,complement(composition(top,top))),zero)) ),[0],$fot(zero)]]) ).
cnf(refute_0_453,plain,
( composition(join(X_122,top),complement(composition(top,top))) != join(composition(X_122,complement(composition(top,top))),zero)
| zero = join(composition(X_122,complement(composition(top,top))),zero) ),
inference(resolve,[$cnf( $equal(composition(join(X_122,top),complement(composition(top,top))),zero) )],[refute_0_451,refute_0_452]) ).
cnf(refute_0_454,plain,
join(join(zero,X_44),zero) = join(zero,join(zero,X_44)),
inference(subst,[],[refute_0_1:[bind(X0,$fot(join(zero,X_44))),bind(X1,$fot(zero))]]) ).
cnf(refute_0_455,plain,
join(zero,join(zero,X_44)) = join(zero,X_44),
inference(subst,[],[refute_0_385:[bind(X2,$fot(X_44))]]) ).
cnf(refute_0_456,plain,
( join(join(zero,X_44),zero) != join(zero,join(zero,X_44))
| join(zero,join(zero,X_44)) != join(zero,X_44)
| join(join(zero,X_44),zero) = join(zero,X_44) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(join(zero,X_44),zero),join(zero,X_44)) ),[0],$fot(join(zero,join(zero,X_44)))]]) ).
cnf(refute_0_457,plain,
( join(join(zero,X_44),zero) != join(zero,join(zero,X_44))
| join(join(zero,X_44),zero) = join(zero,X_44) ),
inference(resolve,[$cnf( $equal(join(zero,join(zero,X_44)),join(zero,X_44)) )],[refute_0_455,refute_0_456]) ).
cnf(refute_0_458,plain,
join(join(zero,X_44),zero) = join(zero,X_44),
inference(resolve,[$cnf( $equal(join(join(zero,X_44),zero),join(zero,join(zero,X_44))) )],[refute_0_454,refute_0_457]) ).
cnf(refute_0_459,plain,
join(join(zero,X_44),zero) = join(zero,join(X_44,zero)),
inference(subst,[],[refute_0_145:[bind(X0,$fot(zero)),bind(X1,$fot(X_44)),bind(X2,$fot(zero))]]) ).
cnf(refute_0_460,plain,
( join(join(zero,X_44),zero) != join(zero,X_44)
| join(join(zero,X_44),zero) != join(zero,join(X_44,zero))
| join(zero,join(X_44,zero)) = join(zero,X_44) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(zero,X_44),zero),join(zero,X_44)) ),[0],$fot(join(zero,join(X_44,zero)))]]) ).
cnf(refute_0_461,plain,
( join(join(zero,X_44),zero) != join(zero,X_44)
| join(zero,join(X_44,zero)) = join(zero,X_44) ),
inference(resolve,[$cnf( $equal(join(join(zero,X_44),zero),join(zero,join(X_44,zero))) )],[refute_0_459,refute_0_460]) ).
cnf(refute_0_462,plain,
join(zero,join(X_44,zero)) = join(zero,X_44),
inference(resolve,[$cnf( $equal(join(join(zero,X_44),zero),join(zero,X_44)) )],[refute_0_458,refute_0_461]) ).
cnf(refute_0_463,plain,
join(zero,join(meet(X_68,top),zero)) = join(zero,meet(X_68,top)),
inference(subst,[],[refute_0_462:[bind(X_44,$fot(meet(X_68,top)))]]) ).
cnf(refute_0_464,plain,
( join(zero,join(meet(X_68,top),zero)) != join(zero,meet(X_68,top))
| join(zero,meet(X_68,top)) != X_68
| join(zero,join(meet(X_68,top),zero)) = X_68 ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(zero,join(meet(X_68,top),zero)),X_68) ),[0],$fot(join(zero,meet(X_68,top)))]]) ).
cnf(refute_0_465,plain,
( join(zero,join(meet(X_68,top),zero)) != join(zero,meet(X_68,top))
| join(zero,join(meet(X_68,top),zero)) = X_68 ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_68,top)),X_68) )],[refute_0_405,refute_0_464]) ).
cnf(refute_0_466,plain,
join(zero,join(meet(X_68,top),zero)) = X_68,
inference(resolve,[$cnf( $equal(join(zero,join(meet(X_68,top),zero)),join(zero,meet(X_68,top))) )],[refute_0_463,refute_0_465]) ).
cnf(refute_0_467,plain,
join(zero,join(meet(X_68,top),X2)) = join(join(zero,meet(X_68,top)),X2),
inference(subst,[],[refute_0_56:[bind(X0,$fot(zero)),bind(X1,$fot(meet(X_68,top)))]]) ).
cnf(refute_0_468,plain,
( join(zero,join(meet(X_68,top),X2)) != join(join(zero,meet(X_68,top)),X2)
| join(zero,meet(X_68,top)) != X_68
| join(zero,join(meet(X_68,top),X2)) = join(X_68,X2) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(meet(X_68,top),X2)),join(join(zero,meet(X_68,top)),X2)) ),[1,0],$fot(X_68)]]) ).
cnf(refute_0_469,plain,
( join(zero,join(meet(X_68,top),X2)) != join(join(zero,meet(X_68,top)),X2)
| join(zero,join(meet(X_68,top),X2)) = join(X_68,X2) ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_68,top)),X_68) )],[refute_0_405,refute_0_468]) ).
cnf(refute_0_470,plain,
join(zero,join(meet(X_68,top),X2)) = join(X_68,X2),
inference(resolve,[$cnf( $equal(join(zero,join(meet(X_68,top),X2)),join(join(zero,meet(X_68,top)),X2)) )],[refute_0_467,refute_0_469]) ).
cnf(refute_0_471,plain,
join(zero,join(meet(X_68,top),zero)) = join(X_68,zero),
inference(subst,[],[refute_0_470:[bind(X2,$fot(zero))]]) ).
cnf(refute_0_472,plain,
( join(zero,join(meet(X_68,top),zero)) != X_68
| join(zero,join(meet(X_68,top),zero)) != join(X_68,zero)
| join(X_68,zero) = X_68 ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(meet(X_68,top),zero)),X_68) ),[0],$fot(join(X_68,zero))]]) ).
cnf(refute_0_473,plain,
( join(zero,join(meet(X_68,top),zero)) != X_68
| join(X_68,zero) = X_68 ),
inference(resolve,[$cnf( $equal(join(zero,join(meet(X_68,top),zero)),join(X_68,zero)) )],[refute_0_471,refute_0_472]) ).
cnf(refute_0_474,plain,
join(X_68,zero) = X_68,
inference(resolve,[$cnf( $equal(join(zero,join(meet(X_68,top),zero)),X_68) )],[refute_0_466,refute_0_473]) ).
cnf(refute_0_475,plain,
join(composition(X_122,complement(composition(top,top))),zero) = composition(X_122,complement(composition(top,top))),
inference(subst,[],[refute_0_474:[bind(X_68,$fot(composition(X_122,complement(composition(top,top)))))]]) ).
cnf(refute_0_476,plain,
( join(composition(X_122,complement(composition(top,top))),zero) != composition(X_122,complement(composition(top,top)))
| zero != join(composition(X_122,complement(composition(top,top))),zero)
| zero = composition(X_122,complement(composition(top,top))) ),
introduced(tautology,[equality,[$cnf( $equal(zero,join(composition(X_122,complement(composition(top,top))),zero)) ),[1],$fot(composition(X_122,complement(composition(top,top))))]]) ).
cnf(refute_0_477,plain,
( zero != join(composition(X_122,complement(composition(top,top))),zero)
| zero = composition(X_122,complement(composition(top,top))) ),
inference(resolve,[$cnf( $equal(join(composition(X_122,complement(composition(top,top))),zero),composition(X_122,complement(composition(top,top)))) )],[refute_0_475,refute_0_476]) ).
cnf(refute_0_478,plain,
( composition(join(X_122,top),complement(composition(top,top))) != join(composition(X_122,complement(composition(top,top))),zero)
| zero = composition(X_122,complement(composition(top,top))) ),
inference(resolve,[$cnf( $equal(zero,join(composition(X_122,complement(composition(top,top))),zero)) )],[refute_0_453,refute_0_477]) ).
cnf(refute_0_479,plain,
zero = composition(X_122,complement(composition(top,top))),
inference(resolve,[$cnf( $equal(composition(join(X_122,top),complement(composition(top,top))),join(composition(X_122,complement(composition(top,top))),zero)) )],[refute_0_443,refute_0_478]) ).
cnf(refute_0_480,plain,
zero = composition(one,complement(composition(top,top))),
inference(subst,[],[refute_0_479:[bind(X_122,$fot(one))]]) ).
cnf(refute_0_481,plain,
( zero != composition(one,complement(composition(top,top)))
| composition(one,complement(composition(top,top))) = zero ),
inference(subst,[],[refute_0_4:[bind(X,$fot(zero)),bind(Y,$fot(composition(one,complement(composition(top,top)))))]]) ).
cnf(refute_0_482,plain,
composition(one,complement(composition(top,top))) = zero,
inference(resolve,[$cnf( $equal(zero,composition(one,complement(composition(top,top)))) )],[refute_0_480,refute_0_481]) ).
cnf(refute_0_483,plain,
( complement(composition(top,top)) != composition(one,complement(composition(top,top)))
| composition(one,complement(composition(top,top))) != zero
| complement(composition(top,top)) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(composition(top,top)),zero) ),[0],$fot(composition(one,complement(composition(top,top))))]]) ).
cnf(refute_0_484,plain,
( complement(composition(top,top)) != composition(one,complement(composition(top,top)))
| complement(composition(top,top)) = zero ),
inference(resolve,[$cnf( $equal(composition(one,complement(composition(top,top))),zero) )],[refute_0_482,refute_0_483]) ).
cnf(refute_0_485,plain,
complement(composition(top,top)) = zero,
inference(resolve,[$cnf( $equal(complement(composition(top,top)),composition(one,complement(composition(top,top)))) )],[refute_0_423,refute_0_484]) ).
cnf(refute_0_486,plain,
( complement(composition(top,top)) != zero
| composition(top,top) != join(composition(top,top),meet(composition(top,top),complement(converse(complement(converse(complement(composition(top,top))))))))
| composition(top,top) = join(composition(top,top),meet(composition(top,top),complement(converse(complement(converse(zero)))))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(top,top),join(composition(top,top),meet(composition(top,top),complement(converse(complement(converse(complement(composition(top,top))))))))) ),[1,1,1,0,0,0,0],$fot(zero)]]) ).
cnf(refute_0_487,plain,
( composition(top,top) != join(composition(top,top),meet(composition(top,top),complement(converse(complement(converse(complement(composition(top,top))))))))
| composition(top,top) = join(composition(top,top),meet(composition(top,top),complement(converse(complement(converse(zero)))))) ),
inference(resolve,[$cnf( $equal(complement(composition(top,top)),zero) )],[refute_0_485,refute_0_486]) ).
cnf(refute_0_488,plain,
composition(top,top) = join(composition(top,top),meet(composition(top,top),complement(converse(complement(converse(zero)))))),
inference(resolve,[$cnf( $equal(composition(top,top),join(composition(top,top),meet(composition(top,top),complement(converse(complement(converse(complement(composition(top,top))))))))) )],[refute_0_422,refute_0_487]) ).
cnf(refute_0_489,plain,
join(X_27,join(converse(complement(converse(X_27))),X_29)) = join(join(X_27,converse(complement(converse(X_27)))),X_29),
inference(subst,[],[refute_0_56:[bind(X0,$fot(X_27)),bind(X1,$fot(converse(complement(converse(X_27))))),bind(X2,$fot(X_29))]]) ).
cnf(refute_0_490,plain,
converse(top) = join(X_27,converse(complement(converse(X_27)))),
inference(subst,[],[refute_0_53:[bind(X_16,$fot(X_27))]]) ).
cnf(refute_0_491,plain,
( converse(top) != join(X_27,converse(complement(converse(X_27))))
| join(X_27,converse(complement(converse(X_27)))) = converse(top) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(converse(top))),bind(Y,$fot(join(X_27,converse(complement(converse(X_27))))))]]) ).
cnf(refute_0_492,plain,
join(X_27,converse(complement(converse(X_27)))) = converse(top),
inference(resolve,[$cnf( $equal(converse(top),join(X_27,converse(complement(converse(X_27))))) )],[refute_0_490,refute_0_491]) ).
cnf(refute_0_493,plain,
( join(X_27,converse(complement(converse(X_27)))) != converse(top)
| join(X_27,join(converse(complement(converse(X_27))),X_29)) != join(join(X_27,converse(complement(converse(X_27)))),X_29)
| join(X_27,join(converse(complement(converse(X_27))),X_29)) = join(converse(top),X_29) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_27,join(converse(complement(converse(X_27))),X_29)),join(join(X_27,converse(complement(converse(X_27)))),X_29)) ),[1,0],$fot(converse(top))]]) ).
cnf(refute_0_494,plain,
( join(X_27,join(converse(complement(converse(X_27))),X_29)) != join(join(X_27,converse(complement(converse(X_27)))),X_29)
| join(X_27,join(converse(complement(converse(X_27))),X_29)) = join(converse(top),X_29) ),
inference(resolve,[$cnf( $equal(join(X_27,converse(complement(converse(X_27)))),converse(top)) )],[refute_0_492,refute_0_493]) ).
cnf(refute_0_495,plain,
join(X_27,join(converse(complement(converse(X_27))),X_29)) = join(converse(top),X_29),
inference(resolve,[$cnf( $equal(join(X_27,join(converse(complement(converse(X_27))),X_29)),join(join(X_27,converse(complement(converse(X_27)))),X_29)) )],[refute_0_489,refute_0_494]) ).
cnf(refute_0_496,plain,
join(top,X_29) = top,
inference(subst,[],[refute_0_322:[bind(X_27,$fot(X_29))]]) ).
cnf(refute_0_497,plain,
join(converse(top),X_29) = join(converse(top),X_29),
introduced(tautology,[refl,[$fot(join(converse(top),X_29))]]) ).
cnf(refute_0_498,plain,
( converse(top) != top
| join(converse(top),X_29) != join(converse(top),X_29)
| join(converse(top),X_29) = join(top,X_29) ),
introduced(tautology,[equality,[$cnf( $equal(join(converse(top),X_29),join(converse(top),X_29)) ),[1,0],$fot(top)]]) ).
cnf(refute_0_499,plain,
( converse(top) != top
| join(converse(top),X_29) = join(top,X_29) ),
inference(resolve,[$cnf( $equal(join(converse(top),X_29),join(converse(top),X_29)) )],[refute_0_497,refute_0_498]) ).
cnf(refute_0_500,plain,
join(converse(top),X_29) = join(top,X_29),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_0_343,refute_0_499]) ).
cnf(refute_0_501,plain,
( join(converse(top),X_29) != join(top,X_29)
| join(top,X_29) != top
| join(converse(top),X_29) = top ),
inference(subst,[],[refute_0_20:[bind(X,$fot(join(converse(top),X_29))),bind(Y,$fot(join(top,X_29))),bind(Z,$fot(top))]]) ).
cnf(refute_0_502,plain,
( join(top,X_29) != top
| join(converse(top),X_29) = top ),
inference(resolve,[$cnf( $equal(join(converse(top),X_29),join(top,X_29)) )],[refute_0_500,refute_0_501]) ).
cnf(refute_0_503,plain,
join(converse(top),X_29) = top,
inference(resolve,[$cnf( $equal(join(top,X_29),top) )],[refute_0_496,refute_0_502]) ).
cnf(refute_0_504,plain,
( join(X_27,join(converse(complement(converse(X_27))),X_29)) != join(converse(top),X_29)
| join(converse(top),X_29) != top
| join(X_27,join(converse(complement(converse(X_27))),X_29)) = top ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_27,join(converse(complement(converse(X_27))),X_29)),top) ),[0],$fot(join(converse(top),X_29))]]) ).
cnf(refute_0_505,plain,
( join(X_27,join(converse(complement(converse(X_27))),X_29)) != join(converse(top),X_29)
| join(X_27,join(converse(complement(converse(X_27))),X_29)) = top ),
inference(resolve,[$cnf( $equal(join(converse(top),X_29),top) )],[refute_0_503,refute_0_504]) ).
cnf(refute_0_506,plain,
join(X_27,join(converse(complement(converse(X_27))),X_29)) = top,
inference(resolve,[$cnf( $equal(join(X_27,join(converse(complement(converse(X_27))),X_29)),join(converse(top),X_29)) )],[refute_0_495,refute_0_505]) ).
cnf(refute_0_507,plain,
join(composition(top,top),join(converse(complement(converse(composition(top,top)))),X_101)) = top,
inference(subst,[],[refute_0_506:[bind(X_27,$fot(composition(top,top))),bind(X_29,$fot(X_101))]]) ).
cnf(refute_0_508,plain,
converse(composition(converse(top),X_20)) = composition(converse(X_20),top),
inference(subst,[],[refute_0_201:[bind(X0,$fot(top))]]) ).
cnf(refute_0_509,plain,
( converse(composition(converse(top),X_20)) != composition(converse(X_20),top)
| converse(top) != top
| converse(composition(top,X_20)) = composition(converse(X_20),top) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(top),X_20)),composition(converse(X_20),top)) ),[0,0,0],$fot(top)]]) ).
cnf(refute_0_510,plain,
( converse(composition(converse(top),X_20)) != composition(converse(X_20),top)
| converse(composition(top,X_20)) = composition(converse(X_20),top) ),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_0_343,refute_0_509]) ).
cnf(refute_0_511,plain,
converse(composition(top,X_20)) = composition(converse(X_20),top),
inference(resolve,[$cnf( $equal(converse(composition(converse(top),X_20)),composition(converse(X_20),top)) )],[refute_0_508,refute_0_510]) ).
cnf(refute_0_512,plain,
converse(composition(top,top)) = composition(converse(top),top),
inference(subst,[],[refute_0_511:[bind(X_20,$fot(top))]]) ).
cnf(refute_0_513,plain,
( converse(composition(top,top)) != composition(converse(top),top)
| converse(top) != top
| converse(composition(top,top)) = composition(top,top) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(top,top)),composition(converse(top),top)) ),[1,0],$fot(top)]]) ).
cnf(refute_0_514,plain,
( converse(composition(top,top)) != composition(converse(top),top)
| converse(composition(top,top)) = composition(top,top) ),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_0_343,refute_0_513]) ).
cnf(refute_0_515,plain,
converse(composition(top,top)) = composition(top,top),
inference(resolve,[$cnf( $equal(converse(composition(top,top)),composition(converse(top),top)) )],[refute_0_512,refute_0_514]) ).
cnf(refute_0_516,plain,
( converse(composition(top,top)) != composition(top,top)
| join(composition(top,top),join(converse(complement(converse(composition(top,top)))),X_101)) != top
| join(composition(top,top),join(converse(complement(composition(top,top))),X_101)) = top ),
introduced(tautology,[equality,[$cnf( $equal(join(composition(top,top),join(converse(complement(converse(composition(top,top)))),X_101)),top) ),[0,1,0,0,0],$fot(composition(top,top))]]) ).
cnf(refute_0_517,plain,
( join(composition(top,top),join(converse(complement(converse(composition(top,top)))),X_101)) != top
| join(composition(top,top),join(converse(complement(composition(top,top))),X_101)) = top ),
inference(resolve,[$cnf( $equal(converse(composition(top,top)),composition(top,top)) )],[refute_0_515,refute_0_516]) ).
cnf(refute_0_518,plain,
join(composition(top,top),join(converse(complement(composition(top,top))),X_101)) = top,
inference(resolve,[$cnf( $equal(join(composition(top,top),join(converse(complement(converse(composition(top,top)))),X_101)),top) )],[refute_0_507,refute_0_517]) ).
cnf(refute_0_519,plain,
join(zero,X_101) = X_101,
inference(subst,[],[refute_0_411:[bind(X_68,$fot(X_101))]]) ).
cnf(refute_0_520,plain,
zero = meet(converse(zero),complement(converse(zero))),
inference(subst,[],[refute_0_59:[bind(X0,$fot(converse(zero)))]]) ).
cnf(refute_0_521,plain,
top = join(complement(converse(zero)),converse(complement(converse(complement(converse(zero)))))),
inference(subst,[],[refute_0_346:[bind(X_16,$fot(complement(converse(zero))))]]) ).
cnf(refute_0_522,plain,
top = join(zero,converse(complement(converse(zero)))),
inference(subst,[],[refute_0_346:[bind(X_16,$fot(zero))]]) ).
cnf(refute_0_523,plain,
join(zero,converse(complement(converse(zero)))) = converse(complement(converse(zero))),
inference(subst,[],[refute_0_411:[bind(X_68,$fot(converse(complement(converse(zero)))))]]) ).
cnf(refute_0_524,plain,
( join(zero,converse(complement(converse(zero)))) != converse(complement(converse(zero)))
| top != join(zero,converse(complement(converse(zero))))
| top = converse(complement(converse(zero))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(zero,converse(complement(converse(zero))))) ),[1],$fot(converse(complement(converse(zero))))]]) ).
cnf(refute_0_525,plain,
( top != join(zero,converse(complement(converse(zero))))
| top = converse(complement(converse(zero))) ),
inference(resolve,[$cnf( $equal(join(zero,converse(complement(converse(zero)))),converse(complement(converse(zero)))) )],[refute_0_523,refute_0_524]) ).
cnf(refute_0_526,plain,
top = converse(complement(converse(zero))),
inference(resolve,[$cnf( $equal(top,join(zero,converse(complement(converse(zero))))) )],[refute_0_522,refute_0_525]) ).
cnf(refute_0_527,plain,
( top != converse(complement(converse(zero)))
| converse(complement(converse(zero))) = top ),
inference(subst,[],[refute_0_4:[bind(X,$fot(top)),bind(Y,$fot(converse(complement(converse(zero)))))]]) ).
cnf(refute_0_528,plain,
converse(complement(converse(zero))) = top,
inference(resolve,[$cnf( $equal(top,converse(complement(converse(zero)))) )],[refute_0_526,refute_0_527]) ).
cnf(refute_0_529,plain,
( converse(complement(converse(zero))) != top
| top != join(complement(converse(zero)),converse(complement(converse(complement(converse(zero))))))
| top = join(complement(converse(zero)),converse(complement(top))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(converse(zero)),converse(complement(converse(complement(converse(zero))))))) ),[1,1,0,0],$fot(top)]]) ).
cnf(refute_0_530,plain,
( top != join(complement(converse(zero)),converse(complement(converse(complement(converse(zero))))))
| top = join(complement(converse(zero)),converse(complement(top))) ),
inference(resolve,[$cnf( $equal(converse(complement(converse(zero))),top) )],[refute_0_528,refute_0_529]) ).
cnf(refute_0_531,plain,
top = join(complement(converse(zero)),converse(complement(top))),
inference(resolve,[$cnf( $equal(top,join(complement(converse(zero)),converse(complement(converse(complement(converse(zero))))))) )],[refute_0_521,refute_0_530]) ).
cnf(refute_0_532,plain,
converse(join(converse(X0),zero)) = join(X0,converse(zero)),
inference(subst,[],[refute_0_45:[bind(X_13,$fot(zero))]]) ).
cnf(refute_0_533,plain,
join(converse(X0),zero) = converse(X0),
inference(subst,[],[refute_0_474:[bind(X_68,$fot(converse(X0)))]]) ).
cnf(refute_0_534,plain,
( converse(join(converse(X0),zero)) != join(X0,converse(zero))
| join(converse(X0),zero) != converse(X0)
| converse(converse(X0)) = join(X0,converse(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(X0),zero)),join(X0,converse(zero))) ),[0,0],$fot(converse(X0))]]) ).
cnf(refute_0_535,plain,
( converse(join(converse(X0),zero)) != join(X0,converse(zero))
| converse(converse(X0)) = join(X0,converse(zero)) ),
inference(resolve,[$cnf( $equal(join(converse(X0),zero),converse(X0)) )],[refute_0_533,refute_0_534]) ).
cnf(refute_0_536,plain,
converse(converse(X0)) = join(X0,converse(zero)),
inference(resolve,[$cnf( $equal(converse(join(converse(X0),zero)),join(X0,converse(zero))) )],[refute_0_532,refute_0_535]) ).
cnf(refute_0_537,plain,
( converse(converse(X0)) != X0
| converse(converse(X0)) != join(X0,converse(zero))
| X0 = join(X0,converse(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(converse(X0)),join(X0,converse(zero))) ),[0],$fot(X0)]]) ).
cnf(refute_0_538,plain,
( converse(converse(X0)) != join(X0,converse(zero))
| X0 = join(X0,converse(zero)) ),
inference(resolve,[$cnf( $equal(converse(converse(X0)),X0) )],[refute_0_42,refute_0_537]) ).
cnf(refute_0_539,plain,
X0 = join(X0,converse(zero)),
inference(resolve,[$cnf( $equal(converse(converse(X0)),join(X0,converse(zero))) )],[refute_0_536,refute_0_538]) ).
cnf(refute_0_540,plain,
( X0 != join(X0,converse(zero))
| join(X0,converse(zero)) = X0 ),
inference(subst,[],[refute_0_4:[bind(X,$fot(X0)),bind(Y,$fot(join(X0,converse(zero))))]]) ).
cnf(refute_0_541,plain,
join(X0,converse(zero)) = X0,
inference(resolve,[$cnf( $equal(X0,join(X0,converse(zero))) )],[refute_0_539,refute_0_540]) ).
cnf(refute_0_542,plain,
join(complement(converse(zero)),converse(zero)) = complement(converse(zero)),
inference(subst,[],[refute_0_541:[bind(X0,$fot(complement(converse(zero))))]]) ).
cnf(refute_0_543,plain,
converse(complement(top)) = converse(complement(top)),
introduced(tautology,[refl,[$fot(converse(complement(top)))]]) ).
cnf(refute_0_544,plain,
( complement(top) != zero
| converse(complement(top)) != converse(complement(top))
| converse(complement(top)) = converse(zero) ),
introduced(tautology,[equality,[$cnf( $equal(converse(complement(top)),converse(complement(top))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_545,plain,
( complement(top) != zero
| converse(complement(top)) = converse(zero) ),
inference(resolve,[$cnf( $equal(converse(complement(top)),converse(complement(top))) )],[refute_0_543,refute_0_544]) ).
cnf(refute_0_546,plain,
converse(complement(top)) = converse(zero),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_86,refute_0_545]) ).
cnf(refute_0_547,plain,
join(complement(converse(zero)),converse(complement(top))) = join(complement(converse(zero)),converse(complement(top))),
introduced(tautology,[refl,[$fot(join(complement(converse(zero)),converse(complement(top))))]]) ).
cnf(refute_0_548,plain,
( converse(complement(top)) != converse(zero)
| join(complement(converse(zero)),converse(complement(top))) != join(complement(converse(zero)),converse(complement(top)))
| join(complement(converse(zero)),converse(complement(top))) = join(complement(converse(zero)),converse(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(converse(zero)),converse(complement(top))),join(complement(converse(zero)),converse(complement(top)))) ),[1,1],$fot(converse(zero))]]) ).
cnf(refute_0_549,plain,
( converse(complement(top)) != converse(zero)
| join(complement(converse(zero)),converse(complement(top))) = join(complement(converse(zero)),converse(zero)) ),
inference(resolve,[$cnf( $equal(join(complement(converse(zero)),converse(complement(top))),join(complement(converse(zero)),converse(complement(top)))) )],[refute_0_547,refute_0_548]) ).
cnf(refute_0_550,plain,
join(complement(converse(zero)),converse(complement(top))) = join(complement(converse(zero)),converse(zero)),
inference(resolve,[$cnf( $equal(converse(complement(top)),converse(zero)) )],[refute_0_546,refute_0_549]) ).
cnf(refute_0_551,plain,
( join(complement(converse(zero)),converse(complement(top))) != join(complement(converse(zero)),converse(zero))
| join(complement(converse(zero)),converse(zero)) != complement(converse(zero))
| join(complement(converse(zero)),converse(complement(top))) = complement(converse(zero)) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(join(complement(converse(zero)),converse(complement(top))))),bind(Y,$fot(join(complement(converse(zero)),converse(zero)))),bind(Z,$fot(complement(converse(zero))))]]) ).
cnf(refute_0_552,plain,
( join(complement(converse(zero)),converse(zero)) != complement(converse(zero))
| join(complement(converse(zero)),converse(complement(top))) = complement(converse(zero)) ),
inference(resolve,[$cnf( $equal(join(complement(converse(zero)),converse(complement(top))),join(complement(converse(zero)),converse(zero))) )],[refute_0_550,refute_0_551]) ).
cnf(refute_0_553,plain,
join(complement(converse(zero)),converse(complement(top))) = complement(converse(zero)),
inference(resolve,[$cnf( $equal(join(complement(converse(zero)),converse(zero)),complement(converse(zero))) )],[refute_0_542,refute_0_552]) ).
cnf(refute_0_554,plain,
( join(complement(converse(zero)),converse(complement(top))) != complement(converse(zero))
| top != join(complement(converse(zero)),converse(complement(top)))
| top = complement(converse(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(converse(zero)),converse(complement(top)))) ),[1],$fot(complement(converse(zero)))]]) ).
cnf(refute_0_555,plain,
( top != join(complement(converse(zero)),converse(complement(top)))
| top = complement(converse(zero)) ),
inference(resolve,[$cnf( $equal(join(complement(converse(zero)),converse(complement(top))),complement(converse(zero))) )],[refute_0_553,refute_0_554]) ).
cnf(refute_0_556,plain,
top = complement(converse(zero)),
inference(resolve,[$cnf( $equal(top,join(complement(converse(zero)),converse(complement(top)))) )],[refute_0_531,refute_0_555]) ).
cnf(refute_0_557,plain,
( top != complement(converse(zero))
| complement(converse(zero)) = top ),
inference(subst,[],[refute_0_4:[bind(X,$fot(top)),bind(Y,$fot(complement(converse(zero))))]]) ).
cnf(refute_0_558,plain,
complement(converse(zero)) = top,
inference(resolve,[$cnf( $equal(top,complement(converse(zero))) )],[refute_0_556,refute_0_557]) ).
cnf(refute_0_559,plain,
( complement(converse(zero)) != top
| zero != meet(converse(zero),complement(converse(zero)))
| zero = meet(converse(zero),top) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(converse(zero),complement(converse(zero)))) ),[1,1],$fot(top)]]) ).
cnf(refute_0_560,plain,
( zero != meet(converse(zero),complement(converse(zero)))
| zero = meet(converse(zero),top) ),
inference(resolve,[$cnf( $equal(complement(converse(zero)),top) )],[refute_0_558,refute_0_559]) ).
cnf(refute_0_561,plain,
zero = meet(converse(zero),top),
inference(resolve,[$cnf( $equal(zero,meet(converse(zero),complement(converse(zero)))) )],[refute_0_520,refute_0_560]) ).
cnf(refute_0_562,plain,
join(zero,meet(X_66,top)) = meet(X_66,top),
inference(subst,[],[refute_0_411:[bind(X_68,$fot(meet(X_66,top)))]]) ).
cnf(refute_0_563,plain,
( X_66 != join(zero,meet(X_66,top))
| join(zero,meet(X_66,top)) != meet(X_66,top)
| X_66 = meet(X_66,top) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_66,meet(X_66,top)) ),[0],$fot(join(zero,meet(X_66,top)))]]) ).
cnf(refute_0_564,plain,
( X_66 != join(zero,meet(X_66,top))
| X_66 = meet(X_66,top) ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_66,top)),meet(X_66,top)) )],[refute_0_562,refute_0_563]) ).
cnf(refute_0_565,plain,
X_66 = meet(X_66,top),
inference(resolve,[$cnf( $equal(X_66,join(zero,meet(X_66,top))) )],[refute_0_402,refute_0_564]) ).
cnf(refute_0_566,plain,
( X_66 != meet(X_66,top)
| meet(X_66,top) = X_66 ),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_66)),bind(Y,$fot(meet(X_66,top)))]]) ).
cnf(refute_0_567,plain,
meet(X_66,top) = X_66,
inference(resolve,[$cnf( $equal(X_66,meet(X_66,top)) )],[refute_0_565,refute_0_566]) ).
cnf(refute_0_568,plain,
meet(converse(zero),top) = converse(zero),
inference(subst,[],[refute_0_567:[bind(X_66,$fot(converse(zero)))]]) ).
cnf(refute_0_569,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_0_570,plain,
( zero != meet(converse(zero),top)
| zero = converse(zero) ),
inference(resolve,[$cnf( $equal(meet(converse(zero),top),converse(zero)) )],[refute_0_568,refute_0_569]) ).
cnf(refute_0_571,plain,
zero = converse(zero),
inference(resolve,[$cnf( $equal(zero,meet(converse(zero),top)) )],[refute_0_561,refute_0_570]) ).
cnf(refute_0_572,plain,
( zero != converse(zero)
| converse(zero) = zero ),
inference(subst,[],[refute_0_4:[bind(X,$fot(zero)),bind(Y,$fot(converse(zero)))]]) ).
cnf(refute_0_573,plain,
converse(zero) = zero,
inference(resolve,[$cnf( $equal(zero,converse(zero)) )],[refute_0_571,refute_0_572]) ).
cnf(refute_0_574,plain,
converse(complement(composition(top,top))) = converse(complement(composition(top,top))),
introduced(tautology,[refl,[$fot(converse(complement(composition(top,top))))]]) ).
cnf(refute_0_575,plain,
( complement(composition(top,top)) != zero
| converse(complement(composition(top,top))) != converse(complement(composition(top,top)))
| converse(complement(composition(top,top))) = converse(zero) ),
introduced(tautology,[equality,[$cnf( $equal(converse(complement(composition(top,top))),converse(complement(composition(top,top)))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_576,plain,
( complement(composition(top,top)) != zero
| converse(complement(composition(top,top))) = converse(zero) ),
inference(resolve,[$cnf( $equal(converse(complement(composition(top,top))),converse(complement(composition(top,top)))) )],[refute_0_574,refute_0_575]) ).
cnf(refute_0_577,plain,
converse(complement(composition(top,top))) = converse(zero),
inference(resolve,[$cnf( $equal(complement(composition(top,top)),zero) )],[refute_0_485,refute_0_576]) ).
cnf(refute_0_578,plain,
( converse(complement(composition(top,top))) != converse(zero)
| converse(zero) != zero
| converse(complement(composition(top,top))) = zero ),
inference(subst,[],[refute_0_20:[bind(X,$fot(converse(complement(composition(top,top))))),bind(Y,$fot(converse(zero))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_579,plain,
( converse(zero) != zero
| converse(complement(composition(top,top))) = zero ),
inference(resolve,[$cnf( $equal(converse(complement(composition(top,top))),converse(zero)) )],[refute_0_577,refute_0_578]) ).
cnf(refute_0_580,plain,
converse(complement(composition(top,top))) = zero,
inference(resolve,[$cnf( $equal(converse(zero),zero) )],[refute_0_573,refute_0_579]) ).
cnf(refute_0_581,plain,
join(converse(complement(composition(top,top))),X_101) = join(converse(complement(composition(top,top))),X_101),
introduced(tautology,[refl,[$fot(join(converse(complement(composition(top,top))),X_101))]]) ).
cnf(refute_0_582,plain,
( converse(complement(composition(top,top))) != zero
| join(converse(complement(composition(top,top))),X_101) != join(converse(complement(composition(top,top))),X_101)
| join(converse(complement(composition(top,top))),X_101) = join(zero,X_101) ),
introduced(tautology,[equality,[$cnf( $equal(join(converse(complement(composition(top,top))),X_101),join(converse(complement(composition(top,top))),X_101)) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_583,plain,
( converse(complement(composition(top,top))) != zero
| join(converse(complement(composition(top,top))),X_101) = join(zero,X_101) ),
inference(resolve,[$cnf( $equal(join(converse(complement(composition(top,top))),X_101),join(converse(complement(composition(top,top))),X_101)) )],[refute_0_581,refute_0_582]) ).
cnf(refute_0_584,plain,
join(converse(complement(composition(top,top))),X_101) = join(zero,X_101),
inference(resolve,[$cnf( $equal(converse(complement(composition(top,top))),zero) )],[refute_0_580,refute_0_583]) ).
cnf(refute_0_585,plain,
( join(converse(complement(composition(top,top))),X_101) != join(zero,X_101)
| join(zero,X_101) != X_101
| join(converse(complement(composition(top,top))),X_101) = X_101 ),
inference(subst,[],[refute_0_20:[bind(X,$fot(join(converse(complement(composition(top,top))),X_101))),bind(Y,$fot(join(zero,X_101))),bind(Z,$fot(X_101))]]) ).
cnf(refute_0_586,plain,
( join(zero,X_101) != X_101
| join(converse(complement(composition(top,top))),X_101) = X_101 ),
inference(resolve,[$cnf( $equal(join(converse(complement(composition(top,top))),X_101),join(zero,X_101)) )],[refute_0_584,refute_0_585]) ).
cnf(refute_0_587,plain,
join(converse(complement(composition(top,top))),X_101) = X_101,
inference(resolve,[$cnf( $equal(join(zero,X_101),X_101) )],[refute_0_519,refute_0_586]) ).
cnf(refute_0_588,plain,
join(composition(top,top),join(converse(complement(composition(top,top))),X_101)) = join(composition(top,top),join(converse(complement(composition(top,top))),X_101)),
introduced(tautology,[refl,[$fot(join(composition(top,top),join(converse(complement(composition(top,top))),X_101)))]]) ).
cnf(refute_0_589,plain,
( join(composition(top,top),join(converse(complement(composition(top,top))),X_101)) != join(composition(top,top),join(converse(complement(composition(top,top))),X_101))
| join(converse(complement(composition(top,top))),X_101) != X_101
| join(composition(top,top),join(converse(complement(composition(top,top))),X_101)) = join(composition(top,top),X_101) ),
introduced(tautology,[equality,[$cnf( $equal(join(composition(top,top),join(converse(complement(composition(top,top))),X_101)),join(composition(top,top),join(converse(complement(composition(top,top))),X_101))) ),[1,1],$fot(X_101)]]) ).
cnf(refute_0_590,plain,
( join(converse(complement(composition(top,top))),X_101) != X_101
| join(composition(top,top),join(converse(complement(composition(top,top))),X_101)) = join(composition(top,top),X_101) ),
inference(resolve,[$cnf( $equal(join(composition(top,top),join(converse(complement(composition(top,top))),X_101)),join(composition(top,top),join(converse(complement(composition(top,top))),X_101))) )],[refute_0_588,refute_0_589]) ).
cnf(refute_0_591,plain,
join(composition(top,top),join(converse(complement(composition(top,top))),X_101)) = join(composition(top,top),X_101),
inference(resolve,[$cnf( $equal(join(converse(complement(composition(top,top))),X_101),X_101) )],[refute_0_587,refute_0_590]) ).
cnf(refute_0_592,plain,
( join(composition(top,top),join(converse(complement(composition(top,top))),X_101)) != join(composition(top,top),X_101)
| join(composition(top,top),join(converse(complement(composition(top,top))),X_101)) != top
| join(composition(top,top),X_101) = top ),
introduced(tautology,[equality,[$cnf( $equal(join(composition(top,top),join(converse(complement(composition(top,top))),X_101)),top) ),[0],$fot(join(composition(top,top),X_101))]]) ).
cnf(refute_0_593,plain,
( join(composition(top,top),join(converse(complement(composition(top,top))),X_101)) != top
| join(composition(top,top),X_101) = top ),
inference(resolve,[$cnf( $equal(join(composition(top,top),join(converse(complement(composition(top,top))),X_101)),join(composition(top,top),X_101)) )],[refute_0_591,refute_0_592]) ).
cnf(refute_0_594,plain,
join(composition(top,top),X_101) = top,
inference(resolve,[$cnf( $equal(join(composition(top,top),join(converse(complement(composition(top,top))),X_101)),top) )],[refute_0_518,refute_0_593]) ).
cnf(refute_0_595,plain,
join(composition(top,top),meet(composition(top,top),complement(converse(complement(converse(zero)))))) = top,
inference(subst,[],[refute_0_594:[bind(X_101,$fot(meet(composition(top,top),complement(converse(complement(converse(zero)))))))]]) ).
cnf(refute_0_596,plain,
( composition(top,top) != join(composition(top,top),meet(composition(top,top),complement(converse(complement(converse(zero))))))
| join(composition(top,top),meet(composition(top,top),complement(converse(complement(converse(zero)))))) != top
| composition(top,top) = top ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(top,top),top) ),[0],$fot(join(composition(top,top),meet(composition(top,top),complement(converse(complement(converse(zero)))))))]]) ).
cnf(refute_0_597,plain,
( composition(top,top) != join(composition(top,top),meet(composition(top,top),complement(converse(complement(converse(zero))))))
| composition(top,top) = top ),
inference(resolve,[$cnf( $equal(join(composition(top,top),meet(composition(top,top),complement(converse(complement(converse(zero)))))),top) )],[refute_0_595,refute_0_596]) ).
cnf(refute_0_598,plain,
composition(top,top) = top,
inference(resolve,[$cnf( $equal(composition(top,top),join(composition(top,top),meet(composition(top,top),complement(converse(complement(converse(zero))))))) )],[refute_0_488,refute_0_597]) ).
cnf(refute_0_599,plain,
composition(top,top) != top,
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_600,plain,
$false,
inference(resolve,[$cnf( $equal(composition(top,top),top) )],[refute_0_598,refute_0_599]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : REL015+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Fri Jul 8 09:01:54 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.74/0.91 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.74/0.91
% 0.74/0.91 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.79/0.97
%------------------------------------------------------------------------------