TSTP Solution File: REL007+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : REL007+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n018.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 19:43:10 EDT 2022
% Result : Theorem 18.57s 18.74s
% Output : CNFRefutation 18.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 109
% Number of leaves : 196
% Syntax : Number of formulae : 835 ( 433 unt; 0 def)
% Number of atoms : 1412 (1411 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 1155 ( 578 ~; 572 |; 2 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 892 ( 20 sgn 63 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(maddux1_join_commutativity,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0) ).
fof(maddux2_join_associativity,axiom,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2) ).
fof(maddux3_a_kind_of_de_Morgan,axiom,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) ).
fof(maddux4_definiton_of_meet,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))) ).
fof(composition_identity,axiom,
! [X0] : composition(X0,one) = X0 ).
fof(converse_idempotence,axiom,
! [X0] : converse(converse(X0)) = X0 ).
fof(converse_additivity,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)) ).
fof(converse_multiplicativity,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)) ).
fof(converse_cancellativity,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1) ).
fof(def_top,axiom,
! [X0] : top = join(X0,complement(X0)) ).
fof(def_zero,axiom,
! [X0] : zero = meet(X0,complement(X0)) ).
fof(goals,conjecture,
! [X0,X1] :
( meet(X0,converse(X1)) = zero
=> meet(converse(X0),X1) = zero ) ).
fof(subgoal_0,plain,
! [X0,X1] :
( meet(X0,converse(X1)) = zero
=> meet(converse(X0),X1) = zero ),
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ! [X0,X1] :
( meet(X0,converse(X1)) = zero
=> meet(converse(X0),X1) = zero ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(canonicalize,[],[maddux4_definiton_of_meet]) ).
fof(normalize_0_1,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(canonicalize,[],[def_zero]) ).
fof(normalize_0_3,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X0] : top = join(X0,complement(X0)),
inference(canonicalize,[],[def_top]) ).
fof(normalize_0_5,plain,
! [X0] : top = join(X0,complement(X0)),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,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_7,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(canonicalize,[],[maddux1_join_commutativity]) ).
fof(normalize_0_9,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(canonicalize,[],[maddux2_join_associativity]) ).
fof(normalize_0_11,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(canonicalize,[],[converse_cancellativity]) ).
fof(normalize_0_13,plain,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(canonicalize,[],[converse_multiplicativity]) ).
fof(normalize_0_15,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [X0] : converse(converse(X0)) = X0,
inference(canonicalize,[],[converse_idempotence]) ).
fof(normalize_0_17,plain,
! [X0] : converse(converse(X0)) = X0,
inference(specialize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [X0] : composition(X0,one) = X0,
inference(canonicalize,[],[composition_identity]) ).
fof(normalize_0_19,plain,
! [X0] : composition(X0,one) = X0,
inference(specialize,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(canonicalize,[],[converse_additivity]) ).
fof(normalize_0_21,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(specialize,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
? [X0,X1] :
( meet(converse(X0),X1) != zero
& meet(X0,converse(X1)) = zero ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_23,plain,
( meet(converse(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) != zero
& meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1)) = zero ),
inference(skolemize,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1)) = zero,
inference(conjunct,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
meet(converse(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) != zero,
inference(conjunct,[],[normalize_0_23]) ).
cnf(refute_0_0,plain,
meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
meet(X0,join(zero,complement(X_25))) = complement(join(complement(X0),complement(join(zero,complement(X_25))))),
inference(subst,[],[refute_0_0:[bind(X1,$fot(join(zero,complement(X_25))))]]) ).
cnf(refute_0_2,plain,
meet(top,X1) = complement(join(complement(top),complement(X1))),
inference(subst,[],[refute_0_0:[bind(X0,$fot(top))]]) ).
cnf(refute_0_3,plain,
zero = meet(X0,complement(X0)),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_4,plain,
zero = meet(join(complement(X_21),complement(X_22)),complement(join(complement(X_21),complement(X_22)))),
inference(subst,[],[refute_0_3:[bind(X0,$fot(join(complement(X_21),complement(X_22))))]]) ).
cnf(refute_0_5,plain,
meet(X_21,X_22) = complement(join(complement(X_21),complement(X_22))),
inference(subst,[],[refute_0_0:[bind(X0,$fot(X_21)),bind(X1,$fot(X_22))]]) ).
cnf(refute_0_6,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_7,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_8,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( meet(X_21,X_22) != complement(join(complement(X_21),complement(X_22)))
| complement(join(complement(X_21),complement(X_22))) = meet(X_21,X_22) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(meet(X_21,X_22))),bind(Y,$fot(complement(join(complement(X_21),complement(X_22)))))]]) ).
cnf(refute_0_10,plain,
complement(join(complement(X_21),complement(X_22))) = meet(X_21,X_22),
inference(resolve,[$cnf( $equal(meet(X_21,X_22),complement(join(complement(X_21),complement(X_22)))) )],[refute_0_5,refute_0_9]) ).
cnf(refute_0_11,plain,
( complement(join(complement(X_21),complement(X_22))) != meet(X_21,X_22)
| zero != meet(join(complement(X_21),complement(X_22)),complement(join(complement(X_21),complement(X_22))))
| zero = meet(join(complement(X_21),complement(X_22)),meet(X_21,X_22)) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(join(complement(X_21),complement(X_22)),complement(join(complement(X_21),complement(X_22))))) ),[1,1],$fot(meet(X_21,X_22))]]) ).
cnf(refute_0_12,plain,
( zero != meet(join(complement(X_21),complement(X_22)),complement(join(complement(X_21),complement(X_22))))
| zero = meet(join(complement(X_21),complement(X_22)),meet(X_21,X_22)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_21),complement(X_22))),meet(X_21,X_22)) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
zero = meet(join(complement(X_21),complement(X_22)),meet(X_21,X_22)),
inference(resolve,[$cnf( $equal(zero,meet(join(complement(X_21),complement(X_22)),complement(join(complement(X_21),complement(X_22))))) )],[refute_0_4,refute_0_12]) ).
cnf(refute_0_14,plain,
top = join(X0,complement(X0)),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_15,plain,
( top != join(X0,complement(X0))
| join(X0,complement(X0)) = top ),
inference(subst,[],[refute_0_8:[bind(X,$fot(top)),bind(Y,$fot(join(X0,complement(X0))))]]) ).
cnf(refute_0_16,plain,
join(X0,complement(X0)) = top,
inference(resolve,[$cnf( $equal(top,join(X0,complement(X0))) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
join(meet(X_21,X_22),complement(meet(X_21,X_22))) = top,
inference(subst,[],[refute_0_16:[bind(X0,$fot(meet(X_21,X_22)))]]) ).
cnf(refute_0_18,plain,
complement(join(meet(X_21,X_22),complement(meet(X_21,X_22)))) = complement(join(meet(X_21,X_22),complement(meet(X_21,X_22)))),
introduced(tautology,[refl,[$fot(complement(join(meet(X_21,X_22),complement(meet(X_21,X_22)))))]]) ).
cnf(refute_0_19,plain,
( complement(join(meet(X_21,X_22),complement(meet(X_21,X_22)))) != complement(join(meet(X_21,X_22),complement(meet(X_21,X_22))))
| join(meet(X_21,X_22),complement(meet(X_21,X_22))) != top
| complement(join(meet(X_21,X_22),complement(meet(X_21,X_22)))) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(meet(X_21,X_22),complement(meet(X_21,X_22)))),complement(join(meet(X_21,X_22),complement(meet(X_21,X_22))))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_20,plain,
( join(meet(X_21,X_22),complement(meet(X_21,X_22))) != top
| complement(join(meet(X_21,X_22),complement(meet(X_21,X_22)))) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(join(meet(X_21,X_22),complement(meet(X_21,X_22)))),complement(join(meet(X_21,X_22),complement(meet(X_21,X_22))))) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
complement(join(meet(X_21,X_22),complement(meet(X_21,X_22)))) = complement(top),
inference(resolve,[$cnf( $equal(join(meet(X_21,X_22),complement(meet(X_21,X_22))),top) )],[refute_0_17,refute_0_20]) ).
cnf(refute_0_22,plain,
meet(join(complement(X_21),complement(X_22)),X1) = complement(join(complement(join(complement(X_21),complement(X_22))),complement(X1))),
inference(subst,[],[refute_0_0:[bind(X0,$fot(join(complement(X_21),complement(X_22))))]]) ).
cnf(refute_0_23,plain,
( complement(join(complement(X_21),complement(X_22))) != meet(X_21,X_22)
| meet(join(complement(X_21),complement(X_22)),X1) != complement(join(complement(join(complement(X_21),complement(X_22))),complement(X1)))
| meet(join(complement(X_21),complement(X_22)),X1) = complement(join(meet(X_21,X_22),complement(X1))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(complement(X_21),complement(X_22)),X1),complement(join(complement(join(complement(X_21),complement(X_22))),complement(X1)))) ),[1,0,0],$fot(meet(X_21,X_22))]]) ).
cnf(refute_0_24,plain,
( meet(join(complement(X_21),complement(X_22)),X1) != complement(join(complement(join(complement(X_21),complement(X_22))),complement(X1)))
| meet(join(complement(X_21),complement(X_22)),X1) = complement(join(meet(X_21,X_22),complement(X1))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_21),complement(X_22))),meet(X_21,X_22)) )],[refute_0_10,refute_0_23]) ).
cnf(refute_0_25,plain,
meet(join(complement(X_21),complement(X_22)),X1) = complement(join(meet(X_21,X_22),complement(X1))),
inference(resolve,[$cnf( $equal(meet(join(complement(X_21),complement(X_22)),X1),complement(join(complement(join(complement(X_21),complement(X_22))),complement(X1)))) )],[refute_0_22,refute_0_24]) ).
cnf(refute_0_26,plain,
meet(join(complement(X_21),complement(X_22)),meet(X_21,X_22)) = complement(join(meet(X_21,X_22),complement(meet(X_21,X_22)))),
inference(subst,[],[refute_0_25:[bind(X1,$fot(meet(X_21,X_22)))]]) ).
cnf(refute_0_27,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_28,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_8,refute_0_27]) ).
cnf(refute_0_29,plain,
( complement(join(meet(X_21,X_22),complement(meet(X_21,X_22)))) != complement(top)
| meet(join(complement(X_21),complement(X_22)),meet(X_21,X_22)) != complement(join(meet(X_21,X_22),complement(meet(X_21,X_22))))
| meet(join(complement(X_21),complement(X_22)),meet(X_21,X_22)) = complement(top) ),
inference(subst,[],[refute_0_28:[bind(X,$fot(meet(join(complement(X_21),complement(X_22)),meet(X_21,X_22)))),bind(Y,$fot(complement(join(meet(X_21,X_22),complement(meet(X_21,X_22)))))),bind(Z,$fot(complement(top)))]]) ).
cnf(refute_0_30,plain,
( complement(join(meet(X_21,X_22),complement(meet(X_21,X_22)))) != complement(top)
| meet(join(complement(X_21),complement(X_22)),meet(X_21,X_22)) = complement(top) ),
inference(resolve,[$cnf( $equal(meet(join(complement(X_21),complement(X_22)),meet(X_21,X_22)),complement(join(meet(X_21,X_22),complement(meet(X_21,X_22))))) )],[refute_0_26,refute_0_29]) ).
cnf(refute_0_31,plain,
meet(join(complement(X_21),complement(X_22)),meet(X_21,X_22)) = complement(top),
inference(resolve,[$cnf( $equal(complement(join(meet(X_21,X_22),complement(meet(X_21,X_22)))),complement(top)) )],[refute_0_21,refute_0_30]) ).
cnf(refute_0_32,plain,
( meet(join(complement(X_21),complement(X_22)),meet(X_21,X_22)) != complement(top)
| zero != meet(join(complement(X_21),complement(X_22)),meet(X_21,X_22))
| zero = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(join(complement(X_21),complement(X_22)),meet(X_21,X_22))) ),[1],$fot(complement(top))]]) ).
cnf(refute_0_33,plain,
( zero != meet(join(complement(X_21),complement(X_22)),meet(X_21,X_22))
| zero = complement(top) ),
inference(resolve,[$cnf( $equal(meet(join(complement(X_21),complement(X_22)),meet(X_21,X_22)),complement(top)) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
zero = complement(top),
inference(resolve,[$cnf( $equal(zero,meet(join(complement(X_21),complement(X_22)),meet(X_21,X_22))) )],[refute_0_13,refute_0_33]) ).
cnf(refute_0_35,plain,
( zero != complement(top)
| complement(top) = zero ),
inference(subst,[],[refute_0_8:[bind(X,$fot(zero)),bind(Y,$fot(complement(top)))]]) ).
cnf(refute_0_36,plain,
complement(top) = zero,
inference(resolve,[$cnf( $equal(zero,complement(top)) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
( complement(top) != zero
| meet(top,X1) != complement(join(complement(top),complement(X1)))
| meet(top,X1) = complement(join(zero,complement(X1))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,X1),complement(join(complement(top),complement(X1)))) ),[1,0,0],$fot(zero)]]) ).
cnf(refute_0_38,plain,
( meet(top,X1) != complement(join(complement(top),complement(X1)))
| meet(top,X1) = complement(join(zero,complement(X1))) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
meet(top,X1) = complement(join(zero,complement(X1))),
inference(resolve,[$cnf( $equal(meet(top,X1),complement(join(complement(top),complement(X1)))) )],[refute_0_2,refute_0_38]) ).
cnf(refute_0_40,plain,
meet(top,X_25) = complement(join(zero,complement(X_25))),
inference(subst,[],[refute_0_39:[bind(X1,$fot(X_25))]]) ).
cnf(refute_0_41,plain,
( meet(top,X_25) != complement(join(zero,complement(X_25)))
| complement(join(zero,complement(X_25))) = meet(top,X_25) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(meet(top,X_25))),bind(Y,$fot(complement(join(zero,complement(X_25)))))]]) ).
cnf(refute_0_42,plain,
complement(join(zero,complement(X_25))) = meet(top,X_25),
inference(resolve,[$cnf( $equal(meet(top,X_25),complement(join(zero,complement(X_25)))) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
( complement(join(zero,complement(X_25))) != meet(top,X_25)
| meet(X0,join(zero,complement(X_25))) != complement(join(complement(X0),complement(join(zero,complement(X_25)))))
| meet(X0,join(zero,complement(X_25))) = complement(join(complement(X0),meet(top,X_25))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X0,join(zero,complement(X_25))),complement(join(complement(X0),complement(join(zero,complement(X_25)))))) ),[1,0,1],$fot(meet(top,X_25))]]) ).
cnf(refute_0_44,plain,
( meet(X0,join(zero,complement(X_25))) != complement(join(complement(X0),complement(join(zero,complement(X_25)))))
| meet(X0,join(zero,complement(X_25))) = complement(join(complement(X0),meet(top,X_25))) ),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(X_25))),meet(top,X_25)) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
meet(X0,join(zero,complement(X_25))) = complement(join(complement(X0),meet(top,X_25))),
inference(resolve,[$cnf( $equal(meet(X0,join(zero,complement(X_25))),complement(join(complement(X0),complement(join(zero,complement(X_25)))))) )],[refute_0_1,refute_0_44]) ).
cnf(refute_0_46,plain,
X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_47,plain,
join(X0,X1) = join(X1,X0),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_48,plain,
( join(X0,X1) != join(X1,X0)
| join(X1,X0) = join(X0,X1) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(join(X0,X1))),bind(Y,$fot(join(X1,X0)))]]) ).
cnf(refute_0_49,plain,
join(X1,X0) = join(X0,X1),
inference(resolve,[$cnf( $equal(join(X0,X1),join(X1,X0)) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),
inference(subst,[],[refute_0_49:[bind(X0,$fot(complement(join(complement(X0),X1)))),bind(X1,$fot(complement(join(complement(X0),complement(X1)))))]]) ).
cnf(refute_0_51,plain,
( X0 != join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1)))
| join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) != join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))
| X0 = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) ),
introduced(tautology,[equality,[$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_52,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( $equal(join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
X0 = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),
inference(resolve,[$cnf( $equal(X0,join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1)))) )],[refute_0_46,refute_0_52]) ).
cnf(refute_0_54,plain,
join(complement(join(complement(X0),X1)),meet(X0,X1)) = join(meet(X0,X1),complement(join(complement(X0),X1))),
inference(subst,[],[refute_0_49:[bind(X0,$fot(meet(X0,X1))),bind(X1,$fot(complement(join(complement(X0),X1))))]]) ).
cnf(refute_0_55,plain,
( meet(X0,X1) != complement(join(complement(X0),complement(X1)))
| complement(join(complement(X0),complement(X1))) = meet(X0,X1) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(meet(X0,X1))),bind(Y,$fot(complement(join(complement(X0),complement(X1)))))]]) ).
cnf(refute_0_56,plain,
complement(join(complement(X0),complement(X1))) = meet(X0,X1),
inference(resolve,[$cnf( $equal(meet(X0,X1),complement(join(complement(X0),complement(X1)))) )],[refute_0_0,refute_0_55]) ).
cnf(refute_0_57,plain,
join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),
introduced(tautology,[refl,[$fot(join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))))]]) ).
cnf(refute_0_58,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_59,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( $equal(join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(complement(join(complement(X0),X1)),meet(X0,X1)),
inference(resolve,[$cnf( $equal(complement(join(complement(X0),complement(X1))),meet(X0,X1)) )],[refute_0_56,refute_0_59]) ).
cnf(refute_0_61,plain,
( join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) != join(complement(join(complement(X0),X1)),meet(X0,X1))
| join(complement(join(complement(X0),X1)),meet(X0,X1)) != join(meet(X0,X1),complement(join(complement(X0),X1)))
| join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(meet(X0,X1),complement(join(complement(X0),X1))) ),
inference(subst,[],[refute_0_28:[bind(X,$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_62,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( $equal(join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),join(complement(join(complement(X0),X1)),meet(X0,X1))) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(meet(X0,X1),complement(join(complement(X0),X1))),
inference(resolve,[$cnf( $equal(join(complement(join(complement(X0),X1)),meet(X0,X1)),join(meet(X0,X1),complement(join(complement(X0),X1)))) )],[refute_0_54,refute_0_62]) ).
cnf(refute_0_64,plain,
( X0 != join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))
| join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) != join(meet(X0,X1),complement(join(complement(X0),X1)))
| X0 = join(meet(X0,X1),complement(join(complement(X0),X1))) ),
introduced(tautology,[equality,[$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_65,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( $equal(join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),join(meet(X0,X1),complement(join(complement(X0),X1)))) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
X0 = join(meet(X0,X1),complement(join(complement(X0),X1))),
inference(resolve,[$cnf( $equal(X0,join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))) )],[refute_0_53,refute_0_65]) ).
cnf(refute_0_67,plain,
X0 = join(meet(X0,zero),complement(join(complement(X0),zero))),
inference(subst,[],[refute_0_66:[bind(X1,$fot(zero))]]) ).
cnf(refute_0_68,plain,
meet(X0,zero) = complement(join(complement(X0),complement(zero))),
inference(subst,[],[refute_0_0:[bind(X1,$fot(zero))]]) ).
cnf(refute_0_69,plain,
X_41 = join(meet(X_41,join(zero,meet(X_41,top))),complement(join(complement(X_41),join(zero,meet(X_41,top))))),
inference(subst,[],[refute_0_66:[bind(X0,$fot(X_41)),bind(X1,$fot(join(zero,meet(X_41,top))))]]) ).
cnf(refute_0_70,plain,
top = join(join(complement(X_21),complement(X_22)),complement(join(complement(X_21),complement(X_22)))),
inference(subst,[],[refute_0_14:[bind(X0,$fot(join(complement(X_21),complement(X_22))))]]) ).
cnf(refute_0_71,plain,
( complement(join(complement(X_21),complement(X_22))) != meet(X_21,X_22)
| top != join(join(complement(X_21),complement(X_22)),complement(join(complement(X_21),complement(X_22))))
| top = join(join(complement(X_21),complement(X_22)),meet(X_21,X_22)) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(join(complement(X_21),complement(X_22)),complement(join(complement(X_21),complement(X_22))))) ),[1,1],$fot(meet(X_21,X_22))]]) ).
cnf(refute_0_72,plain,
( top != join(join(complement(X_21),complement(X_22)),complement(join(complement(X_21),complement(X_22))))
| top = join(join(complement(X_21),complement(X_22)),meet(X_21,X_22)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_21),complement(X_22))),meet(X_21,X_22)) )],[refute_0_10,refute_0_71]) ).
cnf(refute_0_73,plain,
top = join(join(complement(X_21),complement(X_22)),meet(X_21,X_22)),
inference(resolve,[$cnf( $equal(top,join(join(complement(X_21),complement(X_22)),complement(join(complement(X_21),complement(X_22))))) )],[refute_0_70,refute_0_72]) ).
cnf(refute_0_74,plain,
join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_75,plain,
( join(X0,join(X1,X2)) != join(join(X0,X1),X2)
| join(join(X0,X1),X2) = join(X0,join(X1,X2)) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(join(X0,join(X1,X2)))),bind(Y,$fot(join(join(X0,X1),X2)))]]) ).
cnf(refute_0_76,plain,
join(join(X0,X1),X2) = join(X0,join(X1,X2)),
inference(resolve,[$cnf( $equal(join(X0,join(X1,X2)),join(join(X0,X1),X2)) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
join(join(complement(X_21),complement(X_22)),meet(X_21,X_22)) = join(complement(X_21),join(complement(X_22),meet(X_21,X_22))),
inference(subst,[],[refute_0_76:[bind(X0,$fot(complement(X_21))),bind(X1,$fot(complement(X_22))),bind(X2,$fot(meet(X_21,X_22)))]]) ).
cnf(refute_0_78,plain,
( join(join(complement(X_21),complement(X_22)),meet(X_21,X_22)) != join(complement(X_21),join(complement(X_22),meet(X_21,X_22)))
| top != join(join(complement(X_21),complement(X_22)),meet(X_21,X_22))
| top = join(complement(X_21),join(complement(X_22),meet(X_21,X_22))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(join(complement(X_21),complement(X_22)),meet(X_21,X_22))) ),[1],$fot(join(complement(X_21),join(complement(X_22),meet(X_21,X_22))))]]) ).
cnf(refute_0_79,plain,
( top != join(join(complement(X_21),complement(X_22)),meet(X_21,X_22))
| top = join(complement(X_21),join(complement(X_22),meet(X_21,X_22))) ),
inference(resolve,[$cnf( $equal(join(join(complement(X_21),complement(X_22)),meet(X_21,X_22)),join(complement(X_21),join(complement(X_22),meet(X_21,X_22)))) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
top = join(complement(X_21),join(complement(X_22),meet(X_21,X_22))),
inference(resolve,[$cnf( $equal(top,join(join(complement(X_21),complement(X_22)),meet(X_21,X_22))) )],[refute_0_73,refute_0_79]) ).
cnf(refute_0_81,plain,
top = join(complement(X_29),join(complement(top),meet(X_29,top))),
inference(subst,[],[refute_0_80:[bind(X_21,$fot(X_29)),bind(X_22,$fot(top))]]) ).
cnf(refute_0_82,plain,
( complement(top) != zero
| top != join(complement(X_29),join(complement(top),meet(X_29,top)))
| top = join(complement(X_29),join(zero,meet(X_29,top))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(X_29),join(complement(top),meet(X_29,top)))) ),[1,1,0],$fot(zero)]]) ).
cnf(refute_0_83,plain,
( top != join(complement(X_29),join(complement(top),meet(X_29,top)))
| top = join(complement(X_29),join(zero,meet(X_29,top))) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_36,refute_0_82]) ).
cnf(refute_0_84,plain,
top = join(complement(X_29),join(zero,meet(X_29,top))),
inference(resolve,[$cnf( $equal(top,join(complement(X_29),join(complement(top),meet(X_29,top)))) )],[refute_0_81,refute_0_83]) ).
cnf(refute_0_85,plain,
top = join(complement(X_41),join(zero,meet(X_41,top))),
inference(subst,[],[refute_0_84:[bind(X_29,$fot(X_41))]]) ).
cnf(refute_0_86,plain,
( top != join(complement(X_41),join(zero,meet(X_41,top)))
| join(complement(X_41),join(zero,meet(X_41,top))) = top ),
inference(subst,[],[refute_0_8:[bind(X,$fot(top)),bind(Y,$fot(join(complement(X_41),join(zero,meet(X_41,top)))))]]) ).
cnf(refute_0_87,plain,
join(complement(X_41),join(zero,meet(X_41,top))) = top,
inference(resolve,[$cnf( $equal(top,join(complement(X_41),join(zero,meet(X_41,top)))) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
( X_41 != join(meet(X_41,join(zero,meet(X_41,top))),complement(join(complement(X_41),join(zero,meet(X_41,top)))))
| join(complement(X_41),join(zero,meet(X_41,top))) != top
| X_41 = join(meet(X_41,join(zero,meet(X_41,top))),complement(top)) ),
introduced(tautology,[equality,[$cnf( $equal(X_41,join(meet(X_41,join(zero,meet(X_41,top))),complement(join(complement(X_41),join(zero,meet(X_41,top)))))) ),[1,1,0],$fot(top)]]) ).
cnf(refute_0_89,plain,
( X_41 != join(meet(X_41,join(zero,meet(X_41,top))),complement(join(complement(X_41),join(zero,meet(X_41,top)))))
| X_41 = join(meet(X_41,join(zero,meet(X_41,top))),complement(top)) ),
inference(resolve,[$cnf( $equal(join(complement(X_41),join(zero,meet(X_41,top))),top) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
X_41 = join(meet(X_41,join(zero,meet(X_41,top))),complement(top)),
inference(resolve,[$cnf( $equal(X_41,join(meet(X_41,join(zero,meet(X_41,top))),complement(join(complement(X_41),join(zero,meet(X_41,top)))))) )],[refute_0_69,refute_0_89]) ).
cnf(refute_0_91,plain,
join(complement(top),meet(X_41,join(zero,meet(X_41,top)))) = join(complement(top),meet(X_41,join(zero,meet(X_41,top)))),
introduced(tautology,[refl,[$fot(join(complement(top),meet(X_41,join(zero,meet(X_41,top)))))]]) ).
cnf(refute_0_92,plain,
( complement(top) != zero
| join(complement(top),meet(X_41,join(zero,meet(X_41,top)))) != join(complement(top),meet(X_41,join(zero,meet(X_41,top))))
| join(complement(top),meet(X_41,join(zero,meet(X_41,top)))) = join(zero,meet(X_41,join(zero,meet(X_41,top)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(X_41,join(zero,meet(X_41,top)))),join(complement(top),meet(X_41,join(zero,meet(X_41,top))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_93,plain,
( complement(top) != zero
| join(complement(top),meet(X_41,join(zero,meet(X_41,top)))) = join(zero,meet(X_41,join(zero,meet(X_41,top)))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_41,join(zero,meet(X_41,top)))),join(complement(top),meet(X_41,join(zero,meet(X_41,top))))) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
join(complement(top),meet(X_41,join(zero,meet(X_41,top)))) = join(zero,meet(X_41,join(zero,meet(X_41,top)))),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_36,refute_0_93]) ).
cnf(refute_0_95,plain,
join(meet(X_41,join(zero,meet(X_41,top))),complement(top)) = join(complement(top),meet(X_41,join(zero,meet(X_41,top)))),
inference(subst,[],[refute_0_49:[bind(X0,$fot(complement(top))),bind(X1,$fot(meet(X_41,join(zero,meet(X_41,top)))))]]) ).
cnf(refute_0_96,plain,
( join(complement(top),meet(X_41,join(zero,meet(X_41,top)))) != join(zero,meet(X_41,join(zero,meet(X_41,top))))
| join(meet(X_41,join(zero,meet(X_41,top))),complement(top)) != join(complement(top),meet(X_41,join(zero,meet(X_41,top))))
| join(meet(X_41,join(zero,meet(X_41,top))),complement(top)) = join(zero,meet(X_41,join(zero,meet(X_41,top)))) ),
inference(subst,[],[refute_0_28:[bind(X,$fot(join(meet(X_41,join(zero,meet(X_41,top))),complement(top)))),bind(Y,$fot(join(complement(top),meet(X_41,join(zero,meet(X_41,top)))))),bind(Z,$fot(join(zero,meet(X_41,join(zero,meet(X_41,top))))))]]) ).
cnf(refute_0_97,plain,
( join(complement(top),meet(X_41,join(zero,meet(X_41,top)))) != join(zero,meet(X_41,join(zero,meet(X_41,top))))
| join(meet(X_41,join(zero,meet(X_41,top))),complement(top)) = join(zero,meet(X_41,join(zero,meet(X_41,top)))) ),
inference(resolve,[$cnf( $equal(join(meet(X_41,join(zero,meet(X_41,top))),complement(top)),join(complement(top),meet(X_41,join(zero,meet(X_41,top))))) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
join(meet(X_41,join(zero,meet(X_41,top))),complement(top)) = join(zero,meet(X_41,join(zero,meet(X_41,top)))),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_41,join(zero,meet(X_41,top)))),join(zero,meet(X_41,join(zero,meet(X_41,top))))) )],[refute_0_94,refute_0_97]) ).
cnf(refute_0_99,plain,
( X_41 != join(meet(X_41,join(zero,meet(X_41,top))),complement(top))
| join(meet(X_41,join(zero,meet(X_41,top))),complement(top)) != join(zero,meet(X_41,join(zero,meet(X_41,top))))
| X_41 = join(zero,meet(X_41,join(zero,meet(X_41,top)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_41,join(zero,meet(X_41,join(zero,meet(X_41,top))))) ),[0],$fot(join(meet(X_41,join(zero,meet(X_41,top))),complement(top)))]]) ).
cnf(refute_0_100,plain,
( X_41 != join(meet(X_41,join(zero,meet(X_41,top))),complement(top))
| X_41 = join(zero,meet(X_41,join(zero,meet(X_41,top)))) ),
inference(resolve,[$cnf( $equal(join(meet(X_41,join(zero,meet(X_41,top))),complement(top)),join(zero,meet(X_41,join(zero,meet(X_41,top))))) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
X_41 = join(zero,meet(X_41,join(zero,meet(X_41,top)))),
inference(resolve,[$cnf( $equal(X_41,join(meet(X_41,join(zero,meet(X_41,top))),complement(top))) )],[refute_0_90,refute_0_100]) ).
cnf(refute_0_102,plain,
X_46 = join(zero,meet(X_46,join(zero,meet(X_46,top)))),
inference(subst,[],[refute_0_101:[bind(X_41,$fot(X_46))]]) ).
cnf(refute_0_103,plain,
join(complement(X_22),complement(X_21)) = join(complement(X_21),complement(X_22)),
inference(subst,[],[refute_0_47:[bind(X0,$fot(complement(X_22))),bind(X1,$fot(complement(X_21)))]]) ).
cnf(refute_0_104,plain,
( join(complement(X_22),complement(X_21)) != join(complement(X_21),complement(X_22))
| join(complement(X_21),complement(X_22)) = join(complement(X_22),complement(X_21)) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(join(complement(X_22),complement(X_21)))),bind(Y,$fot(join(complement(X_21),complement(X_22))))]]) ).
cnf(refute_0_105,plain,
join(complement(X_21),complement(X_22)) = join(complement(X_22),complement(X_21)),
inference(resolve,[$cnf( $equal(join(complement(X_22),complement(X_21)),join(complement(X_21),complement(X_22))) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
( join(complement(X_21),complement(X_22)) != join(complement(X_22),complement(X_21))
| meet(X_21,X_22) != complement(join(complement(X_21),complement(X_22)))
| meet(X_21,X_22) = complement(join(complement(X_22),complement(X_21))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_21,X_22),complement(join(complement(X_21),complement(X_22)))) ),[1,0],$fot(join(complement(X_22),complement(X_21)))]]) ).
cnf(refute_0_107,plain,
( meet(X_21,X_22) != complement(join(complement(X_21),complement(X_22)))
| meet(X_21,X_22) = complement(join(complement(X_22),complement(X_21))) ),
inference(resolve,[$cnf( $equal(join(complement(X_21),complement(X_22)),join(complement(X_22),complement(X_21))) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
meet(X_21,X_22) = complement(join(complement(X_22),complement(X_21))),
inference(resolve,[$cnf( $equal(meet(X_21,X_22),complement(join(complement(X_21),complement(X_22)))) )],[refute_0_5,refute_0_107]) ).
cnf(refute_0_109,plain,
complement(join(complement(X_22),complement(X_21))) = meet(X_22,X_21),
inference(subst,[],[refute_0_56:[bind(X0,$fot(X_22)),bind(X1,$fot(X_21))]]) ).
cnf(refute_0_110,plain,
( complement(join(complement(X_22),complement(X_21))) != meet(X_22,X_21)
| meet(X_21,X_22) != complement(join(complement(X_22),complement(X_21)))
| meet(X_21,X_22) = meet(X_22,X_21) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_21,X_22),complement(join(complement(X_22),complement(X_21)))) ),[1],$fot(meet(X_22,X_21))]]) ).
cnf(refute_0_111,plain,
( meet(X_21,X_22) != complement(join(complement(X_22),complement(X_21)))
| meet(X_21,X_22) = meet(X_22,X_21) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_22),complement(X_21))),meet(X_22,X_21)) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
meet(X_21,X_22) = meet(X_22,X_21),
inference(resolve,[$cnf( $equal(meet(X_21,X_22),complement(join(complement(X_22),complement(X_21)))) )],[refute_0_108,refute_0_111]) ).
cnf(refute_0_113,plain,
meet(top,X_46) = meet(X_46,top),
inference(subst,[],[refute_0_112:[bind(X_21,$fot(top)),bind(X_22,$fot(X_46))]]) ).
cnf(refute_0_114,plain,
( meet(top,X_46) != meet(X_46,top)
| meet(X_46,top) = meet(top,X_46) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(meet(top,X_46))),bind(Y,$fot(meet(X_46,top)))]]) ).
cnf(refute_0_115,plain,
meet(X_46,top) = meet(top,X_46),
inference(resolve,[$cnf( $equal(meet(top,X_46),meet(X_46,top)) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
( X_46 != join(zero,meet(X_46,join(zero,meet(X_46,top))))
| meet(X_46,top) != meet(top,X_46)
| X_46 = join(zero,meet(X_46,join(zero,meet(top,X_46)))) ),
introduced(tautology,[equality,[$cnf( $equal(X_46,join(zero,meet(X_46,join(zero,meet(X_46,top))))) ),[1,1,1,1],$fot(meet(top,X_46))]]) ).
cnf(refute_0_117,plain,
( X_46 != join(zero,meet(X_46,join(zero,meet(X_46,top))))
| X_46 = join(zero,meet(X_46,join(zero,meet(top,X_46)))) ),
inference(resolve,[$cnf( $equal(meet(X_46,top),meet(top,X_46)) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
X_46 = join(zero,meet(X_46,join(zero,meet(top,X_46)))),
inference(resolve,[$cnf( $equal(X_46,join(zero,meet(X_46,join(zero,meet(X_46,top))))) )],[refute_0_102,refute_0_117]) ).
cnf(refute_0_119,plain,
complement(complement(top)) = join(zero,meet(complement(complement(top)),join(zero,meet(top,complement(complement(top)))))),
inference(subst,[],[refute_0_118:[bind(X_46,$fot(complement(complement(top))))]]) ).
cnf(refute_0_120,plain,
X_41 = join(meet(X_41,complement(complement(X_41))),complement(join(complement(X_41),complement(complement(X_41))))),
inference(subst,[],[refute_0_66:[bind(X0,$fot(X_41)),bind(X1,$fot(complement(complement(X_41))))]]) ).
cnf(refute_0_121,plain,
top = join(complement(X_41),complement(complement(X_41))),
inference(subst,[],[refute_0_14:[bind(X0,$fot(complement(X_41)))]]) ).
cnf(refute_0_122,plain,
( top != join(complement(X_41),complement(complement(X_41)))
| join(complement(X_41),complement(complement(X_41))) = top ),
inference(subst,[],[refute_0_8:[bind(X,$fot(top)),bind(Y,$fot(join(complement(X_41),complement(complement(X_41)))))]]) ).
cnf(refute_0_123,plain,
join(complement(X_41),complement(complement(X_41))) = top,
inference(resolve,[$cnf( $equal(top,join(complement(X_41),complement(complement(X_41)))) )],[refute_0_121,refute_0_122]) ).
cnf(refute_0_124,plain,
( X_41 != join(meet(X_41,complement(complement(X_41))),complement(join(complement(X_41),complement(complement(X_41)))))
| join(complement(X_41),complement(complement(X_41))) != top
| X_41 = join(meet(X_41,complement(complement(X_41))),complement(top)) ),
introduced(tautology,[equality,[$cnf( $equal(X_41,join(meet(X_41,complement(complement(X_41))),complement(join(complement(X_41),complement(complement(X_41)))))) ),[1,1,0],$fot(top)]]) ).
cnf(refute_0_125,plain,
( X_41 != join(meet(X_41,complement(complement(X_41))),complement(join(complement(X_41),complement(complement(X_41)))))
| X_41 = join(meet(X_41,complement(complement(X_41))),complement(top)) ),
inference(resolve,[$cnf( $equal(join(complement(X_41),complement(complement(X_41))),top) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
X_41 = join(meet(X_41,complement(complement(X_41))),complement(top)),
inference(resolve,[$cnf( $equal(X_41,join(meet(X_41,complement(complement(X_41))),complement(join(complement(X_41),complement(complement(X_41)))))) )],[refute_0_120,refute_0_125]) ).
cnf(refute_0_127,plain,
join(complement(top),meet(X_41,complement(complement(X_41)))) = join(complement(top),meet(X_41,complement(complement(X_41)))),
introduced(tautology,[refl,[$fot(join(complement(top),meet(X_41,complement(complement(X_41)))))]]) ).
cnf(refute_0_128,plain,
( complement(top) != zero
| join(complement(top),meet(X_41,complement(complement(X_41)))) != join(complement(top),meet(X_41,complement(complement(X_41))))
| join(complement(top),meet(X_41,complement(complement(X_41)))) = join(zero,meet(X_41,complement(complement(X_41)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(X_41,complement(complement(X_41)))),join(complement(top),meet(X_41,complement(complement(X_41))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_129,plain,
( complement(top) != zero
| join(complement(top),meet(X_41,complement(complement(X_41)))) = join(zero,meet(X_41,complement(complement(X_41)))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_41,complement(complement(X_41)))),join(complement(top),meet(X_41,complement(complement(X_41))))) )],[refute_0_127,refute_0_128]) ).
cnf(refute_0_130,plain,
join(complement(top),meet(X_41,complement(complement(X_41)))) = join(zero,meet(X_41,complement(complement(X_41)))),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_36,refute_0_129]) ).
cnf(refute_0_131,plain,
join(meet(X_41,complement(complement(X_41))),complement(top)) = join(complement(top),meet(X_41,complement(complement(X_41)))),
inference(subst,[],[refute_0_49:[bind(X0,$fot(complement(top))),bind(X1,$fot(meet(X_41,complement(complement(X_41)))))]]) ).
cnf(refute_0_132,plain,
( join(complement(top),meet(X_41,complement(complement(X_41)))) != join(zero,meet(X_41,complement(complement(X_41))))
| join(meet(X_41,complement(complement(X_41))),complement(top)) != join(complement(top),meet(X_41,complement(complement(X_41))))
| join(meet(X_41,complement(complement(X_41))),complement(top)) = join(zero,meet(X_41,complement(complement(X_41)))) ),
inference(subst,[],[refute_0_28:[bind(X,$fot(join(meet(X_41,complement(complement(X_41))),complement(top)))),bind(Y,$fot(join(complement(top),meet(X_41,complement(complement(X_41)))))),bind(Z,$fot(join(zero,meet(X_41,complement(complement(X_41))))))]]) ).
cnf(refute_0_133,plain,
( join(complement(top),meet(X_41,complement(complement(X_41)))) != join(zero,meet(X_41,complement(complement(X_41))))
| join(meet(X_41,complement(complement(X_41))),complement(top)) = join(zero,meet(X_41,complement(complement(X_41)))) ),
inference(resolve,[$cnf( $equal(join(meet(X_41,complement(complement(X_41))),complement(top)),join(complement(top),meet(X_41,complement(complement(X_41))))) )],[refute_0_131,refute_0_132]) ).
cnf(refute_0_134,plain,
join(meet(X_41,complement(complement(X_41))),complement(top)) = join(zero,meet(X_41,complement(complement(X_41)))),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_41,complement(complement(X_41)))),join(zero,meet(X_41,complement(complement(X_41))))) )],[refute_0_130,refute_0_133]) ).
cnf(refute_0_135,plain,
( X_41 != join(meet(X_41,complement(complement(X_41))),complement(top))
| join(meet(X_41,complement(complement(X_41))),complement(top)) != join(zero,meet(X_41,complement(complement(X_41))))
| X_41 = join(zero,meet(X_41,complement(complement(X_41)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_41,join(zero,meet(X_41,complement(complement(X_41))))) ),[0],$fot(join(meet(X_41,complement(complement(X_41))),complement(top)))]]) ).
cnf(refute_0_136,plain,
( X_41 != join(meet(X_41,complement(complement(X_41))),complement(top))
| X_41 = join(zero,meet(X_41,complement(complement(X_41)))) ),
inference(resolve,[$cnf( $equal(join(meet(X_41,complement(complement(X_41))),complement(top)),join(zero,meet(X_41,complement(complement(X_41))))) )],[refute_0_134,refute_0_135]) ).
cnf(refute_0_137,plain,
X_41 = join(zero,meet(X_41,complement(complement(X_41)))),
inference(resolve,[$cnf( $equal(X_41,join(meet(X_41,complement(complement(X_41))),complement(top))) )],[refute_0_126,refute_0_136]) ).
cnf(refute_0_138,plain,
top = join(zero,meet(top,complement(complement(top)))),
inference(subst,[],[refute_0_137:[bind(X_41,$fot(top))]]) ).
cnf(refute_0_139,plain,
( top != join(zero,meet(top,complement(complement(top))))
| join(zero,meet(top,complement(complement(top)))) = top ),
inference(subst,[],[refute_0_8:[bind(X,$fot(top)),bind(Y,$fot(join(zero,meet(top,complement(complement(top))))))]]) ).
cnf(refute_0_140,plain,
join(zero,meet(top,complement(complement(top)))) = top,
inference(resolve,[$cnf( $equal(top,join(zero,meet(top,complement(complement(top))))) )],[refute_0_138,refute_0_139]) ).
cnf(refute_0_141,plain,
( complement(complement(top)) != join(zero,meet(complement(complement(top)),join(zero,meet(top,complement(complement(top))))))
| join(zero,meet(top,complement(complement(top)))) != top
| complement(complement(top)) = join(zero,meet(complement(complement(top)),top)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(complement(top)),join(zero,meet(complement(complement(top)),join(zero,meet(top,complement(complement(top))))))) ),[1,1,1],$fot(top)]]) ).
cnf(refute_0_142,plain,
( complement(complement(top)) != join(zero,meet(complement(complement(top)),join(zero,meet(top,complement(complement(top))))))
| complement(complement(top)) = join(zero,meet(complement(complement(top)),top)) ),
inference(resolve,[$cnf( $equal(join(zero,meet(top,complement(complement(top)))),top) )],[refute_0_140,refute_0_141]) ).
cnf(refute_0_143,plain,
complement(complement(top)) = join(zero,meet(complement(complement(top)),top)),
inference(resolve,[$cnf( $equal(complement(complement(top)),join(zero,meet(complement(complement(top)),join(zero,meet(top,complement(complement(top))))))) )],[refute_0_119,refute_0_142]) ).
cnf(refute_0_144,plain,
complement(complement(top)) = complement(complement(top)),
introduced(tautology,[refl,[$fot(complement(complement(top)))]]) ).
cnf(refute_0_145,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_146,plain,
( complement(top) != zero
| complement(complement(top)) = complement(zero) ),
inference(resolve,[$cnf( $equal(complement(complement(top)),complement(complement(top))) )],[refute_0_144,refute_0_145]) ).
cnf(refute_0_147,plain,
complement(complement(top)) = complement(zero),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_36,refute_0_146]) ).
cnf(refute_0_148,plain,
( complement(complement(top)) != complement(zero)
| complement(complement(top)) != join(zero,meet(complement(complement(top)),top))
| complement(zero) = join(zero,meet(complement(complement(top)),top)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(complement(top)),join(zero,meet(complement(complement(top)),top))) ),[0],$fot(complement(zero))]]) ).
cnf(refute_0_149,plain,
( complement(complement(top)) != join(zero,meet(complement(complement(top)),top))
| complement(zero) = join(zero,meet(complement(complement(top)),top)) ),
inference(resolve,[$cnf( $equal(complement(complement(top)),complement(zero)) )],[refute_0_147,refute_0_148]) ).
cnf(refute_0_150,plain,
join(zero,complement(zero)) = top,
inference(subst,[],[refute_0_16:[bind(X0,$fot(zero))]]) ).
cnf(refute_0_151,plain,
meet(top,complement(X_44)) = complement(join(zero,complement(complement(X_44)))),
inference(subst,[],[refute_0_39:[bind(X1,$fot(complement(X_44)))]]) ).
cnf(refute_0_152,plain,
X_41 = join(meet(X_41,complement(X_41)),complement(join(complement(X_41),complement(X_41)))),
inference(subst,[],[refute_0_66:[bind(X0,$fot(X_41)),bind(X1,$fot(complement(X_41)))]]) ).
cnf(refute_0_153,plain,
join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_154,plain,
join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))),
inference(subst,[],[refute_0_49:[bind(X0,$fot(complement(X1))),bind(X1,$fot(composition(converse(X0),complement(composition(X0,X1)))))]]) ).
cnf(refute_0_155,plain,
( join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) != complement(X1)
| join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) != join(complement(X1),composition(converse(X0),complement(composition(X0,X1))))
| join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))) = complement(X1) ),
introduced(tautology,[equality,[$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_156,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( $equal(join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),join(complement(X1),composition(converse(X0),complement(composition(X0,X1))))) )],[refute_0_154,refute_0_155]) ).
cnf(refute_0_157,plain,
join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))) = complement(X1),
inference(resolve,[$cnf( $equal(join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),complement(X1)) )],[refute_0_153,refute_0_156]) ).
cnf(refute_0_158,plain,
join(complement(X_33),composition(converse(one),complement(composition(one,X_33)))) = complement(X_33),
inference(subst,[],[refute_0_157:[bind(X0,$fot(one)),bind(X1,$fot(X_33))]]) ).
cnf(refute_0_159,plain,
converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_160,plain,
converse(composition(converse(X0),X_7)) = composition(converse(X_7),converse(converse(X0))),
inference(subst,[],[refute_0_159:[bind(X0,$fot(converse(X0))),bind(X1,$fot(X_7))]]) ).
cnf(refute_0_161,plain,
converse(converse(X0)) = X0,
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_162,plain,
( converse(composition(converse(X0),X_7)) != composition(converse(X_7),converse(converse(X0)))
| converse(converse(X0)) != X0
| converse(composition(converse(X0),X_7)) = composition(converse(X_7),X0) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(X0),X_7)),composition(converse(X_7),converse(converse(X0)))) ),[1,1],$fot(X0)]]) ).
cnf(refute_0_163,plain,
( converse(composition(converse(X0),X_7)) != composition(converse(X_7),converse(converse(X0)))
| converse(composition(converse(X0),X_7)) = composition(converse(X_7),X0) ),
inference(resolve,[$cnf( $equal(converse(converse(X0)),X0) )],[refute_0_161,refute_0_162]) ).
cnf(refute_0_164,plain,
converse(composition(converse(X0),X_7)) = composition(converse(X_7),X0),
inference(resolve,[$cnf( $equal(converse(composition(converse(X0),X_7)),composition(converse(X_7),converse(converse(X0)))) )],[refute_0_160,refute_0_163]) ).
cnf(refute_0_165,plain,
converse(composition(converse(X_15),one)) = composition(converse(one),X_15),
inference(subst,[],[refute_0_164:[bind(X0,$fot(X_15)),bind(X_7,$fot(one))]]) ).
cnf(refute_0_166,plain,
composition(X0,one) = X0,
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_167,plain,
composition(converse(X_15),one) = converse(X_15),
inference(subst,[],[refute_0_166:[bind(X0,$fot(converse(X_15)))]]) ).
cnf(refute_0_168,plain,
( composition(converse(X_15),one) != converse(X_15)
| converse(composition(converse(X_15),one)) != composition(converse(one),X_15)
| converse(converse(X_15)) = composition(converse(one),X_15) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(X_15),one)),composition(converse(one),X_15)) ),[0,0],$fot(converse(X_15))]]) ).
cnf(refute_0_169,plain,
( converse(composition(converse(X_15),one)) != composition(converse(one),X_15)
| converse(converse(X_15)) = composition(converse(one),X_15) ),
inference(resolve,[$cnf( $equal(composition(converse(X_15),one),converse(X_15)) )],[refute_0_167,refute_0_168]) ).
cnf(refute_0_170,plain,
converse(converse(X_15)) = composition(converse(one),X_15),
inference(resolve,[$cnf( $equal(converse(composition(converse(X_15),one)),composition(converse(one),X_15)) )],[refute_0_165,refute_0_169]) ).
cnf(refute_0_171,plain,
converse(converse(X_15)) = X_15,
inference(subst,[],[refute_0_161:[bind(X0,$fot(X_15))]]) ).
cnf(refute_0_172,plain,
( converse(converse(X_15)) != X_15
| converse(converse(X_15)) != composition(converse(one),X_15)
| X_15 = composition(converse(one),X_15) ),
introduced(tautology,[equality,[$cnf( $equal(converse(converse(X_15)),composition(converse(one),X_15)) ),[0],$fot(X_15)]]) ).
cnf(refute_0_173,plain,
( converse(converse(X_15)) != composition(converse(one),X_15)
| X_15 = composition(converse(one),X_15) ),
inference(resolve,[$cnf( $equal(converse(converse(X_15)),X_15) )],[refute_0_171,refute_0_172]) ).
cnf(refute_0_174,plain,
X_15 = composition(converse(one),X_15),
inference(resolve,[$cnf( $equal(converse(converse(X_15)),composition(converse(one),X_15)) )],[refute_0_170,refute_0_173]) ).
cnf(refute_0_175,plain,
composition(converse(one),one) = converse(one),
inference(subst,[],[refute_0_166:[bind(X0,$fot(converse(one)))]]) ).
cnf(refute_0_176,plain,
one = composition(converse(one),one),
inference(subst,[],[refute_0_174:[bind(X_15,$fot(one))]]) ).
cnf(refute_0_177,plain,
( one != composition(converse(one),one)
| composition(converse(one),one) = one ),
inference(subst,[],[refute_0_8:[bind(X,$fot(one)),bind(Y,$fot(composition(converse(one),one)))]]) ).
cnf(refute_0_178,plain,
composition(converse(one),one) = one,
inference(resolve,[$cnf( $equal(one,composition(converse(one),one)) )],[refute_0_176,refute_0_177]) ).
cnf(refute_0_179,plain,
( composition(converse(one),one) != converse(one)
| composition(converse(one),one) != one
| one = converse(one) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(one),one),converse(one)) ),[0],$fot(one)]]) ).
cnf(refute_0_180,plain,
( composition(converse(one),one) != converse(one)
| one = converse(one) ),
inference(resolve,[$cnf( $equal(composition(converse(one),one),one) )],[refute_0_178,refute_0_179]) ).
cnf(refute_0_181,plain,
one = converse(one),
inference(resolve,[$cnf( $equal(composition(converse(one),one),converse(one)) )],[refute_0_175,refute_0_180]) ).
cnf(refute_0_182,plain,
( one != converse(one)
| converse(one) = one ),
inference(subst,[],[refute_0_8:[bind(X,$fot(one)),bind(Y,$fot(converse(one)))]]) ).
cnf(refute_0_183,plain,
converse(one) = one,
inference(resolve,[$cnf( $equal(one,converse(one)) )],[refute_0_181,refute_0_182]) ).
cnf(refute_0_184,plain,
composition(converse(one),X_15) = composition(converse(one),X_15),
introduced(tautology,[refl,[$fot(composition(converse(one),X_15))]]) ).
cnf(refute_0_185,plain,
( composition(converse(one),X_15) != composition(converse(one),X_15)
| converse(one) != one
| composition(converse(one),X_15) = composition(one,X_15) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(one),X_15),composition(converse(one),X_15)) ),[1,0],$fot(one)]]) ).
cnf(refute_0_186,plain,
( converse(one) != one
| composition(converse(one),X_15) = composition(one,X_15) ),
inference(resolve,[$cnf( $equal(composition(converse(one),X_15),composition(converse(one),X_15)) )],[refute_0_184,refute_0_185]) ).
cnf(refute_0_187,plain,
composition(converse(one),X_15) = composition(one,X_15),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_183,refute_0_186]) ).
cnf(refute_0_188,plain,
( X_15 != composition(converse(one),X_15)
| composition(converse(one),X_15) != composition(one,X_15)
| X_15 = composition(one,X_15) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_15,composition(one,X_15)) ),[0],$fot(composition(converse(one),X_15))]]) ).
cnf(refute_0_189,plain,
( X_15 != composition(converse(one),X_15)
| X_15 = composition(one,X_15) ),
inference(resolve,[$cnf( $equal(composition(converse(one),X_15),composition(one,X_15)) )],[refute_0_187,refute_0_188]) ).
cnf(refute_0_190,plain,
X_15 = composition(one,X_15),
inference(resolve,[$cnf( $equal(X_15,composition(converse(one),X_15)) )],[refute_0_174,refute_0_189]) ).
cnf(refute_0_191,plain,
X_33 = composition(one,X_33),
inference(subst,[],[refute_0_190:[bind(X_15,$fot(X_33))]]) ).
cnf(refute_0_192,plain,
( X_33 != composition(one,X_33)
| composition(one,X_33) = X_33 ),
inference(subst,[],[refute_0_8:[bind(X,$fot(X_33)),bind(Y,$fot(composition(one,X_33)))]]) ).
cnf(refute_0_193,plain,
composition(one,X_33) = X_33,
inference(resolve,[$cnf( $equal(X_33,composition(one,X_33)) )],[refute_0_191,refute_0_192]) ).
cnf(refute_0_194,plain,
( composition(one,X_33) != X_33
| join(complement(X_33),composition(converse(one),complement(composition(one,X_33)))) != complement(X_33)
| join(complement(X_33),composition(converse(one),complement(X_33))) = complement(X_33) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_33),composition(converse(one),complement(composition(one,X_33)))),complement(X_33)) ),[0,1,1,0],$fot(X_33)]]) ).
cnf(refute_0_195,plain,
( join(complement(X_33),composition(converse(one),complement(composition(one,X_33)))) != complement(X_33)
| join(complement(X_33),composition(converse(one),complement(X_33))) = complement(X_33) ),
inference(resolve,[$cnf( $equal(composition(one,X_33),X_33) )],[refute_0_193,refute_0_194]) ).
cnf(refute_0_196,plain,
join(complement(X_33),composition(converse(one),complement(X_33))) = complement(X_33),
inference(resolve,[$cnf( $equal(join(complement(X_33),composition(converse(one),complement(composition(one,X_33)))),complement(X_33)) )],[refute_0_158,refute_0_195]) ).
cnf(refute_0_197,plain,
( X_15 != composition(one,X_15)
| composition(one,X_15) = X_15 ),
inference(subst,[],[refute_0_8:[bind(X,$fot(X_15)),bind(Y,$fot(composition(one,X_15)))]]) ).
cnf(refute_0_198,plain,
composition(one,X_15) = X_15,
inference(resolve,[$cnf( $equal(X_15,composition(one,X_15)) )],[refute_0_190,refute_0_197]) ).
cnf(refute_0_199,plain,
composition(one,complement(X_33)) = complement(X_33),
inference(subst,[],[refute_0_198:[bind(X_15,$fot(complement(X_33)))]]) ).
cnf(refute_0_200,plain,
composition(converse(one),complement(X_33)) = composition(converse(one),complement(X_33)),
introduced(tautology,[refl,[$fot(composition(converse(one),complement(X_33)))]]) ).
cnf(refute_0_201,plain,
( composition(converse(one),complement(X_33)) != composition(converse(one),complement(X_33))
| converse(one) != one
| composition(converse(one),complement(X_33)) = composition(one,complement(X_33)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(one),complement(X_33)),composition(converse(one),complement(X_33))) ),[1,0],$fot(one)]]) ).
cnf(refute_0_202,plain,
( converse(one) != one
| composition(converse(one),complement(X_33)) = composition(one,complement(X_33)) ),
inference(resolve,[$cnf( $equal(composition(converse(one),complement(X_33)),composition(converse(one),complement(X_33))) )],[refute_0_200,refute_0_201]) ).
cnf(refute_0_203,plain,
composition(converse(one),complement(X_33)) = composition(one,complement(X_33)),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_183,refute_0_202]) ).
cnf(refute_0_204,plain,
( composition(converse(one),complement(X_33)) != composition(one,complement(X_33))
| composition(one,complement(X_33)) != complement(X_33)
| composition(converse(one),complement(X_33)) = complement(X_33) ),
inference(subst,[],[refute_0_28:[bind(X,$fot(composition(converse(one),complement(X_33)))),bind(Y,$fot(composition(one,complement(X_33)))),bind(Z,$fot(complement(X_33)))]]) ).
cnf(refute_0_205,plain,
( composition(one,complement(X_33)) != complement(X_33)
| composition(converse(one),complement(X_33)) = complement(X_33) ),
inference(resolve,[$cnf( $equal(composition(converse(one),complement(X_33)),composition(one,complement(X_33))) )],[refute_0_203,refute_0_204]) ).
cnf(refute_0_206,plain,
composition(converse(one),complement(X_33)) = complement(X_33),
inference(resolve,[$cnf( $equal(composition(one,complement(X_33)),complement(X_33)) )],[refute_0_199,refute_0_205]) ).
cnf(refute_0_207,plain,
join(complement(X_33),composition(converse(one),complement(X_33))) = join(complement(X_33),composition(converse(one),complement(X_33))),
introduced(tautology,[refl,[$fot(join(complement(X_33),composition(converse(one),complement(X_33))))]]) ).
cnf(refute_0_208,plain,
( composition(converse(one),complement(X_33)) != complement(X_33)
| join(complement(X_33),composition(converse(one),complement(X_33))) != join(complement(X_33),composition(converse(one),complement(X_33)))
| join(complement(X_33),composition(converse(one),complement(X_33))) = join(complement(X_33),complement(X_33)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_33),composition(converse(one),complement(X_33))),join(complement(X_33),composition(converse(one),complement(X_33)))) ),[1,1],$fot(complement(X_33))]]) ).
cnf(refute_0_209,plain,
( composition(converse(one),complement(X_33)) != complement(X_33)
| join(complement(X_33),composition(converse(one),complement(X_33))) = join(complement(X_33),complement(X_33)) ),
inference(resolve,[$cnf( $equal(join(complement(X_33),composition(converse(one),complement(X_33))),join(complement(X_33),composition(converse(one),complement(X_33)))) )],[refute_0_207,refute_0_208]) ).
cnf(refute_0_210,plain,
join(complement(X_33),composition(converse(one),complement(X_33))) = join(complement(X_33),complement(X_33)),
inference(resolve,[$cnf( $equal(composition(converse(one),complement(X_33)),complement(X_33)) )],[refute_0_206,refute_0_209]) ).
cnf(refute_0_211,plain,
( join(complement(X_33),composition(converse(one),complement(X_33))) != complement(X_33)
| join(complement(X_33),composition(converse(one),complement(X_33))) != join(complement(X_33),complement(X_33))
| join(complement(X_33),complement(X_33)) = complement(X_33) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_33),composition(converse(one),complement(X_33))),complement(X_33)) ),[0],$fot(join(complement(X_33),complement(X_33)))]]) ).
cnf(refute_0_212,plain,
( join(complement(X_33),composition(converse(one),complement(X_33))) != complement(X_33)
| join(complement(X_33),complement(X_33)) = complement(X_33) ),
inference(resolve,[$cnf( $equal(join(complement(X_33),composition(converse(one),complement(X_33))),join(complement(X_33),complement(X_33))) )],[refute_0_210,refute_0_211]) ).
cnf(refute_0_213,plain,
join(complement(X_33),complement(X_33)) = complement(X_33),
inference(resolve,[$cnf( $equal(join(complement(X_33),composition(converse(one),complement(X_33))),complement(X_33)) )],[refute_0_196,refute_0_212]) ).
cnf(refute_0_214,plain,
join(complement(X_41),complement(X_41)) = complement(X_41),
inference(subst,[],[refute_0_213:[bind(X_33,$fot(X_41))]]) ).
cnf(refute_0_215,plain,
( X_41 != join(meet(X_41,complement(X_41)),complement(join(complement(X_41),complement(X_41))))
| join(complement(X_41),complement(X_41)) != complement(X_41)
| X_41 = join(meet(X_41,complement(X_41)),complement(complement(X_41))) ),
introduced(tautology,[equality,[$cnf( $equal(X_41,join(meet(X_41,complement(X_41)),complement(join(complement(X_41),complement(X_41))))) ),[1,1,0],$fot(complement(X_41))]]) ).
cnf(refute_0_216,plain,
( X_41 != join(meet(X_41,complement(X_41)),complement(join(complement(X_41),complement(X_41))))
| X_41 = join(meet(X_41,complement(X_41)),complement(complement(X_41))) ),
inference(resolve,[$cnf( $equal(join(complement(X_41),complement(X_41)),complement(X_41)) )],[refute_0_214,refute_0_215]) ).
cnf(refute_0_217,plain,
X_41 = join(meet(X_41,complement(X_41)),complement(complement(X_41))),
inference(resolve,[$cnf( $equal(X_41,join(meet(X_41,complement(X_41)),complement(join(complement(X_41),complement(X_41))))) )],[refute_0_152,refute_0_216]) ).
cnf(refute_0_218,plain,
join(complement(complement(X_41)),zero) = join(zero,complement(complement(X_41))),
inference(subst,[],[refute_0_49:[bind(X0,$fot(zero)),bind(X1,$fot(complement(complement(X_41))))]]) ).
cnf(refute_0_219,plain,
( zero != meet(X0,complement(X0))
| meet(X0,complement(X0)) = zero ),
inference(subst,[],[refute_0_8:[bind(X,$fot(zero)),bind(Y,$fot(meet(X0,complement(X0))))]]) ).
cnf(refute_0_220,plain,
meet(X0,complement(X0)) = zero,
inference(resolve,[$cnf( $equal(zero,meet(X0,complement(X0))) )],[refute_0_3,refute_0_219]) ).
cnf(refute_0_221,plain,
meet(X_41,complement(X_41)) = zero,
inference(subst,[],[refute_0_220:[bind(X0,$fot(X_41))]]) ).
cnf(refute_0_222,plain,
join(complement(complement(X_41)),meet(X_41,complement(X_41))) = join(complement(complement(X_41)),meet(X_41,complement(X_41))),
introduced(tautology,[refl,[$fot(join(complement(complement(X_41)),meet(X_41,complement(X_41))))]]) ).
cnf(refute_0_223,plain,
( join(complement(complement(X_41)),meet(X_41,complement(X_41))) != join(complement(complement(X_41)),meet(X_41,complement(X_41)))
| meet(X_41,complement(X_41)) != zero
| join(complement(complement(X_41)),meet(X_41,complement(X_41))) = join(complement(complement(X_41)),zero) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(complement(X_41)),meet(X_41,complement(X_41))),join(complement(complement(X_41)),meet(X_41,complement(X_41)))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_224,plain,
( meet(X_41,complement(X_41)) != zero
| join(complement(complement(X_41)),meet(X_41,complement(X_41))) = join(complement(complement(X_41)),zero) ),
inference(resolve,[$cnf( $equal(join(complement(complement(X_41)),meet(X_41,complement(X_41))),join(complement(complement(X_41)),meet(X_41,complement(X_41)))) )],[refute_0_222,refute_0_223]) ).
cnf(refute_0_225,plain,
join(complement(complement(X_41)),meet(X_41,complement(X_41))) = join(complement(complement(X_41)),zero),
inference(resolve,[$cnf( $equal(meet(X_41,complement(X_41)),zero) )],[refute_0_221,refute_0_224]) ).
cnf(refute_0_226,plain,
( join(complement(complement(X_41)),meet(X_41,complement(X_41))) != join(complement(complement(X_41)),zero)
| join(complement(complement(X_41)),zero) != join(zero,complement(complement(X_41)))
| join(complement(complement(X_41)),meet(X_41,complement(X_41))) = join(zero,complement(complement(X_41))) ),
inference(subst,[],[refute_0_28:[bind(X,$fot(join(complement(complement(X_41)),meet(X_41,complement(X_41))))),bind(Y,$fot(join(complement(complement(X_41)),zero))),bind(Z,$fot(join(zero,complement(complement(X_41)))))]]) ).
cnf(refute_0_227,plain,
( join(complement(complement(X_41)),zero) != join(zero,complement(complement(X_41)))
| join(complement(complement(X_41)),meet(X_41,complement(X_41))) = join(zero,complement(complement(X_41))) ),
inference(resolve,[$cnf( $equal(join(complement(complement(X_41)),meet(X_41,complement(X_41))),join(complement(complement(X_41)),zero)) )],[refute_0_225,refute_0_226]) ).
cnf(refute_0_228,plain,
join(complement(complement(X_41)),meet(X_41,complement(X_41))) = join(zero,complement(complement(X_41))),
inference(resolve,[$cnf( $equal(join(complement(complement(X_41)),zero),join(zero,complement(complement(X_41)))) )],[refute_0_218,refute_0_227]) ).
cnf(refute_0_229,plain,
join(meet(X_41,complement(X_41)),complement(complement(X_41))) = join(complement(complement(X_41)),meet(X_41,complement(X_41))),
inference(subst,[],[refute_0_49:[bind(X0,$fot(complement(complement(X_41)))),bind(X1,$fot(meet(X_41,complement(X_41))))]]) ).
cnf(refute_0_230,plain,
( join(complement(complement(X_41)),meet(X_41,complement(X_41))) != join(zero,complement(complement(X_41)))
| join(meet(X_41,complement(X_41)),complement(complement(X_41))) != join(complement(complement(X_41)),meet(X_41,complement(X_41)))
| join(meet(X_41,complement(X_41)),complement(complement(X_41))) = join(zero,complement(complement(X_41))) ),
inference(subst,[],[refute_0_28:[bind(X,$fot(join(meet(X_41,complement(X_41)),complement(complement(X_41))))),bind(Y,$fot(join(complement(complement(X_41)),meet(X_41,complement(X_41))))),bind(Z,$fot(join(zero,complement(complement(X_41)))))]]) ).
cnf(refute_0_231,plain,
( join(complement(complement(X_41)),meet(X_41,complement(X_41))) != join(zero,complement(complement(X_41)))
| join(meet(X_41,complement(X_41)),complement(complement(X_41))) = join(zero,complement(complement(X_41))) ),
inference(resolve,[$cnf( $equal(join(meet(X_41,complement(X_41)),complement(complement(X_41))),join(complement(complement(X_41)),meet(X_41,complement(X_41)))) )],[refute_0_229,refute_0_230]) ).
cnf(refute_0_232,plain,
join(meet(X_41,complement(X_41)),complement(complement(X_41))) = join(zero,complement(complement(X_41))),
inference(resolve,[$cnf( $equal(join(complement(complement(X_41)),meet(X_41,complement(X_41))),join(zero,complement(complement(X_41)))) )],[refute_0_228,refute_0_231]) ).
cnf(refute_0_233,plain,
( X_41 != join(meet(X_41,complement(X_41)),complement(complement(X_41)))
| join(meet(X_41,complement(X_41)),complement(complement(X_41))) != join(zero,complement(complement(X_41)))
| X_41 = join(zero,complement(complement(X_41))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_41,join(zero,complement(complement(X_41)))) ),[0],$fot(join(meet(X_41,complement(X_41)),complement(complement(X_41))))]]) ).
cnf(refute_0_234,plain,
( X_41 != join(meet(X_41,complement(X_41)),complement(complement(X_41)))
| X_41 = join(zero,complement(complement(X_41))) ),
inference(resolve,[$cnf( $equal(join(meet(X_41,complement(X_41)),complement(complement(X_41))),join(zero,complement(complement(X_41)))) )],[refute_0_232,refute_0_233]) ).
cnf(refute_0_235,plain,
X_41 = join(zero,complement(complement(X_41))),
inference(resolve,[$cnf( $equal(X_41,join(meet(X_41,complement(X_41)),complement(complement(X_41)))) )],[refute_0_217,refute_0_234]) ).
cnf(refute_0_236,plain,
X_44 = join(zero,complement(complement(X_44))),
inference(subst,[],[refute_0_235:[bind(X_41,$fot(X_44))]]) ).
cnf(refute_0_237,plain,
( X_44 != join(zero,complement(complement(X_44)))
| join(zero,complement(complement(X_44))) = X_44 ),
inference(subst,[],[refute_0_8:[bind(X,$fot(X_44)),bind(Y,$fot(join(zero,complement(complement(X_44)))))]]) ).
cnf(refute_0_238,plain,
join(zero,complement(complement(X_44))) = X_44,
inference(resolve,[$cnf( $equal(X_44,join(zero,complement(complement(X_44)))) )],[refute_0_236,refute_0_237]) ).
cnf(refute_0_239,plain,
( join(zero,complement(complement(X_44))) != X_44
| meet(top,complement(X_44)) != complement(join(zero,complement(complement(X_44))))
| meet(top,complement(X_44)) = complement(X_44) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,complement(X_44)),complement(join(zero,complement(complement(X_44))))) ),[1,0],$fot(X_44)]]) ).
cnf(refute_0_240,plain,
( meet(top,complement(X_44)) != complement(join(zero,complement(complement(X_44))))
| meet(top,complement(X_44)) = complement(X_44) ),
inference(resolve,[$cnf( $equal(join(zero,complement(complement(X_44))),X_44) )],[refute_0_238,refute_0_239]) ).
cnf(refute_0_241,plain,
meet(top,complement(X_44)) = complement(X_44),
inference(resolve,[$cnf( $equal(meet(top,complement(X_44)),complement(join(zero,complement(complement(X_44))))) )],[refute_0_151,refute_0_240]) ).
cnf(refute_0_242,plain,
meet(top,complement(complement(top))) = complement(complement(top)),
inference(subst,[],[refute_0_241:[bind(X_44,$fot(complement(top)))]]) ).
cnf(refute_0_243,plain,
meet(X0,top) = complement(join(complement(X0),complement(top))),
inference(subst,[],[refute_0_0:[bind(X1,$fot(top))]]) ).
cnf(refute_0_244,plain,
( complement(top) != zero
| meet(X0,top) != complement(join(complement(X0),complement(top)))
| meet(X0,top) = complement(join(complement(X0),zero)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X0,top),complement(join(complement(X0),complement(top)))) ),[1,0,1],$fot(zero)]]) ).
cnf(refute_0_245,plain,
( meet(X0,top) != complement(join(complement(X0),complement(top)))
| meet(X0,top) = complement(join(complement(X0),zero)) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_36,refute_0_244]) ).
cnf(refute_0_246,plain,
meet(X0,top) = complement(join(complement(X0),zero)),
inference(resolve,[$cnf( $equal(meet(X0,top),complement(join(complement(X0),complement(top)))) )],[refute_0_243,refute_0_245]) ).
cnf(refute_0_247,plain,
( meet(top,X1) != complement(join(zero,complement(X1)))
| complement(join(zero,complement(X1))) = meet(top,X1) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(meet(top,X1))),bind(Y,$fot(complement(join(zero,complement(X1)))))]]) ).
cnf(refute_0_248,plain,
complement(join(zero,complement(X1))) = meet(top,X1),
inference(resolve,[$cnf( $equal(meet(top,X1),complement(join(zero,complement(X1)))) )],[refute_0_39,refute_0_247]) ).
cnf(refute_0_249,plain,
complement(join(zero,complement(X0))) = meet(top,X0),
inference(subst,[],[refute_0_248:[bind(X1,$fot(X0))]]) ).
cnf(refute_0_250,plain,
join(complement(X0),zero) = join(zero,complement(X0)),
inference(subst,[],[refute_0_49:[bind(X0,$fot(zero)),bind(X1,$fot(complement(X0)))]]) ).
cnf(refute_0_251,plain,
complement(join(complement(X0),zero)) = complement(join(complement(X0),zero)),
introduced(tautology,[refl,[$fot(complement(join(complement(X0),zero)))]]) ).
cnf(refute_0_252,plain,
( complement(join(complement(X0),zero)) != complement(join(complement(X0),zero))
| join(complement(X0),zero) != join(zero,complement(X0))
| complement(join(complement(X0),zero)) = complement(join(zero,complement(X0))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(X0),zero)),complement(join(complement(X0),zero))) ),[1,0],$fot(join(zero,complement(X0)))]]) ).
cnf(refute_0_253,plain,
( join(complement(X0),zero) != join(zero,complement(X0))
| complement(join(complement(X0),zero)) = complement(join(zero,complement(X0))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X0),zero)),complement(join(complement(X0),zero))) )],[refute_0_251,refute_0_252]) ).
cnf(refute_0_254,plain,
complement(join(complement(X0),zero)) = complement(join(zero,complement(X0))),
inference(resolve,[$cnf( $equal(join(complement(X0),zero),join(zero,complement(X0))) )],[refute_0_250,refute_0_253]) ).
cnf(refute_0_255,plain,
( complement(join(complement(X0),zero)) != complement(join(zero,complement(X0)))
| complement(join(zero,complement(X0))) != meet(top,X0)
| complement(join(complement(X0),zero)) = meet(top,X0) ),
inference(subst,[],[refute_0_28:[bind(X,$fot(complement(join(complement(X0),zero)))),bind(Y,$fot(complement(join(zero,complement(X0))))),bind(Z,$fot(meet(top,X0)))]]) ).
cnf(refute_0_256,plain,
( complement(join(zero,complement(X0))) != meet(top,X0)
| complement(join(complement(X0),zero)) = meet(top,X0) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X0),zero)),complement(join(zero,complement(X0)))) )],[refute_0_254,refute_0_255]) ).
cnf(refute_0_257,plain,
complement(join(complement(X0),zero)) = meet(top,X0),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(X0))),meet(top,X0)) )],[refute_0_249,refute_0_256]) ).
cnf(refute_0_258,plain,
( complement(join(complement(X0),zero)) != meet(top,X0)
| meet(X0,top) != complement(join(complement(X0),zero))
| meet(X0,top) = meet(top,X0) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X0,top),complement(join(complement(X0),zero))) ),[1],$fot(meet(top,X0))]]) ).
cnf(refute_0_259,plain,
( meet(X0,top) != complement(join(complement(X0),zero))
| meet(X0,top) = meet(top,X0) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X0),zero)),meet(top,X0)) )],[refute_0_257,refute_0_258]) ).
cnf(refute_0_260,plain,
meet(X0,top) = meet(top,X0),
inference(resolve,[$cnf( $equal(meet(X0,top),complement(join(complement(X0),zero))) )],[refute_0_246,refute_0_259]) ).
cnf(refute_0_261,plain,
meet(complement(complement(top)),top) = meet(top,complement(complement(top))),
inference(subst,[],[refute_0_260:[bind(X0,$fot(complement(complement(top))))]]) ).
cnf(refute_0_262,plain,
( meet(complement(complement(top)),top) != meet(top,complement(complement(top)))
| meet(top,complement(complement(top))) != complement(complement(top))
| meet(complement(complement(top)),top) = complement(complement(top)) ),
inference(subst,[],[refute_0_28:[bind(X,$fot(meet(complement(complement(top)),top))),bind(Y,$fot(meet(top,complement(complement(top))))),bind(Z,$fot(complement(complement(top))))]]) ).
cnf(refute_0_263,plain,
( meet(top,complement(complement(top))) != complement(complement(top))
| meet(complement(complement(top)),top) = complement(complement(top)) ),
inference(resolve,[$cnf( $equal(meet(complement(complement(top)),top),meet(top,complement(complement(top)))) )],[refute_0_261,refute_0_262]) ).
cnf(refute_0_264,plain,
meet(complement(complement(top)),top) = complement(complement(top)),
inference(resolve,[$cnf( $equal(meet(top,complement(complement(top))),complement(complement(top))) )],[refute_0_242,refute_0_263]) ).
cnf(refute_0_265,plain,
( complement(complement(top)) != complement(zero)
| meet(complement(complement(top)),top) != complement(complement(top))
| meet(complement(complement(top)),top) = complement(zero) ),
inference(subst,[],[refute_0_28:[bind(X,$fot(meet(complement(complement(top)),top))),bind(Y,$fot(complement(complement(top)))),bind(Z,$fot(complement(zero)))]]) ).
cnf(refute_0_266,plain,
( complement(complement(top)) != complement(zero)
| meet(complement(complement(top)),top) = complement(zero) ),
inference(resolve,[$cnf( $equal(meet(complement(complement(top)),top),complement(complement(top))) )],[refute_0_264,refute_0_265]) ).
cnf(refute_0_267,plain,
meet(complement(complement(top)),top) = complement(zero),
inference(resolve,[$cnf( $equal(complement(complement(top)),complement(zero)) )],[refute_0_147,refute_0_266]) ).
cnf(refute_0_268,plain,
join(zero,meet(complement(complement(top)),top)) = join(zero,meet(complement(complement(top)),top)),
introduced(tautology,[refl,[$fot(join(zero,meet(complement(complement(top)),top)))]]) ).
cnf(refute_0_269,plain,
( join(zero,meet(complement(complement(top)),top)) != join(zero,meet(complement(complement(top)),top))
| meet(complement(complement(top)),top) != complement(zero)
| join(zero,meet(complement(complement(top)),top)) = join(zero,complement(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,meet(complement(complement(top)),top)),join(zero,meet(complement(complement(top)),top))) ),[1,1],$fot(complement(zero))]]) ).
cnf(refute_0_270,plain,
( meet(complement(complement(top)),top) != complement(zero)
| join(zero,meet(complement(complement(top)),top)) = join(zero,complement(zero)) ),
inference(resolve,[$cnf( $equal(join(zero,meet(complement(complement(top)),top)),join(zero,meet(complement(complement(top)),top))) )],[refute_0_268,refute_0_269]) ).
cnf(refute_0_271,plain,
join(zero,meet(complement(complement(top)),top)) = join(zero,complement(zero)),
inference(resolve,[$cnf( $equal(meet(complement(complement(top)),top),complement(zero)) )],[refute_0_267,refute_0_270]) ).
cnf(refute_0_272,plain,
( join(zero,complement(zero)) != top
| join(zero,meet(complement(complement(top)),top)) != join(zero,complement(zero))
| join(zero,meet(complement(complement(top)),top)) = top ),
inference(subst,[],[refute_0_28:[bind(X,$fot(join(zero,meet(complement(complement(top)),top)))),bind(Y,$fot(join(zero,complement(zero)))),bind(Z,$fot(top))]]) ).
cnf(refute_0_273,plain,
( join(zero,complement(zero)) != top
| join(zero,meet(complement(complement(top)),top)) = top ),
inference(resolve,[$cnf( $equal(join(zero,meet(complement(complement(top)),top)),join(zero,complement(zero))) )],[refute_0_271,refute_0_272]) ).
cnf(refute_0_274,plain,
join(zero,meet(complement(complement(top)),top)) = top,
inference(resolve,[$cnf( $equal(join(zero,complement(zero)),top) )],[refute_0_150,refute_0_273]) ).
cnf(refute_0_275,plain,
( complement(zero) != join(zero,meet(complement(complement(top)),top))
| join(zero,meet(complement(complement(top)),top)) != top
| complement(zero) = top ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(zero),top) ),[0],$fot(join(zero,meet(complement(complement(top)),top)))]]) ).
cnf(refute_0_276,plain,
( complement(zero) != join(zero,meet(complement(complement(top)),top))
| complement(zero) = top ),
inference(resolve,[$cnf( $equal(join(zero,meet(complement(complement(top)),top)),top) )],[refute_0_274,refute_0_275]) ).
cnf(refute_0_277,plain,
( complement(complement(top)) != join(zero,meet(complement(complement(top)),top))
| complement(zero) = top ),
inference(resolve,[$cnf( $equal(complement(zero),join(zero,meet(complement(complement(top)),top))) )],[refute_0_149,refute_0_276]) ).
cnf(refute_0_278,plain,
complement(zero) = top,
inference(resolve,[$cnf( $equal(complement(complement(top)),join(zero,meet(complement(complement(top)),top))) )],[refute_0_143,refute_0_277]) ).
cnf(refute_0_279,plain,
( complement(zero) != top
| meet(X0,zero) != complement(join(complement(X0),complement(zero)))
| meet(X0,zero) = complement(join(complement(X0),top)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X0,zero),complement(join(complement(X0),complement(zero)))) ),[1,0,1],$fot(top)]]) ).
cnf(refute_0_280,plain,
( meet(X0,zero) != complement(join(complement(X0),complement(zero)))
| meet(X0,zero) = complement(join(complement(X0),top)) ),
inference(resolve,[$cnf( $equal(complement(zero),top) )],[refute_0_278,refute_0_279]) ).
cnf(refute_0_281,plain,
meet(X0,zero) = complement(join(complement(X0),top)),
inference(resolve,[$cnf( $equal(meet(X0,zero),complement(join(complement(X0),complement(zero)))) )],[refute_0_68,refute_0_280]) ).
cnf(refute_0_282,plain,
top = join(complement(X_22),join(complement(X_22),meet(X_22,X_22))),
inference(subst,[],[refute_0_80:[bind(X_21,$fot(X_22))]]) ).
cnf(refute_0_283,plain,
meet(X1,X1) = complement(join(complement(X1),complement(X1))),
inference(subst,[],[refute_0_0:[bind(X0,$fot(X1))]]) ).
cnf(refute_0_284,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(subst,[],[refute_0_213:[bind(X_33,$fot(X1))]]) ).
cnf(refute_0_285,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_286,plain,
( meet(X1,X1) != complement(join(complement(X1),complement(X1)))
| meet(X1,X1) = complement(complement(X1)) ),
inference(resolve,[$cnf( $equal(join(complement(X1),complement(X1)),complement(X1)) )],[refute_0_284,refute_0_285]) ).
cnf(refute_0_287,plain,
meet(X1,X1) = complement(complement(X1)),
inference(resolve,[$cnf( $equal(meet(X1,X1),complement(join(complement(X1),complement(X1)))) )],[refute_0_283,refute_0_286]) ).
cnf(refute_0_288,plain,
meet(X_22,X_22) = complement(complement(X_22)),
inference(subst,[],[refute_0_287:[bind(X1,$fot(X_22))]]) ).
cnf(refute_0_289,plain,
( meet(X_22,X_22) != complement(complement(X_22))
| top != join(complement(X_22),join(complement(X_22),meet(X_22,X_22)))
| top = join(complement(X_22),join(complement(X_22),complement(complement(X_22)))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(X_22),join(complement(X_22),meet(X_22,X_22)))) ),[1,1,1],$fot(complement(complement(X_22)))]]) ).
cnf(refute_0_290,plain,
( top != join(complement(X_22),join(complement(X_22),meet(X_22,X_22)))
| top = join(complement(X_22),join(complement(X_22),complement(complement(X_22)))) ),
inference(resolve,[$cnf( $equal(meet(X_22,X_22),complement(complement(X_22))) )],[refute_0_288,refute_0_289]) ).
cnf(refute_0_291,plain,
top = join(complement(X_22),join(complement(X_22),complement(complement(X_22)))),
inference(resolve,[$cnf( $equal(top,join(complement(X_22),join(complement(X_22),meet(X_22,X_22)))) )],[refute_0_282,refute_0_290]) ).
cnf(refute_0_292,plain,
join(complement(X_22),top) = join(top,complement(X_22)),
inference(subst,[],[refute_0_49:[bind(X0,$fot(top)),bind(X1,$fot(complement(X_22)))]]) ).
cnf(refute_0_293,plain,
join(complement(X_22),complement(complement(X_22))) = top,
inference(subst,[],[refute_0_16:[bind(X0,$fot(complement(X_22)))]]) ).
cnf(refute_0_294,plain,
join(complement(X_22),join(complement(X_22),complement(complement(X_22)))) = join(complement(X_22),join(complement(X_22),complement(complement(X_22)))),
introduced(tautology,[refl,[$fot(join(complement(X_22),join(complement(X_22),complement(complement(X_22)))))]]) ).
cnf(refute_0_295,plain,
( join(complement(X_22),complement(complement(X_22))) != top
| join(complement(X_22),join(complement(X_22),complement(complement(X_22)))) != join(complement(X_22),join(complement(X_22),complement(complement(X_22))))
| join(complement(X_22),join(complement(X_22),complement(complement(X_22)))) = join(complement(X_22),top) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_22),join(complement(X_22),complement(complement(X_22)))),join(complement(X_22),join(complement(X_22),complement(complement(X_22))))) ),[1,1],$fot(top)]]) ).
cnf(refute_0_296,plain,
( join(complement(X_22),complement(complement(X_22))) != top
| join(complement(X_22),join(complement(X_22),complement(complement(X_22)))) = join(complement(X_22),top) ),
inference(resolve,[$cnf( $equal(join(complement(X_22),join(complement(X_22),complement(complement(X_22)))),join(complement(X_22),join(complement(X_22),complement(complement(X_22))))) )],[refute_0_294,refute_0_295]) ).
cnf(refute_0_297,plain,
join(complement(X_22),join(complement(X_22),complement(complement(X_22)))) = join(complement(X_22),top),
inference(resolve,[$cnf( $equal(join(complement(X_22),complement(complement(X_22))),top) )],[refute_0_293,refute_0_296]) ).
cnf(refute_0_298,plain,
( join(complement(X_22),join(complement(X_22),complement(complement(X_22)))) != join(complement(X_22),top)
| join(complement(X_22),top) != join(top,complement(X_22))
| join(complement(X_22),join(complement(X_22),complement(complement(X_22)))) = join(top,complement(X_22)) ),
inference(subst,[],[refute_0_28:[bind(X,$fot(join(complement(X_22),join(complement(X_22),complement(complement(X_22)))))),bind(Y,$fot(join(complement(X_22),top))),bind(Z,$fot(join(top,complement(X_22))))]]) ).
cnf(refute_0_299,plain,
( join(complement(X_22),top) != join(top,complement(X_22))
| join(complement(X_22),join(complement(X_22),complement(complement(X_22)))) = join(top,complement(X_22)) ),
inference(resolve,[$cnf( $equal(join(complement(X_22),join(complement(X_22),complement(complement(X_22)))),join(complement(X_22),top)) )],[refute_0_297,refute_0_298]) ).
cnf(refute_0_300,plain,
join(complement(X_22),join(complement(X_22),complement(complement(X_22)))) = join(top,complement(X_22)),
inference(resolve,[$cnf( $equal(join(complement(X_22),top),join(top,complement(X_22))) )],[refute_0_292,refute_0_299]) ).
cnf(refute_0_301,plain,
( join(complement(X_22),join(complement(X_22),complement(complement(X_22)))) != join(top,complement(X_22))
| top != join(complement(X_22),join(complement(X_22),complement(complement(X_22))))
| top = join(top,complement(X_22)) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(X_22),join(complement(X_22),complement(complement(X_22))))) ),[1],$fot(join(top,complement(X_22)))]]) ).
cnf(refute_0_302,plain,
( top != join(complement(X_22),join(complement(X_22),complement(complement(X_22))))
| top = join(top,complement(X_22)) ),
inference(resolve,[$cnf( $equal(join(complement(X_22),join(complement(X_22),complement(complement(X_22)))),join(top,complement(X_22))) )],[refute_0_300,refute_0_301]) ).
cnf(refute_0_303,plain,
top = join(top,complement(X_22)),
inference(resolve,[$cnf( $equal(top,join(complement(X_22),join(complement(X_22),complement(complement(X_22))))) )],[refute_0_291,refute_0_302]) ).
cnf(refute_0_304,plain,
( top != join(top,complement(X_22))
| join(top,complement(X_22)) = top ),
inference(subst,[],[refute_0_8:[bind(X,$fot(top)),bind(Y,$fot(join(top,complement(X_22))))]]) ).
cnf(refute_0_305,plain,
join(top,complement(X_22)) = top,
inference(resolve,[$cnf( $equal(top,join(top,complement(X_22))) )],[refute_0_303,refute_0_304]) ).
cnf(refute_0_306,plain,
join(top,complement(X0)) = top,
inference(subst,[],[refute_0_305:[bind(X_22,$fot(X0))]]) ).
cnf(refute_0_307,plain,
join(complement(X0),top) = join(top,complement(X0)),
inference(subst,[],[refute_0_49:[bind(X0,$fot(top)),bind(X1,$fot(complement(X0)))]]) ).
cnf(refute_0_308,plain,
( join(complement(X0),top) != join(top,complement(X0))
| join(top,complement(X0)) != top
| join(complement(X0),top) = top ),
inference(subst,[],[refute_0_28:[bind(X,$fot(join(complement(X0),top))),bind(Y,$fot(join(top,complement(X0)))),bind(Z,$fot(top))]]) ).
cnf(refute_0_309,plain,
( join(top,complement(X0)) != top
| join(complement(X0),top) = top ),
inference(resolve,[$cnf( $equal(join(complement(X0),top),join(top,complement(X0))) )],[refute_0_307,refute_0_308]) ).
cnf(refute_0_310,plain,
join(complement(X0),top) = top,
inference(resolve,[$cnf( $equal(join(top,complement(X0)),top) )],[refute_0_306,refute_0_309]) ).
cnf(refute_0_311,plain,
complement(join(complement(X0),top)) = complement(join(complement(X0),top)),
introduced(tautology,[refl,[$fot(complement(join(complement(X0),top)))]]) ).
cnf(refute_0_312,plain,
( complement(join(complement(X0),top)) != complement(join(complement(X0),top))
| join(complement(X0),top) != top
| complement(join(complement(X0),top)) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(X0),top)),complement(join(complement(X0),top))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_313,plain,
( join(complement(X0),top) != top
| complement(join(complement(X0),top)) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X0),top)),complement(join(complement(X0),top))) )],[refute_0_311,refute_0_312]) ).
cnf(refute_0_314,plain,
complement(join(complement(X0),top)) = complement(top),
inference(resolve,[$cnf( $equal(join(complement(X0),top),top) )],[refute_0_310,refute_0_313]) ).
cnf(refute_0_315,plain,
( complement(join(complement(X0),top)) != complement(top)
| complement(top) != zero
| complement(join(complement(X0),top)) = zero ),
inference(subst,[],[refute_0_28:[bind(X,$fot(complement(join(complement(X0),top)))),bind(Y,$fot(complement(top))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_316,plain,
( complement(top) != zero
| complement(join(complement(X0),top)) = zero ),
inference(resolve,[$cnf( $equal(complement(join(complement(X0),top)),complement(top)) )],[refute_0_314,refute_0_315]) ).
cnf(refute_0_317,plain,
complement(join(complement(X0),top)) = zero,
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_36,refute_0_316]) ).
cnf(refute_0_318,plain,
( complement(join(complement(X0),top)) != zero
| meet(X0,zero) != complement(join(complement(X0),top))
| meet(X0,zero) = zero ),
introduced(tautology,[equality,[$cnf( $equal(meet(X0,zero),complement(join(complement(X0),top))) ),[1],$fot(zero)]]) ).
cnf(refute_0_319,plain,
( meet(X0,zero) != complement(join(complement(X0),top))
| meet(X0,zero) = zero ),
inference(resolve,[$cnf( $equal(complement(join(complement(X0),top)),zero) )],[refute_0_317,refute_0_318]) ).
cnf(refute_0_320,plain,
meet(X0,zero) = zero,
inference(resolve,[$cnf( $equal(meet(X0,zero),complement(join(complement(X0),top))) )],[refute_0_281,refute_0_319]) ).
cnf(refute_0_321,plain,
( X0 != join(meet(X0,zero),complement(join(complement(X0),zero)))
| meet(X0,zero) != zero
| X0 = join(zero,complement(join(complement(X0),zero))) ),
introduced(tautology,[equality,[$cnf( $equal(X0,join(meet(X0,zero),complement(join(complement(X0),zero)))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_322,plain,
( X0 != join(meet(X0,zero),complement(join(complement(X0),zero)))
| X0 = join(zero,complement(join(complement(X0),zero))) ),
inference(resolve,[$cnf( $equal(meet(X0,zero),zero) )],[refute_0_320,refute_0_321]) ).
cnf(refute_0_323,plain,
X0 = join(zero,complement(join(complement(X0),zero))),
inference(resolve,[$cnf( $equal(X0,join(meet(X0,zero),complement(join(complement(X0),zero)))) )],[refute_0_67,refute_0_322]) ).
cnf(refute_0_324,plain,
join(zero,complement(join(complement(X0),zero))) = join(zero,complement(join(complement(X0),zero))),
introduced(tautology,[refl,[$fot(join(zero,complement(join(complement(X0),zero))))]]) ).
cnf(refute_0_325,plain,
( complement(join(complement(X0),zero)) != meet(top,X0)
| join(zero,complement(join(complement(X0),zero))) != join(zero,complement(join(complement(X0),zero)))
| join(zero,complement(join(complement(X0),zero))) = join(zero,meet(top,X0)) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(join(complement(X0),zero))),join(zero,complement(join(complement(X0),zero)))) ),[1,1],$fot(meet(top,X0))]]) ).
cnf(refute_0_326,plain,
( complement(join(complement(X0),zero)) != meet(top,X0)
| join(zero,complement(join(complement(X0),zero))) = join(zero,meet(top,X0)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(complement(X0),zero))),join(zero,complement(join(complement(X0),zero)))) )],[refute_0_324,refute_0_325]) ).
cnf(refute_0_327,plain,
join(zero,complement(join(complement(X0),zero))) = join(zero,meet(top,X0)),
inference(resolve,[$cnf( $equal(complement(join(complement(X0),zero)),meet(top,X0)) )],[refute_0_257,refute_0_326]) ).
cnf(refute_0_328,plain,
( X0 != join(zero,complement(join(complement(X0),zero)))
| join(zero,complement(join(complement(X0),zero))) != join(zero,meet(top,X0))
| X0 = join(zero,meet(top,X0)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X0,join(zero,meet(top,X0))) ),[0],$fot(join(zero,complement(join(complement(X0),zero))))]]) ).
cnf(refute_0_329,plain,
( X0 != join(zero,complement(join(complement(X0),zero)))
| X0 = join(zero,meet(top,X0)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(complement(X0),zero))),join(zero,meet(top,X0))) )],[refute_0_327,refute_0_328]) ).
cnf(refute_0_330,plain,
X0 = join(zero,meet(top,X0)),
inference(resolve,[$cnf( $equal(X0,join(zero,complement(join(complement(X0),zero)))) )],[refute_0_323,refute_0_329]) ).
cnf(refute_0_331,plain,
complement(X_44) = join(zero,meet(top,complement(X_44))),
inference(subst,[],[refute_0_330:[bind(X0,$fot(complement(X_44)))]]) ).
cnf(refute_0_332,plain,
( complement(X_44) != join(zero,meet(top,complement(X_44)))
| meet(top,complement(X_44)) != complement(X_44)
| complement(X_44) = join(zero,complement(X_44)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(X_44),join(zero,meet(top,complement(X_44)))) ),[1,1],$fot(complement(X_44))]]) ).
cnf(refute_0_333,plain,
( complement(X_44) != join(zero,meet(top,complement(X_44)))
| complement(X_44) = join(zero,complement(X_44)) ),
inference(resolve,[$cnf( $equal(meet(top,complement(X_44)),complement(X_44)) )],[refute_0_241,refute_0_332]) ).
cnf(refute_0_334,plain,
complement(X_44) = join(zero,complement(X_44)),
inference(resolve,[$cnf( $equal(complement(X_44),join(zero,meet(top,complement(X_44)))) )],[refute_0_331,refute_0_333]) ).
cnf(refute_0_335,plain,
( complement(X_44) != join(zero,complement(X_44))
| join(zero,complement(X_44)) = complement(X_44) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(complement(X_44))),bind(Y,$fot(join(zero,complement(X_44))))]]) ).
cnf(refute_0_336,plain,
join(zero,complement(X_44)) = complement(X_44),
inference(resolve,[$cnf( $equal(complement(X_44),join(zero,complement(X_44))) )],[refute_0_334,refute_0_335]) ).
cnf(refute_0_337,plain,
join(zero,complement(X_25)) = complement(X_25),
inference(subst,[],[refute_0_336:[bind(X_44,$fot(X_25))]]) ).
cnf(refute_0_338,plain,
meet(X0,join(zero,complement(X_25))) = meet(X0,join(zero,complement(X_25))),
introduced(tautology,[refl,[$fot(meet(X0,join(zero,complement(X_25))))]]) ).
cnf(refute_0_339,plain,
( join(zero,complement(X_25)) != complement(X_25)
| meet(X0,join(zero,complement(X_25))) != meet(X0,join(zero,complement(X_25)))
| meet(X0,join(zero,complement(X_25))) = meet(X0,complement(X_25)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X0,join(zero,complement(X_25))),meet(X0,join(zero,complement(X_25)))) ),[1,1],$fot(complement(X_25))]]) ).
cnf(refute_0_340,plain,
( join(zero,complement(X_25)) != complement(X_25)
| meet(X0,join(zero,complement(X_25))) = meet(X0,complement(X_25)) ),
inference(resolve,[$cnf( $equal(meet(X0,join(zero,complement(X_25))),meet(X0,join(zero,complement(X_25)))) )],[refute_0_338,refute_0_339]) ).
cnf(refute_0_341,plain,
meet(X0,join(zero,complement(X_25))) = meet(X0,complement(X_25)),
inference(resolve,[$cnf( $equal(join(zero,complement(X_25)),complement(X_25)) )],[refute_0_337,refute_0_340]) ).
cnf(refute_0_342,plain,
( meet(X0,join(zero,complement(X_25))) != complement(join(complement(X0),meet(top,X_25)))
| meet(X0,join(zero,complement(X_25))) != meet(X0,complement(X_25))
| meet(X0,complement(X_25)) = complement(join(complement(X0),meet(top,X_25))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X0,join(zero,complement(X_25))),complement(join(complement(X0),meet(top,X_25)))) ),[0],$fot(meet(X0,complement(X_25)))]]) ).
cnf(refute_0_343,plain,
( meet(X0,join(zero,complement(X_25))) != complement(join(complement(X0),meet(top,X_25)))
| meet(X0,complement(X_25)) = complement(join(complement(X0),meet(top,X_25))) ),
inference(resolve,[$cnf( $equal(meet(X0,join(zero,complement(X_25))),meet(X0,complement(X_25))) )],[refute_0_341,refute_0_342]) ).
cnf(refute_0_344,plain,
join(zero,complement(complement(X_41))) = complement(complement(X_41)),
inference(subst,[],[refute_0_336:[bind(X_44,$fot(complement(X_41)))]]) ).
cnf(refute_0_345,plain,
meet(X_41,X_41) = complement(complement(X_41)),
inference(subst,[],[refute_0_287:[bind(X1,$fot(X_41))]]) ).
cnf(refute_0_346,plain,
X_53 = join(zero,meet(top,X_53)),
inference(subst,[],[refute_0_330:[bind(X0,$fot(X_53))]]) ).
cnf(refute_0_347,plain,
meet(X_53,top) = meet(top,X_53),
inference(subst,[],[refute_0_112:[bind(X_21,$fot(X_53)),bind(X_22,$fot(top))]]) ).
cnf(refute_0_348,plain,
( meet(X_53,top) != meet(top,X_53)
| meet(top,X_53) = meet(X_53,top) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(meet(X_53,top))),bind(Y,$fot(meet(top,X_53)))]]) ).
cnf(refute_0_349,plain,
meet(top,X_53) = meet(X_53,top),
inference(resolve,[$cnf( $equal(meet(X_53,top),meet(top,X_53)) )],[refute_0_347,refute_0_348]) ).
cnf(refute_0_350,plain,
( X_53 != join(zero,meet(top,X_53))
| meet(top,X_53) != meet(X_53,top)
| X_53 = join(zero,meet(X_53,top)) ),
introduced(tautology,[equality,[$cnf( $equal(X_53,join(zero,meet(top,X_53))) ),[1,1],$fot(meet(X_53,top))]]) ).
cnf(refute_0_351,plain,
( X_53 != join(zero,meet(top,X_53))
| X_53 = join(zero,meet(X_53,top)) ),
inference(resolve,[$cnf( $equal(meet(top,X_53),meet(X_53,top)) )],[refute_0_349,refute_0_350]) ).
cnf(refute_0_352,plain,
X_53 = join(zero,meet(X_53,top)),
inference(resolve,[$cnf( $equal(X_53,join(zero,meet(top,X_53))) )],[refute_0_346,refute_0_351]) ).
cnf(refute_0_353,plain,
( X_53 != join(zero,meet(X_53,top))
| join(zero,meet(X_53,top)) = X_53 ),
inference(subst,[],[refute_0_8:[bind(X,$fot(X_53)),bind(Y,$fot(join(zero,meet(X_53,top))))]]) ).
cnf(refute_0_354,plain,
join(zero,meet(X_53,top)) = X_53,
inference(resolve,[$cnf( $equal(X_53,join(zero,meet(X_53,top))) )],[refute_0_352,refute_0_353]) ).
cnf(refute_0_355,plain,
join(zero,meet(X_41,top)) = X_41,
inference(subst,[],[refute_0_354:[bind(X_53,$fot(X_41))]]) ).
cnf(refute_0_356,plain,
meet(X_41,join(zero,meet(X_41,top))) = meet(X_41,join(zero,meet(X_41,top))),
introduced(tautology,[refl,[$fot(meet(X_41,join(zero,meet(X_41,top))))]]) ).
cnf(refute_0_357,plain,
( join(zero,meet(X_41,top)) != X_41
| meet(X_41,join(zero,meet(X_41,top))) != meet(X_41,join(zero,meet(X_41,top)))
| meet(X_41,join(zero,meet(X_41,top))) = meet(X_41,X_41) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_41,join(zero,meet(X_41,top))),meet(X_41,join(zero,meet(X_41,top)))) ),[1,1],$fot(X_41)]]) ).
cnf(refute_0_358,plain,
( join(zero,meet(X_41,top)) != X_41
| meet(X_41,join(zero,meet(X_41,top))) = meet(X_41,X_41) ),
inference(resolve,[$cnf( $equal(meet(X_41,join(zero,meet(X_41,top))),meet(X_41,join(zero,meet(X_41,top)))) )],[refute_0_356,refute_0_357]) ).
cnf(refute_0_359,plain,
meet(X_41,join(zero,meet(X_41,top))) = meet(X_41,X_41),
inference(resolve,[$cnf( $equal(join(zero,meet(X_41,top)),X_41) )],[refute_0_355,refute_0_358]) ).
cnf(refute_0_360,plain,
( meet(X_41,X_41) != complement(complement(X_41))
| meet(X_41,join(zero,meet(X_41,top))) != meet(X_41,X_41)
| meet(X_41,join(zero,meet(X_41,top))) = complement(complement(X_41)) ),
inference(subst,[],[refute_0_28:[bind(X,$fot(meet(X_41,join(zero,meet(X_41,top))))),bind(Y,$fot(meet(X_41,X_41))),bind(Z,$fot(complement(complement(X_41))))]]) ).
cnf(refute_0_361,plain,
( meet(X_41,X_41) != complement(complement(X_41))
| meet(X_41,join(zero,meet(X_41,top))) = complement(complement(X_41)) ),
inference(resolve,[$cnf( $equal(meet(X_41,join(zero,meet(X_41,top))),meet(X_41,X_41)) )],[refute_0_359,refute_0_360]) ).
cnf(refute_0_362,plain,
meet(X_41,join(zero,meet(X_41,top))) = complement(complement(X_41)),
inference(resolve,[$cnf( $equal(meet(X_41,X_41),complement(complement(X_41))) )],[refute_0_345,refute_0_361]) ).
cnf(refute_0_363,plain,
join(zero,meet(X_41,join(zero,meet(X_41,top)))) = join(zero,meet(X_41,join(zero,meet(X_41,top)))),
introduced(tautology,[refl,[$fot(join(zero,meet(X_41,join(zero,meet(X_41,top)))))]]) ).
cnf(refute_0_364,plain,
( join(zero,meet(X_41,join(zero,meet(X_41,top)))) != join(zero,meet(X_41,join(zero,meet(X_41,top))))
| meet(X_41,join(zero,meet(X_41,top))) != complement(complement(X_41))
| join(zero,meet(X_41,join(zero,meet(X_41,top)))) = join(zero,complement(complement(X_41))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,meet(X_41,join(zero,meet(X_41,top)))),join(zero,meet(X_41,join(zero,meet(X_41,top))))) ),[1,1],$fot(complement(complement(X_41)))]]) ).
cnf(refute_0_365,plain,
( meet(X_41,join(zero,meet(X_41,top))) != complement(complement(X_41))
| join(zero,meet(X_41,join(zero,meet(X_41,top)))) = join(zero,complement(complement(X_41))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_41,join(zero,meet(X_41,top)))),join(zero,meet(X_41,join(zero,meet(X_41,top))))) )],[refute_0_363,refute_0_364]) ).
cnf(refute_0_366,plain,
join(zero,meet(X_41,join(zero,meet(X_41,top)))) = join(zero,complement(complement(X_41))),
inference(resolve,[$cnf( $equal(meet(X_41,join(zero,meet(X_41,top))),complement(complement(X_41))) )],[refute_0_362,refute_0_365]) ).
cnf(refute_0_367,plain,
( join(zero,complement(complement(X_41))) != complement(complement(X_41))
| join(zero,meet(X_41,join(zero,meet(X_41,top)))) != join(zero,complement(complement(X_41)))
| join(zero,meet(X_41,join(zero,meet(X_41,top)))) = complement(complement(X_41)) ),
inference(subst,[],[refute_0_28:[bind(X,$fot(join(zero,meet(X_41,join(zero,meet(X_41,top)))))),bind(Y,$fot(join(zero,complement(complement(X_41))))),bind(Z,$fot(complement(complement(X_41))))]]) ).
cnf(refute_0_368,plain,
( join(zero,complement(complement(X_41))) != complement(complement(X_41))
| join(zero,meet(X_41,join(zero,meet(X_41,top)))) = complement(complement(X_41)) ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_41,join(zero,meet(X_41,top)))),join(zero,complement(complement(X_41)))) )],[refute_0_366,refute_0_367]) ).
cnf(refute_0_369,plain,
join(zero,meet(X_41,join(zero,meet(X_41,top)))) = complement(complement(X_41)),
inference(resolve,[$cnf( $equal(join(zero,complement(complement(X_41))),complement(complement(X_41))) )],[refute_0_344,refute_0_368]) ).
cnf(refute_0_370,plain,
( X_41 != join(zero,meet(X_41,join(zero,meet(X_41,top))))
| join(zero,meet(X_41,join(zero,meet(X_41,top)))) != complement(complement(X_41))
| X_41 = complement(complement(X_41)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_41,complement(complement(X_41))) ),[0],$fot(join(zero,meet(X_41,join(zero,meet(X_41,top)))))]]) ).
cnf(refute_0_371,plain,
( X_41 != join(zero,meet(X_41,join(zero,meet(X_41,top))))
| X_41 = complement(complement(X_41)) ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_41,join(zero,meet(X_41,top)))),complement(complement(X_41))) )],[refute_0_369,refute_0_370]) ).
cnf(refute_0_372,plain,
X_41 = complement(complement(X_41)),
inference(resolve,[$cnf( $equal(X_41,join(zero,meet(X_41,join(zero,meet(X_41,top))))) )],[refute_0_101,refute_0_371]) ).
cnf(refute_0_373,plain,
( X_41 != complement(complement(X_41))
| complement(complement(X_41)) = X_41 ),
inference(subst,[],[refute_0_8:[bind(X,$fot(X_41)),bind(Y,$fot(complement(complement(X_41))))]]) ).
cnf(refute_0_374,plain,
complement(complement(X_41)) = X_41,
inference(resolve,[$cnf( $equal(X_41,complement(complement(X_41))) )],[refute_0_372,refute_0_373]) ).
cnf(refute_0_375,plain,
complement(complement(X1)) = X1,
inference(subst,[],[refute_0_374:[bind(X_41,$fot(X1))]]) ).
cnf(refute_0_376,plain,
join(zero,complement(X1)) = complement(X1),
inference(subst,[],[refute_0_336:[bind(X_44,$fot(X1))]]) ).
cnf(refute_0_377,plain,
complement(join(zero,complement(X1))) = complement(join(zero,complement(X1))),
introduced(tautology,[refl,[$fot(complement(join(zero,complement(X1))))]]) ).
cnf(refute_0_378,plain,
( complement(join(zero,complement(X1))) != complement(join(zero,complement(X1)))
| join(zero,complement(X1)) != complement(X1)
| complement(join(zero,complement(X1))) = complement(complement(X1)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(zero,complement(X1))),complement(join(zero,complement(X1)))) ),[1,0],$fot(complement(X1))]]) ).
cnf(refute_0_379,plain,
( join(zero,complement(X1)) != complement(X1)
| complement(join(zero,complement(X1))) = complement(complement(X1)) ),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(X1))),complement(join(zero,complement(X1)))) )],[refute_0_377,refute_0_378]) ).
cnf(refute_0_380,plain,
complement(join(zero,complement(X1))) = complement(complement(X1)),
inference(resolve,[$cnf( $equal(join(zero,complement(X1)),complement(X1)) )],[refute_0_376,refute_0_379]) ).
cnf(refute_0_381,plain,
( complement(complement(X1)) != X1
| complement(join(zero,complement(X1))) != complement(complement(X1))
| complement(join(zero,complement(X1))) = X1 ),
inference(subst,[],[refute_0_28:[bind(X,$fot(complement(join(zero,complement(X1))))),bind(Y,$fot(complement(complement(X1)))),bind(Z,$fot(X1))]]) ).
cnf(refute_0_382,plain,
( complement(complement(X1)) != X1
| complement(join(zero,complement(X1))) = X1 ),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(X1))),complement(complement(X1))) )],[refute_0_380,refute_0_381]) ).
cnf(refute_0_383,plain,
complement(join(zero,complement(X1))) = X1,
inference(resolve,[$cnf( $equal(complement(complement(X1)),X1) )],[refute_0_375,refute_0_382]) ).
cnf(refute_0_384,plain,
( complement(join(zero,complement(X1))) != X1
| meet(top,X1) != complement(join(zero,complement(X1)))
| meet(top,X1) = X1 ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,X1),complement(join(zero,complement(X1)))) ),[1],$fot(X1)]]) ).
cnf(refute_0_385,plain,
( meet(top,X1) != complement(join(zero,complement(X1)))
| meet(top,X1) = X1 ),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(X1))),X1) )],[refute_0_383,refute_0_384]) ).
cnf(refute_0_386,plain,
meet(top,X1) = X1,
inference(resolve,[$cnf( $equal(meet(top,X1),complement(join(zero,complement(X1)))) )],[refute_0_39,refute_0_385]) ).
cnf(refute_0_387,plain,
meet(top,X_25) = X_25,
inference(subst,[],[refute_0_386:[bind(X1,$fot(X_25))]]) ).
cnf(refute_0_388,plain,
join(complement(X0),meet(top,X_25)) = join(complement(X0),meet(top,X_25)),
introduced(tautology,[refl,[$fot(join(complement(X0),meet(top,X_25)))]]) ).
cnf(refute_0_389,plain,
( join(complement(X0),meet(top,X_25)) != join(complement(X0),meet(top,X_25))
| meet(top,X_25) != X_25
| join(complement(X0),meet(top,X_25)) = join(complement(X0),X_25) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X0),meet(top,X_25)),join(complement(X0),meet(top,X_25))) ),[1,1],$fot(X_25)]]) ).
cnf(refute_0_390,plain,
( meet(top,X_25) != X_25
| join(complement(X0),meet(top,X_25)) = join(complement(X0),X_25) ),
inference(resolve,[$cnf( $equal(join(complement(X0),meet(top,X_25)),join(complement(X0),meet(top,X_25))) )],[refute_0_388,refute_0_389]) ).
cnf(refute_0_391,plain,
join(complement(X0),meet(top,X_25)) = join(complement(X0),X_25),
inference(resolve,[$cnf( $equal(meet(top,X_25),X_25) )],[refute_0_387,refute_0_390]) ).
cnf(refute_0_392,plain,
complement(join(complement(X0),meet(top,X_25))) = complement(join(complement(X0),meet(top,X_25))),
introduced(tautology,[refl,[$fot(complement(join(complement(X0),meet(top,X_25))))]]) ).
cnf(refute_0_393,plain,
( complement(join(complement(X0),meet(top,X_25))) != complement(join(complement(X0),meet(top,X_25)))
| join(complement(X0),meet(top,X_25)) != join(complement(X0),X_25)
| complement(join(complement(X0),meet(top,X_25))) = complement(join(complement(X0),X_25)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(X0),meet(top,X_25))),complement(join(complement(X0),meet(top,X_25)))) ),[1,0],$fot(join(complement(X0),X_25))]]) ).
cnf(refute_0_394,plain,
( join(complement(X0),meet(top,X_25)) != join(complement(X0),X_25)
| complement(join(complement(X0),meet(top,X_25))) = complement(join(complement(X0),X_25)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X0),meet(top,X_25))),complement(join(complement(X0),meet(top,X_25)))) )],[refute_0_392,refute_0_393]) ).
cnf(refute_0_395,plain,
complement(join(complement(X0),meet(top,X_25))) = complement(join(complement(X0),X_25)),
inference(resolve,[$cnf( $equal(join(complement(X0),meet(top,X_25)),join(complement(X0),X_25)) )],[refute_0_391,refute_0_394]) ).
cnf(refute_0_396,plain,
( complement(join(complement(X0),meet(top,X_25))) != complement(join(complement(X0),X_25))
| meet(X0,complement(X_25)) != complement(join(complement(X0),meet(top,X_25)))
| meet(X0,complement(X_25)) = complement(join(complement(X0),X_25)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X0,complement(X_25)),complement(join(complement(X0),meet(top,X_25)))) ),[1],$fot(complement(join(complement(X0),X_25)))]]) ).
cnf(refute_0_397,plain,
( meet(X0,complement(X_25)) != complement(join(complement(X0),meet(top,X_25)))
| meet(X0,complement(X_25)) = complement(join(complement(X0),X_25)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X0),meet(top,X_25))),complement(join(complement(X0),X_25))) )],[refute_0_395,refute_0_396]) ).
cnf(refute_0_398,plain,
( meet(X0,join(zero,complement(X_25))) != complement(join(complement(X0),meet(top,X_25)))
| meet(X0,complement(X_25)) = complement(join(complement(X0),X_25)) ),
inference(resolve,[$cnf( $equal(meet(X0,complement(X_25)),complement(join(complement(X0),meet(top,X_25)))) )],[refute_0_343,refute_0_397]) ).
cnf(refute_0_399,plain,
meet(X0,complement(X_25)) = complement(join(complement(X0),X_25)),
inference(resolve,[$cnf( $equal(meet(X0,join(zero,complement(X_25))),complement(join(complement(X0),meet(top,X_25)))) )],[refute_0_45,refute_0_398]) ).
cnf(refute_0_400,plain,
meet(X_405,complement(join(complement(complement(X_405)),X_64))) = complement(join(complement(X_405),join(complement(complement(X_405)),X_64))),
inference(subst,[],[refute_0_399:[bind(X0,$fot(X_405)),bind(X_25,$fot(join(complement(complement(X_405)),X_64)))]]) ).
cnf(refute_0_401,plain,
join(X_62,join(complement(X_62),X_64)) = join(join(X_62,complement(X_62)),X_64),
inference(subst,[],[refute_0_74:[bind(X0,$fot(X_62)),bind(X1,$fot(complement(X_62))),bind(X2,$fot(X_64))]]) ).
cnf(refute_0_402,plain,
top = join(X_62,complement(X_62)),
inference(subst,[],[refute_0_14:[bind(X0,$fot(X_62))]]) ).
cnf(refute_0_403,plain,
( top != join(X_62,complement(X_62))
| join(X_62,complement(X_62)) = top ),
inference(subst,[],[refute_0_8:[bind(X,$fot(top)),bind(Y,$fot(join(X_62,complement(X_62))))]]) ).
cnf(refute_0_404,plain,
join(X_62,complement(X_62)) = top,
inference(resolve,[$cnf( $equal(top,join(X_62,complement(X_62))) )],[refute_0_402,refute_0_403]) ).
cnf(refute_0_405,plain,
( join(X_62,complement(X_62)) != top
| join(X_62,join(complement(X_62),X_64)) != join(join(X_62,complement(X_62)),X_64)
| join(X_62,join(complement(X_62),X_64)) = join(top,X_64) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_62,join(complement(X_62),X_64)),join(join(X_62,complement(X_62)),X_64)) ),[1,0],$fot(top)]]) ).
cnf(refute_0_406,plain,
( join(X_62,join(complement(X_62),X_64)) != join(join(X_62,complement(X_62)),X_64)
| join(X_62,join(complement(X_62),X_64)) = join(top,X_64) ),
inference(resolve,[$cnf( $equal(join(X_62,complement(X_62)),top) )],[refute_0_404,refute_0_405]) ).
cnf(refute_0_407,plain,
join(X_62,join(complement(X_62),X_64)) = join(top,X_64),
inference(resolve,[$cnf( $equal(join(X_62,join(complement(X_62),X_64)),join(join(X_62,complement(X_62)),X_64)) )],[refute_0_401,refute_0_406]) ).
cnf(refute_0_408,plain,
top = join(top,complement(join(complement(X0),complement(X1)))),
inference(subst,[],[refute_0_303:[bind(X_22,$fot(join(complement(X0),complement(X1))))]]) ).
cnf(refute_0_409,plain,
( complement(join(complement(X0),complement(X1))) != meet(X0,X1)
| top != join(top,complement(join(complement(X0),complement(X1))))
| top = join(top,meet(X0,X1)) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(top,complement(join(complement(X0),complement(X1))))) ),[1,1],$fot(meet(X0,X1))]]) ).
cnf(refute_0_410,plain,
( top != join(top,complement(join(complement(X0),complement(X1))))
| top = join(top,meet(X0,X1)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X0),complement(X1))),meet(X0,X1)) )],[refute_0_56,refute_0_409]) ).
cnf(refute_0_411,plain,
top = join(top,meet(X0,X1)),
inference(resolve,[$cnf( $equal(top,join(top,complement(join(complement(X0),complement(X1))))) )],[refute_0_408,refute_0_410]) ).
cnf(refute_0_412,plain,
top = join(top,meet(top,X1)),
inference(subst,[],[refute_0_411:[bind(X0,$fot(top))]]) ).
cnf(refute_0_413,plain,
( meet(top,X1) != X1
| top != join(top,meet(top,X1))
| top = join(top,X1) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(top,meet(top,X1))) ),[1,1],$fot(X1)]]) ).
cnf(refute_0_414,plain,
( top != join(top,meet(top,X1))
| top = join(top,X1) ),
inference(resolve,[$cnf( $equal(meet(top,X1),X1) )],[refute_0_386,refute_0_413]) ).
cnf(refute_0_415,plain,
top = join(top,X1),
inference(resolve,[$cnf( $equal(top,join(top,meet(top,X1))) )],[refute_0_412,refute_0_414]) ).
cnf(refute_0_416,plain,
( top != join(top,X1)
| join(top,X1) = top ),
inference(subst,[],[refute_0_8:[bind(X,$fot(top)),bind(Y,$fot(join(top,X1)))]]) ).
cnf(refute_0_417,plain,
join(top,X1) = top,
inference(resolve,[$cnf( $equal(top,join(top,X1)) )],[refute_0_415,refute_0_416]) ).
cnf(refute_0_418,plain,
join(top,X_64) = top,
inference(subst,[],[refute_0_417:[bind(X1,$fot(X_64))]]) ).
cnf(refute_0_419,plain,
( join(X_62,join(complement(X_62),X_64)) != join(top,X_64)
| join(top,X_64) != top
| join(X_62,join(complement(X_62),X_64)) = top ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_62,join(complement(X_62),X_64)),top) ),[0],$fot(join(top,X_64))]]) ).
cnf(refute_0_420,plain,
( join(X_62,join(complement(X_62),X_64)) != join(top,X_64)
| join(X_62,join(complement(X_62),X_64)) = top ),
inference(resolve,[$cnf( $equal(join(top,X_64),top) )],[refute_0_418,refute_0_419]) ).
cnf(refute_0_421,plain,
join(X_62,join(complement(X_62),X_64)) = top,
inference(resolve,[$cnf( $equal(join(X_62,join(complement(X_62),X_64)),join(top,X_64)) )],[refute_0_407,refute_0_420]) ).
cnf(refute_0_422,plain,
join(complement(X_405),join(complement(complement(X_405)),X_64)) = top,
inference(subst,[],[refute_0_421:[bind(X_62,$fot(complement(X_405)))]]) ).
cnf(refute_0_423,plain,
( join(complement(X_405),join(complement(complement(X_405)),X_64)) != top
| meet(X_405,complement(join(complement(complement(X_405)),X_64))) != complement(join(complement(X_405),join(complement(complement(X_405)),X_64)))
| meet(X_405,complement(join(complement(complement(X_405)),X_64))) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_405,complement(join(complement(complement(X_405)),X_64))),complement(join(complement(X_405),join(complement(complement(X_405)),X_64)))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_424,plain,
( meet(X_405,complement(join(complement(complement(X_405)),X_64))) != complement(join(complement(X_405),join(complement(complement(X_405)),X_64)))
| meet(X_405,complement(join(complement(complement(X_405)),X_64))) = complement(top) ),
inference(resolve,[$cnf( $equal(join(complement(X_405),join(complement(complement(X_405)),X_64)),top) )],[refute_0_422,refute_0_423]) ).
cnf(refute_0_425,plain,
meet(X_405,complement(join(complement(complement(X_405)),X_64))) = complement(top),
inference(resolve,[$cnf( $equal(meet(X_405,complement(join(complement(complement(X_405)),X_64))),complement(join(complement(X_405),join(complement(complement(X_405)),X_64)))) )],[refute_0_400,refute_0_424]) ).
cnf(refute_0_426,plain,
meet(join(zero,complement(X_25)),X1) = complement(join(complement(join(zero,complement(X_25))),complement(X1))),
inference(subst,[],[refute_0_0:[bind(X0,$fot(join(zero,complement(X_25))))]]) ).
cnf(refute_0_427,plain,
( complement(join(zero,complement(X_25))) != meet(top,X_25)
| meet(join(zero,complement(X_25)),X1) != complement(join(complement(join(zero,complement(X_25))),complement(X1)))
| meet(join(zero,complement(X_25)),X1) = complement(join(meet(top,X_25),complement(X1))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(zero,complement(X_25)),X1),complement(join(complement(join(zero,complement(X_25))),complement(X1)))) ),[1,0,0],$fot(meet(top,X_25))]]) ).
cnf(refute_0_428,plain,
( meet(join(zero,complement(X_25)),X1) != complement(join(complement(join(zero,complement(X_25))),complement(X1)))
| meet(join(zero,complement(X_25)),X1) = complement(join(meet(top,X_25),complement(X1))) ),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(X_25))),meet(top,X_25)) )],[refute_0_42,refute_0_427]) ).
cnf(refute_0_429,plain,
meet(join(zero,complement(X_25)),X1) = complement(join(meet(top,X_25),complement(X1))),
inference(resolve,[$cnf( $equal(meet(join(zero,complement(X_25)),X1),complement(join(complement(join(zero,complement(X_25))),complement(X1)))) )],[refute_0_426,refute_0_428]) ).
cnf(refute_0_430,plain,
meet(join(zero,complement(X_25)),X1) = meet(join(zero,complement(X_25)),X1),
introduced(tautology,[refl,[$fot(meet(join(zero,complement(X_25)),X1))]]) ).
cnf(refute_0_431,plain,
( join(zero,complement(X_25)) != complement(X_25)
| meet(join(zero,complement(X_25)),X1) != meet(join(zero,complement(X_25)),X1)
| meet(join(zero,complement(X_25)),X1) = meet(complement(X_25),X1) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(zero,complement(X_25)),X1),meet(join(zero,complement(X_25)),X1)) ),[1,0],$fot(complement(X_25))]]) ).
cnf(refute_0_432,plain,
( join(zero,complement(X_25)) != complement(X_25)
| meet(join(zero,complement(X_25)),X1) = meet(complement(X_25),X1) ),
inference(resolve,[$cnf( $equal(meet(join(zero,complement(X_25)),X1),meet(join(zero,complement(X_25)),X1)) )],[refute_0_430,refute_0_431]) ).
cnf(refute_0_433,plain,
meet(join(zero,complement(X_25)),X1) = meet(complement(X_25),X1),
inference(resolve,[$cnf( $equal(join(zero,complement(X_25)),complement(X_25)) )],[refute_0_337,refute_0_432]) ).
cnf(refute_0_434,plain,
( meet(join(zero,complement(X_25)),X1) != complement(join(meet(top,X_25),complement(X1)))
| meet(join(zero,complement(X_25)),X1) != meet(complement(X_25),X1)
| meet(complement(X_25),X1) = complement(join(meet(top,X_25),complement(X1))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(zero,complement(X_25)),X1),complement(join(meet(top,X_25),complement(X1)))) ),[0],$fot(meet(complement(X_25),X1))]]) ).
cnf(refute_0_435,plain,
( meet(join(zero,complement(X_25)),X1) != complement(join(meet(top,X_25),complement(X1)))
| meet(complement(X_25),X1) = complement(join(meet(top,X_25),complement(X1))) ),
inference(resolve,[$cnf( $equal(meet(join(zero,complement(X_25)),X1),meet(complement(X_25),X1)) )],[refute_0_433,refute_0_434]) ).
cnf(refute_0_436,plain,
join(meet(top,X_25),complement(X1)) = join(meet(top,X_25),complement(X1)),
introduced(tautology,[refl,[$fot(join(meet(top,X_25),complement(X1)))]]) ).
cnf(refute_0_437,plain,
( join(meet(top,X_25),complement(X1)) != join(meet(top,X_25),complement(X1))
| meet(top,X_25) != X_25
| join(meet(top,X_25),complement(X1)) = join(X_25,complement(X1)) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(top,X_25),complement(X1)),join(meet(top,X_25),complement(X1))) ),[1,0],$fot(X_25)]]) ).
cnf(refute_0_438,plain,
( meet(top,X_25) != X_25
| join(meet(top,X_25),complement(X1)) = join(X_25,complement(X1)) ),
inference(resolve,[$cnf( $equal(join(meet(top,X_25),complement(X1)),join(meet(top,X_25),complement(X1))) )],[refute_0_436,refute_0_437]) ).
cnf(refute_0_439,plain,
join(meet(top,X_25),complement(X1)) = join(X_25,complement(X1)),
inference(resolve,[$cnf( $equal(meet(top,X_25),X_25) )],[refute_0_387,refute_0_438]) ).
cnf(refute_0_440,plain,
complement(join(meet(top,X_25),complement(X1))) = complement(join(meet(top,X_25),complement(X1))),
introduced(tautology,[refl,[$fot(complement(join(meet(top,X_25),complement(X1))))]]) ).
cnf(refute_0_441,plain,
( complement(join(meet(top,X_25),complement(X1))) != complement(join(meet(top,X_25),complement(X1)))
| join(meet(top,X_25),complement(X1)) != join(X_25,complement(X1))
| complement(join(meet(top,X_25),complement(X1))) = complement(join(X_25,complement(X1))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(meet(top,X_25),complement(X1))),complement(join(meet(top,X_25),complement(X1)))) ),[1,0],$fot(join(X_25,complement(X1)))]]) ).
cnf(refute_0_442,plain,
( join(meet(top,X_25),complement(X1)) != join(X_25,complement(X1))
| complement(join(meet(top,X_25),complement(X1))) = complement(join(X_25,complement(X1))) ),
inference(resolve,[$cnf( $equal(complement(join(meet(top,X_25),complement(X1))),complement(join(meet(top,X_25),complement(X1)))) )],[refute_0_440,refute_0_441]) ).
cnf(refute_0_443,plain,
complement(join(meet(top,X_25),complement(X1))) = complement(join(X_25,complement(X1))),
inference(resolve,[$cnf( $equal(join(meet(top,X_25),complement(X1)),join(X_25,complement(X1))) )],[refute_0_439,refute_0_442]) ).
cnf(refute_0_444,plain,
( complement(join(meet(top,X_25),complement(X1))) != complement(join(X_25,complement(X1)))
| meet(complement(X_25),X1) != complement(join(meet(top,X_25),complement(X1)))
| meet(complement(X_25),X1) = complement(join(X_25,complement(X1))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(complement(X_25),X1),complement(join(meet(top,X_25),complement(X1)))) ),[1],$fot(complement(join(X_25,complement(X1))))]]) ).
cnf(refute_0_445,plain,
( meet(complement(X_25),X1) != complement(join(meet(top,X_25),complement(X1)))
| meet(complement(X_25),X1) = complement(join(X_25,complement(X1))) ),
inference(resolve,[$cnf( $equal(complement(join(meet(top,X_25),complement(X1))),complement(join(X_25,complement(X1)))) )],[refute_0_443,refute_0_444]) ).
cnf(refute_0_446,plain,
( meet(join(zero,complement(X_25)),X1) != complement(join(meet(top,X_25),complement(X1)))
| meet(complement(X_25),X1) = complement(join(X_25,complement(X1))) ),
inference(resolve,[$cnf( $equal(meet(complement(X_25),X1),complement(join(meet(top,X_25),complement(X1)))) )],[refute_0_435,refute_0_445]) ).
cnf(refute_0_447,plain,
meet(complement(X_25),X1) = complement(join(X_25,complement(X1))),
inference(resolve,[$cnf( $equal(meet(join(zero,complement(X_25)),X1),complement(join(meet(top,X_25),complement(X1)))) )],[refute_0_429,refute_0_446]) ).
cnf(refute_0_448,plain,
meet(complement(X_396),complement(X_41)) = complement(join(X_396,complement(complement(X_41)))),
inference(subst,[],[refute_0_447:[bind(X1,$fot(complement(X_41))),bind(X_25,$fot(X_396))]]) ).
cnf(refute_0_449,plain,
( complement(complement(X_41)) != X_41
| meet(complement(X_396),complement(X_41)) != complement(join(X_396,complement(complement(X_41))))
| meet(complement(X_396),complement(X_41)) = complement(join(X_396,X_41)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(complement(X_396),complement(X_41)),complement(join(X_396,complement(complement(X_41))))) ),[1,0,1],$fot(X_41)]]) ).
cnf(refute_0_450,plain,
( meet(complement(X_396),complement(X_41)) != complement(join(X_396,complement(complement(X_41))))
| meet(complement(X_396),complement(X_41)) = complement(join(X_396,X_41)) ),
inference(resolve,[$cnf( $equal(complement(complement(X_41)),X_41) )],[refute_0_374,refute_0_449]) ).
cnf(refute_0_451,plain,
meet(complement(X_396),complement(X_41)) = complement(join(X_396,X_41)),
inference(resolve,[$cnf( $equal(meet(complement(X_396),complement(X_41)),complement(join(X_396,complement(complement(X_41))))) )],[refute_0_448,refute_0_450]) ).
cnf(refute_0_452,plain,
meet(complement(X_405),complement(X_64)) = complement(join(X_405,X_64)),
inference(subst,[],[refute_0_451:[bind(X_396,$fot(X_405)),bind(X_41,$fot(X_64))]]) ).
cnf(refute_0_453,plain,
( meet(X0,complement(X_25)) != complement(join(complement(X0),X_25))
| complement(join(complement(X0),X_25)) = meet(X0,complement(X_25)) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(meet(X0,complement(X_25)))),bind(Y,$fot(complement(join(complement(X0),X_25))))]]) ).
cnf(refute_0_454,plain,
complement(join(complement(X0),X_25)) = meet(X0,complement(X_25)),
inference(resolve,[$cnf( $equal(meet(X0,complement(X_25)),complement(join(complement(X0),X_25))) )],[refute_0_399,refute_0_453]) ).
cnf(refute_0_455,plain,
complement(join(complement(complement(X_405)),X_64)) = meet(complement(X_405),complement(X_64)),
inference(subst,[],[refute_0_454:[bind(X0,$fot(complement(X_405))),bind(X_25,$fot(X_64))]]) ).
cnf(refute_0_456,plain,
( complement(join(complement(complement(X_405)),X_64)) != meet(complement(X_405),complement(X_64))
| meet(complement(X_405),complement(X_64)) != complement(join(X_405,X_64))
| complement(join(complement(complement(X_405)),X_64)) = complement(join(X_405,X_64)) ),
inference(subst,[],[refute_0_28:[bind(X,$fot(complement(join(complement(complement(X_405)),X_64)))),bind(Y,$fot(meet(complement(X_405),complement(X_64)))),bind(Z,$fot(complement(join(X_405,X_64))))]]) ).
cnf(refute_0_457,plain,
( meet(complement(X_405),complement(X_64)) != complement(join(X_405,X_64))
| complement(join(complement(complement(X_405)),X_64)) = complement(join(X_405,X_64)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(complement(X_405)),X_64)),meet(complement(X_405),complement(X_64))) )],[refute_0_455,refute_0_456]) ).
cnf(refute_0_458,plain,
complement(join(complement(complement(X_405)),X_64)) = complement(join(X_405,X_64)),
inference(resolve,[$cnf( $equal(meet(complement(X_405),complement(X_64)),complement(join(X_405,X_64))) )],[refute_0_452,refute_0_457]) ).
cnf(refute_0_459,plain,
meet(X_405,complement(join(complement(complement(X_405)),X_64))) = meet(X_405,complement(join(complement(complement(X_405)),X_64))),
introduced(tautology,[refl,[$fot(meet(X_405,complement(join(complement(complement(X_405)),X_64))))]]) ).
cnf(refute_0_460,plain,
( complement(join(complement(complement(X_405)),X_64)) != complement(join(X_405,X_64))
| meet(X_405,complement(join(complement(complement(X_405)),X_64))) != meet(X_405,complement(join(complement(complement(X_405)),X_64)))
| meet(X_405,complement(join(complement(complement(X_405)),X_64))) = meet(X_405,complement(join(X_405,X_64))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_405,complement(join(complement(complement(X_405)),X_64))),meet(X_405,complement(join(complement(complement(X_405)),X_64)))) ),[1,1],$fot(complement(join(X_405,X_64)))]]) ).
cnf(refute_0_461,plain,
( complement(join(complement(complement(X_405)),X_64)) != complement(join(X_405,X_64))
| meet(X_405,complement(join(complement(complement(X_405)),X_64))) = meet(X_405,complement(join(X_405,X_64))) ),
inference(resolve,[$cnf( $equal(meet(X_405,complement(join(complement(complement(X_405)),X_64))),meet(X_405,complement(join(complement(complement(X_405)),X_64)))) )],[refute_0_459,refute_0_460]) ).
cnf(refute_0_462,plain,
meet(X_405,complement(join(complement(complement(X_405)),X_64))) = meet(X_405,complement(join(X_405,X_64))),
inference(resolve,[$cnf( $equal(complement(join(complement(complement(X_405)),X_64)),complement(join(X_405,X_64))) )],[refute_0_458,refute_0_461]) ).
cnf(refute_0_463,plain,
( meet(X_405,complement(join(complement(complement(X_405)),X_64))) != complement(top)
| meet(X_405,complement(join(complement(complement(X_405)),X_64))) != meet(X_405,complement(join(X_405,X_64)))
| meet(X_405,complement(join(X_405,X_64))) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_405,complement(join(complement(complement(X_405)),X_64))),complement(top)) ),[0],$fot(meet(X_405,complement(join(X_405,X_64))))]]) ).
cnf(refute_0_464,plain,
( meet(X_405,complement(join(complement(complement(X_405)),X_64))) != complement(top)
| meet(X_405,complement(join(X_405,X_64))) = complement(top) ),
inference(resolve,[$cnf( $equal(meet(X_405,complement(join(complement(complement(X_405)),X_64))),meet(X_405,complement(join(X_405,X_64)))) )],[refute_0_462,refute_0_463]) ).
cnf(refute_0_465,plain,
( complement(top) != zero
| meet(X_405,complement(join(X_405,X_64))) != complement(top)
| meet(X_405,complement(join(X_405,X_64))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_405,complement(join(X_405,X_64))),complement(top)) ),[1],$fot(zero)]]) ).
cnf(refute_0_466,plain,
( meet(X_405,complement(join(X_405,X_64))) != complement(top)
| meet(X_405,complement(join(X_405,X_64))) = zero ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_36,refute_0_465]) ).
cnf(refute_0_467,plain,
( meet(X_405,complement(join(complement(complement(X_405)),X_64))) != complement(top)
| meet(X_405,complement(join(X_405,X_64))) = zero ),
inference(resolve,[$cnf( $equal(meet(X_405,complement(join(X_405,X_64))),complement(top)) )],[refute_0_464,refute_0_466]) ).
cnf(refute_0_468,plain,
meet(X_405,complement(join(X_405,X_64))) = zero,
inference(resolve,[$cnf( $equal(meet(X_405,complement(join(complement(complement(X_405)),X_64))),complement(top)) )],[refute_0_425,refute_0_467]) ).
cnf(refute_0_469,plain,
meet(skolemFOFtoCNF_X1,complement(join(skolemFOFtoCNF_X1,complement(converse(skolemFOFtoCNF_X0))))) = zero,
inference(subst,[],[refute_0_468:[bind(X_405,$fot(skolemFOFtoCNF_X1)),bind(X_64,$fot(complement(converse(skolemFOFtoCNF_X0))))]]) ).
cnf(refute_0_470,plain,
join(skolemFOFtoCNF_X1,join(converse(complement(skolemFOFtoCNF_X0)),X_64)) = join(join(skolemFOFtoCNF_X1,converse(complement(skolemFOFtoCNF_X0))),X_64),
inference(subst,[],[refute_0_74:[bind(X0,$fot(skolemFOFtoCNF_X1)),bind(X1,$fot(converse(complement(skolemFOFtoCNF_X0)))),bind(X2,$fot(X_64))]]) ).
cnf(refute_0_471,plain,
converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_472,plain,
join(converse(X0),converse(X1)) = join(converse(X1),converse(X0)),
inference(subst,[],[refute_0_47:[bind(X0,$fot(converse(X0))),bind(X1,$fot(converse(X1)))]]) ).
cnf(refute_0_473,plain,
( converse(join(X0,X1)) != join(converse(X0),converse(X1))
| join(converse(X0),converse(X1)) != join(converse(X1),converse(X0))
| converse(join(X0,X1)) = join(converse(X1),converse(X0)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(join(X0,X1)),join(converse(X1),converse(X0))) ),[0],$fot(join(converse(X0),converse(X1)))]]) ).
cnf(refute_0_474,plain,
( converse(join(X0,X1)) != join(converse(X0),converse(X1))
| converse(join(X0,X1)) = join(converse(X1),converse(X0)) ),
inference(resolve,[$cnf( $equal(join(converse(X0),converse(X1)),join(converse(X1),converse(X0))) )],[refute_0_472,refute_0_473]) ).
cnf(refute_0_475,plain,
converse(join(X0,X1)) = join(converse(X1),converse(X0)),
inference(resolve,[$cnf( $equal(converse(join(X0,X1)),join(converse(X0),converse(X1))) )],[refute_0_471,refute_0_474]) ).
cnf(refute_0_476,plain,
( converse(join(X0,X1)) != join(converse(X0),converse(X1))
| join(converse(X0),converse(X1)) = converse(join(X0,X1)) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(converse(join(X0,X1)))),bind(Y,$fot(join(converse(X0),converse(X1))))]]) ).
cnf(refute_0_477,plain,
join(converse(X0),converse(X1)) = converse(join(X0,X1)),
inference(resolve,[$cnf( $equal(converse(join(X0,X1)),join(converse(X0),converse(X1))) )],[refute_0_471,refute_0_476]) ).
cnf(refute_0_478,plain,
join(converse(X1),converse(X0)) = converse(join(X1,X0)),
inference(subst,[],[refute_0_477:[bind(X0,$fot(X1)),bind(X1,$fot(X0))]]) ).
cnf(refute_0_479,plain,
( converse(join(X0,X1)) != join(converse(X1),converse(X0))
| join(converse(X1),converse(X0)) != converse(join(X1,X0))
| converse(join(X0,X1)) = converse(join(X1,X0)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(join(X0,X1)),converse(join(X1,X0))) ),[0],$fot(join(converse(X1),converse(X0)))]]) ).
cnf(refute_0_480,plain,
( converse(join(X0,X1)) != join(converse(X1),converse(X0))
| converse(join(X0,X1)) = converse(join(X1,X0)) ),
inference(resolve,[$cnf( $equal(join(converse(X1),converse(X0)),converse(join(X1,X0))) )],[refute_0_478,refute_0_479]) ).
cnf(refute_0_481,plain,
converse(join(X0,X1)) = converse(join(X1,X0)),
inference(resolve,[$cnf( $equal(converse(join(X0,X1)),join(converse(X1),converse(X0))) )],[refute_0_475,refute_0_480]) ).
cnf(refute_0_482,plain,
converse(join(converse(skolemFOFtoCNF_X1),complement(skolemFOFtoCNF_X0))) = converse(join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1))),
inference(subst,[],[refute_0_481:[bind(X0,$fot(converse(skolemFOFtoCNF_X1))),bind(X1,$fot(complement(skolemFOFtoCNF_X0)))]]) ).
cnf(refute_0_483,plain,
join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1)) = join(zero,meet(top,join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1)))),
inference(subst,[],[refute_0_330:[bind(X0,$fot(join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1))))]]) ).
cnf(refute_0_484,plain,
meet(top,join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1))) = complement(join(zero,complement(join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1))))),
inference(subst,[],[refute_0_39:[bind(X1,$fot(join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1))))]]) ).
cnf(refute_0_485,plain,
skolemFOFtoCNF_X0 = join(meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1)),complement(join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1)))),
inference(subst,[],[refute_0_66:[bind(X0,$fot(skolemFOFtoCNF_X0)),bind(X1,$fot(converse(skolemFOFtoCNF_X1)))]]) ).
cnf(refute_0_486,plain,
meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1)) = zero,
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_487,plain,
( meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1)) != zero
| skolemFOFtoCNF_X0 != join(meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1)),complement(join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1))))
| skolemFOFtoCNF_X0 = join(zero,complement(join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1)))) ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_X0,join(meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1)),complement(join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_488,plain,
( skolemFOFtoCNF_X0 != join(meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1)),complement(join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1))))
| skolemFOFtoCNF_X0 = join(zero,complement(join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1)))) ),
inference(resolve,[$cnf( $equal(meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1)),zero) )],[refute_0_486,refute_0_487]) ).
cnf(refute_0_489,plain,
skolemFOFtoCNF_X0 = join(zero,complement(join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1)))),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X0,join(meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1)),complement(join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1))))) )],[refute_0_485,refute_0_488]) ).
cnf(refute_0_490,plain,
( skolemFOFtoCNF_X0 != join(zero,complement(join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1))))
| join(zero,complement(join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1)))) = skolemFOFtoCNF_X0 ),
inference(subst,[],[refute_0_8:[bind(X,$fot(skolemFOFtoCNF_X0)),bind(Y,$fot(join(zero,complement(join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1))))))]]) ).
cnf(refute_0_491,plain,
join(zero,complement(join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1)))) = skolemFOFtoCNF_X0,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X0,join(zero,complement(join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1))))) )],[refute_0_489,refute_0_490]) ).
cnf(refute_0_492,plain,
( join(zero,complement(join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1)))) != skolemFOFtoCNF_X0
| meet(top,join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1))) != complement(join(zero,complement(join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1)))))
| meet(top,join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1))) = complement(skolemFOFtoCNF_X0) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1))),complement(join(zero,complement(join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1)))))) ),[1,0],$fot(skolemFOFtoCNF_X0)]]) ).
cnf(refute_0_493,plain,
( meet(top,join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1))) != complement(join(zero,complement(join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1)))))
| meet(top,join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1))) = complement(skolemFOFtoCNF_X0) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1)))),skolemFOFtoCNF_X0) )],[refute_0_491,refute_0_492]) ).
cnf(refute_0_494,plain,
meet(top,join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1))) = complement(skolemFOFtoCNF_X0),
inference(resolve,[$cnf( $equal(meet(top,join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1))),complement(join(zero,complement(join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1)))))) )],[refute_0_484,refute_0_493]) ).
cnf(refute_0_495,plain,
( join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1)) != join(zero,meet(top,join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1))))
| meet(top,join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1))) != complement(skolemFOFtoCNF_X0)
| join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1)) = join(zero,complement(skolemFOFtoCNF_X0)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1)),join(zero,meet(top,join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1))))) ),[1,1],$fot(complement(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_496,plain,
( join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1)) != join(zero,meet(top,join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1))))
| join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1)) = join(zero,complement(skolemFOFtoCNF_X0)) ),
inference(resolve,[$cnf( $equal(meet(top,join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1))),complement(skolemFOFtoCNF_X0)) )],[refute_0_494,refute_0_495]) ).
cnf(refute_0_497,plain,
join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1)) = join(zero,complement(skolemFOFtoCNF_X0)),
inference(resolve,[$cnf( $equal(join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1)),join(zero,meet(top,join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1))))) )],[refute_0_483,refute_0_496]) ).
cnf(refute_0_498,plain,
join(zero,complement(skolemFOFtoCNF_X0)) = complement(skolemFOFtoCNF_X0),
inference(subst,[],[refute_0_336:[bind(X_44,$fot(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_499,plain,
( join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1)) != join(zero,complement(skolemFOFtoCNF_X0))
| join(zero,complement(skolemFOFtoCNF_X0)) != complement(skolemFOFtoCNF_X0)
| join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1)) = complement(skolemFOFtoCNF_X0) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1)),complement(skolemFOFtoCNF_X0)) ),[0],$fot(join(zero,complement(skolemFOFtoCNF_X0)))]]) ).
cnf(refute_0_500,plain,
( join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1)) != join(zero,complement(skolemFOFtoCNF_X0))
| join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1)) = complement(skolemFOFtoCNF_X0) ),
inference(resolve,[$cnf( $equal(join(zero,complement(skolemFOFtoCNF_X0)),complement(skolemFOFtoCNF_X0)) )],[refute_0_498,refute_0_499]) ).
cnf(refute_0_501,plain,
join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1)) = complement(skolemFOFtoCNF_X0),
inference(resolve,[$cnf( $equal(join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1)),join(zero,complement(skolemFOFtoCNF_X0))) )],[refute_0_497,refute_0_500]) ).
cnf(refute_0_502,plain,
( converse(join(converse(skolemFOFtoCNF_X1),complement(skolemFOFtoCNF_X0))) != converse(join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1)))
| join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1)) != complement(skolemFOFtoCNF_X0)
| converse(join(converse(skolemFOFtoCNF_X1),complement(skolemFOFtoCNF_X0))) = converse(complement(skolemFOFtoCNF_X0)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(skolemFOFtoCNF_X1),complement(skolemFOFtoCNF_X0))),converse(join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1)))) ),[1,0],$fot(complement(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_503,plain,
( converse(join(converse(skolemFOFtoCNF_X1),complement(skolemFOFtoCNF_X0))) != converse(join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1)))
| converse(join(converse(skolemFOFtoCNF_X1),complement(skolemFOFtoCNF_X0))) = converse(complement(skolemFOFtoCNF_X0)) ),
inference(resolve,[$cnf( $equal(join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1)),complement(skolemFOFtoCNF_X0)) )],[refute_0_501,refute_0_502]) ).
cnf(refute_0_504,plain,
converse(join(converse(skolemFOFtoCNF_X1),complement(skolemFOFtoCNF_X0))) = converse(complement(skolemFOFtoCNF_X0)),
inference(resolve,[$cnf( $equal(converse(join(converse(skolemFOFtoCNF_X1),complement(skolemFOFtoCNF_X0))),converse(join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1)))) )],[refute_0_482,refute_0_503]) ).
cnf(refute_0_505,plain,
join(converse(complement(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1) = join(skolemFOFtoCNF_X1,converse(complement(skolemFOFtoCNF_X0))),
inference(subst,[],[refute_0_49:[bind(X0,$fot(skolemFOFtoCNF_X1)),bind(X1,$fot(converse(complement(skolemFOFtoCNF_X0))))]]) ).
cnf(refute_0_506,plain,
converse(join(X_4,converse(X0))) = join(converse(X_4),converse(converse(X0))),
inference(subst,[],[refute_0_471:[bind(X0,$fot(X_4)),bind(X1,$fot(converse(X0)))]]) ).
cnf(refute_0_507,plain,
( converse(converse(X0)) != X0
| converse(join(X_4,converse(X0))) != join(converse(X_4),converse(converse(X0)))
| converse(join(X_4,converse(X0))) = join(converse(X_4),X0) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(X_4,converse(X0))),join(converse(X_4),converse(converse(X0)))) ),[1,1],$fot(X0)]]) ).
cnf(refute_0_508,plain,
( converse(join(X_4,converse(X0))) != join(converse(X_4),converse(converse(X0)))
| converse(join(X_4,converse(X0))) = join(converse(X_4),X0) ),
inference(resolve,[$cnf( $equal(converse(converse(X0)),X0) )],[refute_0_161,refute_0_507]) ).
cnf(refute_0_509,plain,
converse(join(X_4,converse(X0))) = join(converse(X_4),X0),
inference(resolve,[$cnf( $equal(converse(join(X_4,converse(X0))),join(converse(X_4),converse(converse(X0)))) )],[refute_0_506,refute_0_508]) ).
cnf(refute_0_510,plain,
converse(join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1))) = join(converse(complement(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1),
inference(subst,[],[refute_0_509:[bind(X0,$fot(skolemFOFtoCNF_X1)),bind(X_4,$fot(complement(skolemFOFtoCNF_X0)))]]) ).
cnf(refute_0_511,plain,
( converse(join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1))) != join(converse(complement(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1)
| join(converse(complement(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1) != join(skolemFOFtoCNF_X1,converse(complement(skolemFOFtoCNF_X0)))
| converse(join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1))) = join(skolemFOFtoCNF_X1,converse(complement(skolemFOFtoCNF_X0))) ),
inference(subst,[],[refute_0_28:[bind(X,$fot(converse(join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1))))),bind(Y,$fot(join(converse(complement(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1))),bind(Z,$fot(join(skolemFOFtoCNF_X1,converse(complement(skolemFOFtoCNF_X0)))))]]) ).
cnf(refute_0_512,plain,
( join(converse(complement(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1) != join(skolemFOFtoCNF_X1,converse(complement(skolemFOFtoCNF_X0)))
| converse(join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1))) = join(skolemFOFtoCNF_X1,converse(complement(skolemFOFtoCNF_X0))) ),
inference(resolve,[$cnf( $equal(converse(join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1))),join(converse(complement(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1)) )],[refute_0_510,refute_0_511]) ).
cnf(refute_0_513,plain,
converse(join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1))) = join(skolemFOFtoCNF_X1,converse(complement(skolemFOFtoCNF_X0))),
inference(resolve,[$cnf( $equal(join(converse(complement(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1),join(skolemFOFtoCNF_X1,converse(complement(skolemFOFtoCNF_X0)))) )],[refute_0_505,refute_0_512]) ).
cnf(refute_0_514,plain,
( converse(join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1))) != join(skolemFOFtoCNF_X1,converse(complement(skolemFOFtoCNF_X0)))
| converse(join(converse(skolemFOFtoCNF_X1),complement(skolemFOFtoCNF_X0))) != converse(join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1)))
| converse(join(converse(skolemFOFtoCNF_X1),complement(skolemFOFtoCNF_X0))) = join(skolemFOFtoCNF_X1,converse(complement(skolemFOFtoCNF_X0))) ),
inference(subst,[],[refute_0_28:[bind(X,$fot(converse(join(converse(skolemFOFtoCNF_X1),complement(skolemFOFtoCNF_X0))))),bind(Y,$fot(converse(join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1))))),bind(Z,$fot(join(skolemFOFtoCNF_X1,converse(complement(skolemFOFtoCNF_X0)))))]]) ).
cnf(refute_0_515,plain,
( converse(join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1))) != join(skolemFOFtoCNF_X1,converse(complement(skolemFOFtoCNF_X0)))
| converse(join(converse(skolemFOFtoCNF_X1),complement(skolemFOFtoCNF_X0))) = join(skolemFOFtoCNF_X1,converse(complement(skolemFOFtoCNF_X0))) ),
inference(resolve,[$cnf( $equal(converse(join(converse(skolemFOFtoCNF_X1),complement(skolemFOFtoCNF_X0))),converse(join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1)))) )],[refute_0_482,refute_0_514]) ).
cnf(refute_0_516,plain,
converse(join(converse(skolemFOFtoCNF_X1),complement(skolemFOFtoCNF_X0))) = join(skolemFOFtoCNF_X1,converse(complement(skolemFOFtoCNF_X0))),
inference(resolve,[$cnf( $equal(converse(join(complement(skolemFOFtoCNF_X0),converse(skolemFOFtoCNF_X1))),join(skolemFOFtoCNF_X1,converse(complement(skolemFOFtoCNF_X0)))) )],[refute_0_513,refute_0_515]) ).
cnf(refute_0_517,plain,
( converse(join(converse(skolemFOFtoCNF_X1),complement(skolemFOFtoCNF_X0))) != converse(complement(skolemFOFtoCNF_X0))
| converse(join(converse(skolemFOFtoCNF_X1),complement(skolemFOFtoCNF_X0))) != join(skolemFOFtoCNF_X1,converse(complement(skolemFOFtoCNF_X0)))
| join(skolemFOFtoCNF_X1,converse(complement(skolemFOFtoCNF_X0))) = converse(complement(skolemFOFtoCNF_X0)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(skolemFOFtoCNF_X1),complement(skolemFOFtoCNF_X0))),converse(complement(skolemFOFtoCNF_X0))) ),[0],$fot(join(skolemFOFtoCNF_X1,converse(complement(skolemFOFtoCNF_X0))))]]) ).
cnf(refute_0_518,plain,
( converse(join(converse(skolemFOFtoCNF_X1),complement(skolemFOFtoCNF_X0))) != converse(complement(skolemFOFtoCNF_X0))
| join(skolemFOFtoCNF_X1,converse(complement(skolemFOFtoCNF_X0))) = converse(complement(skolemFOFtoCNF_X0)) ),
inference(resolve,[$cnf( $equal(converse(join(converse(skolemFOFtoCNF_X1),complement(skolemFOFtoCNF_X0))),join(skolemFOFtoCNF_X1,converse(complement(skolemFOFtoCNF_X0)))) )],[refute_0_516,refute_0_517]) ).
cnf(refute_0_519,plain,
join(skolemFOFtoCNF_X1,converse(complement(skolemFOFtoCNF_X0))) = converse(complement(skolemFOFtoCNF_X0)),
inference(resolve,[$cnf( $equal(converse(join(converse(skolemFOFtoCNF_X1),complement(skolemFOFtoCNF_X0))),converse(complement(skolemFOFtoCNF_X0))) )],[refute_0_504,refute_0_518]) ).
cnf(refute_0_520,plain,
( join(skolemFOFtoCNF_X1,converse(complement(skolemFOFtoCNF_X0))) != converse(complement(skolemFOFtoCNF_X0))
| join(skolemFOFtoCNF_X1,join(converse(complement(skolemFOFtoCNF_X0)),X_64)) != join(join(skolemFOFtoCNF_X1,converse(complement(skolemFOFtoCNF_X0))),X_64)
| join(skolemFOFtoCNF_X1,join(converse(complement(skolemFOFtoCNF_X0)),X_64)) = join(converse(complement(skolemFOFtoCNF_X0)),X_64) ),
introduced(tautology,[equality,[$cnf( $equal(join(skolemFOFtoCNF_X1,join(converse(complement(skolemFOFtoCNF_X0)),X_64)),join(join(skolemFOFtoCNF_X1,converse(complement(skolemFOFtoCNF_X0))),X_64)) ),[1,0],$fot(converse(complement(skolemFOFtoCNF_X0)))]]) ).
cnf(refute_0_521,plain,
( join(skolemFOFtoCNF_X1,join(converse(complement(skolemFOFtoCNF_X0)),X_64)) != join(join(skolemFOFtoCNF_X1,converse(complement(skolemFOFtoCNF_X0))),X_64)
| join(skolemFOFtoCNF_X1,join(converse(complement(skolemFOFtoCNF_X0)),X_64)) = join(converse(complement(skolemFOFtoCNF_X0)),X_64) ),
inference(resolve,[$cnf( $equal(join(skolemFOFtoCNF_X1,converse(complement(skolemFOFtoCNF_X0))),converse(complement(skolemFOFtoCNF_X0))) )],[refute_0_519,refute_0_520]) ).
cnf(refute_0_522,plain,
join(skolemFOFtoCNF_X1,join(converse(complement(skolemFOFtoCNF_X0)),X_64)) = join(converse(complement(skolemFOFtoCNF_X0)),X_64),
inference(resolve,[$cnf( $equal(join(skolemFOFtoCNF_X1,join(converse(complement(skolemFOFtoCNF_X0)),X_64)),join(join(skolemFOFtoCNF_X1,converse(complement(skolemFOFtoCNF_X0))),X_64)) )],[refute_0_470,refute_0_521]) ).
cnf(refute_0_523,plain,
join(skolemFOFtoCNF_X1,join(converse(complement(skolemFOFtoCNF_X0)),converse(X1))) = join(converse(complement(skolemFOFtoCNF_X0)),converse(X1)),
inference(subst,[],[refute_0_522:[bind(X_64,$fot(converse(X1)))]]) ).
cnf(refute_0_524,plain,
converse(join(complement(skolemFOFtoCNF_X0),X1)) = join(converse(complement(skolemFOFtoCNF_X0)),converse(X1)),
inference(subst,[],[refute_0_471:[bind(X0,$fot(complement(skolemFOFtoCNF_X0)))]]) ).
cnf(refute_0_525,plain,
( converse(join(complement(skolemFOFtoCNF_X0),X1)) != join(converse(complement(skolemFOFtoCNF_X0)),converse(X1))
| join(converse(complement(skolemFOFtoCNF_X0)),converse(X1)) = converse(join(complement(skolemFOFtoCNF_X0),X1)) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(converse(join(complement(skolemFOFtoCNF_X0),X1)))),bind(Y,$fot(join(converse(complement(skolemFOFtoCNF_X0)),converse(X1))))]]) ).
cnf(refute_0_526,plain,
join(converse(complement(skolemFOFtoCNF_X0)),converse(X1)) = converse(join(complement(skolemFOFtoCNF_X0),X1)),
inference(resolve,[$cnf( $equal(converse(join(complement(skolemFOFtoCNF_X0),X1)),join(converse(complement(skolemFOFtoCNF_X0)),converse(X1))) )],[refute_0_524,refute_0_525]) ).
cnf(refute_0_527,plain,
( join(converse(complement(skolemFOFtoCNF_X0)),converse(X1)) != converse(join(complement(skolemFOFtoCNF_X0),X1))
| join(skolemFOFtoCNF_X1,join(converse(complement(skolemFOFtoCNF_X0)),converse(X1))) != join(converse(complement(skolemFOFtoCNF_X0)),converse(X1))
| join(skolemFOFtoCNF_X1,converse(join(complement(skolemFOFtoCNF_X0),X1))) = join(converse(complement(skolemFOFtoCNF_X0)),converse(X1)) ),
introduced(tautology,[equality,[$cnf( $equal(join(skolemFOFtoCNF_X1,join(converse(complement(skolemFOFtoCNF_X0)),converse(X1))),join(converse(complement(skolemFOFtoCNF_X0)),converse(X1))) ),[0,1],$fot(converse(join(complement(skolemFOFtoCNF_X0),X1)))]]) ).
cnf(refute_0_528,plain,
( join(skolemFOFtoCNF_X1,join(converse(complement(skolemFOFtoCNF_X0)),converse(X1))) != join(converse(complement(skolemFOFtoCNF_X0)),converse(X1))
| join(skolemFOFtoCNF_X1,converse(join(complement(skolemFOFtoCNF_X0),X1))) = join(converse(complement(skolemFOFtoCNF_X0)),converse(X1)) ),
inference(resolve,[$cnf( $equal(join(converse(complement(skolemFOFtoCNF_X0)),converse(X1)),converse(join(complement(skolemFOFtoCNF_X0),X1))) )],[refute_0_526,refute_0_527]) ).
cnf(refute_0_529,plain,
join(skolemFOFtoCNF_X1,converse(join(complement(skolemFOFtoCNF_X0),X1))) = join(converse(complement(skolemFOFtoCNF_X0)),converse(X1)),
inference(resolve,[$cnf( $equal(join(skolemFOFtoCNF_X1,join(converse(complement(skolemFOFtoCNF_X0)),converse(X1))),join(converse(complement(skolemFOFtoCNF_X0)),converse(X1))) )],[refute_0_523,refute_0_528]) ).
cnf(refute_0_530,plain,
( join(converse(complement(skolemFOFtoCNF_X0)),converse(X1)) != converse(join(complement(skolemFOFtoCNF_X0),X1))
| join(skolemFOFtoCNF_X1,converse(join(complement(skolemFOFtoCNF_X0),X1))) != join(converse(complement(skolemFOFtoCNF_X0)),converse(X1))
| join(skolemFOFtoCNF_X1,converse(join(complement(skolemFOFtoCNF_X0),X1))) = converse(join(complement(skolemFOFtoCNF_X0),X1)) ),
introduced(tautology,[equality,[$cnf( $equal(join(skolemFOFtoCNF_X1,converse(join(complement(skolemFOFtoCNF_X0),X1))),join(converse(complement(skolemFOFtoCNF_X0)),converse(X1))) ),[1],$fot(converse(join(complement(skolemFOFtoCNF_X0),X1)))]]) ).
cnf(refute_0_531,plain,
( join(skolemFOFtoCNF_X1,converse(join(complement(skolemFOFtoCNF_X0),X1))) != join(converse(complement(skolemFOFtoCNF_X0)),converse(X1))
| join(skolemFOFtoCNF_X1,converse(join(complement(skolemFOFtoCNF_X0),X1))) = converse(join(complement(skolemFOFtoCNF_X0),X1)) ),
inference(resolve,[$cnf( $equal(join(converse(complement(skolemFOFtoCNF_X0)),converse(X1)),converse(join(complement(skolemFOFtoCNF_X0),X1))) )],[refute_0_526,refute_0_530]) ).
cnf(refute_0_532,plain,
join(skolemFOFtoCNF_X1,converse(join(complement(skolemFOFtoCNF_X0),X1))) = converse(join(complement(skolemFOFtoCNF_X0),X1)),
inference(resolve,[$cnf( $equal(join(skolemFOFtoCNF_X1,converse(join(complement(skolemFOFtoCNF_X0),X1))),join(converse(complement(skolemFOFtoCNF_X0)),converse(X1))) )],[refute_0_529,refute_0_531]) ).
cnf(refute_0_533,plain,
join(skolemFOFtoCNF_X1,converse(join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))))) = converse(join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0)))))))),
inference(subst,[],[refute_0_532:[bind(X1,$fot(meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))))]]) ).
cnf(refute_0_534,plain,
X_41 = join(meet(X_41,X_42),complement(join(complement(X_41),X_42))),
inference(subst,[],[refute_0_66:[bind(X0,$fot(X_41)),bind(X1,$fot(X_42))]]) ).
cnf(refute_0_535,plain,
meet(X_42,X_41) = meet(X_41,X_42),
inference(subst,[],[refute_0_112:[bind(X_21,$fot(X_42)),bind(X_22,$fot(X_41))]]) ).
cnf(refute_0_536,plain,
( meet(X_42,X_41) != meet(X_41,X_42)
| meet(X_41,X_42) = meet(X_42,X_41) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(meet(X_42,X_41))),bind(Y,$fot(meet(X_41,X_42)))]]) ).
cnf(refute_0_537,plain,
meet(X_41,X_42) = meet(X_42,X_41),
inference(resolve,[$cnf( $equal(meet(X_42,X_41),meet(X_41,X_42)) )],[refute_0_535,refute_0_536]) ).
cnf(refute_0_538,plain,
( X_41 != join(meet(X_41,X_42),complement(join(complement(X_41),X_42)))
| meet(X_41,X_42) != meet(X_42,X_41)
| X_41 = join(meet(X_42,X_41),complement(join(complement(X_41),X_42))) ),
introduced(tautology,[equality,[$cnf( $equal(X_41,join(meet(X_41,X_42),complement(join(complement(X_41),X_42)))) ),[1,0],$fot(meet(X_42,X_41))]]) ).
cnf(refute_0_539,plain,
( X_41 != join(meet(X_41,X_42),complement(join(complement(X_41),X_42)))
| X_41 = join(meet(X_42,X_41),complement(join(complement(X_41),X_42))) ),
inference(resolve,[$cnf( $equal(meet(X_41,X_42),meet(X_42,X_41)) )],[refute_0_537,refute_0_538]) ).
cnf(refute_0_540,plain,
X_41 = join(meet(X_42,X_41),complement(join(complement(X_41),X_42))),
inference(resolve,[$cnf( $equal(X_41,join(meet(X_41,X_42),complement(join(complement(X_41),X_42)))) )],[refute_0_534,refute_0_539]) ).
cnf(refute_0_541,plain,
complement(join(complement(X_41),X_42)) = meet(X_41,complement(X_42)),
inference(subst,[],[refute_0_454:[bind(X0,$fot(X_41)),bind(X_25,$fot(X_42))]]) ).
cnf(refute_0_542,plain,
join(meet(X_42,X_41),complement(join(complement(X_41),X_42))) = join(meet(X_42,X_41),complement(join(complement(X_41),X_42))),
introduced(tautology,[refl,[$fot(join(meet(X_42,X_41),complement(join(complement(X_41),X_42))))]]) ).
cnf(refute_0_543,plain,
( complement(join(complement(X_41),X_42)) != meet(X_41,complement(X_42))
| join(meet(X_42,X_41),complement(join(complement(X_41),X_42))) != join(meet(X_42,X_41),complement(join(complement(X_41),X_42)))
| join(meet(X_42,X_41),complement(join(complement(X_41),X_42))) = join(meet(X_42,X_41),meet(X_41,complement(X_42))) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_42,X_41),complement(join(complement(X_41),X_42))),join(meet(X_42,X_41),complement(join(complement(X_41),X_42)))) ),[1,1],$fot(meet(X_41,complement(X_42)))]]) ).
cnf(refute_0_544,plain,
( complement(join(complement(X_41),X_42)) != meet(X_41,complement(X_42))
| join(meet(X_42,X_41),complement(join(complement(X_41),X_42))) = join(meet(X_42,X_41),meet(X_41,complement(X_42))) ),
inference(resolve,[$cnf( $equal(join(meet(X_42,X_41),complement(join(complement(X_41),X_42))),join(meet(X_42,X_41),complement(join(complement(X_41),X_42)))) )],[refute_0_542,refute_0_543]) ).
cnf(refute_0_545,plain,
join(meet(X_42,X_41),complement(join(complement(X_41),X_42))) = join(meet(X_42,X_41),meet(X_41,complement(X_42))),
inference(resolve,[$cnf( $equal(complement(join(complement(X_41),X_42)),meet(X_41,complement(X_42))) )],[refute_0_541,refute_0_544]) ).
cnf(refute_0_546,plain,
( X_41 != join(meet(X_42,X_41),complement(join(complement(X_41),X_42)))
| join(meet(X_42,X_41),complement(join(complement(X_41),X_42))) != join(meet(X_42,X_41),meet(X_41,complement(X_42)))
| X_41 = join(meet(X_42,X_41),meet(X_41,complement(X_42))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_41,join(meet(X_42,X_41),meet(X_41,complement(X_42)))) ),[0],$fot(join(meet(X_42,X_41),complement(join(complement(X_41),X_42))))]]) ).
cnf(refute_0_547,plain,
( X_41 != join(meet(X_42,X_41),complement(join(complement(X_41),X_42)))
| X_41 = join(meet(X_42,X_41),meet(X_41,complement(X_42))) ),
inference(resolve,[$cnf( $equal(join(meet(X_42,X_41),complement(join(complement(X_41),X_42))),join(meet(X_42,X_41),meet(X_41,complement(X_42)))) )],[refute_0_545,refute_0_546]) ).
cnf(refute_0_548,plain,
X_41 = join(meet(X_42,X_41),meet(X_41,complement(X_42))),
inference(resolve,[$cnf( $equal(X_41,join(meet(X_42,X_41),complement(join(complement(X_41),X_42)))) )],[refute_0_540,refute_0_547]) ).
cnf(refute_0_549,plain,
converse(complement(converse(complement(X_80)))) = join(meet(X_80,converse(complement(converse(complement(X_80))))),meet(converse(complement(converse(complement(X_80)))),complement(X_80))),
inference(subst,[],[refute_0_548:[bind(X_41,$fot(converse(complement(converse(complement(X_80)))))),bind(X_42,$fot(X_80))]]) ).
cnf(refute_0_550,plain,
X_41 = join(meet(X_41,converse(complement(converse(complement(X_41))))),complement(join(complement(X_41),converse(complement(converse(complement(X_41))))))),
inference(subst,[],[refute_0_66:[bind(X0,$fot(X_41)),bind(X1,$fot(converse(complement(converse(complement(X_41))))))]]) ).
cnf(refute_0_551,plain,
converse(join(converse(X0),X_5)) = join(converse(converse(X0)),converse(X_5)),
inference(subst,[],[refute_0_471:[bind(X0,$fot(converse(X0))),bind(X1,$fot(X_5))]]) ).
cnf(refute_0_552,plain,
( converse(converse(X0)) != X0
| converse(join(converse(X0),X_5)) != join(converse(converse(X0)),converse(X_5))
| converse(join(converse(X0),X_5)) = join(X0,converse(X_5)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(X0),X_5)),join(converse(converse(X0)),converse(X_5))) ),[1,0],$fot(X0)]]) ).
cnf(refute_0_553,plain,
( converse(join(converse(X0),X_5)) != join(converse(converse(X0)),converse(X_5))
| converse(join(converse(X0),X_5)) = join(X0,converse(X_5)) ),
inference(resolve,[$cnf( $equal(converse(converse(X0)),X0) )],[refute_0_161,refute_0_552]) ).
cnf(refute_0_554,plain,
converse(join(converse(X0),X_5)) = join(X0,converse(X_5)),
inference(resolve,[$cnf( $equal(converse(join(converse(X0),X_5)),join(converse(converse(X0)),converse(X_5))) )],[refute_0_551,refute_0_553]) ).
cnf(refute_0_555,plain,
converse(join(converse(X_12),complement(converse(X_12)))) = join(X_12,converse(complement(converse(X_12)))),
inference(subst,[],[refute_0_554:[bind(X0,$fot(X_12)),bind(X_5,$fot(complement(converse(X_12))))]]) ).
cnf(refute_0_556,plain,
top = join(converse(X_12),complement(converse(X_12))),
inference(subst,[],[refute_0_14:[bind(X0,$fot(converse(X_12)))]]) ).
cnf(refute_0_557,plain,
( top != join(converse(X_12),complement(converse(X_12)))
| join(converse(X_12),complement(converse(X_12))) = top ),
inference(subst,[],[refute_0_8:[bind(X,$fot(top)),bind(Y,$fot(join(converse(X_12),complement(converse(X_12)))))]]) ).
cnf(refute_0_558,plain,
join(converse(X_12),complement(converse(X_12))) = top,
inference(resolve,[$cnf( $equal(top,join(converse(X_12),complement(converse(X_12)))) )],[refute_0_556,refute_0_557]) ).
cnf(refute_0_559,plain,
( converse(join(converse(X_12),complement(converse(X_12)))) != join(X_12,converse(complement(converse(X_12))))
| join(converse(X_12),complement(converse(X_12))) != top
| converse(top) = join(X_12,converse(complement(converse(X_12)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(X_12),complement(converse(X_12)))),join(X_12,converse(complement(converse(X_12))))) ),[0,0],$fot(top)]]) ).
cnf(refute_0_560,plain,
( converse(join(converse(X_12),complement(converse(X_12)))) != join(X_12,converse(complement(converse(X_12))))
| converse(top) = join(X_12,converse(complement(converse(X_12)))) ),
inference(resolve,[$cnf( $equal(join(converse(X_12),complement(converse(X_12))),top) )],[refute_0_558,refute_0_559]) ).
cnf(refute_0_561,plain,
converse(top) = join(X_12,converse(complement(converse(X_12)))),
inference(resolve,[$cnf( $equal(converse(join(converse(X_12),complement(converse(X_12)))),join(X_12,converse(complement(converse(X_12))))) )],[refute_0_555,refute_0_560]) ).
cnf(refute_0_562,plain,
converse(top) = join(complement(X_41),converse(complement(converse(complement(X_41))))),
inference(subst,[],[refute_0_561:[bind(X_12,$fot(complement(X_41)))]]) ).
cnf(refute_0_563,plain,
( converse(top) != join(complement(X_41),converse(complement(converse(complement(X_41)))))
| join(complement(X_41),converse(complement(converse(complement(X_41))))) = converse(top) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(converse(top))),bind(Y,$fot(join(complement(X_41),converse(complement(converse(complement(X_41)))))))]]) ).
cnf(refute_0_564,plain,
join(complement(X_41),converse(complement(converse(complement(X_41))))) = converse(top),
inference(resolve,[$cnf( $equal(converse(top),join(complement(X_41),converse(complement(converse(complement(X_41)))))) )],[refute_0_562,refute_0_563]) ).
cnf(refute_0_565,plain,
( X_41 != join(meet(X_41,converse(complement(converse(complement(X_41))))),complement(join(complement(X_41),converse(complement(converse(complement(X_41)))))))
| join(complement(X_41),converse(complement(converse(complement(X_41))))) != converse(top)
| X_41 = join(meet(X_41,converse(complement(converse(complement(X_41))))),complement(converse(top))) ),
introduced(tautology,[equality,[$cnf( $equal(X_41,join(meet(X_41,converse(complement(converse(complement(X_41))))),complement(join(complement(X_41),converse(complement(converse(complement(X_41)))))))) ),[1,1,0],$fot(converse(top))]]) ).
cnf(refute_0_566,plain,
( X_41 != join(meet(X_41,converse(complement(converse(complement(X_41))))),complement(join(complement(X_41),converse(complement(converse(complement(X_41)))))))
| X_41 = join(meet(X_41,converse(complement(converse(complement(X_41))))),complement(converse(top))) ),
inference(resolve,[$cnf( $equal(join(complement(X_41),converse(complement(converse(complement(X_41))))),converse(top)) )],[refute_0_564,refute_0_565]) ).
cnf(refute_0_567,plain,
X_41 = join(meet(X_41,converse(complement(converse(complement(X_41))))),complement(converse(top))),
inference(resolve,[$cnf( $equal(X_41,join(meet(X_41,converse(complement(converse(complement(X_41))))),complement(join(complement(X_41),converse(complement(converse(complement(X_41)))))))) )],[refute_0_550,refute_0_566]) ).
cnf(refute_0_568,plain,
join(meet(X_41,converse(complement(converse(complement(X_41))))),complement(converse(top))) = join(complement(converse(top)),meet(X_41,converse(complement(converse(complement(X_41)))))),
inference(subst,[],[refute_0_49:[bind(X0,$fot(complement(converse(top)))),bind(X1,$fot(meet(X_41,converse(complement(converse(complement(X_41)))))))]]) ).
cnf(refute_0_569,plain,
( X_41 != join(meet(X_41,converse(complement(converse(complement(X_41))))),complement(converse(top)))
| join(meet(X_41,converse(complement(converse(complement(X_41))))),complement(converse(top))) != join(complement(converse(top)),meet(X_41,converse(complement(converse(complement(X_41))))))
| X_41 = join(complement(converse(top)),meet(X_41,converse(complement(converse(complement(X_41)))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_41,join(complement(converse(top)),meet(X_41,converse(complement(converse(complement(X_41))))))) ),[0],$fot(join(meet(X_41,converse(complement(converse(complement(X_41))))),complement(converse(top))))]]) ).
cnf(refute_0_570,plain,
( X_41 != join(meet(X_41,converse(complement(converse(complement(X_41))))),complement(converse(top)))
| X_41 = join(complement(converse(top)),meet(X_41,converse(complement(converse(complement(X_41)))))) ),
inference(resolve,[$cnf( $equal(join(meet(X_41,converse(complement(converse(complement(X_41))))),complement(converse(top))),join(complement(converse(top)),meet(X_41,converse(complement(converse(complement(X_41))))))) )],[refute_0_568,refute_0_569]) ).
cnf(refute_0_571,plain,
X_41 = join(complement(converse(top)),meet(X_41,converse(complement(converse(complement(X_41)))))),
inference(resolve,[$cnf( $equal(X_41,join(meet(X_41,converse(complement(converse(complement(X_41))))),complement(converse(top)))) )],[refute_0_567,refute_0_570]) ).
cnf(refute_0_572,plain,
( complement(complement(X1)) != X1
| meet(X1,X1) != complement(complement(X1))
| meet(X1,X1) = X1 ),
introduced(tautology,[equality,[$cnf( $equal(meet(X1,X1),complement(complement(X1))) ),[1],$fot(X1)]]) ).
cnf(refute_0_573,plain,
( meet(X1,X1) != complement(complement(X1))
| meet(X1,X1) = X1 ),
inference(resolve,[$cnf( $equal(complement(complement(X1)),X1) )],[refute_0_375,refute_0_572]) ).
cnf(refute_0_574,plain,
meet(X1,X1) = X1,
inference(resolve,[$cnf( $equal(meet(X1,X1),complement(complement(X1))) )],[refute_0_287,refute_0_573]) ).
cnf(refute_0_575,plain,
meet(X_41,X_41) = X_41,
inference(subst,[],[refute_0_574:[bind(X1,$fot(X_41))]]) ).
cnf(refute_0_576,plain,
meet(X_41,complement(complement(X_41))) = meet(X_41,complement(complement(X_41))),
introduced(tautology,[refl,[$fot(meet(X_41,complement(complement(X_41))))]]) ).
cnf(refute_0_577,plain,
( complement(complement(X_41)) != X_41
| meet(X_41,complement(complement(X_41))) != meet(X_41,complement(complement(X_41)))
| meet(X_41,complement(complement(X_41))) = meet(X_41,X_41) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_41,complement(complement(X_41))),meet(X_41,complement(complement(X_41)))) ),[1,1],$fot(X_41)]]) ).
cnf(refute_0_578,plain,
( complement(complement(X_41)) != X_41
| meet(X_41,complement(complement(X_41))) = meet(X_41,X_41) ),
inference(resolve,[$cnf( $equal(meet(X_41,complement(complement(X_41))),meet(X_41,complement(complement(X_41)))) )],[refute_0_576,refute_0_577]) ).
cnf(refute_0_579,plain,
meet(X_41,complement(complement(X_41))) = meet(X_41,X_41),
inference(resolve,[$cnf( $equal(complement(complement(X_41)),X_41) )],[refute_0_374,refute_0_578]) ).
cnf(refute_0_580,plain,
( meet(X_41,X_41) != X_41
| meet(X_41,complement(complement(X_41))) != meet(X_41,X_41)
| meet(X_41,complement(complement(X_41))) = X_41 ),
inference(subst,[],[refute_0_28:[bind(X,$fot(meet(X_41,complement(complement(X_41))))),bind(Y,$fot(meet(X_41,X_41))),bind(Z,$fot(X_41))]]) ).
cnf(refute_0_581,plain,
( meet(X_41,X_41) != X_41
| meet(X_41,complement(complement(X_41))) = X_41 ),
inference(resolve,[$cnf( $equal(meet(X_41,complement(complement(X_41))),meet(X_41,X_41)) )],[refute_0_579,refute_0_580]) ).
cnf(refute_0_582,plain,
meet(X_41,complement(complement(X_41))) = X_41,
inference(resolve,[$cnf( $equal(meet(X_41,X_41),X_41) )],[refute_0_575,refute_0_581]) ).
cnf(refute_0_583,plain,
join(zero,meet(X_41,complement(complement(X_41)))) = join(zero,meet(X_41,complement(complement(X_41)))),
introduced(tautology,[refl,[$fot(join(zero,meet(X_41,complement(complement(X_41)))))]]) ).
cnf(refute_0_584,plain,
( join(zero,meet(X_41,complement(complement(X_41)))) != join(zero,meet(X_41,complement(complement(X_41))))
| meet(X_41,complement(complement(X_41))) != X_41
| join(zero,meet(X_41,complement(complement(X_41)))) = join(zero,X_41) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,meet(X_41,complement(complement(X_41)))),join(zero,meet(X_41,complement(complement(X_41))))) ),[1,1],$fot(X_41)]]) ).
cnf(refute_0_585,plain,
( meet(X_41,complement(complement(X_41))) != X_41
| join(zero,meet(X_41,complement(complement(X_41)))) = join(zero,X_41) ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_41,complement(complement(X_41)))),join(zero,meet(X_41,complement(complement(X_41))))) )],[refute_0_583,refute_0_584]) ).
cnf(refute_0_586,plain,
join(zero,meet(X_41,complement(complement(X_41)))) = join(zero,X_41),
inference(resolve,[$cnf( $equal(meet(X_41,complement(complement(X_41))),X_41) )],[refute_0_582,refute_0_585]) ).
cnf(refute_0_587,plain,
( X_41 != join(zero,meet(X_41,complement(complement(X_41))))
| join(zero,meet(X_41,complement(complement(X_41)))) != join(zero,X_41)
| X_41 = join(zero,X_41) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_41,join(zero,X_41)) ),[0],$fot(join(zero,meet(X_41,complement(complement(X_41)))))]]) ).
cnf(refute_0_588,plain,
( X_41 != join(zero,meet(X_41,complement(complement(X_41))))
| X_41 = join(zero,X_41) ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_41,complement(complement(X_41)))),join(zero,X_41)) )],[refute_0_586,refute_0_587]) ).
cnf(refute_0_589,plain,
X_41 = join(zero,X_41),
inference(resolve,[$cnf( $equal(X_41,join(zero,meet(X_41,complement(complement(X_41))))) )],[refute_0_137,refute_0_588]) ).
cnf(refute_0_590,plain,
( X_41 != join(zero,X_41)
| join(zero,X_41) = X_41 ),
inference(subst,[],[refute_0_8:[bind(X,$fot(X_41)),bind(Y,$fot(join(zero,X_41)))]]) ).
cnf(refute_0_591,plain,
join(zero,X_41) = X_41,
inference(resolve,[$cnf( $equal(X_41,join(zero,X_41)) )],[refute_0_589,refute_0_590]) ).
cnf(refute_0_592,plain,
join(zero,meet(X_41,converse(complement(converse(complement(X_41)))))) = meet(X_41,converse(complement(converse(complement(X_41))))),
inference(subst,[],[refute_0_591:[bind(X_41,$fot(meet(X_41,converse(complement(converse(complement(X_41)))))))]]) ).
cnf(refute_0_593,plain,
converse(join(join(converse(top),complement(converse(complement(converse(zero))))),complement(converse(top)))) = converse(join(complement(converse(top)),join(converse(top),complement(converse(complement(converse(zero))))))),
inference(subst,[],[refute_0_481:[bind(X0,$fot(join(converse(top),complement(converse(complement(converse(zero))))))),bind(X1,$fot(complement(converse(top))))]]) ).
cnf(refute_0_594,plain,
top = join(complement(converse(top)),join(complement(converse(complement(converse(zero)))),meet(converse(top),converse(complement(converse(zero)))))),
inference(subst,[],[refute_0_80:[bind(X_21,$fot(converse(top))),bind(X_22,$fot(converse(complement(converse(zero)))))]]) ).
cnf(refute_0_595,plain,
converse(top) = join(meet(converse(top),meet(top,converse(complement(converse(zero))))),complement(join(complement(converse(top)),meet(top,converse(complement(converse(zero))))))),
inference(subst,[],[refute_0_66:[bind(X0,$fot(converse(top))),bind(X1,$fot(meet(top,converse(complement(converse(zero))))))]]) ).
cnf(refute_0_596,plain,
top = join(meet(top,X_42),complement(join(complement(top),X_42))),
inference(subst,[],[refute_0_66:[bind(X0,$fot(top)),bind(X1,$fot(X_42))]]) ).
cnf(refute_0_597,plain,
( complement(top) != zero
| top != join(meet(top,X_42),complement(join(complement(top),X_42)))
| top = join(meet(top,X_42),complement(join(zero,X_42))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(meet(top,X_42),complement(join(complement(top),X_42)))) ),[1,1,0,0],$fot(zero)]]) ).
cnf(refute_0_598,plain,
( top != join(meet(top,X_42),complement(join(complement(top),X_42)))
| top = join(meet(top,X_42),complement(join(zero,X_42))) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_36,refute_0_597]) ).
cnf(refute_0_599,plain,
top = join(meet(top,X_42),complement(join(zero,X_42))),
inference(resolve,[$cnf( $equal(top,join(meet(top,X_42),complement(join(complement(top),X_42)))) )],[refute_0_596,refute_0_598]) ).
cnf(refute_0_600,plain,
top = join(meet(top,converse(complement(converse(zero)))),complement(join(zero,converse(complement(converse(zero)))))),
inference(subst,[],[refute_0_599:[bind(X_42,$fot(converse(complement(converse(zero)))))]]) ).
cnf(refute_0_601,plain,
converse(top) = join(zero,converse(complement(converse(zero)))),
inference(subst,[],[refute_0_561:[bind(X_12,$fot(zero))]]) ).
cnf(refute_0_602,plain,
( converse(top) != join(zero,converse(complement(converse(zero))))
| join(zero,converse(complement(converse(zero)))) = converse(top) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(converse(top))),bind(Y,$fot(join(zero,converse(complement(converse(zero))))))]]) ).
cnf(refute_0_603,plain,
join(zero,converse(complement(converse(zero)))) = converse(top),
inference(resolve,[$cnf( $equal(converse(top),join(zero,converse(complement(converse(zero))))) )],[refute_0_601,refute_0_602]) ).
cnf(refute_0_604,plain,
( join(zero,converse(complement(converse(zero)))) != converse(top)
| top != join(meet(top,converse(complement(converse(zero)))),complement(join(zero,converse(complement(converse(zero))))))
| top = join(meet(top,converse(complement(converse(zero)))),complement(converse(top))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(meet(top,converse(complement(converse(zero)))),complement(join(zero,converse(complement(converse(zero))))))) ),[1,1,0],$fot(converse(top))]]) ).
cnf(refute_0_605,plain,
( top != join(meet(top,converse(complement(converse(zero)))),complement(join(zero,converse(complement(converse(zero))))))
| top = join(meet(top,converse(complement(converse(zero)))),complement(converse(top))) ),
inference(resolve,[$cnf( $equal(join(zero,converse(complement(converse(zero)))),converse(top)) )],[refute_0_603,refute_0_604]) ).
cnf(refute_0_606,plain,
top = join(meet(top,converse(complement(converse(zero)))),complement(converse(top))),
inference(resolve,[$cnf( $equal(top,join(meet(top,converse(complement(converse(zero)))),complement(join(zero,converse(complement(converse(zero))))))) )],[refute_0_600,refute_0_605]) ).
cnf(refute_0_607,plain,
join(meet(top,converse(complement(converse(zero)))),complement(converse(top))) = join(complement(converse(top)),meet(top,converse(complement(converse(zero))))),
inference(subst,[],[refute_0_49:[bind(X0,$fot(complement(converse(top)))),bind(X1,$fot(meet(top,converse(complement(converse(zero))))))]]) ).
cnf(refute_0_608,plain,
( join(meet(top,converse(complement(converse(zero)))),complement(converse(top))) != join(complement(converse(top)),meet(top,converse(complement(converse(zero)))))
| top != join(meet(top,converse(complement(converse(zero)))),complement(converse(top)))
| top = join(complement(converse(top)),meet(top,converse(complement(converse(zero))))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(meet(top,converse(complement(converse(zero)))),complement(converse(top)))) ),[1],$fot(join(complement(converse(top)),meet(top,converse(complement(converse(zero))))))]]) ).
cnf(refute_0_609,plain,
( top != join(meet(top,converse(complement(converse(zero)))),complement(converse(top)))
| top = join(complement(converse(top)),meet(top,converse(complement(converse(zero))))) ),
inference(resolve,[$cnf( $equal(join(meet(top,converse(complement(converse(zero)))),complement(converse(top))),join(complement(converse(top)),meet(top,converse(complement(converse(zero)))))) )],[refute_0_607,refute_0_608]) ).
cnf(refute_0_610,plain,
top = join(complement(converse(top)),meet(top,converse(complement(converse(zero))))),
inference(resolve,[$cnf( $equal(top,join(meet(top,converse(complement(converse(zero)))),complement(converse(top)))) )],[refute_0_606,refute_0_609]) ).
cnf(refute_0_611,plain,
( top != join(complement(converse(top)),meet(top,converse(complement(converse(zero)))))
| join(complement(converse(top)),meet(top,converse(complement(converse(zero))))) = top ),
inference(subst,[],[refute_0_8:[bind(X,$fot(top)),bind(Y,$fot(join(complement(converse(top)),meet(top,converse(complement(converse(zero)))))))]]) ).
cnf(refute_0_612,plain,
join(complement(converse(top)),meet(top,converse(complement(converse(zero))))) = top,
inference(resolve,[$cnf( $equal(top,join(complement(converse(top)),meet(top,converse(complement(converse(zero)))))) )],[refute_0_610,refute_0_611]) ).
cnf(refute_0_613,plain,
( converse(top) != join(meet(converse(top),meet(top,converse(complement(converse(zero))))),complement(join(complement(converse(top)),meet(top,converse(complement(converse(zero)))))))
| join(complement(converse(top)),meet(top,converse(complement(converse(zero))))) != top
| converse(top) = join(meet(converse(top),meet(top,converse(complement(converse(zero))))),complement(top)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(top),join(meet(converse(top),meet(top,converse(complement(converse(zero))))),complement(join(complement(converse(top)),meet(top,converse(complement(converse(zero)))))))) ),[1,1,0],$fot(top)]]) ).
cnf(refute_0_614,plain,
( converse(top) != join(meet(converse(top),meet(top,converse(complement(converse(zero))))),complement(join(complement(converse(top)),meet(top,converse(complement(converse(zero)))))))
| converse(top) = join(meet(converse(top),meet(top,converse(complement(converse(zero))))),complement(top)) ),
inference(resolve,[$cnf( $equal(join(complement(converse(top)),meet(top,converse(complement(converse(zero))))),top) )],[refute_0_612,refute_0_613]) ).
cnf(refute_0_615,plain,
converse(top) = join(meet(converse(top),meet(top,converse(complement(converse(zero))))),complement(top)),
inference(resolve,[$cnf( $equal(converse(top),join(meet(converse(top),meet(top,converse(complement(converse(zero))))),complement(join(complement(converse(top)),meet(top,converse(complement(converse(zero)))))))) )],[refute_0_595,refute_0_614]) ).
cnf(refute_0_616,plain,
join(complement(top),meet(converse(top),meet(top,converse(complement(converse(zero)))))) = join(complement(top),meet(converse(top),meet(top,converse(complement(converse(zero)))))),
introduced(tautology,[refl,[$fot(join(complement(top),meet(converse(top),meet(top,converse(complement(converse(zero)))))))]]) ).
cnf(refute_0_617,plain,
( complement(top) != zero
| join(complement(top),meet(converse(top),meet(top,converse(complement(converse(zero)))))) != join(complement(top),meet(converse(top),meet(top,converse(complement(converse(zero))))))
| join(complement(top),meet(converse(top),meet(top,converse(complement(converse(zero)))))) = join(zero,meet(converse(top),meet(top,converse(complement(converse(zero)))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(converse(top),meet(top,converse(complement(converse(zero)))))),join(complement(top),meet(converse(top),meet(top,converse(complement(converse(zero))))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_618,plain,
( complement(top) != zero
| join(complement(top),meet(converse(top),meet(top,converse(complement(converse(zero)))))) = join(zero,meet(converse(top),meet(top,converse(complement(converse(zero)))))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(converse(top),meet(top,converse(complement(converse(zero)))))),join(complement(top),meet(converse(top),meet(top,converse(complement(converse(zero))))))) )],[refute_0_616,refute_0_617]) ).
cnf(refute_0_619,plain,
join(complement(top),meet(converse(top),meet(top,converse(complement(converse(zero)))))) = join(zero,meet(converse(top),meet(top,converse(complement(converse(zero)))))),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_36,refute_0_618]) ).
cnf(refute_0_620,plain,
join(meet(converse(top),meet(top,converse(complement(converse(zero))))),complement(top)) = join(complement(top),meet(converse(top),meet(top,converse(complement(converse(zero)))))),
inference(subst,[],[refute_0_49:[bind(X0,$fot(complement(top))),bind(X1,$fot(meet(converse(top),meet(top,converse(complement(converse(zero)))))))]]) ).
cnf(refute_0_621,plain,
( join(complement(top),meet(converse(top),meet(top,converse(complement(converse(zero)))))) != join(zero,meet(converse(top),meet(top,converse(complement(converse(zero))))))
| join(meet(converse(top),meet(top,converse(complement(converse(zero))))),complement(top)) != join(complement(top),meet(converse(top),meet(top,converse(complement(converse(zero))))))
| join(meet(converse(top),meet(top,converse(complement(converse(zero))))),complement(top)) = join(zero,meet(converse(top),meet(top,converse(complement(converse(zero)))))) ),
inference(subst,[],[refute_0_28:[bind(X,$fot(join(meet(converse(top),meet(top,converse(complement(converse(zero))))),complement(top)))),bind(Y,$fot(join(complement(top),meet(converse(top),meet(top,converse(complement(converse(zero)))))))),bind(Z,$fot(join(zero,meet(converse(top),meet(top,converse(complement(converse(zero))))))))]]) ).
cnf(refute_0_622,plain,
( join(complement(top),meet(converse(top),meet(top,converse(complement(converse(zero)))))) != join(zero,meet(converse(top),meet(top,converse(complement(converse(zero))))))
| join(meet(converse(top),meet(top,converse(complement(converse(zero))))),complement(top)) = join(zero,meet(converse(top),meet(top,converse(complement(converse(zero)))))) ),
inference(resolve,[$cnf( $equal(join(meet(converse(top),meet(top,converse(complement(converse(zero))))),complement(top)),join(complement(top),meet(converse(top),meet(top,converse(complement(converse(zero))))))) )],[refute_0_620,refute_0_621]) ).
cnf(refute_0_623,plain,
join(meet(converse(top),meet(top,converse(complement(converse(zero))))),complement(top)) = join(zero,meet(converse(top),meet(top,converse(complement(converse(zero)))))),
inference(resolve,[$cnf( $equal(join(complement(top),meet(converse(top),meet(top,converse(complement(converse(zero)))))),join(zero,meet(converse(top),meet(top,converse(complement(converse(zero))))))) )],[refute_0_619,refute_0_622]) ).
cnf(refute_0_624,plain,
( converse(top) != join(meet(converse(top),meet(top,converse(complement(converse(zero))))),complement(top))
| join(meet(converse(top),meet(top,converse(complement(converse(zero))))),complement(top)) != join(zero,meet(converse(top),meet(top,converse(complement(converse(zero))))))
| converse(top) = join(zero,meet(converse(top),meet(top,converse(complement(converse(zero)))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(top),join(zero,meet(converse(top),meet(top,converse(complement(converse(zero))))))) ),[0],$fot(join(meet(converse(top),meet(top,converse(complement(converse(zero))))),complement(top)))]]) ).
cnf(refute_0_625,plain,
( converse(top) != join(meet(converse(top),meet(top,converse(complement(converse(zero))))),complement(top))
| converse(top) = join(zero,meet(converse(top),meet(top,converse(complement(converse(zero)))))) ),
inference(resolve,[$cnf( $equal(join(meet(converse(top),meet(top,converse(complement(converse(zero))))),complement(top)),join(zero,meet(converse(top),meet(top,converse(complement(converse(zero))))))) )],[refute_0_623,refute_0_624]) ).
cnf(refute_0_626,plain,
converse(top) = join(zero,meet(converse(top),meet(top,converse(complement(converse(zero)))))),
inference(resolve,[$cnf( $equal(converse(top),join(meet(converse(top),meet(top,converse(complement(converse(zero))))),complement(top))) )],[refute_0_615,refute_0_625]) ).
cnf(refute_0_627,plain,
meet(top,converse(complement(converse(zero)))) = converse(complement(converse(zero))),
inference(subst,[],[refute_0_386:[bind(X1,$fot(converse(complement(converse(zero)))))]]) ).
cnf(refute_0_628,plain,
meet(converse(top),meet(top,converse(complement(converse(zero))))) = meet(converse(top),meet(top,converse(complement(converse(zero))))),
introduced(tautology,[refl,[$fot(meet(converse(top),meet(top,converse(complement(converse(zero))))))]]) ).
cnf(refute_0_629,plain,
( meet(converse(top),meet(top,converse(complement(converse(zero))))) != meet(converse(top),meet(top,converse(complement(converse(zero)))))
| meet(top,converse(complement(converse(zero)))) != converse(complement(converse(zero)))
| meet(converse(top),meet(top,converse(complement(converse(zero))))) = meet(converse(top),converse(complement(converse(zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(converse(top),meet(top,converse(complement(converse(zero))))),meet(converse(top),meet(top,converse(complement(converse(zero)))))) ),[1,1],$fot(converse(complement(converse(zero))))]]) ).
cnf(refute_0_630,plain,
( meet(top,converse(complement(converse(zero)))) != converse(complement(converse(zero)))
| meet(converse(top),meet(top,converse(complement(converse(zero))))) = meet(converse(top),converse(complement(converse(zero)))) ),
inference(resolve,[$cnf( $equal(meet(converse(top),meet(top,converse(complement(converse(zero))))),meet(converse(top),meet(top,converse(complement(converse(zero)))))) )],[refute_0_628,refute_0_629]) ).
cnf(refute_0_631,plain,
meet(converse(top),meet(top,converse(complement(converse(zero))))) = meet(converse(top),converse(complement(converse(zero)))),
inference(resolve,[$cnf( $equal(meet(top,converse(complement(converse(zero)))),converse(complement(converse(zero)))) )],[refute_0_627,refute_0_630]) ).
cnf(refute_0_632,plain,
join(zero,meet(converse(top),meet(top,converse(complement(converse(zero)))))) = meet(converse(top),meet(top,converse(complement(converse(zero))))),
inference(subst,[],[refute_0_591:[bind(X_41,$fot(meet(converse(top),meet(top,converse(complement(converse(zero)))))))]]) ).
cnf(refute_0_633,plain,
( join(zero,meet(converse(top),meet(top,converse(complement(converse(zero)))))) != meet(converse(top),meet(top,converse(complement(converse(zero)))))
| meet(converse(top),meet(top,converse(complement(converse(zero))))) != meet(converse(top),converse(complement(converse(zero))))
| join(zero,meet(converse(top),meet(top,converse(complement(converse(zero)))))) = meet(converse(top),converse(complement(converse(zero)))) ),
inference(subst,[],[refute_0_28:[bind(X,$fot(join(zero,meet(converse(top),meet(top,converse(complement(converse(zero)))))))),bind(Y,$fot(meet(converse(top),meet(top,converse(complement(converse(zero))))))),bind(Z,$fot(meet(converse(top),converse(complement(converse(zero))))))]]) ).
cnf(refute_0_634,plain,
( meet(converse(top),meet(top,converse(complement(converse(zero))))) != meet(converse(top),converse(complement(converse(zero))))
| join(zero,meet(converse(top),meet(top,converse(complement(converse(zero)))))) = meet(converse(top),converse(complement(converse(zero)))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(converse(top),meet(top,converse(complement(converse(zero)))))),meet(converse(top),meet(top,converse(complement(converse(zero)))))) )],[refute_0_632,refute_0_633]) ).
cnf(refute_0_635,plain,
join(zero,meet(converse(top),meet(top,converse(complement(converse(zero)))))) = meet(converse(top),converse(complement(converse(zero)))),
inference(resolve,[$cnf( $equal(meet(converse(top),meet(top,converse(complement(converse(zero))))),meet(converse(top),converse(complement(converse(zero))))) )],[refute_0_631,refute_0_634]) ).
cnf(refute_0_636,plain,
( converse(top) != join(zero,meet(converse(top),meet(top,converse(complement(converse(zero))))))
| join(zero,meet(converse(top),meet(top,converse(complement(converse(zero)))))) != meet(converse(top),converse(complement(converse(zero))))
| converse(top) = meet(converse(top),converse(complement(converse(zero)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(top),meet(converse(top),converse(complement(converse(zero))))) ),[0],$fot(join(zero,meet(converse(top),meet(top,converse(complement(converse(zero)))))))]]) ).
cnf(refute_0_637,plain,
( converse(top) != join(zero,meet(converse(top),meet(top,converse(complement(converse(zero))))))
| converse(top) = meet(converse(top),converse(complement(converse(zero)))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(converse(top),meet(top,converse(complement(converse(zero)))))),meet(converse(top),converse(complement(converse(zero))))) )],[refute_0_635,refute_0_636]) ).
cnf(refute_0_638,plain,
converse(top) = meet(converse(top),converse(complement(converse(zero)))),
inference(resolve,[$cnf( $equal(converse(top),join(zero,meet(converse(top),meet(top,converse(complement(converse(zero))))))) )],[refute_0_626,refute_0_637]) ).
cnf(refute_0_639,plain,
( converse(top) != meet(converse(top),converse(complement(converse(zero))))
| meet(converse(top),converse(complement(converse(zero)))) = converse(top) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(converse(top))),bind(Y,$fot(meet(converse(top),converse(complement(converse(zero))))))]]) ).
cnf(refute_0_640,plain,
meet(converse(top),converse(complement(converse(zero)))) = converse(top),
inference(resolve,[$cnf( $equal(converse(top),meet(converse(top),converse(complement(converse(zero))))) )],[refute_0_638,refute_0_639]) ).
cnf(refute_0_641,plain,
( meet(converse(top),converse(complement(converse(zero)))) != converse(top)
| top != join(complement(converse(top)),join(complement(converse(complement(converse(zero)))),meet(converse(top),converse(complement(converse(zero))))))
| top = join(complement(converse(top)),join(complement(converse(complement(converse(zero)))),converse(top))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(converse(top)),join(complement(converse(complement(converse(zero)))),meet(converse(top),converse(complement(converse(zero))))))) ),[1,1,1],$fot(converse(top))]]) ).
cnf(refute_0_642,plain,
( top != join(complement(converse(top)),join(complement(converse(complement(converse(zero)))),meet(converse(top),converse(complement(converse(zero))))))
| top = join(complement(converse(top)),join(complement(converse(complement(converse(zero)))),converse(top))) ),
inference(resolve,[$cnf( $equal(meet(converse(top),converse(complement(converse(zero)))),converse(top)) )],[refute_0_640,refute_0_641]) ).
cnf(refute_0_643,plain,
top = join(complement(converse(top)),join(complement(converse(complement(converse(zero)))),converse(top))),
inference(resolve,[$cnf( $equal(top,join(complement(converse(top)),join(complement(converse(complement(converse(zero)))),meet(converse(top),converse(complement(converse(zero))))))) )],[refute_0_594,refute_0_642]) ).
cnf(refute_0_644,plain,
join(complement(converse(complement(converse(zero)))),converse(top)) = join(converse(top),complement(converse(complement(converse(zero))))),
inference(subst,[],[refute_0_49:[bind(X0,$fot(converse(top))),bind(X1,$fot(complement(converse(complement(converse(zero))))))]]) ).
cnf(refute_0_645,plain,
join(complement(converse(top)),join(complement(converse(complement(converse(zero)))),converse(top))) = join(complement(converse(top)),join(complement(converse(complement(converse(zero)))),converse(top))),
introduced(tautology,[refl,[$fot(join(complement(converse(top)),join(complement(converse(complement(converse(zero)))),converse(top))))]]) ).
cnf(refute_0_646,plain,
( join(complement(converse(complement(converse(zero)))),converse(top)) != join(converse(top),complement(converse(complement(converse(zero)))))
| join(complement(converse(top)),join(complement(converse(complement(converse(zero)))),converse(top))) != join(complement(converse(top)),join(complement(converse(complement(converse(zero)))),converse(top)))
| join(complement(converse(top)),join(complement(converse(complement(converse(zero)))),converse(top))) = join(complement(converse(top)),join(converse(top),complement(converse(complement(converse(zero)))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(converse(top)),join(complement(converse(complement(converse(zero)))),converse(top))),join(complement(converse(top)),join(complement(converse(complement(converse(zero)))),converse(top)))) ),[1,1],$fot(join(converse(top),complement(converse(complement(converse(zero))))))]]) ).
cnf(refute_0_647,plain,
( join(complement(converse(complement(converse(zero)))),converse(top)) != join(converse(top),complement(converse(complement(converse(zero)))))
| join(complement(converse(top)),join(complement(converse(complement(converse(zero)))),converse(top))) = join(complement(converse(top)),join(converse(top),complement(converse(complement(converse(zero)))))) ),
inference(resolve,[$cnf( $equal(join(complement(converse(top)),join(complement(converse(complement(converse(zero)))),converse(top))),join(complement(converse(top)),join(complement(converse(complement(converse(zero)))),converse(top)))) )],[refute_0_645,refute_0_646]) ).
cnf(refute_0_648,plain,
join(complement(converse(top)),join(complement(converse(complement(converse(zero)))),converse(top))) = join(complement(converse(top)),join(converse(top),complement(converse(complement(converse(zero)))))),
inference(resolve,[$cnf( $equal(join(complement(converse(complement(converse(zero)))),converse(top)),join(converse(top),complement(converse(complement(converse(zero)))))) )],[refute_0_644,refute_0_647]) ).
cnf(refute_0_649,plain,
( join(complement(converse(top)),join(complement(converse(complement(converse(zero)))),converse(top))) != join(complement(converse(top)),join(converse(top),complement(converse(complement(converse(zero))))))
| top != join(complement(converse(top)),join(complement(converse(complement(converse(zero)))),converse(top)))
| top = join(complement(converse(top)),join(converse(top),complement(converse(complement(converse(zero)))))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(converse(top)),join(complement(converse(complement(converse(zero)))),converse(top)))) ),[1],$fot(join(complement(converse(top)),join(converse(top),complement(converse(complement(converse(zero)))))))]]) ).
cnf(refute_0_650,plain,
( top != join(complement(converse(top)),join(complement(converse(complement(converse(zero)))),converse(top)))
| top = join(complement(converse(top)),join(converse(top),complement(converse(complement(converse(zero)))))) ),
inference(resolve,[$cnf( $equal(join(complement(converse(top)),join(complement(converse(complement(converse(zero)))),converse(top))),join(complement(converse(top)),join(converse(top),complement(converse(complement(converse(zero))))))) )],[refute_0_648,refute_0_649]) ).
cnf(refute_0_651,plain,
top = join(complement(converse(top)),join(converse(top),complement(converse(complement(converse(zero)))))),
inference(resolve,[$cnf( $equal(top,join(complement(converse(top)),join(complement(converse(complement(converse(zero)))),converse(top)))) )],[refute_0_643,refute_0_650]) ).
cnf(refute_0_652,plain,
( top != join(complement(converse(top)),join(converse(top),complement(converse(complement(converse(zero))))))
| join(complement(converse(top)),join(converse(top),complement(converse(complement(converse(zero)))))) = top ),
inference(subst,[],[refute_0_8:[bind(X,$fot(top)),bind(Y,$fot(join(complement(converse(top)),join(converse(top),complement(converse(complement(converse(zero))))))))]]) ).
cnf(refute_0_653,plain,
join(complement(converse(top)),join(converse(top),complement(converse(complement(converse(zero)))))) = top,
inference(resolve,[$cnf( $equal(top,join(complement(converse(top)),join(converse(top),complement(converse(complement(converse(zero))))))) )],[refute_0_651,refute_0_652]) ).
cnf(refute_0_654,plain,
( converse(join(join(converse(top),complement(converse(complement(converse(zero))))),complement(converse(top)))) != converse(join(complement(converse(top)),join(converse(top),complement(converse(complement(converse(zero)))))))
| join(complement(converse(top)),join(converse(top),complement(converse(complement(converse(zero)))))) != top
| converse(join(join(converse(top),complement(converse(complement(converse(zero))))),complement(converse(top)))) = converse(top) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(join(converse(top),complement(converse(complement(converse(zero))))),complement(converse(top)))),converse(join(complement(converse(top)),join(converse(top),complement(converse(complement(converse(zero)))))))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_655,plain,
( converse(join(join(converse(top),complement(converse(complement(converse(zero))))),complement(converse(top)))) != converse(join(complement(converse(top)),join(converse(top),complement(converse(complement(converse(zero)))))))
| converse(join(join(converse(top),complement(converse(complement(converse(zero))))),complement(converse(top)))) = converse(top) ),
inference(resolve,[$cnf( $equal(join(complement(converse(top)),join(converse(top),complement(converse(complement(converse(zero)))))),top) )],[refute_0_653,refute_0_654]) ).
cnf(refute_0_656,plain,
converse(join(join(converse(top),complement(converse(complement(converse(zero))))),complement(converse(top)))) = converse(top),
inference(resolve,[$cnf( $equal(converse(join(join(converse(top),complement(converse(complement(converse(zero))))),complement(converse(top)))),converse(join(complement(converse(top)),join(converse(top),complement(converse(complement(converse(zero)))))))) )],[refute_0_593,refute_0_655]) ).
cnf(refute_0_657,plain,
join(top,converse(join(complement(converse(top)),complement(converse(complement(converse(zero))))))) = top,
inference(subst,[],[refute_0_417:[bind(X1,$fot(converse(join(complement(converse(top)),complement(converse(complement(converse(zero))))))))]]) ).
cnf(refute_0_658,plain,
converse(join(converse(top),join(complement(converse(top)),complement(converse(complement(converse(zero))))))) = join(top,converse(join(complement(converse(top)),complement(converse(complement(converse(zero))))))),
inference(subst,[],[refute_0_554:[bind(X0,$fot(top)),bind(X_5,$fot(join(complement(converse(top)),complement(converse(complement(converse(zero)))))))]]) ).
cnf(refute_0_659,plain,
( converse(join(converse(top),join(complement(converse(top)),complement(converse(complement(converse(zero))))))) != join(top,converse(join(complement(converse(top)),complement(converse(complement(converse(zero)))))))
| join(top,converse(join(complement(converse(top)),complement(converse(complement(converse(zero))))))) != top
| converse(join(converse(top),join(complement(converse(top)),complement(converse(complement(converse(zero))))))) = top ),
inference(subst,[],[refute_0_28:[bind(X,$fot(converse(join(converse(top),join(complement(converse(top)),complement(converse(complement(converse(zero))))))))),bind(Y,$fot(join(top,converse(join(complement(converse(top)),complement(converse(complement(converse(zero))))))))),bind(Z,$fot(top))]]) ).
cnf(refute_0_660,plain,
( join(top,converse(join(complement(converse(top)),complement(converse(complement(converse(zero))))))) != top
| converse(join(converse(top),join(complement(converse(top)),complement(converse(complement(converse(zero))))))) = top ),
inference(resolve,[$cnf( $equal(converse(join(converse(top),join(complement(converse(top)),complement(converse(complement(converse(zero))))))),join(top,converse(join(complement(converse(top)),complement(converse(complement(converse(zero)))))))) )],[refute_0_658,refute_0_659]) ).
cnf(refute_0_661,plain,
converse(join(converse(top),join(complement(converse(top)),complement(converse(complement(converse(zero))))))) = top,
inference(resolve,[$cnf( $equal(join(top,converse(join(complement(converse(top)),complement(converse(complement(converse(zero))))))),top) )],[refute_0_657,refute_0_660]) ).
cnf(refute_0_662,plain,
converse(join(join(X_27,X_28),X1)) = join(converse(join(X_27,X_28)),converse(X1)),
inference(subst,[],[refute_0_471:[bind(X0,$fot(join(X_27,X_28)))]]) ).
cnf(refute_0_663,plain,
converse(join(X_27,X_28)) = converse(join(X_28,X_27)),
inference(subst,[],[refute_0_481:[bind(X0,$fot(X_27)),bind(X1,$fot(X_28))]]) ).
cnf(refute_0_664,plain,
( converse(join(X_27,X_28)) != converse(join(X_28,X_27))
| converse(join(join(X_27,X_28),X1)) != join(converse(join(X_27,X_28)),converse(X1))
| converse(join(join(X_27,X_28),X1)) = join(converse(join(X_28,X_27)),converse(X1)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(join(X_27,X_28),X1)),join(converse(join(X_27,X_28)),converse(X1))) ),[1,0],$fot(converse(join(X_28,X_27)))]]) ).
cnf(refute_0_665,plain,
( converse(join(join(X_27,X_28),X1)) != join(converse(join(X_27,X_28)),converse(X1))
| converse(join(join(X_27,X_28),X1)) = join(converse(join(X_28,X_27)),converse(X1)) ),
inference(resolve,[$cnf( $equal(converse(join(X_27,X_28)),converse(join(X_28,X_27))) )],[refute_0_663,refute_0_664]) ).
cnf(refute_0_666,plain,
converse(join(join(X_27,X_28),X1)) = join(converse(join(X_28,X_27)),converse(X1)),
inference(resolve,[$cnf( $equal(converse(join(join(X_27,X_28),X1)),join(converse(join(X_27,X_28)),converse(X1))) )],[refute_0_662,refute_0_665]) ).
cnf(refute_0_667,plain,
join(join(X_27,X_28),X1) = join(X_27,join(X_28,X1)),
inference(subst,[],[refute_0_76:[bind(X0,$fot(X_27)),bind(X1,$fot(X_28)),bind(X2,$fot(X1))]]) ).
cnf(refute_0_668,plain,
converse(join(join(X_27,X_28),X1)) = converse(join(join(X_27,X_28),X1)),
introduced(tautology,[refl,[$fot(converse(join(join(X_27,X_28),X1)))]]) ).
cnf(refute_0_669,plain,
( converse(join(join(X_27,X_28),X1)) != converse(join(join(X_27,X_28),X1))
| join(join(X_27,X_28),X1) != join(X_27,join(X_28,X1))
| converse(join(join(X_27,X_28),X1)) = converse(join(X_27,join(X_28,X1))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(join(X_27,X_28),X1)),converse(join(join(X_27,X_28),X1))) ),[1,0],$fot(join(X_27,join(X_28,X1)))]]) ).
cnf(refute_0_670,plain,
( join(join(X_27,X_28),X1) != join(X_27,join(X_28,X1))
| converse(join(join(X_27,X_28),X1)) = converse(join(X_27,join(X_28,X1))) ),
inference(resolve,[$cnf( $equal(converse(join(join(X_27,X_28),X1)),converse(join(join(X_27,X_28),X1))) )],[refute_0_668,refute_0_669]) ).
cnf(refute_0_671,plain,
converse(join(join(X_27,X_28),X1)) = converse(join(X_27,join(X_28,X1))),
inference(resolve,[$cnf( $equal(join(join(X_27,X_28),X1),join(X_27,join(X_28,X1))) )],[refute_0_667,refute_0_670]) ).
cnf(refute_0_672,plain,
( converse(join(join(X_27,X_28),X1)) != converse(join(X_27,join(X_28,X1)))
| converse(join(join(X_27,X_28),X1)) != join(converse(join(X_28,X_27)),converse(X1))
| converse(join(X_27,join(X_28,X1))) = join(converse(join(X_28,X_27)),converse(X1)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(join(X_27,X_28),X1)),join(converse(join(X_28,X_27)),converse(X1))) ),[0],$fot(converse(join(X_27,join(X_28,X1))))]]) ).
cnf(refute_0_673,plain,
( converse(join(join(X_27,X_28),X1)) != join(converse(join(X_28,X_27)),converse(X1))
| converse(join(X_27,join(X_28,X1))) = join(converse(join(X_28,X_27)),converse(X1)) ),
inference(resolve,[$cnf( $equal(converse(join(join(X_27,X_28),X1)),converse(join(X_27,join(X_28,X1)))) )],[refute_0_671,refute_0_672]) ).
cnf(refute_0_674,plain,
join(join(X_28,X_27),X1) = join(X_28,join(X_27,X1)),
inference(subst,[],[refute_0_76:[bind(X0,$fot(X_28)),bind(X1,$fot(X_27)),bind(X2,$fot(X1))]]) ).
cnf(refute_0_675,plain,
converse(join(join(X_28,X_27),X1)) = converse(join(join(X_28,X_27),X1)),
introduced(tautology,[refl,[$fot(converse(join(join(X_28,X_27),X1)))]]) ).
cnf(refute_0_676,plain,
( converse(join(join(X_28,X_27),X1)) != converse(join(join(X_28,X_27),X1))
| join(join(X_28,X_27),X1) != join(X_28,join(X_27,X1))
| converse(join(join(X_28,X_27),X1)) = converse(join(X_28,join(X_27,X1))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(join(X_28,X_27),X1)),converse(join(join(X_28,X_27),X1))) ),[1,0],$fot(join(X_28,join(X_27,X1)))]]) ).
cnf(refute_0_677,plain,
( join(join(X_28,X_27),X1) != join(X_28,join(X_27,X1))
| converse(join(join(X_28,X_27),X1)) = converse(join(X_28,join(X_27,X1))) ),
inference(resolve,[$cnf( $equal(converse(join(join(X_28,X_27),X1)),converse(join(join(X_28,X_27),X1))) )],[refute_0_675,refute_0_676]) ).
cnf(refute_0_678,plain,
converse(join(join(X_28,X_27),X1)) = converse(join(X_28,join(X_27,X1))),
inference(resolve,[$cnf( $equal(join(join(X_28,X_27),X1),join(X_28,join(X_27,X1))) )],[refute_0_674,refute_0_677]) ).
cnf(refute_0_679,plain,
join(converse(join(X_28,X_27)),converse(X1)) = converse(join(join(X_28,X_27),X1)),
inference(subst,[],[refute_0_477:[bind(X0,$fot(join(X_28,X_27)))]]) ).
cnf(refute_0_680,plain,
( converse(join(join(X_28,X_27),X1)) != converse(join(X_28,join(X_27,X1)))
| join(converse(join(X_28,X_27)),converse(X1)) != converse(join(join(X_28,X_27),X1))
| join(converse(join(X_28,X_27)),converse(X1)) = converse(join(X_28,join(X_27,X1))) ),
inference(subst,[],[refute_0_28:[bind(X,$fot(join(converse(join(X_28,X_27)),converse(X1)))),bind(Y,$fot(converse(join(join(X_28,X_27),X1)))),bind(Z,$fot(converse(join(X_28,join(X_27,X1)))))]]) ).
cnf(refute_0_681,plain,
( converse(join(join(X_28,X_27),X1)) != converse(join(X_28,join(X_27,X1)))
| join(converse(join(X_28,X_27)),converse(X1)) = converse(join(X_28,join(X_27,X1))) ),
inference(resolve,[$cnf( $equal(join(converse(join(X_28,X_27)),converse(X1)),converse(join(join(X_28,X_27),X1))) )],[refute_0_679,refute_0_680]) ).
cnf(refute_0_682,plain,
join(converse(join(X_28,X_27)),converse(X1)) = converse(join(X_28,join(X_27,X1))),
inference(resolve,[$cnf( $equal(converse(join(join(X_28,X_27),X1)),converse(join(X_28,join(X_27,X1)))) )],[refute_0_678,refute_0_681]) ).
cnf(refute_0_683,plain,
( converse(join(X_27,join(X_28,X1))) != join(converse(join(X_28,X_27)),converse(X1))
| join(converse(join(X_28,X_27)),converse(X1)) != converse(join(X_28,join(X_27,X1)))
| converse(join(X_27,join(X_28,X1))) = converse(join(X_28,join(X_27,X1))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(join(X_27,join(X_28,X1))),converse(join(X_28,join(X_27,X1)))) ),[0],$fot(join(converse(join(X_28,X_27)),converse(X1)))]]) ).
cnf(refute_0_684,plain,
( converse(join(X_27,join(X_28,X1))) != join(converse(join(X_28,X_27)),converse(X1))
| converse(join(X_27,join(X_28,X1))) = converse(join(X_28,join(X_27,X1))) ),
inference(resolve,[$cnf( $equal(join(converse(join(X_28,X_27)),converse(X1)),converse(join(X_28,join(X_27,X1)))) )],[refute_0_682,refute_0_683]) ).
cnf(refute_0_685,plain,
( converse(join(join(X_27,X_28),X1)) != join(converse(join(X_28,X_27)),converse(X1))
| converse(join(X_27,join(X_28,X1))) = converse(join(X_28,join(X_27,X1))) ),
inference(resolve,[$cnf( $equal(converse(join(X_27,join(X_28,X1))),join(converse(join(X_28,X_27)),converse(X1))) )],[refute_0_673,refute_0_684]) ).
cnf(refute_0_686,plain,
converse(join(X_27,join(X_28,X1))) = converse(join(X_28,join(X_27,X1))),
inference(resolve,[$cnf( $equal(converse(join(join(X_27,X_28),X1)),join(converse(join(X_28,X_27)),converse(X1))) )],[refute_0_666,refute_0_685]) ).
cnf(refute_0_687,plain,
( converse(join(X_27,join(X_28,X1))) != converse(join(X_28,join(X_27,X1)))
| converse(join(X_28,join(X_27,X1))) = converse(join(X_27,join(X_28,X1))) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(converse(join(X_27,join(X_28,X1))))),bind(Y,$fot(converse(join(X_28,join(X_27,X1)))))]]) ).
cnf(refute_0_688,plain,
converse(join(X_28,join(X_27,X1))) = converse(join(X_27,join(X_28,X1))),
inference(resolve,[$cnf( $equal(converse(join(X_27,join(X_28,X1))),converse(join(X_28,join(X_27,X1)))) )],[refute_0_686,refute_0_687]) ).
cnf(refute_0_689,plain,
converse(join(complement(converse(top)),join(converse(top),complement(converse(complement(converse(zero))))))) = converse(join(converse(top),join(complement(converse(top)),complement(converse(complement(converse(zero))))))),
inference(subst,[],[refute_0_688:[bind(X1,$fot(complement(converse(complement(converse(zero)))))),bind(X_27,$fot(converse(top))),bind(X_28,$fot(complement(converse(top))))]]) ).
cnf(refute_0_690,plain,
( converse(join(complement(converse(top)),join(converse(top),complement(converse(complement(converse(zero))))))) != converse(join(converse(top),join(complement(converse(top)),complement(converse(complement(converse(zero)))))))
| converse(join(converse(top),join(complement(converse(top)),complement(converse(complement(converse(zero))))))) != top
| converse(join(complement(converse(top)),join(converse(top),complement(converse(complement(converse(zero))))))) = top ),
inference(subst,[],[refute_0_28:[bind(X,$fot(converse(join(complement(converse(top)),join(converse(top),complement(converse(complement(converse(zero))))))))),bind(Y,$fot(converse(join(converse(top),join(complement(converse(top)),complement(converse(complement(converse(zero))))))))),bind(Z,$fot(top))]]) ).
cnf(refute_0_691,plain,
( converse(join(converse(top),join(complement(converse(top)),complement(converse(complement(converse(zero))))))) != top
| converse(join(complement(converse(top)),join(converse(top),complement(converse(complement(converse(zero))))))) = top ),
inference(resolve,[$cnf( $equal(converse(join(complement(converse(top)),join(converse(top),complement(converse(complement(converse(zero))))))),converse(join(converse(top),join(complement(converse(top)),complement(converse(complement(converse(zero)))))))) )],[refute_0_689,refute_0_690]) ).
cnf(refute_0_692,plain,
converse(join(complement(converse(top)),join(converse(top),complement(converse(complement(converse(zero))))))) = top,
inference(resolve,[$cnf( $equal(converse(join(converse(top),join(complement(converse(top)),complement(converse(complement(converse(zero))))))),top) )],[refute_0_661,refute_0_691]) ).
cnf(refute_0_693,plain,
( converse(join(complement(converse(top)),join(converse(top),complement(converse(complement(converse(zero))))))) != top
| converse(join(join(converse(top),complement(converse(complement(converse(zero))))),complement(converse(top)))) != converse(join(complement(converse(top)),join(converse(top),complement(converse(complement(converse(zero)))))))
| converse(join(join(converse(top),complement(converse(complement(converse(zero))))),complement(converse(top)))) = top ),
inference(subst,[],[refute_0_28:[bind(X,$fot(converse(join(join(converse(top),complement(converse(complement(converse(zero))))),complement(converse(top)))))),bind(Y,$fot(converse(join(complement(converse(top)),join(converse(top),complement(converse(complement(converse(zero))))))))),bind(Z,$fot(top))]]) ).
cnf(refute_0_694,plain,
( converse(join(complement(converse(top)),join(converse(top),complement(converse(complement(converse(zero))))))) != top
| converse(join(join(converse(top),complement(converse(complement(converse(zero))))),complement(converse(top)))) = top ),
inference(resolve,[$cnf( $equal(converse(join(join(converse(top),complement(converse(complement(converse(zero))))),complement(converse(top)))),converse(join(complement(converse(top)),join(converse(top),complement(converse(complement(converse(zero)))))))) )],[refute_0_593,refute_0_693]) ).
cnf(refute_0_695,plain,
converse(join(join(converse(top),complement(converse(complement(converse(zero))))),complement(converse(top)))) = top,
inference(resolve,[$cnf( $equal(converse(join(complement(converse(top)),join(converse(top),complement(converse(complement(converse(zero))))))),top) )],[refute_0_692,refute_0_694]) ).
cnf(refute_0_696,plain,
( converse(join(join(converse(top),complement(converse(complement(converse(zero))))),complement(converse(top)))) != converse(top)
| converse(join(join(converse(top),complement(converse(complement(converse(zero))))),complement(converse(top)))) != top
| top = converse(top) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(join(converse(top),complement(converse(complement(converse(zero))))),complement(converse(top)))),converse(top)) ),[0],$fot(top)]]) ).
cnf(refute_0_697,plain,
( converse(join(join(converse(top),complement(converse(complement(converse(zero))))),complement(converse(top)))) != converse(top)
| top = converse(top) ),
inference(resolve,[$cnf( $equal(converse(join(join(converse(top),complement(converse(complement(converse(zero))))),complement(converse(top)))),top) )],[refute_0_695,refute_0_696]) ).
cnf(refute_0_698,plain,
top = converse(top),
inference(resolve,[$cnf( $equal(converse(join(join(converse(top),complement(converse(complement(converse(zero))))),complement(converse(top)))),converse(top)) )],[refute_0_656,refute_0_697]) ).
cnf(refute_0_699,plain,
( top != converse(top)
| converse(top) = top ),
inference(subst,[],[refute_0_8:[bind(X,$fot(top)),bind(Y,$fot(converse(top)))]]) ).
cnf(refute_0_700,plain,
converse(top) = top,
inference(resolve,[$cnf( $equal(top,converse(top)) )],[refute_0_698,refute_0_699]) ).
cnf(refute_0_701,plain,
complement(converse(top)) = complement(converse(top)),
introduced(tautology,[refl,[$fot(complement(converse(top)))]]) ).
cnf(refute_0_702,plain,
( complement(converse(top)) != complement(converse(top))
| converse(top) != top
| complement(converse(top)) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(complement(converse(top)),complement(converse(top))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_703,plain,
( converse(top) != top
| complement(converse(top)) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(converse(top)),complement(converse(top))) )],[refute_0_701,refute_0_702]) ).
cnf(refute_0_704,plain,
complement(converse(top)) = complement(top),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_0_700,refute_0_703]) ).
cnf(refute_0_705,plain,
( complement(converse(top)) != complement(top)
| complement(top) != zero
| complement(converse(top)) = zero ),
inference(subst,[],[refute_0_28:[bind(X,$fot(complement(converse(top)))),bind(Y,$fot(complement(top))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_706,plain,
( complement(top) != zero
| complement(converse(top)) = zero ),
inference(resolve,[$cnf( $equal(complement(converse(top)),complement(top)) )],[refute_0_704,refute_0_705]) ).
cnf(refute_0_707,plain,
complement(converse(top)) = zero,
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_36,refute_0_706]) ).
cnf(refute_0_708,plain,
join(complement(converse(top)),meet(X_41,converse(complement(converse(complement(X_41)))))) = join(complement(converse(top)),meet(X_41,converse(complement(converse(complement(X_41)))))),
introduced(tautology,[refl,[$fot(join(complement(converse(top)),meet(X_41,converse(complement(converse(complement(X_41)))))))]]) ).
cnf(refute_0_709,plain,
( complement(converse(top)) != zero
| join(complement(converse(top)),meet(X_41,converse(complement(converse(complement(X_41)))))) != join(complement(converse(top)),meet(X_41,converse(complement(converse(complement(X_41))))))
| join(complement(converse(top)),meet(X_41,converse(complement(converse(complement(X_41)))))) = join(zero,meet(X_41,converse(complement(converse(complement(X_41)))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(converse(top)),meet(X_41,converse(complement(converse(complement(X_41)))))),join(complement(converse(top)),meet(X_41,converse(complement(converse(complement(X_41))))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_710,plain,
( complement(converse(top)) != zero
| join(complement(converse(top)),meet(X_41,converse(complement(converse(complement(X_41)))))) = join(zero,meet(X_41,converse(complement(converse(complement(X_41)))))) ),
inference(resolve,[$cnf( $equal(join(complement(converse(top)),meet(X_41,converse(complement(converse(complement(X_41)))))),join(complement(converse(top)),meet(X_41,converse(complement(converse(complement(X_41))))))) )],[refute_0_708,refute_0_709]) ).
cnf(refute_0_711,plain,
join(complement(converse(top)),meet(X_41,converse(complement(converse(complement(X_41)))))) = join(zero,meet(X_41,converse(complement(converse(complement(X_41)))))),
inference(resolve,[$cnf( $equal(complement(converse(top)),zero) )],[refute_0_707,refute_0_710]) ).
cnf(refute_0_712,plain,
( join(complement(converse(top)),meet(X_41,converse(complement(converse(complement(X_41)))))) != join(zero,meet(X_41,converse(complement(converse(complement(X_41))))))
| join(zero,meet(X_41,converse(complement(converse(complement(X_41)))))) != meet(X_41,converse(complement(converse(complement(X_41)))))
| join(complement(converse(top)),meet(X_41,converse(complement(converse(complement(X_41)))))) = meet(X_41,converse(complement(converse(complement(X_41))))) ),
inference(subst,[],[refute_0_28:[bind(X,$fot(join(complement(converse(top)),meet(X_41,converse(complement(converse(complement(X_41)))))))),bind(Y,$fot(join(zero,meet(X_41,converse(complement(converse(complement(X_41)))))))),bind(Z,$fot(meet(X_41,converse(complement(converse(complement(X_41)))))))]]) ).
cnf(refute_0_713,plain,
( join(zero,meet(X_41,converse(complement(converse(complement(X_41)))))) != meet(X_41,converse(complement(converse(complement(X_41)))))
| join(complement(converse(top)),meet(X_41,converse(complement(converse(complement(X_41)))))) = meet(X_41,converse(complement(converse(complement(X_41))))) ),
inference(resolve,[$cnf( $equal(join(complement(converse(top)),meet(X_41,converse(complement(converse(complement(X_41)))))),join(zero,meet(X_41,converse(complement(converse(complement(X_41))))))) )],[refute_0_711,refute_0_712]) ).
cnf(refute_0_714,plain,
join(complement(converse(top)),meet(X_41,converse(complement(converse(complement(X_41)))))) = meet(X_41,converse(complement(converse(complement(X_41))))),
inference(resolve,[$cnf( $equal(join(zero,meet(X_41,converse(complement(converse(complement(X_41)))))),meet(X_41,converse(complement(converse(complement(X_41)))))) )],[refute_0_592,refute_0_713]) ).
cnf(refute_0_715,plain,
( X_41 != join(complement(converse(top)),meet(X_41,converse(complement(converse(complement(X_41))))))
| join(complement(converse(top)),meet(X_41,converse(complement(converse(complement(X_41)))))) != meet(X_41,converse(complement(converse(complement(X_41)))))
| X_41 = meet(X_41,converse(complement(converse(complement(X_41))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_41,meet(X_41,converse(complement(converse(complement(X_41)))))) ),[0],$fot(join(complement(converse(top)),meet(X_41,converse(complement(converse(complement(X_41)))))))]]) ).
cnf(refute_0_716,plain,
( X_41 != join(complement(converse(top)),meet(X_41,converse(complement(converse(complement(X_41))))))
| X_41 = meet(X_41,converse(complement(converse(complement(X_41))))) ),
inference(resolve,[$cnf( $equal(join(complement(converse(top)),meet(X_41,converse(complement(converse(complement(X_41)))))),meet(X_41,converse(complement(converse(complement(X_41)))))) )],[refute_0_714,refute_0_715]) ).
cnf(refute_0_717,plain,
X_41 = meet(X_41,converse(complement(converse(complement(X_41))))),
inference(resolve,[$cnf( $equal(X_41,join(complement(converse(top)),meet(X_41,converse(complement(converse(complement(X_41))))))) )],[refute_0_571,refute_0_716]) ).
cnf(refute_0_718,plain,
X_80 = meet(X_80,converse(complement(converse(complement(X_80))))),
inference(subst,[],[refute_0_717:[bind(X_41,$fot(X_80))]]) ).
cnf(refute_0_719,plain,
( X_80 != meet(X_80,converse(complement(converse(complement(X_80)))))
| meet(X_80,converse(complement(converse(complement(X_80))))) = X_80 ),
inference(subst,[],[refute_0_8:[bind(X,$fot(X_80)),bind(Y,$fot(meet(X_80,converse(complement(converse(complement(X_80)))))))]]) ).
cnf(refute_0_720,plain,
meet(X_80,converse(complement(converse(complement(X_80))))) = X_80,
inference(resolve,[$cnf( $equal(X_80,meet(X_80,converse(complement(converse(complement(X_80)))))) )],[refute_0_718,refute_0_719]) ).
cnf(refute_0_721,plain,
( converse(complement(converse(complement(X_80)))) != join(meet(X_80,converse(complement(converse(complement(X_80))))),meet(converse(complement(converse(complement(X_80)))),complement(X_80)))
| meet(X_80,converse(complement(converse(complement(X_80))))) != X_80
| converse(complement(converse(complement(X_80)))) = join(X_80,meet(converse(complement(converse(complement(X_80)))),complement(X_80))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(complement(converse(complement(X_80)))),join(meet(X_80,converse(complement(converse(complement(X_80))))),meet(converse(complement(converse(complement(X_80)))),complement(X_80)))) ),[1,0],$fot(X_80)]]) ).
cnf(refute_0_722,plain,
( converse(complement(converse(complement(X_80)))) != join(meet(X_80,converse(complement(converse(complement(X_80))))),meet(converse(complement(converse(complement(X_80)))),complement(X_80)))
| converse(complement(converse(complement(X_80)))) = join(X_80,meet(converse(complement(converse(complement(X_80)))),complement(X_80))) ),
inference(resolve,[$cnf( $equal(meet(X_80,converse(complement(converse(complement(X_80))))),X_80) )],[refute_0_720,refute_0_721]) ).
cnf(refute_0_723,plain,
converse(complement(converse(complement(X_80)))) = join(X_80,meet(converse(complement(converse(complement(X_80)))),complement(X_80))),
inference(resolve,[$cnf( $equal(converse(complement(converse(complement(X_80)))),join(meet(X_80,converse(complement(converse(complement(X_80))))),meet(converse(complement(converse(complement(X_80)))),complement(X_80)))) )],[refute_0_549,refute_0_722]) ).
cnf(refute_0_724,plain,
( meet(X_21,X_22) != meet(X_22,X_21)
| meet(X_22,X_21) = meet(X_21,X_22) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(meet(X_21,X_22))),bind(Y,$fot(meet(X_22,X_21)))]]) ).
cnf(refute_0_725,plain,
meet(X_22,X_21) = meet(X_21,X_22),
inference(resolve,[$cnf( $equal(meet(X_21,X_22),meet(X_22,X_21)) )],[refute_0_112,refute_0_724]) ).
cnf(refute_0_726,plain,
meet(converse(complement(converse(complement(X_80)))),complement(X_80)) = meet(complement(X_80),converse(complement(converse(complement(X_80))))),
inference(subst,[],[refute_0_725:[bind(X_21,$fot(complement(X_80))),bind(X_22,$fot(converse(complement(converse(complement(X_80))))))]]) ).
cnf(refute_0_727,plain,
join(X_80,meet(converse(complement(converse(complement(X_80)))),complement(X_80))) = join(X_80,meet(converse(complement(converse(complement(X_80)))),complement(X_80))),
introduced(tautology,[refl,[$fot(join(X_80,meet(converse(complement(converse(complement(X_80)))),complement(X_80))))]]) ).
cnf(refute_0_728,plain,
( join(X_80,meet(converse(complement(converse(complement(X_80)))),complement(X_80))) != join(X_80,meet(converse(complement(converse(complement(X_80)))),complement(X_80)))
| meet(converse(complement(converse(complement(X_80)))),complement(X_80)) != meet(complement(X_80),converse(complement(converse(complement(X_80)))))
| join(X_80,meet(converse(complement(converse(complement(X_80)))),complement(X_80))) = join(X_80,meet(complement(X_80),converse(complement(converse(complement(X_80)))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_80,meet(converse(complement(converse(complement(X_80)))),complement(X_80))),join(X_80,meet(converse(complement(converse(complement(X_80)))),complement(X_80)))) ),[1,1],$fot(meet(complement(X_80),converse(complement(converse(complement(X_80))))))]]) ).
cnf(refute_0_729,plain,
( meet(converse(complement(converse(complement(X_80)))),complement(X_80)) != meet(complement(X_80),converse(complement(converse(complement(X_80)))))
| join(X_80,meet(converse(complement(converse(complement(X_80)))),complement(X_80))) = join(X_80,meet(complement(X_80),converse(complement(converse(complement(X_80)))))) ),
inference(resolve,[$cnf( $equal(join(X_80,meet(converse(complement(converse(complement(X_80)))),complement(X_80))),join(X_80,meet(converse(complement(converse(complement(X_80)))),complement(X_80)))) )],[refute_0_727,refute_0_728]) ).
cnf(refute_0_730,plain,
join(X_80,meet(converse(complement(converse(complement(X_80)))),complement(X_80))) = join(X_80,meet(complement(X_80),converse(complement(converse(complement(X_80)))))),
inference(resolve,[$cnf( $equal(meet(converse(complement(converse(complement(X_80)))),complement(X_80)),meet(complement(X_80),converse(complement(converse(complement(X_80)))))) )],[refute_0_726,refute_0_729]) ).
cnf(refute_0_731,plain,
( converse(complement(converse(complement(X_80)))) != join(X_80,meet(converse(complement(converse(complement(X_80)))),complement(X_80)))
| join(X_80,meet(converse(complement(converse(complement(X_80)))),complement(X_80))) != join(X_80,meet(complement(X_80),converse(complement(converse(complement(X_80))))))
| converse(complement(converse(complement(X_80)))) = join(X_80,meet(complement(X_80),converse(complement(converse(complement(X_80)))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(complement(converse(complement(X_80)))),join(X_80,meet(complement(X_80),converse(complement(converse(complement(X_80))))))) ),[0],$fot(join(X_80,meet(converse(complement(converse(complement(X_80)))),complement(X_80))))]]) ).
cnf(refute_0_732,plain,
( converse(complement(converse(complement(X_80)))) != join(X_80,meet(converse(complement(converse(complement(X_80)))),complement(X_80)))
| converse(complement(converse(complement(X_80)))) = join(X_80,meet(complement(X_80),converse(complement(converse(complement(X_80)))))) ),
inference(resolve,[$cnf( $equal(join(X_80,meet(converse(complement(converse(complement(X_80)))),complement(X_80))),join(X_80,meet(complement(X_80),converse(complement(converse(complement(X_80))))))) )],[refute_0_730,refute_0_731]) ).
cnf(refute_0_733,plain,
converse(complement(converse(complement(X_80)))) = join(X_80,meet(complement(X_80),converse(complement(converse(complement(X_80)))))),
inference(resolve,[$cnf( $equal(converse(complement(converse(complement(X_80)))),join(X_80,meet(converse(complement(converse(complement(X_80)))),complement(X_80)))) )],[refute_0_723,refute_0_732]) ).
cnf(refute_0_734,plain,
converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))) = join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))),
inference(subst,[],[refute_0_733:[bind(X_80,$fot(complement(skolemFOFtoCNF_X0)))]]) ).
cnf(refute_0_735,plain,
( converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))) != join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0)))))))
| join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))) = converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))),bind(Y,$fot(join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0)))))))))]]) ).
cnf(refute_0_736,plain,
join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))) = converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))),
inference(resolve,[$cnf( $equal(converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))),join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0)))))))) )],[refute_0_734,refute_0_735]) ).
cnf(refute_0_737,plain,
( join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))) != converse(complement(converse(complement(complement(skolemFOFtoCNF_X0)))))
| join(skolemFOFtoCNF_X1,converse(join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))))) != converse(join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))))
| join(skolemFOFtoCNF_X1,converse(converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))) = converse(join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0)))))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(skolemFOFtoCNF_X1,converse(join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))))),converse(join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))))) ),[0,1,0],$fot(converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))]]) ).
cnf(refute_0_738,plain,
( join(skolemFOFtoCNF_X1,converse(join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))))) != converse(join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))))
| join(skolemFOFtoCNF_X1,converse(converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))) = converse(join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0)))))))) ),
inference(resolve,[$cnf( $equal(join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0)))))) )],[refute_0_736,refute_0_737]) ).
cnf(refute_0_739,plain,
join(skolemFOFtoCNF_X1,converse(converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))) = converse(join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0)))))))),
inference(resolve,[$cnf( $equal(join(skolemFOFtoCNF_X1,converse(join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))))),converse(join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))))) )],[refute_0_533,refute_0_738]) ).
cnf(refute_0_740,plain,
complement(complement(skolemFOFtoCNF_X0)) = skolemFOFtoCNF_X0,
inference(subst,[],[refute_0_374:[bind(X_41,$fot(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_741,plain,
converse(complement(complement(skolemFOFtoCNF_X0))) = converse(complement(complement(skolemFOFtoCNF_X0))),
introduced(tautology,[refl,[$fot(converse(complement(complement(skolemFOFtoCNF_X0))))]]) ).
cnf(refute_0_742,plain,
( complement(complement(skolemFOFtoCNF_X0)) != skolemFOFtoCNF_X0
| converse(complement(complement(skolemFOFtoCNF_X0))) != converse(complement(complement(skolemFOFtoCNF_X0)))
| converse(complement(complement(skolemFOFtoCNF_X0))) = converse(skolemFOFtoCNF_X0) ),
introduced(tautology,[equality,[$cnf( $equal(converse(complement(complement(skolemFOFtoCNF_X0))),converse(complement(complement(skolemFOFtoCNF_X0)))) ),[1,0],$fot(skolemFOFtoCNF_X0)]]) ).
cnf(refute_0_743,plain,
( complement(complement(skolemFOFtoCNF_X0)) != skolemFOFtoCNF_X0
| converse(complement(complement(skolemFOFtoCNF_X0))) = converse(skolemFOFtoCNF_X0) ),
inference(resolve,[$cnf( $equal(converse(complement(complement(skolemFOFtoCNF_X0))),converse(complement(complement(skolemFOFtoCNF_X0)))) )],[refute_0_741,refute_0_742]) ).
cnf(refute_0_744,plain,
converse(complement(complement(skolemFOFtoCNF_X0))) = converse(skolemFOFtoCNF_X0),
inference(resolve,[$cnf( $equal(complement(complement(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X0) )],[refute_0_740,refute_0_743]) ).
cnf(refute_0_745,plain,
complement(converse(complement(complement(skolemFOFtoCNF_X0)))) = complement(converse(complement(complement(skolemFOFtoCNF_X0)))),
introduced(tautology,[refl,[$fot(complement(converse(complement(complement(skolemFOFtoCNF_X0)))))]]) ).
cnf(refute_0_746,plain,
( complement(converse(complement(complement(skolemFOFtoCNF_X0)))) != complement(converse(complement(complement(skolemFOFtoCNF_X0))))
| converse(complement(complement(skolemFOFtoCNF_X0))) != converse(skolemFOFtoCNF_X0)
| complement(converse(complement(complement(skolemFOFtoCNF_X0)))) = complement(converse(skolemFOFtoCNF_X0)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(converse(complement(complement(skolemFOFtoCNF_X0)))),complement(converse(complement(complement(skolemFOFtoCNF_X0))))) ),[1,0],$fot(converse(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_747,plain,
( converse(complement(complement(skolemFOFtoCNF_X0))) != converse(skolemFOFtoCNF_X0)
| complement(converse(complement(complement(skolemFOFtoCNF_X0)))) = complement(converse(skolemFOFtoCNF_X0)) ),
inference(resolve,[$cnf( $equal(complement(converse(complement(complement(skolemFOFtoCNF_X0)))),complement(converse(complement(complement(skolemFOFtoCNF_X0))))) )],[refute_0_745,refute_0_746]) ).
cnf(refute_0_748,plain,
complement(converse(complement(complement(skolemFOFtoCNF_X0)))) = complement(converse(skolemFOFtoCNF_X0)),
inference(resolve,[$cnf( $equal(converse(complement(complement(skolemFOFtoCNF_X0))),converse(skolemFOFtoCNF_X0)) )],[refute_0_744,refute_0_747]) ).
cnf(refute_0_749,plain,
converse(converse(complement(converse(complement(complement(skolemFOFtoCNF_X0)))))) = complement(converse(complement(complement(skolemFOFtoCNF_X0)))),
inference(subst,[],[refute_0_161:[bind(X0,$fot(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))]]) ).
cnf(refute_0_750,plain,
( complement(converse(complement(complement(skolemFOFtoCNF_X0)))) != complement(converse(skolemFOFtoCNF_X0))
| converse(converse(complement(converse(complement(complement(skolemFOFtoCNF_X0)))))) != complement(converse(complement(complement(skolemFOFtoCNF_X0))))
| converse(converse(complement(converse(complement(complement(skolemFOFtoCNF_X0)))))) = complement(converse(skolemFOFtoCNF_X0)) ),
inference(subst,[],[refute_0_28:[bind(X,$fot(converse(converse(complement(converse(complement(complement(skolemFOFtoCNF_X0)))))))),bind(Y,$fot(complement(converse(complement(complement(skolemFOFtoCNF_X0)))))),bind(Z,$fot(complement(converse(skolemFOFtoCNF_X0))))]]) ).
cnf(refute_0_751,plain,
( complement(converse(complement(complement(skolemFOFtoCNF_X0)))) != complement(converse(skolemFOFtoCNF_X0))
| converse(converse(complement(converse(complement(complement(skolemFOFtoCNF_X0)))))) = complement(converse(skolemFOFtoCNF_X0)) ),
inference(resolve,[$cnf( $equal(converse(converse(complement(converse(complement(complement(skolemFOFtoCNF_X0)))))),complement(converse(complement(complement(skolemFOFtoCNF_X0))))) )],[refute_0_749,refute_0_750]) ).
cnf(refute_0_752,plain,
converse(converse(complement(converse(complement(complement(skolemFOFtoCNF_X0)))))) = complement(converse(skolemFOFtoCNF_X0)),
inference(resolve,[$cnf( $equal(complement(converse(complement(complement(skolemFOFtoCNF_X0)))),complement(converse(skolemFOFtoCNF_X0))) )],[refute_0_748,refute_0_751]) ).
cnf(refute_0_753,plain,
join(skolemFOFtoCNF_X1,converse(converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))) = join(skolemFOFtoCNF_X1,converse(converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))),
introduced(tautology,[refl,[$fot(join(skolemFOFtoCNF_X1,converse(converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))))]]) ).
cnf(refute_0_754,plain,
( converse(converse(complement(converse(complement(complement(skolemFOFtoCNF_X0)))))) != complement(converse(skolemFOFtoCNF_X0))
| join(skolemFOFtoCNF_X1,converse(converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))) != join(skolemFOFtoCNF_X1,converse(converse(complement(converse(complement(complement(skolemFOFtoCNF_X0)))))))
| join(skolemFOFtoCNF_X1,converse(converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))) = join(skolemFOFtoCNF_X1,complement(converse(skolemFOFtoCNF_X0))) ),
introduced(tautology,[equality,[$cnf( $equal(join(skolemFOFtoCNF_X1,converse(converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))),join(skolemFOFtoCNF_X1,converse(converse(complement(converse(complement(complement(skolemFOFtoCNF_X0)))))))) ),[1,1],$fot(complement(converse(skolemFOFtoCNF_X0)))]]) ).
cnf(refute_0_755,plain,
( converse(converse(complement(converse(complement(complement(skolemFOFtoCNF_X0)))))) != complement(converse(skolemFOFtoCNF_X0))
| join(skolemFOFtoCNF_X1,converse(converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))) = join(skolemFOFtoCNF_X1,complement(converse(skolemFOFtoCNF_X0))) ),
inference(resolve,[$cnf( $equal(join(skolemFOFtoCNF_X1,converse(converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))),join(skolemFOFtoCNF_X1,converse(converse(complement(converse(complement(complement(skolemFOFtoCNF_X0)))))))) )],[refute_0_753,refute_0_754]) ).
cnf(refute_0_756,plain,
join(skolemFOFtoCNF_X1,converse(converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))) = join(skolemFOFtoCNF_X1,complement(converse(skolemFOFtoCNF_X0))),
inference(resolve,[$cnf( $equal(converse(converse(complement(converse(complement(complement(skolemFOFtoCNF_X0)))))),complement(converse(skolemFOFtoCNF_X0))) )],[refute_0_752,refute_0_755]) ).
cnf(refute_0_757,plain,
( join(skolemFOFtoCNF_X1,converse(converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))) != converse(join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))))
| join(skolemFOFtoCNF_X1,converse(converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))) != join(skolemFOFtoCNF_X1,complement(converse(skolemFOFtoCNF_X0)))
| join(skolemFOFtoCNF_X1,complement(converse(skolemFOFtoCNF_X0))) = converse(join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0)))))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(skolemFOFtoCNF_X1,converse(converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))),converse(join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))))) ),[0],$fot(join(skolemFOFtoCNF_X1,complement(converse(skolemFOFtoCNF_X0))))]]) ).
cnf(refute_0_758,plain,
( join(skolemFOFtoCNF_X1,converse(converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))) != converse(join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))))
| join(skolemFOFtoCNF_X1,complement(converse(skolemFOFtoCNF_X0))) = converse(join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0)))))))) ),
inference(resolve,[$cnf( $equal(join(skolemFOFtoCNF_X1,converse(converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))),join(skolemFOFtoCNF_X1,complement(converse(skolemFOFtoCNF_X0)))) )],[refute_0_756,refute_0_757]) ).
cnf(refute_0_759,plain,
converse(converse(complement(converse(skolemFOFtoCNF_X0)))) = complement(converse(skolemFOFtoCNF_X0)),
inference(subst,[],[refute_0_161:[bind(X0,$fot(complement(converse(skolemFOFtoCNF_X0))))]]) ).
cnf(refute_0_760,plain,
converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))) = converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))),
introduced(tautology,[refl,[$fot(converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))]]) ).
cnf(refute_0_761,plain,
( complement(converse(complement(complement(skolemFOFtoCNF_X0)))) != complement(converse(skolemFOFtoCNF_X0))
| converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))) != converse(complement(converse(complement(complement(skolemFOFtoCNF_X0)))))
| converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))) = converse(complement(converse(skolemFOFtoCNF_X0))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0)))))) ),[1,0],$fot(complement(converse(skolemFOFtoCNF_X0)))]]) ).
cnf(refute_0_762,plain,
( complement(converse(complement(complement(skolemFOFtoCNF_X0)))) != complement(converse(skolemFOFtoCNF_X0))
| converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))) = converse(complement(converse(skolemFOFtoCNF_X0))) ),
inference(resolve,[$cnf( $equal(converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0)))))) )],[refute_0_760,refute_0_761]) ).
cnf(refute_0_763,plain,
converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))) = converse(complement(converse(skolemFOFtoCNF_X0))),
inference(resolve,[$cnf( $equal(complement(converse(complement(complement(skolemFOFtoCNF_X0)))),complement(converse(skolemFOFtoCNF_X0))) )],[refute_0_748,refute_0_762]) ).
cnf(refute_0_764,plain,
( converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))) != converse(complement(converse(skolemFOFtoCNF_X0)))
| join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))) != converse(complement(converse(complement(complement(skolemFOFtoCNF_X0)))))
| join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))) = converse(complement(converse(skolemFOFtoCNF_X0))) ),
inference(subst,[],[refute_0_28:[bind(X,$fot(join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))))),bind(Y,$fot(converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))),bind(Z,$fot(converse(complement(converse(skolemFOFtoCNF_X0)))))]]) ).
cnf(refute_0_765,plain,
( converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))) != converse(complement(converse(skolemFOFtoCNF_X0)))
| join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))) = converse(complement(converse(skolemFOFtoCNF_X0))) ),
inference(resolve,[$cnf( $equal(join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0)))))) )],[refute_0_736,refute_0_764]) ).
cnf(refute_0_766,plain,
join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))) = converse(complement(converse(skolemFOFtoCNF_X0))),
inference(resolve,[$cnf( $equal(converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))),converse(complement(converse(skolemFOFtoCNF_X0)))) )],[refute_0_763,refute_0_765]) ).
cnf(refute_0_767,plain,
converse(join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0)))))))) = converse(join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0)))))))),
introduced(tautology,[refl,[$fot(converse(join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0)))))))))]]) ).
cnf(refute_0_768,plain,
( converse(join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0)))))))) != converse(join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))))
| join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))) != converse(complement(converse(skolemFOFtoCNF_X0)))
| converse(join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0)))))))) = converse(converse(complement(converse(skolemFOFtoCNF_X0)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0)))))))),converse(join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))))) ),[1,0],$fot(converse(complement(converse(skolemFOFtoCNF_X0))))]]) ).
cnf(refute_0_769,plain,
( join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))) != converse(complement(converse(skolemFOFtoCNF_X0)))
| converse(join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0)))))))) = converse(converse(complement(converse(skolemFOFtoCNF_X0)))) ),
inference(resolve,[$cnf( $equal(converse(join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0)))))))),converse(join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))))) )],[refute_0_767,refute_0_768]) ).
cnf(refute_0_770,plain,
converse(join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0)))))))) = converse(converse(complement(converse(skolemFOFtoCNF_X0)))),
inference(resolve,[$cnf( $equal(join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))),converse(complement(converse(skolemFOFtoCNF_X0)))) )],[refute_0_766,refute_0_769]) ).
cnf(refute_0_771,plain,
( converse(converse(complement(converse(skolemFOFtoCNF_X0)))) != complement(converse(skolemFOFtoCNF_X0))
| converse(join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0)))))))) != converse(converse(complement(converse(skolemFOFtoCNF_X0))))
| converse(join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0)))))))) = complement(converse(skolemFOFtoCNF_X0)) ),
inference(subst,[],[refute_0_28:[bind(X,$fot(converse(join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0)))))))))),bind(Y,$fot(converse(converse(complement(converse(skolemFOFtoCNF_X0)))))),bind(Z,$fot(complement(converse(skolemFOFtoCNF_X0))))]]) ).
cnf(refute_0_772,plain,
( converse(converse(complement(converse(skolemFOFtoCNF_X0)))) != complement(converse(skolemFOFtoCNF_X0))
| converse(join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0)))))))) = complement(converse(skolemFOFtoCNF_X0)) ),
inference(resolve,[$cnf( $equal(converse(join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0)))))))),converse(converse(complement(converse(skolemFOFtoCNF_X0))))) )],[refute_0_770,refute_0_771]) ).
cnf(refute_0_773,plain,
converse(join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0)))))))) = complement(converse(skolemFOFtoCNF_X0)),
inference(resolve,[$cnf( $equal(converse(converse(complement(converse(skolemFOFtoCNF_X0)))),complement(converse(skolemFOFtoCNF_X0))) )],[refute_0_759,refute_0_772]) ).
cnf(refute_0_774,plain,
( converse(join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0)))))))) != complement(converse(skolemFOFtoCNF_X0))
| join(skolemFOFtoCNF_X1,complement(converse(skolemFOFtoCNF_X0))) != converse(join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))))
| join(skolemFOFtoCNF_X1,complement(converse(skolemFOFtoCNF_X0))) = complement(converse(skolemFOFtoCNF_X0)) ),
introduced(tautology,[equality,[$cnf( $equal(join(skolemFOFtoCNF_X1,complement(converse(skolemFOFtoCNF_X0))),converse(join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))))) ),[1],$fot(complement(converse(skolemFOFtoCNF_X0)))]]) ).
cnf(refute_0_775,plain,
( join(skolemFOFtoCNF_X1,complement(converse(skolemFOFtoCNF_X0))) != converse(join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))))
| join(skolemFOFtoCNF_X1,complement(converse(skolemFOFtoCNF_X0))) = complement(converse(skolemFOFtoCNF_X0)) ),
inference(resolve,[$cnf( $equal(converse(join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0)))))))),complement(converse(skolemFOFtoCNF_X0))) )],[refute_0_773,refute_0_774]) ).
cnf(refute_0_776,plain,
( join(skolemFOFtoCNF_X1,converse(converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))) != converse(join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))))
| join(skolemFOFtoCNF_X1,complement(converse(skolemFOFtoCNF_X0))) = complement(converse(skolemFOFtoCNF_X0)) ),
inference(resolve,[$cnf( $equal(join(skolemFOFtoCNF_X1,complement(converse(skolemFOFtoCNF_X0))),converse(join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))))) )],[refute_0_758,refute_0_775]) ).
cnf(refute_0_777,plain,
join(skolemFOFtoCNF_X1,complement(converse(skolemFOFtoCNF_X0))) = complement(converse(skolemFOFtoCNF_X0)),
inference(resolve,[$cnf( $equal(join(skolemFOFtoCNF_X1,converse(converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))),converse(join(complement(skolemFOFtoCNF_X0),meet(complement(complement(skolemFOFtoCNF_X0)),converse(complement(converse(complement(complement(skolemFOFtoCNF_X0))))))))) )],[refute_0_739,refute_0_776]) ).
cnf(refute_0_778,plain,
( join(skolemFOFtoCNF_X1,complement(converse(skolemFOFtoCNF_X0))) != complement(converse(skolemFOFtoCNF_X0))
| meet(skolemFOFtoCNF_X1,complement(join(skolemFOFtoCNF_X1,complement(converse(skolemFOFtoCNF_X0))))) != zero
| meet(skolemFOFtoCNF_X1,complement(complement(converse(skolemFOFtoCNF_X0)))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(meet(skolemFOFtoCNF_X1,complement(join(skolemFOFtoCNF_X1,complement(converse(skolemFOFtoCNF_X0))))),zero) ),[0,1,0],$fot(complement(converse(skolemFOFtoCNF_X0)))]]) ).
cnf(refute_0_779,plain,
( meet(skolemFOFtoCNF_X1,complement(join(skolemFOFtoCNF_X1,complement(converse(skolemFOFtoCNF_X0))))) != zero
| meet(skolemFOFtoCNF_X1,complement(complement(converse(skolemFOFtoCNF_X0)))) = zero ),
inference(resolve,[$cnf( $equal(join(skolemFOFtoCNF_X1,complement(converse(skolemFOFtoCNF_X0))),complement(converse(skolemFOFtoCNF_X0))) )],[refute_0_777,refute_0_778]) ).
cnf(refute_0_780,plain,
meet(skolemFOFtoCNF_X1,complement(complement(converse(skolemFOFtoCNF_X0)))) = zero,
inference(resolve,[$cnf( $equal(meet(skolemFOFtoCNF_X1,complement(join(skolemFOFtoCNF_X1,complement(converse(skolemFOFtoCNF_X0))))),zero) )],[refute_0_469,refute_0_779]) ).
cnf(refute_0_781,plain,
complement(complement(converse(skolemFOFtoCNF_X0))) = converse(skolemFOFtoCNF_X0),
inference(subst,[],[refute_0_374:[bind(X_41,$fot(converse(skolemFOFtoCNF_X0)))]]) ).
cnf(refute_0_782,plain,
meet(skolemFOFtoCNF_X1,complement(complement(converse(skolemFOFtoCNF_X0)))) = meet(skolemFOFtoCNF_X1,complement(complement(converse(skolemFOFtoCNF_X0)))),
introduced(tautology,[refl,[$fot(meet(skolemFOFtoCNF_X1,complement(complement(converse(skolemFOFtoCNF_X0)))))]]) ).
cnf(refute_0_783,plain,
( complement(complement(converse(skolemFOFtoCNF_X0))) != converse(skolemFOFtoCNF_X0)
| meet(skolemFOFtoCNF_X1,complement(complement(converse(skolemFOFtoCNF_X0)))) != meet(skolemFOFtoCNF_X1,complement(complement(converse(skolemFOFtoCNF_X0))))
| meet(skolemFOFtoCNF_X1,complement(complement(converse(skolemFOFtoCNF_X0)))) = meet(skolemFOFtoCNF_X1,converse(skolemFOFtoCNF_X0)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(skolemFOFtoCNF_X1,complement(complement(converse(skolemFOFtoCNF_X0)))),meet(skolemFOFtoCNF_X1,complement(complement(converse(skolemFOFtoCNF_X0))))) ),[1,1],$fot(converse(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_784,plain,
( complement(complement(converse(skolemFOFtoCNF_X0))) != converse(skolemFOFtoCNF_X0)
| meet(skolemFOFtoCNF_X1,complement(complement(converse(skolemFOFtoCNF_X0)))) = meet(skolemFOFtoCNF_X1,converse(skolemFOFtoCNF_X0)) ),
inference(resolve,[$cnf( $equal(meet(skolemFOFtoCNF_X1,complement(complement(converse(skolemFOFtoCNF_X0)))),meet(skolemFOFtoCNF_X1,complement(complement(converse(skolemFOFtoCNF_X0))))) )],[refute_0_782,refute_0_783]) ).
cnf(refute_0_785,plain,
meet(skolemFOFtoCNF_X1,complement(complement(converse(skolemFOFtoCNF_X0)))) = meet(skolemFOFtoCNF_X1,converse(skolemFOFtoCNF_X0)),
inference(resolve,[$cnf( $equal(complement(complement(converse(skolemFOFtoCNF_X0))),converse(skolemFOFtoCNF_X0)) )],[refute_0_781,refute_0_784]) ).
cnf(refute_0_786,plain,
( meet(skolemFOFtoCNF_X1,complement(complement(converse(skolemFOFtoCNF_X0)))) != meet(skolemFOFtoCNF_X1,converse(skolemFOFtoCNF_X0))
| meet(skolemFOFtoCNF_X1,complement(complement(converse(skolemFOFtoCNF_X0)))) != zero
| meet(skolemFOFtoCNF_X1,converse(skolemFOFtoCNF_X0)) = zero ),
introduced(tautology,[equality,[$cnf( $equal(meet(skolemFOFtoCNF_X1,complement(complement(converse(skolemFOFtoCNF_X0)))),zero) ),[0],$fot(meet(skolemFOFtoCNF_X1,converse(skolemFOFtoCNF_X0)))]]) ).
cnf(refute_0_787,plain,
( meet(skolemFOFtoCNF_X1,complement(complement(converse(skolemFOFtoCNF_X0)))) != zero
| meet(skolemFOFtoCNF_X1,converse(skolemFOFtoCNF_X0)) = zero ),
inference(resolve,[$cnf( $equal(meet(skolemFOFtoCNF_X1,complement(complement(converse(skolemFOFtoCNF_X0)))),meet(skolemFOFtoCNF_X1,converse(skolemFOFtoCNF_X0))) )],[refute_0_785,refute_0_786]) ).
cnf(refute_0_788,plain,
meet(skolemFOFtoCNF_X1,converse(skolemFOFtoCNF_X0)) = zero,
inference(resolve,[$cnf( $equal(meet(skolemFOFtoCNF_X1,complement(complement(converse(skolemFOFtoCNF_X0)))),zero) )],[refute_0_780,refute_0_787]) ).
cnf(refute_0_789,plain,
meet(converse(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) != zero,
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_790,plain,
meet(converse(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) = meet(skolemFOFtoCNF_X1,converse(skolemFOFtoCNF_X0)),
inference(subst,[],[refute_0_725:[bind(X_21,$fot(skolemFOFtoCNF_X1)),bind(X_22,$fot(converse(skolemFOFtoCNF_X0)))]]) ).
cnf(refute_0_791,plain,
( meet(converse(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) != meet(skolemFOFtoCNF_X1,converse(skolemFOFtoCNF_X0))
| meet(skolemFOFtoCNF_X1,converse(skolemFOFtoCNF_X0)) != zero
| meet(converse(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(meet(converse(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1),zero) ),[0],$fot(meet(skolemFOFtoCNF_X1,converse(skolemFOFtoCNF_X0)))]]) ).
cnf(refute_0_792,plain,
( meet(skolemFOFtoCNF_X1,converse(skolemFOFtoCNF_X0)) != zero
| meet(converse(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) = zero ),
inference(resolve,[$cnf( $equal(meet(converse(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1),meet(skolemFOFtoCNF_X1,converse(skolemFOFtoCNF_X0))) )],[refute_0_790,refute_0_791]) ).
cnf(refute_0_793,plain,
meet(skolemFOFtoCNF_X1,converse(skolemFOFtoCNF_X0)) != zero,
inference(resolve,[$cnf( $equal(meet(converse(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1),zero) )],[refute_0_792,refute_0_789]) ).
cnf(refute_0_794,plain,
$false,
inference(resolve,[$cnf( $equal(meet(skolemFOFtoCNF_X1,converse(skolemFOFtoCNF_X0)),zero) )],[refute_0_788,refute_0_793]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : REL007+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n018.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Fri Jul 8 13:44:55 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 18.57/18.74 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.57/18.74
% 18.57/18.74 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 18.64/18.80
%------------------------------------------------------------------------------