TSTP Solution File: REL023+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : REL023+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n012.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 19:43:53 EDT 2022
% Result : Theorem 0.89s 1.08s
% Output : CNFRefutation 0.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 62
% Number of leaves : 84
% Syntax : Number of formulae : 382 ( 215 unt; 0 def)
% Number of atoms : 619 ( 618 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 480 ( 243 ~; 237 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 507 ( 1 sgn 69 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(maddux1_join_commutativity,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0) ).
fof(maddux2_join_associativity,axiom,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2) ).
fof(maddux3_a_kind_of_de_Morgan,axiom,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) ).
fof(maddux4_definiton_of_meet,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))) ).
fof(composition_identity,axiom,
! [X0] : composition(X0,one) = X0 ).
fof(composition_distributivity,axiom,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)) ).
fof(converse_idempotence,axiom,
! [X0] : converse(converse(X0)) = X0 ).
fof(converse_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,X2] : join(composition(meet(X0,converse(X1)),meet(X1,X2)),composition(X0,meet(X1,X2))) = composition(X0,meet(X1,X2)) ).
fof(subgoal_0,plain,
! [X0,X1,X2] : join(composition(meet(X0,converse(X1)),meet(X1,X2)),composition(X0,meet(X1,X2))) = composition(X0,meet(X1,X2)),
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ! [X0,X1,X2] : join(composition(meet(X0,converse(X1)),meet(X1,X2)),composition(X0,meet(X1,X2))) = composition(X0,meet(X1,X2)),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X0,X1,X2] : join(composition(meet(X0,converse(X1)),meet(X1,X2)),composition(X0,meet(X1,X2))) != composition(X0,meet(X1,X2)),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
join(composition(meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1)),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),composition(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2))) != composition(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(canonicalize,[],[maddux1_join_commutativity]) ).
fof(normalize_0_3,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(canonicalize,[],[composition_distributivity]) ).
fof(normalize_0_5,plain,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(canonicalize,[],[maddux2_join_associativity]) ).
fof(normalize_0_7,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(canonicalize,[],[converse_cancellativity]) ).
fof(normalize_0_9,plain,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(canonicalize,[],[converse_multiplicativity]) ).
fof(normalize_0_11,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [X0] : converse(converse(X0)) = X0,
inference(canonicalize,[],[converse_idempotence]) ).
fof(normalize_0_13,plain,
! [X0] : converse(converse(X0)) = X0,
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [X0] : composition(X0,one) = X0,
inference(canonicalize,[],[composition_identity]) ).
fof(normalize_0_15,plain,
! [X0] : composition(X0,one) = X0,
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,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_17,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(specialize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(canonicalize,[],[maddux4_definiton_of_meet]) ).
fof(normalize_0_19,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(specialize,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(canonicalize,[],[def_zero]) ).
fof(normalize_0_21,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(specialize,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [X0] : top = join(X0,complement(X0)),
inference(canonicalize,[],[def_top]) ).
fof(normalize_0_23,plain,
! [X0] : top = join(X0,complement(X0)),
inference(specialize,[],[normalize_0_22]) ).
cnf(refute_0_0,plain,
join(composition(meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1)),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),composition(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2))) != composition(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
join(X0,X1) = join(X1,X0),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_3,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_4,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( join(X0,X1) != join(X1,X0)
| join(X1,X0) = join(X0,X1) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(join(X0,X1))),bind(Y,$fot(join(X1,X0)))]]) ).
cnf(refute_0_6,plain,
join(X1,X0) = join(X0,X1),
inference(resolve,[$cnf( $equal(join(X0,X1),join(X1,X0)) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
join(meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1)),skolemFOFtoCNF_X0) = join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1))),
inference(subst,[],[refute_0_6:[bind(X0,$fot(skolemFOFtoCNF_X0)),bind(X1,$fot(meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1))))]]) ).
cnf(refute_0_8,plain,
composition(join(meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1)),skolemFOFtoCNF_X0),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)) = composition(join(meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1)),skolemFOFtoCNF_X0),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),
introduced(tautology,[refl,[$fot(composition(join(meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1)),skolemFOFtoCNF_X0),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)))]]) ).
cnf(refute_0_9,plain,
( composition(join(meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1)),skolemFOFtoCNF_X0),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)) != composition(join(meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1)),skolemFOFtoCNF_X0),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2))
| join(meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1)),skolemFOFtoCNF_X0) != join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1)))
| composition(join(meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1)),skolemFOFtoCNF_X0),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)) = composition(join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1))),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1)),skolemFOFtoCNF_X0),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),composition(join(meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1)),skolemFOFtoCNF_X0),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2))) ),[1,0],$fot(join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1))))]]) ).
cnf(refute_0_10,plain,
( join(meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1)),skolemFOFtoCNF_X0) != join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1)))
| composition(join(meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1)),skolemFOFtoCNF_X0),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)) = composition(join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1))),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)) ),
inference(resolve,[$cnf( $equal(composition(join(meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1)),skolemFOFtoCNF_X0),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),composition(join(meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1)),skolemFOFtoCNF_X0),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2))) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
composition(join(meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1)),skolemFOFtoCNF_X0),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)) = composition(join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1))),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),
inference(resolve,[$cnf( $equal(join(meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1)),skolemFOFtoCNF_X0),join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1)))) )],[refute_0_7,refute_0_10]) ).
cnf(refute_0_12,plain,
composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_13,plain,
( composition(join(X0,X1),X2) != join(composition(X0,X2),composition(X1,X2))
| join(composition(X0,X2),composition(X1,X2)) = composition(join(X0,X1),X2) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(composition(join(X0,X1),X2))),bind(Y,$fot(join(composition(X0,X2),composition(X1,X2))))]]) ).
cnf(refute_0_14,plain,
join(composition(X0,X2),composition(X1,X2)) = composition(join(X0,X1),X2),
inference(resolve,[$cnf( $equal(composition(join(X0,X1),X2),join(composition(X0,X2),composition(X1,X2))) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
join(composition(meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1)),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),composition(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2))) = composition(join(meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1)),skolemFOFtoCNF_X0),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),
inference(subst,[],[refute_0_14:[bind(X0,$fot(meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1)))),bind(X1,$fot(skolemFOFtoCNF_X0)),bind(X2,$fot(meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)))]]) ).
cnf(refute_0_16,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_17,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_4,refute_0_16]) ).
cnf(refute_0_18,plain,
( composition(join(meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1)),skolemFOFtoCNF_X0),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)) != composition(join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1))),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2))
| join(composition(meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1)),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),composition(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2))) != composition(join(meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1)),skolemFOFtoCNF_X0),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2))
| join(composition(meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1)),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),composition(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2))) = composition(join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1))),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(composition(meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1)),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),composition(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2))))),bind(Y,$fot(composition(join(meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1)),skolemFOFtoCNF_X0),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)))),bind(Z,$fot(composition(join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1))),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2))))]]) ).
cnf(refute_0_19,plain,
( composition(join(meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1)),skolemFOFtoCNF_X0),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)) != composition(join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1))),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2))
| join(composition(meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1)),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),composition(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2))) = composition(join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1))),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)) ),
inference(resolve,[$cnf( $equal(join(composition(meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1)),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),composition(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2))),composition(join(meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1)),skolemFOFtoCNF_X0),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2))) )],[refute_0_15,refute_0_18]) ).
cnf(refute_0_20,plain,
join(composition(meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1)),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),composition(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2))) = composition(join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1))),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),
inference(resolve,[$cnf( $equal(composition(join(meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1)),skolemFOFtoCNF_X0),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),composition(join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1))),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2))) )],[refute_0_11,refute_0_19]) ).
cnf(refute_0_21,plain,
( composition(join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1))),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)) != composition(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2))
| join(composition(meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1)),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),composition(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2))) != composition(join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1))),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2))
| join(composition(meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1)),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),composition(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2))) = composition(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)) ),
introduced(tautology,[equality,[$cnf( $equal(join(composition(meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1)),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),composition(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2))),composition(join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1))),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2))) ),[1],$fot(composition(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)))]]) ).
cnf(refute_0_22,plain,
( composition(join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1))),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)) != composition(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2))
| join(composition(meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1)),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),composition(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2))) = composition(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)) ),
inference(resolve,[$cnf( $equal(join(composition(meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1)),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),composition(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2))),composition(join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1))),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2))) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
composition(join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1))),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)) != composition(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),
inference(resolve,[$cnf( $equal(join(composition(meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1)),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),composition(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2))),composition(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2))) )],[refute_0_22,refute_0_0]) ).
cnf(refute_0_24,plain,
join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_25,plain,
join(X_95,join(X_95,X_96)) = join(join(X_95,X_95),X_96),
inference(subst,[],[refute_0_24:[bind(X0,$fot(X_95)),bind(X1,$fot(X_95)),bind(X2,$fot(X_96))]]) ).
cnf(refute_0_26,plain,
join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_27,plain,
join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))),
inference(subst,[],[refute_0_6:[bind(X0,$fot(complement(X1))),bind(X1,$fot(composition(converse(X0),complement(composition(X0,X1)))))]]) ).
cnf(refute_0_28,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_29,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( $equal(join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),join(complement(X1),composition(converse(X0),complement(composition(X0,X1))))) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))) = complement(X1),
inference(resolve,[$cnf( $equal(join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),complement(X1)) )],[refute_0_26,refute_0_29]) ).
cnf(refute_0_31,plain,
join(complement(X_67),composition(converse(one),complement(composition(one,X_67)))) = complement(X_67),
inference(subst,[],[refute_0_30:[bind(X0,$fot(one)),bind(X1,$fot(X_67))]]) ).
cnf(refute_0_32,plain,
converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_33,plain,
converse(composition(converse(X0),X_16)) = composition(converse(X_16),converse(converse(X0))),
inference(subst,[],[refute_0_32:[bind(X0,$fot(converse(X0))),bind(X1,$fot(X_16))]]) ).
cnf(refute_0_34,plain,
converse(converse(X0)) = X0,
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_35,plain,
( converse(composition(converse(X0),X_16)) != composition(converse(X_16),converse(converse(X0)))
| converse(converse(X0)) != X0
| converse(composition(converse(X0),X_16)) = composition(converse(X_16),X0) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(X0),X_16)),composition(converse(X_16),converse(converse(X0)))) ),[1,1],$fot(X0)]]) ).
cnf(refute_0_36,plain,
( converse(composition(converse(X0),X_16)) != composition(converse(X_16),converse(converse(X0)))
| converse(composition(converse(X0),X_16)) = composition(converse(X_16),X0) ),
inference(resolve,[$cnf( $equal(converse(converse(X0)),X0) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
converse(composition(converse(X0),X_16)) = composition(converse(X_16),X0),
inference(resolve,[$cnf( $equal(converse(composition(converse(X0),X_16)),composition(converse(X_16),converse(converse(X0)))) )],[refute_0_33,refute_0_36]) ).
cnf(refute_0_38,plain,
converse(composition(converse(X_17),one)) = composition(converse(one),X_17),
inference(subst,[],[refute_0_37:[bind(X0,$fot(X_17)),bind(X_16,$fot(one))]]) ).
cnf(refute_0_39,plain,
composition(X0,one) = X0,
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_40,plain,
composition(converse(X_17),one) = converse(X_17),
inference(subst,[],[refute_0_39:[bind(X0,$fot(converse(X_17)))]]) ).
cnf(refute_0_41,plain,
( composition(converse(X_17),one) != converse(X_17)
| converse(composition(converse(X_17),one)) != composition(converse(one),X_17)
| converse(converse(X_17)) = composition(converse(one),X_17) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(X_17),one)),composition(converse(one),X_17)) ),[0,0],$fot(converse(X_17))]]) ).
cnf(refute_0_42,plain,
( converse(composition(converse(X_17),one)) != composition(converse(one),X_17)
| converse(converse(X_17)) = composition(converse(one),X_17) ),
inference(resolve,[$cnf( $equal(composition(converse(X_17),one),converse(X_17)) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
converse(converse(X_17)) = composition(converse(one),X_17),
inference(resolve,[$cnf( $equal(converse(composition(converse(X_17),one)),composition(converse(one),X_17)) )],[refute_0_38,refute_0_42]) ).
cnf(refute_0_44,plain,
converse(converse(X_17)) = X_17,
inference(subst,[],[refute_0_34:[bind(X0,$fot(X_17))]]) ).
cnf(refute_0_45,plain,
( converse(converse(X_17)) != X_17
| converse(converse(X_17)) != composition(converse(one),X_17)
| X_17 = composition(converse(one),X_17) ),
introduced(tautology,[equality,[$cnf( $equal(converse(converse(X_17)),composition(converse(one),X_17)) ),[0],$fot(X_17)]]) ).
cnf(refute_0_46,plain,
( converse(converse(X_17)) != composition(converse(one),X_17)
| X_17 = composition(converse(one),X_17) ),
inference(resolve,[$cnf( $equal(converse(converse(X_17)),X_17) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
X_17 = composition(converse(one),X_17),
inference(resolve,[$cnf( $equal(converse(converse(X_17)),composition(converse(one),X_17)) )],[refute_0_43,refute_0_46]) ).
cnf(refute_0_48,plain,
composition(converse(one),one) = converse(one),
inference(subst,[],[refute_0_39:[bind(X0,$fot(converse(one)))]]) ).
cnf(refute_0_49,plain,
one = composition(converse(one),one),
inference(subst,[],[refute_0_47:[bind(X_17,$fot(one))]]) ).
cnf(refute_0_50,plain,
( one != composition(converse(one),one)
| composition(converse(one),one) = one ),
inference(subst,[],[refute_0_4:[bind(X,$fot(one)),bind(Y,$fot(composition(converse(one),one)))]]) ).
cnf(refute_0_51,plain,
composition(converse(one),one) = one,
inference(resolve,[$cnf( $equal(one,composition(converse(one),one)) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
( composition(converse(one),one) != converse(one)
| composition(converse(one),one) != one
| one = converse(one) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(one),one),converse(one)) ),[0],$fot(one)]]) ).
cnf(refute_0_53,plain,
( composition(converse(one),one) != converse(one)
| one = converse(one) ),
inference(resolve,[$cnf( $equal(composition(converse(one),one),one) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
one = converse(one),
inference(resolve,[$cnf( $equal(composition(converse(one),one),converse(one)) )],[refute_0_48,refute_0_53]) ).
cnf(refute_0_55,plain,
( one != converse(one)
| converse(one) = one ),
inference(subst,[],[refute_0_4:[bind(X,$fot(one)),bind(Y,$fot(converse(one)))]]) ).
cnf(refute_0_56,plain,
converse(one) = one,
inference(resolve,[$cnf( $equal(one,converse(one)) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
composition(converse(one),X_17) = composition(converse(one),X_17),
introduced(tautology,[refl,[$fot(composition(converse(one),X_17))]]) ).
cnf(refute_0_58,plain,
( composition(converse(one),X_17) != composition(converse(one),X_17)
| converse(one) != one
| composition(converse(one),X_17) = composition(one,X_17) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(one),X_17),composition(converse(one),X_17)) ),[1,0],$fot(one)]]) ).
cnf(refute_0_59,plain,
( converse(one) != one
| composition(converse(one),X_17) = composition(one,X_17) ),
inference(resolve,[$cnf( $equal(composition(converse(one),X_17),composition(converse(one),X_17)) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
composition(converse(one),X_17) = composition(one,X_17),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_56,refute_0_59]) ).
cnf(refute_0_61,plain,
( X_17 != composition(converse(one),X_17)
| composition(converse(one),X_17) != composition(one,X_17)
| X_17 = composition(one,X_17) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_17,composition(one,X_17)) ),[0],$fot(composition(converse(one),X_17))]]) ).
cnf(refute_0_62,plain,
( X_17 != composition(converse(one),X_17)
| X_17 = composition(one,X_17) ),
inference(resolve,[$cnf( $equal(composition(converse(one),X_17),composition(one,X_17)) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
X_17 = composition(one,X_17),
inference(resolve,[$cnf( $equal(X_17,composition(converse(one),X_17)) )],[refute_0_47,refute_0_62]) ).
cnf(refute_0_64,plain,
X_67 = composition(one,X_67),
inference(subst,[],[refute_0_63:[bind(X_17,$fot(X_67))]]) ).
cnf(refute_0_65,plain,
( X_67 != composition(one,X_67)
| composition(one,X_67) = X_67 ),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_67)),bind(Y,$fot(composition(one,X_67)))]]) ).
cnf(refute_0_66,plain,
composition(one,X_67) = X_67,
inference(resolve,[$cnf( $equal(X_67,composition(one,X_67)) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
( composition(one,X_67) != X_67
| join(complement(X_67),composition(converse(one),complement(composition(one,X_67)))) != complement(X_67)
| join(complement(X_67),composition(converse(one),complement(X_67))) = complement(X_67) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_67),composition(converse(one),complement(composition(one,X_67)))),complement(X_67)) ),[0,1,1,0],$fot(X_67)]]) ).
cnf(refute_0_68,plain,
( join(complement(X_67),composition(converse(one),complement(composition(one,X_67)))) != complement(X_67)
| join(complement(X_67),composition(converse(one),complement(X_67))) = complement(X_67) ),
inference(resolve,[$cnf( $equal(composition(one,X_67),X_67) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
join(complement(X_67),composition(converse(one),complement(X_67))) = complement(X_67),
inference(resolve,[$cnf( $equal(join(complement(X_67),composition(converse(one),complement(composition(one,X_67)))),complement(X_67)) )],[refute_0_31,refute_0_68]) ).
cnf(refute_0_70,plain,
( X_17 != composition(one,X_17)
| composition(one,X_17) = X_17 ),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_17)),bind(Y,$fot(composition(one,X_17)))]]) ).
cnf(refute_0_71,plain,
composition(one,X_17) = X_17,
inference(resolve,[$cnf( $equal(X_17,composition(one,X_17)) )],[refute_0_63,refute_0_70]) ).
cnf(refute_0_72,plain,
composition(one,complement(X_67)) = complement(X_67),
inference(subst,[],[refute_0_71:[bind(X_17,$fot(complement(X_67)))]]) ).
cnf(refute_0_73,plain,
composition(converse(one),complement(X_67)) = composition(converse(one),complement(X_67)),
introduced(tautology,[refl,[$fot(composition(converse(one),complement(X_67)))]]) ).
cnf(refute_0_74,plain,
( composition(converse(one),complement(X_67)) != composition(converse(one),complement(X_67))
| converse(one) != one
| composition(converse(one),complement(X_67)) = composition(one,complement(X_67)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(one),complement(X_67)),composition(converse(one),complement(X_67))) ),[1,0],$fot(one)]]) ).
cnf(refute_0_75,plain,
( converse(one) != one
| composition(converse(one),complement(X_67)) = composition(one,complement(X_67)) ),
inference(resolve,[$cnf( $equal(composition(converse(one),complement(X_67)),composition(converse(one),complement(X_67))) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
composition(converse(one),complement(X_67)) = composition(one,complement(X_67)),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_56,refute_0_75]) ).
cnf(refute_0_77,plain,
( composition(converse(one),complement(X_67)) != composition(one,complement(X_67))
| composition(one,complement(X_67)) != complement(X_67)
| composition(converse(one),complement(X_67)) = complement(X_67) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(composition(converse(one),complement(X_67)))),bind(Y,$fot(composition(one,complement(X_67)))),bind(Z,$fot(complement(X_67)))]]) ).
cnf(refute_0_78,plain,
( composition(one,complement(X_67)) != complement(X_67)
| composition(converse(one),complement(X_67)) = complement(X_67) ),
inference(resolve,[$cnf( $equal(composition(converse(one),complement(X_67)),composition(one,complement(X_67))) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
composition(converse(one),complement(X_67)) = complement(X_67),
inference(resolve,[$cnf( $equal(composition(one,complement(X_67)),complement(X_67)) )],[refute_0_72,refute_0_78]) ).
cnf(refute_0_80,plain,
join(complement(X_67),composition(converse(one),complement(X_67))) = join(complement(X_67),composition(converse(one),complement(X_67))),
introduced(tautology,[refl,[$fot(join(complement(X_67),composition(converse(one),complement(X_67))))]]) ).
cnf(refute_0_81,plain,
( composition(converse(one),complement(X_67)) != complement(X_67)
| join(complement(X_67),composition(converse(one),complement(X_67))) != join(complement(X_67),composition(converse(one),complement(X_67)))
| join(complement(X_67),composition(converse(one),complement(X_67))) = join(complement(X_67),complement(X_67)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_67),composition(converse(one),complement(X_67))),join(complement(X_67),composition(converse(one),complement(X_67)))) ),[1,1],$fot(complement(X_67))]]) ).
cnf(refute_0_82,plain,
( composition(converse(one),complement(X_67)) != complement(X_67)
| join(complement(X_67),composition(converse(one),complement(X_67))) = join(complement(X_67),complement(X_67)) ),
inference(resolve,[$cnf( $equal(join(complement(X_67),composition(converse(one),complement(X_67))),join(complement(X_67),composition(converse(one),complement(X_67)))) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
join(complement(X_67),composition(converse(one),complement(X_67))) = join(complement(X_67),complement(X_67)),
inference(resolve,[$cnf( $equal(composition(converse(one),complement(X_67)),complement(X_67)) )],[refute_0_79,refute_0_82]) ).
cnf(refute_0_84,plain,
( join(complement(X_67),composition(converse(one),complement(X_67))) != complement(X_67)
| join(complement(X_67),composition(converse(one),complement(X_67))) != join(complement(X_67),complement(X_67))
| join(complement(X_67),complement(X_67)) = complement(X_67) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_67),composition(converse(one),complement(X_67))),complement(X_67)) ),[0],$fot(join(complement(X_67),complement(X_67)))]]) ).
cnf(refute_0_85,plain,
( join(complement(X_67),composition(converse(one),complement(X_67))) != complement(X_67)
| join(complement(X_67),complement(X_67)) = complement(X_67) ),
inference(resolve,[$cnf( $equal(join(complement(X_67),composition(converse(one),complement(X_67))),join(complement(X_67),complement(X_67))) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
join(complement(X_67),complement(X_67)) = complement(X_67),
inference(resolve,[$cnf( $equal(join(complement(X_67),composition(converse(one),complement(X_67))),complement(X_67)) )],[refute_0_69,refute_0_85]) ).
cnf(refute_0_87,plain,
join(complement(meet(top,complement(X_69))),complement(meet(top,complement(X_69)))) = complement(meet(top,complement(X_69))),
inference(subst,[],[refute_0_86:[bind(X_67,$fot(meet(top,complement(X_69))))]]) ).
cnf(refute_0_88,plain,
X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_89,plain,
join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),
inference(subst,[],[refute_0_6:[bind(X0,$fot(complement(join(complement(X0),X1)))),bind(X1,$fot(complement(join(complement(X0),complement(X1)))))]]) ).
cnf(refute_0_90,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_91,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( $equal(join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
X0 = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),
inference(resolve,[$cnf( $equal(X0,join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1)))) )],[refute_0_88,refute_0_91]) ).
cnf(refute_0_93,plain,
join(complement(join(complement(X0),X1)),meet(X0,X1)) = join(meet(X0,X1),complement(join(complement(X0),X1))),
inference(subst,[],[refute_0_6:[bind(X0,$fot(meet(X0,X1))),bind(X1,$fot(complement(join(complement(X0),X1))))]]) ).
cnf(refute_0_94,plain,
meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_95,plain,
( meet(X0,X1) != complement(join(complement(X0),complement(X1)))
| complement(join(complement(X0),complement(X1))) = meet(X0,X1) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(meet(X0,X1))),bind(Y,$fot(complement(join(complement(X0),complement(X1)))))]]) ).
cnf(refute_0_96,plain,
complement(join(complement(X0),complement(X1))) = meet(X0,X1),
inference(resolve,[$cnf( $equal(meet(X0,X1),complement(join(complement(X0),complement(X1)))) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),
introduced(tautology,[refl,[$fot(join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))))]]) ).
cnf(refute_0_98,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_99,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( $equal(join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(complement(join(complement(X0),X1)),meet(X0,X1)),
inference(resolve,[$cnf( $equal(complement(join(complement(X0),complement(X1))),meet(X0,X1)) )],[refute_0_96,refute_0_99]) ).
cnf(refute_0_101,plain,
( join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) != join(complement(join(complement(X0),X1)),meet(X0,X1))
| join(complement(join(complement(X0),X1)),meet(X0,X1)) != join(meet(X0,X1),complement(join(complement(X0),X1)))
| join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(meet(X0,X1),complement(join(complement(X0),X1))) ),
inference(subst,[],[refute_0_17:[bind(X,$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_102,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( $equal(join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),join(complement(join(complement(X0),X1)),meet(X0,X1))) )],[refute_0_100,refute_0_101]) ).
cnf(refute_0_103,plain,
join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(meet(X0,X1),complement(join(complement(X0),X1))),
inference(resolve,[$cnf( $equal(join(complement(join(complement(X0),X1)),meet(X0,X1)),join(meet(X0,X1),complement(join(complement(X0),X1)))) )],[refute_0_93,refute_0_102]) ).
cnf(refute_0_104,plain,
( X0 != join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))
| join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) != join(meet(X0,X1),complement(join(complement(X0),X1)))
| X0 = join(meet(X0,X1),complement(join(complement(X0),X1))) ),
introduced(tautology,[equality,[$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_105,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( $equal(join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),join(meet(X0,X1),complement(join(complement(X0),X1)))) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
X0 = join(meet(X0,X1),complement(join(complement(X0),X1))),
inference(resolve,[$cnf( $equal(X0,join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))) )],[refute_0_92,refute_0_105]) ).
cnf(refute_0_107,plain,
X_37 = join(meet(X_37,X_38),complement(join(complement(X_37),X_38))),
inference(subst,[],[refute_0_106:[bind(X0,$fot(X_37)),bind(X1,$fot(X_38))]]) ).
cnf(refute_0_108,plain,
join(X_38,complement(X_37)) = join(complement(X_37),X_38),
inference(subst,[],[refute_0_1:[bind(X0,$fot(X_38)),bind(X1,$fot(complement(X_37)))]]) ).
cnf(refute_0_109,plain,
( join(X_38,complement(X_37)) != join(complement(X_37),X_38)
| join(complement(X_37),X_38) = join(X_38,complement(X_37)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(join(X_38,complement(X_37)))),bind(Y,$fot(join(complement(X_37),X_38)))]]) ).
cnf(refute_0_110,plain,
join(complement(X_37),X_38) = join(X_38,complement(X_37)),
inference(resolve,[$cnf( $equal(join(X_38,complement(X_37)),join(complement(X_37),X_38)) )],[refute_0_108,refute_0_109]) ).
cnf(refute_0_111,plain,
( X_37 != join(meet(X_37,X_38),complement(join(complement(X_37),X_38)))
| join(complement(X_37),X_38) != join(X_38,complement(X_37))
| X_37 = join(meet(X_37,X_38),complement(join(X_38,complement(X_37)))) ),
introduced(tautology,[equality,[$cnf( $equal(X_37,join(meet(X_37,X_38),complement(join(complement(X_37),X_38)))) ),[1,1,0],$fot(join(X_38,complement(X_37)))]]) ).
cnf(refute_0_112,plain,
( X_37 != join(meet(X_37,X_38),complement(join(complement(X_37),X_38)))
| X_37 = join(meet(X_37,X_38),complement(join(X_38,complement(X_37)))) ),
inference(resolve,[$cnf( $equal(join(complement(X_37),X_38),join(X_38,complement(X_37))) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
X_37 = join(meet(X_37,X_38),complement(join(X_38,complement(X_37)))),
inference(resolve,[$cnf( $equal(X_37,join(meet(X_37,X_38),complement(join(complement(X_37),X_38)))) )],[refute_0_107,refute_0_112]) ).
cnf(refute_0_114,plain,
X_37 = join(meet(X_37,complement(X_37)),complement(join(complement(X_37),complement(X_37)))),
inference(subst,[],[refute_0_113:[bind(X_38,$fot(complement(X_37)))]]) ).
cnf(refute_0_115,plain,
join(complement(X_37),complement(X_37)) = complement(X_37),
inference(subst,[],[refute_0_86:[bind(X_67,$fot(X_37))]]) ).
cnf(refute_0_116,plain,
( X_37 != join(meet(X_37,complement(X_37)),complement(join(complement(X_37),complement(X_37))))
| join(complement(X_37),complement(X_37)) != complement(X_37)
| X_37 = join(meet(X_37,complement(X_37)),complement(complement(X_37))) ),
introduced(tautology,[equality,[$cnf( $equal(X_37,join(meet(X_37,complement(X_37)),complement(join(complement(X_37),complement(X_37))))) ),[1,1,0],$fot(complement(X_37))]]) ).
cnf(refute_0_117,plain,
( X_37 != join(meet(X_37,complement(X_37)),complement(join(complement(X_37),complement(X_37))))
| X_37 = join(meet(X_37,complement(X_37)),complement(complement(X_37))) ),
inference(resolve,[$cnf( $equal(join(complement(X_37),complement(X_37)),complement(X_37)) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
X_37 = join(meet(X_37,complement(X_37)),complement(complement(X_37))),
inference(resolve,[$cnf( $equal(X_37,join(meet(X_37,complement(X_37)),complement(join(complement(X_37),complement(X_37))))) )],[refute_0_114,refute_0_117]) ).
cnf(refute_0_119,plain,
meet(top,X_9) = join(meet(meet(top,X_9),join(zero,complement(X_9))),complement(join(complement(meet(top,X_9)),join(zero,complement(X_9))))),
inference(subst,[],[refute_0_106:[bind(X0,$fot(meet(top,X_9))),bind(X1,$fot(join(zero,complement(X_9))))]]) ).
cnf(refute_0_120,plain,
zero = meet(X0,complement(X0)),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_121,plain,
zero = meet(join(zero,complement(X_9)),complement(join(zero,complement(X_9)))),
inference(subst,[],[refute_0_120:[bind(X0,$fot(join(zero,complement(X_9))))]]) ).
cnf(refute_0_122,plain,
meet(top,X1) = complement(join(complement(top),complement(X1))),
inference(subst,[],[refute_0_94:[bind(X0,$fot(top))]]) ).
cnf(refute_0_123,plain,
zero = meet(join(complement(X_6),complement(X_7)),complement(join(complement(X_6),complement(X_7)))),
inference(subst,[],[refute_0_120:[bind(X0,$fot(join(complement(X_6),complement(X_7))))]]) ).
cnf(refute_0_124,plain,
meet(X_6,X_7) = complement(join(complement(X_6),complement(X_7))),
inference(subst,[],[refute_0_94:[bind(X0,$fot(X_6)),bind(X1,$fot(X_7))]]) ).
cnf(refute_0_125,plain,
( meet(X_6,X_7) != complement(join(complement(X_6),complement(X_7)))
| complement(join(complement(X_6),complement(X_7))) = meet(X_6,X_7) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(meet(X_6,X_7))),bind(Y,$fot(complement(join(complement(X_6),complement(X_7)))))]]) ).
cnf(refute_0_126,plain,
complement(join(complement(X_6),complement(X_7))) = meet(X_6,X_7),
inference(resolve,[$cnf( $equal(meet(X_6,X_7),complement(join(complement(X_6),complement(X_7)))) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
( complement(join(complement(X_6),complement(X_7))) != meet(X_6,X_7)
| zero != meet(join(complement(X_6),complement(X_7)),complement(join(complement(X_6),complement(X_7))))
| zero = meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(join(complement(X_6),complement(X_7)),complement(join(complement(X_6),complement(X_7))))) ),[1,1],$fot(meet(X_6,X_7))]]) ).
cnf(refute_0_128,plain,
( zero != meet(join(complement(X_6),complement(X_7)),complement(join(complement(X_6),complement(X_7))))
| zero = meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_6),complement(X_7))),meet(X_6,X_7)) )],[refute_0_126,refute_0_127]) ).
cnf(refute_0_129,plain,
zero = meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)),
inference(resolve,[$cnf( $equal(zero,meet(join(complement(X_6),complement(X_7)),complement(join(complement(X_6),complement(X_7))))) )],[refute_0_123,refute_0_128]) ).
cnf(refute_0_130,plain,
top = join(X0,complement(X0)),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_131,plain,
( top != join(X0,complement(X0))
| join(X0,complement(X0)) = top ),
inference(subst,[],[refute_0_4:[bind(X,$fot(top)),bind(Y,$fot(join(X0,complement(X0))))]]) ).
cnf(refute_0_132,plain,
join(X0,complement(X0)) = top,
inference(resolve,[$cnf( $equal(top,join(X0,complement(X0))) )],[refute_0_130,refute_0_131]) ).
cnf(refute_0_133,plain,
join(meet(X_6,X_7),complement(meet(X_6,X_7))) = top,
inference(subst,[],[refute_0_132:[bind(X0,$fot(meet(X_6,X_7)))]]) ).
cnf(refute_0_134,plain,
complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))) = complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))),
introduced(tautology,[refl,[$fot(complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))))]]) ).
cnf(refute_0_135,plain,
( complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))) != complement(join(meet(X_6,X_7),complement(meet(X_6,X_7))))
| join(meet(X_6,X_7),complement(meet(X_6,X_7))) != top
| complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))),complement(join(meet(X_6,X_7),complement(meet(X_6,X_7))))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_136,plain,
( join(meet(X_6,X_7),complement(meet(X_6,X_7))) != top
| complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))),complement(join(meet(X_6,X_7),complement(meet(X_6,X_7))))) )],[refute_0_134,refute_0_135]) ).
cnf(refute_0_137,plain,
complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))) = complement(top),
inference(resolve,[$cnf( $equal(join(meet(X_6,X_7),complement(meet(X_6,X_7))),top) )],[refute_0_133,refute_0_136]) ).
cnf(refute_0_138,plain,
meet(join(complement(X_6),complement(X_7)),X1) = complement(join(complement(join(complement(X_6),complement(X_7))),complement(X1))),
inference(subst,[],[refute_0_94:[bind(X0,$fot(join(complement(X_6),complement(X_7))))]]) ).
cnf(refute_0_139,plain,
( complement(join(complement(X_6),complement(X_7))) != meet(X_6,X_7)
| meet(join(complement(X_6),complement(X_7)),X1) != complement(join(complement(join(complement(X_6),complement(X_7))),complement(X1)))
| meet(join(complement(X_6),complement(X_7)),X1) = complement(join(meet(X_6,X_7),complement(X1))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(complement(X_6),complement(X_7)),X1),complement(join(complement(join(complement(X_6),complement(X_7))),complement(X1)))) ),[1,0,0],$fot(meet(X_6,X_7))]]) ).
cnf(refute_0_140,plain,
( meet(join(complement(X_6),complement(X_7)),X1) != complement(join(complement(join(complement(X_6),complement(X_7))),complement(X1)))
| meet(join(complement(X_6),complement(X_7)),X1) = complement(join(meet(X_6,X_7),complement(X1))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_6),complement(X_7))),meet(X_6,X_7)) )],[refute_0_126,refute_0_139]) ).
cnf(refute_0_141,plain,
meet(join(complement(X_6),complement(X_7)),X1) = complement(join(meet(X_6,X_7),complement(X1))),
inference(resolve,[$cnf( $equal(meet(join(complement(X_6),complement(X_7)),X1),complement(join(complement(join(complement(X_6),complement(X_7))),complement(X1)))) )],[refute_0_138,refute_0_140]) ).
cnf(refute_0_142,plain,
meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)) = complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))),
inference(subst,[],[refute_0_141:[bind(X1,$fot(meet(X_6,X_7)))]]) ).
cnf(refute_0_143,plain,
( complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))) != complement(top)
| meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)) != complement(join(meet(X_6,X_7),complement(meet(X_6,X_7))))
| meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)) = complement(top) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)))),bind(Y,$fot(complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))))),bind(Z,$fot(complement(top)))]]) ).
cnf(refute_0_144,plain,
( complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))) != complement(top)
| meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)) = complement(top) ),
inference(resolve,[$cnf( $equal(meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)),complement(join(meet(X_6,X_7),complement(meet(X_6,X_7))))) )],[refute_0_142,refute_0_143]) ).
cnf(refute_0_145,plain,
meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)) = complement(top),
inference(resolve,[$cnf( $equal(complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))),complement(top)) )],[refute_0_137,refute_0_144]) ).
cnf(refute_0_146,plain,
( meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)) != complement(top)
| zero != meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7))
| zero = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7))) ),[1],$fot(complement(top))]]) ).
cnf(refute_0_147,plain,
( zero != meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7))
| zero = complement(top) ),
inference(resolve,[$cnf( $equal(meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)),complement(top)) )],[refute_0_145,refute_0_146]) ).
cnf(refute_0_148,plain,
zero = complement(top),
inference(resolve,[$cnf( $equal(zero,meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7))) )],[refute_0_129,refute_0_147]) ).
cnf(refute_0_149,plain,
( zero != complement(top)
| complement(top) = zero ),
inference(subst,[],[refute_0_4:[bind(X,$fot(zero)),bind(Y,$fot(complement(top)))]]) ).
cnf(refute_0_150,plain,
complement(top) = zero,
inference(resolve,[$cnf( $equal(zero,complement(top)) )],[refute_0_148,refute_0_149]) ).
cnf(refute_0_151,plain,
( complement(top) != zero
| meet(top,X1) != complement(join(complement(top),complement(X1)))
| meet(top,X1) = complement(join(zero,complement(X1))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,X1),complement(join(complement(top),complement(X1)))) ),[1,0,0],$fot(zero)]]) ).
cnf(refute_0_152,plain,
( meet(top,X1) != complement(join(complement(top),complement(X1)))
| meet(top,X1) = complement(join(zero,complement(X1))) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_150,refute_0_151]) ).
cnf(refute_0_153,plain,
meet(top,X1) = complement(join(zero,complement(X1))),
inference(resolve,[$cnf( $equal(meet(top,X1),complement(join(complement(top),complement(X1)))) )],[refute_0_122,refute_0_152]) ).
cnf(refute_0_154,plain,
meet(top,X_9) = complement(join(zero,complement(X_9))),
inference(subst,[],[refute_0_153:[bind(X1,$fot(X_9))]]) ).
cnf(refute_0_155,plain,
( meet(top,X_9) != complement(join(zero,complement(X_9)))
| complement(join(zero,complement(X_9))) = meet(top,X_9) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(meet(top,X_9))),bind(Y,$fot(complement(join(zero,complement(X_9)))))]]) ).
cnf(refute_0_156,plain,
complement(join(zero,complement(X_9))) = meet(top,X_9),
inference(resolve,[$cnf( $equal(meet(top,X_9),complement(join(zero,complement(X_9)))) )],[refute_0_154,refute_0_155]) ).
cnf(refute_0_157,plain,
( complement(join(zero,complement(X_9))) != meet(top,X_9)
| zero != meet(join(zero,complement(X_9)),complement(join(zero,complement(X_9))))
| zero = meet(join(zero,complement(X_9)),meet(top,X_9)) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(join(zero,complement(X_9)),complement(join(zero,complement(X_9))))) ),[1,1],$fot(meet(top,X_9))]]) ).
cnf(refute_0_158,plain,
( zero != meet(join(zero,complement(X_9)),complement(join(zero,complement(X_9))))
| zero = meet(join(zero,complement(X_9)),meet(top,X_9)) ),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(X_9))),meet(top,X_9)) )],[refute_0_156,refute_0_157]) ).
cnf(refute_0_159,plain,
zero = meet(join(zero,complement(X_9)),meet(top,X_9)),
inference(resolve,[$cnf( $equal(zero,meet(join(zero,complement(X_9)),complement(join(zero,complement(X_9))))) )],[refute_0_121,refute_0_158]) ).
cnf(refute_0_160,plain,
join(complement(X_7),complement(X_6)) = join(complement(X_6),complement(X_7)),
inference(subst,[],[refute_0_1:[bind(X0,$fot(complement(X_7))),bind(X1,$fot(complement(X_6)))]]) ).
cnf(refute_0_161,plain,
( join(complement(X_7),complement(X_6)) != join(complement(X_6),complement(X_7))
| join(complement(X_6),complement(X_7)) = join(complement(X_7),complement(X_6)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(join(complement(X_7),complement(X_6)))),bind(Y,$fot(join(complement(X_6),complement(X_7))))]]) ).
cnf(refute_0_162,plain,
join(complement(X_6),complement(X_7)) = join(complement(X_7),complement(X_6)),
inference(resolve,[$cnf( $equal(join(complement(X_7),complement(X_6)),join(complement(X_6),complement(X_7))) )],[refute_0_160,refute_0_161]) ).
cnf(refute_0_163,plain,
( join(complement(X_6),complement(X_7)) != join(complement(X_7),complement(X_6))
| meet(X_6,X_7) != complement(join(complement(X_6),complement(X_7)))
| meet(X_6,X_7) = complement(join(complement(X_7),complement(X_6))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_6,X_7),complement(join(complement(X_6),complement(X_7)))) ),[1,0],$fot(join(complement(X_7),complement(X_6)))]]) ).
cnf(refute_0_164,plain,
( meet(X_6,X_7) != complement(join(complement(X_6),complement(X_7)))
| meet(X_6,X_7) = complement(join(complement(X_7),complement(X_6))) ),
inference(resolve,[$cnf( $equal(join(complement(X_6),complement(X_7)),join(complement(X_7),complement(X_6))) )],[refute_0_162,refute_0_163]) ).
cnf(refute_0_165,plain,
meet(X_6,X_7) = complement(join(complement(X_7),complement(X_6))),
inference(resolve,[$cnf( $equal(meet(X_6,X_7),complement(join(complement(X_6),complement(X_7)))) )],[refute_0_124,refute_0_164]) ).
cnf(refute_0_166,plain,
complement(join(complement(X_7),complement(X_6))) = meet(X_7,X_6),
inference(subst,[],[refute_0_96:[bind(X0,$fot(X_7)),bind(X1,$fot(X_6))]]) ).
cnf(refute_0_167,plain,
( complement(join(complement(X_7),complement(X_6))) != meet(X_7,X_6)
| meet(X_6,X_7) != complement(join(complement(X_7),complement(X_6)))
| meet(X_6,X_7) = meet(X_7,X_6) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_6,X_7),complement(join(complement(X_7),complement(X_6)))) ),[1],$fot(meet(X_7,X_6))]]) ).
cnf(refute_0_168,plain,
( meet(X_6,X_7) != complement(join(complement(X_7),complement(X_6)))
| meet(X_6,X_7) = meet(X_7,X_6) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_7),complement(X_6))),meet(X_7,X_6)) )],[refute_0_166,refute_0_167]) ).
cnf(refute_0_169,plain,
meet(X_6,X_7) = meet(X_7,X_6),
inference(resolve,[$cnf( $equal(meet(X_6,X_7),complement(join(complement(X_7),complement(X_6)))) )],[refute_0_165,refute_0_168]) ).
cnf(refute_0_170,plain,
( meet(X_6,X_7) != meet(X_7,X_6)
| meet(X_7,X_6) = meet(X_6,X_7) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(meet(X_6,X_7))),bind(Y,$fot(meet(X_7,X_6)))]]) ).
cnf(refute_0_171,plain,
meet(X_7,X_6) = meet(X_6,X_7),
inference(resolve,[$cnf( $equal(meet(X_6,X_7),meet(X_7,X_6)) )],[refute_0_169,refute_0_170]) ).
cnf(refute_0_172,plain,
meet(join(zero,complement(X_9)),meet(top,X_9)) = meet(meet(top,X_9),join(zero,complement(X_9))),
inference(subst,[],[refute_0_171:[bind(X_6,$fot(meet(top,X_9))),bind(X_7,$fot(join(zero,complement(X_9))))]]) ).
cnf(refute_0_173,plain,
( meet(join(zero,complement(X_9)),meet(top,X_9)) != meet(meet(top,X_9),join(zero,complement(X_9)))
| zero != meet(join(zero,complement(X_9)),meet(top,X_9))
| zero = meet(meet(top,X_9),join(zero,complement(X_9))) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(join(zero,complement(X_9)),meet(top,X_9))) ),[1],$fot(meet(meet(top,X_9),join(zero,complement(X_9))))]]) ).
cnf(refute_0_174,plain,
( zero != meet(join(zero,complement(X_9)),meet(top,X_9))
| zero = meet(meet(top,X_9),join(zero,complement(X_9))) ),
inference(resolve,[$cnf( $equal(meet(join(zero,complement(X_9)),meet(top,X_9)),meet(meet(top,X_9),join(zero,complement(X_9)))) )],[refute_0_172,refute_0_173]) ).
cnf(refute_0_175,plain,
zero = meet(meet(top,X_9),join(zero,complement(X_9))),
inference(resolve,[$cnf( $equal(zero,meet(join(zero,complement(X_9)),meet(top,X_9))) )],[refute_0_159,refute_0_174]) ).
cnf(refute_0_176,plain,
( zero != meet(meet(top,X_9),join(zero,complement(X_9)))
| meet(meet(top,X_9),join(zero,complement(X_9))) = zero ),
inference(subst,[],[refute_0_4:[bind(X,$fot(zero)),bind(Y,$fot(meet(meet(top,X_9),join(zero,complement(X_9)))))]]) ).
cnf(refute_0_177,plain,
meet(meet(top,X_9),join(zero,complement(X_9))) = zero,
inference(resolve,[$cnf( $equal(zero,meet(meet(top,X_9),join(zero,complement(X_9)))) )],[refute_0_175,refute_0_176]) ).
cnf(refute_0_178,plain,
( meet(meet(top,X_9),join(zero,complement(X_9))) != zero
| meet(top,X_9) != join(meet(meet(top,X_9),join(zero,complement(X_9))),complement(join(complement(meet(top,X_9)),join(zero,complement(X_9)))))
| meet(top,X_9) = join(zero,complement(join(complement(meet(top,X_9)),join(zero,complement(X_9))))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,X_9),join(meet(meet(top,X_9),join(zero,complement(X_9))),complement(join(complement(meet(top,X_9)),join(zero,complement(X_9)))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_179,plain,
( meet(top,X_9) != join(meet(meet(top,X_9),join(zero,complement(X_9))),complement(join(complement(meet(top,X_9)),join(zero,complement(X_9)))))
| meet(top,X_9) = join(zero,complement(join(complement(meet(top,X_9)),join(zero,complement(X_9))))) ),
inference(resolve,[$cnf( $equal(meet(meet(top,X_9),join(zero,complement(X_9))),zero) )],[refute_0_177,refute_0_178]) ).
cnf(refute_0_180,plain,
meet(top,X_9) = join(zero,complement(join(complement(meet(top,X_9)),join(zero,complement(X_9))))),
inference(resolve,[$cnf( $equal(meet(top,X_9),join(meet(meet(top,X_9),join(zero,complement(X_9))),complement(join(complement(meet(top,X_9)),join(zero,complement(X_9)))))) )],[refute_0_119,refute_0_179]) ).
cnf(refute_0_181,plain,
meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9)))) = join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),join(zero,complement(join(complement(meet(top,X_9)),join(zero,complement(X_9)))))))),
inference(subst,[],[refute_0_180:[bind(X_9,$fot(join(complement(meet(top,X_9)),join(zero,complement(X_9)))))]]) ).
cnf(refute_0_182,plain,
( meet(top,X_9) != join(zero,complement(join(complement(meet(top,X_9)),join(zero,complement(X_9)))))
| join(zero,complement(join(complement(meet(top,X_9)),join(zero,complement(X_9))))) = meet(top,X_9) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(meet(top,X_9))),bind(Y,$fot(join(zero,complement(join(complement(meet(top,X_9)),join(zero,complement(X_9)))))))]]) ).
cnf(refute_0_183,plain,
join(zero,complement(join(complement(meet(top,X_9)),join(zero,complement(X_9))))) = meet(top,X_9),
inference(resolve,[$cnf( $equal(meet(top,X_9),join(zero,complement(join(complement(meet(top,X_9)),join(zero,complement(X_9)))))) )],[refute_0_180,refute_0_182]) ).
cnf(refute_0_184,plain,
( join(zero,complement(join(complement(meet(top,X_9)),join(zero,complement(X_9))))) != meet(top,X_9)
| meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9)))) != join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),join(zero,complement(join(complement(meet(top,X_9)),join(zero,complement(X_9))))))))
| meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9)))) = join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(top,X_9)))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9)))),join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),join(zero,complement(join(complement(meet(top,X_9)),join(zero,complement(X_9))))))))) ),[1,1,0,1],$fot(meet(top,X_9))]]) ).
cnf(refute_0_185,plain,
( meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9)))) != join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),join(zero,complement(join(complement(meet(top,X_9)),join(zero,complement(X_9))))))))
| meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9)))) = join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(top,X_9)))) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(top,X_9)) )],[refute_0_183,refute_0_184]) ).
cnf(refute_0_186,plain,
meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9)))) = join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(top,X_9)))),
inference(resolve,[$cnf( $equal(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9)))),join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),join(zero,complement(join(complement(meet(top,X_9)),join(zero,complement(X_9))))))))) )],[refute_0_181,refute_0_185]) ).
cnf(refute_0_187,plain,
meet(top,join(complement(meet(top,X_60)),join(zero,complement(X_60)))) = complement(join(zero,complement(join(complement(meet(top,X_60)),join(zero,complement(X_60)))))),
inference(subst,[],[refute_0_153:[bind(X1,$fot(join(complement(meet(top,X_60)),join(zero,complement(X_60)))))]]) ).
cnf(refute_0_188,plain,
meet(top,X_60) = join(zero,complement(join(complement(meet(top,X_60)),join(zero,complement(X_60))))),
inference(subst,[],[refute_0_180:[bind(X_9,$fot(X_60))]]) ).
cnf(refute_0_189,plain,
( meet(top,X_60) != join(zero,complement(join(complement(meet(top,X_60)),join(zero,complement(X_60)))))
| join(zero,complement(join(complement(meet(top,X_60)),join(zero,complement(X_60))))) = meet(top,X_60) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(meet(top,X_60))),bind(Y,$fot(join(zero,complement(join(complement(meet(top,X_60)),join(zero,complement(X_60)))))))]]) ).
cnf(refute_0_190,plain,
join(zero,complement(join(complement(meet(top,X_60)),join(zero,complement(X_60))))) = meet(top,X_60),
inference(resolve,[$cnf( $equal(meet(top,X_60),join(zero,complement(join(complement(meet(top,X_60)),join(zero,complement(X_60)))))) )],[refute_0_188,refute_0_189]) ).
cnf(refute_0_191,plain,
( join(zero,complement(join(complement(meet(top,X_60)),join(zero,complement(X_60))))) != meet(top,X_60)
| meet(top,join(complement(meet(top,X_60)),join(zero,complement(X_60)))) != complement(join(zero,complement(join(complement(meet(top,X_60)),join(zero,complement(X_60))))))
| meet(top,join(complement(meet(top,X_60)),join(zero,complement(X_60)))) = complement(meet(top,X_60)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,join(complement(meet(top,X_60)),join(zero,complement(X_60)))),complement(join(zero,complement(join(complement(meet(top,X_60)),join(zero,complement(X_60))))))) ),[1,0],$fot(meet(top,X_60))]]) ).
cnf(refute_0_192,plain,
( meet(top,join(complement(meet(top,X_60)),join(zero,complement(X_60)))) != complement(join(zero,complement(join(complement(meet(top,X_60)),join(zero,complement(X_60))))))
| meet(top,join(complement(meet(top,X_60)),join(zero,complement(X_60)))) = complement(meet(top,X_60)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(complement(meet(top,X_60)),join(zero,complement(X_60))))),meet(top,X_60)) )],[refute_0_190,refute_0_191]) ).
cnf(refute_0_193,plain,
meet(top,join(complement(meet(top,X_60)),join(zero,complement(X_60)))) = complement(meet(top,X_60)),
inference(resolve,[$cnf( $equal(meet(top,join(complement(meet(top,X_60)),join(zero,complement(X_60)))),complement(join(zero,complement(join(complement(meet(top,X_60)),join(zero,complement(X_60))))))) )],[refute_0_187,refute_0_192]) ).
cnf(refute_0_194,plain,
meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9)))) = complement(meet(top,X_9)),
inference(subst,[],[refute_0_193:[bind(X_60,$fot(X_9))]]) ).
cnf(refute_0_195,plain,
( meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9)))) != complement(meet(top,X_9))
| meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9)))) != join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(top,X_9))))
| complement(meet(top,X_9)) = join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(top,X_9)))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9)))),join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(top,X_9))))) ),[0],$fot(complement(meet(top,X_9)))]]) ).
cnf(refute_0_196,plain,
( meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9)))) != join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(top,X_9))))
| complement(meet(top,X_9)) = join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(top,X_9)))) ),
inference(resolve,[$cnf( $equal(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9)))),complement(meet(top,X_9))) )],[refute_0_194,refute_0_195]) ).
cnf(refute_0_197,plain,
X_37 = join(meet(X_37,complement(complement(X_37))),complement(join(complement(X_37),complement(complement(X_37))))),
inference(subst,[],[refute_0_106:[bind(X0,$fot(X_37)),bind(X1,$fot(complement(complement(X_37))))]]) ).
cnf(refute_0_198,plain,
top = join(complement(X_37),complement(complement(X_37))),
inference(subst,[],[refute_0_130:[bind(X0,$fot(complement(X_37)))]]) ).
cnf(refute_0_199,plain,
( top != join(complement(X_37),complement(complement(X_37)))
| join(complement(X_37),complement(complement(X_37))) = top ),
inference(subst,[],[refute_0_4:[bind(X,$fot(top)),bind(Y,$fot(join(complement(X_37),complement(complement(X_37)))))]]) ).
cnf(refute_0_200,plain,
join(complement(X_37),complement(complement(X_37))) = top,
inference(resolve,[$cnf( $equal(top,join(complement(X_37),complement(complement(X_37)))) )],[refute_0_198,refute_0_199]) ).
cnf(refute_0_201,plain,
( X_37 != join(meet(X_37,complement(complement(X_37))),complement(join(complement(X_37),complement(complement(X_37)))))
| join(complement(X_37),complement(complement(X_37))) != top
| X_37 = join(meet(X_37,complement(complement(X_37))),complement(top)) ),
introduced(tautology,[equality,[$cnf( $equal(X_37,join(meet(X_37,complement(complement(X_37))),complement(join(complement(X_37),complement(complement(X_37)))))) ),[1,1,0],$fot(top)]]) ).
cnf(refute_0_202,plain,
( X_37 != join(meet(X_37,complement(complement(X_37))),complement(join(complement(X_37),complement(complement(X_37)))))
| X_37 = join(meet(X_37,complement(complement(X_37))),complement(top)) ),
inference(resolve,[$cnf( $equal(join(complement(X_37),complement(complement(X_37))),top) )],[refute_0_200,refute_0_201]) ).
cnf(refute_0_203,plain,
X_37 = join(meet(X_37,complement(complement(X_37))),complement(top)),
inference(resolve,[$cnf( $equal(X_37,join(meet(X_37,complement(complement(X_37))),complement(join(complement(X_37),complement(complement(X_37)))))) )],[refute_0_197,refute_0_202]) ).
cnf(refute_0_204,plain,
join(complement(top),meet(X_37,complement(complement(X_37)))) = join(complement(top),meet(X_37,complement(complement(X_37)))),
introduced(tautology,[refl,[$fot(join(complement(top),meet(X_37,complement(complement(X_37)))))]]) ).
cnf(refute_0_205,plain,
( complement(top) != zero
| join(complement(top),meet(X_37,complement(complement(X_37)))) != join(complement(top),meet(X_37,complement(complement(X_37))))
| join(complement(top),meet(X_37,complement(complement(X_37)))) = join(zero,meet(X_37,complement(complement(X_37)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(X_37,complement(complement(X_37)))),join(complement(top),meet(X_37,complement(complement(X_37))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_206,plain,
( complement(top) != zero
| join(complement(top),meet(X_37,complement(complement(X_37)))) = join(zero,meet(X_37,complement(complement(X_37)))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_37,complement(complement(X_37)))),join(complement(top),meet(X_37,complement(complement(X_37))))) )],[refute_0_204,refute_0_205]) ).
cnf(refute_0_207,plain,
join(complement(top),meet(X_37,complement(complement(X_37)))) = join(zero,meet(X_37,complement(complement(X_37)))),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_150,refute_0_206]) ).
cnf(refute_0_208,plain,
join(meet(X_37,complement(complement(X_37))),complement(top)) = join(complement(top),meet(X_37,complement(complement(X_37)))),
inference(subst,[],[refute_0_6:[bind(X0,$fot(complement(top))),bind(X1,$fot(meet(X_37,complement(complement(X_37)))))]]) ).
cnf(refute_0_209,plain,
( join(complement(top),meet(X_37,complement(complement(X_37)))) != join(zero,meet(X_37,complement(complement(X_37))))
| join(meet(X_37,complement(complement(X_37))),complement(top)) != join(complement(top),meet(X_37,complement(complement(X_37))))
| join(meet(X_37,complement(complement(X_37))),complement(top)) = join(zero,meet(X_37,complement(complement(X_37)))) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(meet(X_37,complement(complement(X_37))),complement(top)))),bind(Y,$fot(join(complement(top),meet(X_37,complement(complement(X_37)))))),bind(Z,$fot(join(zero,meet(X_37,complement(complement(X_37))))))]]) ).
cnf(refute_0_210,plain,
( join(complement(top),meet(X_37,complement(complement(X_37)))) != join(zero,meet(X_37,complement(complement(X_37))))
| join(meet(X_37,complement(complement(X_37))),complement(top)) = join(zero,meet(X_37,complement(complement(X_37)))) ),
inference(resolve,[$cnf( $equal(join(meet(X_37,complement(complement(X_37))),complement(top)),join(complement(top),meet(X_37,complement(complement(X_37))))) )],[refute_0_208,refute_0_209]) ).
cnf(refute_0_211,plain,
join(meet(X_37,complement(complement(X_37))),complement(top)) = join(zero,meet(X_37,complement(complement(X_37)))),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_37,complement(complement(X_37)))),join(zero,meet(X_37,complement(complement(X_37))))) )],[refute_0_207,refute_0_210]) ).
cnf(refute_0_212,plain,
( X_37 != join(meet(X_37,complement(complement(X_37))),complement(top))
| join(meet(X_37,complement(complement(X_37))),complement(top)) != join(zero,meet(X_37,complement(complement(X_37))))
| X_37 = join(zero,meet(X_37,complement(complement(X_37)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_37,join(zero,meet(X_37,complement(complement(X_37))))) ),[0],$fot(join(meet(X_37,complement(complement(X_37))),complement(top)))]]) ).
cnf(refute_0_213,plain,
( X_37 != join(meet(X_37,complement(complement(X_37))),complement(top))
| X_37 = join(zero,meet(X_37,complement(complement(X_37)))) ),
inference(resolve,[$cnf( $equal(join(meet(X_37,complement(complement(X_37))),complement(top)),join(zero,meet(X_37,complement(complement(X_37))))) )],[refute_0_211,refute_0_212]) ).
cnf(refute_0_214,plain,
X_37 = join(zero,meet(X_37,complement(complement(X_37)))),
inference(resolve,[$cnf( $equal(X_37,join(meet(X_37,complement(complement(X_37))),complement(top))) )],[refute_0_203,refute_0_213]) ).
cnf(refute_0_215,plain,
join(zero,complement(X1)) = join(zero,meet(join(zero,complement(X1)),complement(complement(join(zero,complement(X1)))))),
inference(subst,[],[refute_0_214:[bind(X_37,$fot(join(zero,complement(X1))))]]) ).
cnf(refute_0_216,plain,
( meet(top,X1) != complement(join(zero,complement(X1)))
| complement(join(zero,complement(X1))) = meet(top,X1) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(meet(top,X1))),bind(Y,$fot(complement(join(zero,complement(X1)))))]]) ).
cnf(refute_0_217,plain,
complement(join(zero,complement(X1))) = meet(top,X1),
inference(resolve,[$cnf( $equal(meet(top,X1),complement(join(zero,complement(X1)))) )],[refute_0_153,refute_0_216]) ).
cnf(refute_0_218,plain,
( complement(join(zero,complement(X1))) != meet(top,X1)
| join(zero,complement(X1)) != join(zero,meet(join(zero,complement(X1)),complement(complement(join(zero,complement(X1))))))
| join(zero,complement(X1)) = join(zero,meet(join(zero,complement(X1)),complement(meet(top,X1)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(X1)),join(zero,meet(join(zero,complement(X1)),complement(complement(join(zero,complement(X1))))))) ),[1,1,1,0],$fot(meet(top,X1))]]) ).
cnf(refute_0_219,plain,
( join(zero,complement(X1)) != join(zero,meet(join(zero,complement(X1)),complement(complement(join(zero,complement(X1))))))
| join(zero,complement(X1)) = join(zero,meet(join(zero,complement(X1)),complement(meet(top,X1)))) ),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(X1))),meet(top,X1)) )],[refute_0_217,refute_0_218]) ).
cnf(refute_0_220,plain,
join(zero,complement(X1)) = join(zero,meet(join(zero,complement(X1)),complement(meet(top,X1)))),
inference(resolve,[$cnf( $equal(join(zero,complement(X1)),join(zero,meet(join(zero,complement(X1)),complement(complement(join(zero,complement(X1))))))) )],[refute_0_215,refute_0_219]) ).
cnf(refute_0_221,plain,
meet(join(zero,complement(X1)),complement(meet(top,X1))) = meet(complement(meet(top,X1)),join(zero,complement(X1))),
inference(subst,[],[refute_0_171:[bind(X_6,$fot(complement(meet(top,X1)))),bind(X_7,$fot(join(zero,complement(X1))))]]) ).
cnf(refute_0_222,plain,
join(zero,meet(join(zero,complement(X1)),complement(meet(top,X1)))) = join(zero,meet(join(zero,complement(X1)),complement(meet(top,X1)))),
introduced(tautology,[refl,[$fot(join(zero,meet(join(zero,complement(X1)),complement(meet(top,X1)))))]]) ).
cnf(refute_0_223,plain,
( join(zero,meet(join(zero,complement(X1)),complement(meet(top,X1)))) != join(zero,meet(join(zero,complement(X1)),complement(meet(top,X1))))
| meet(join(zero,complement(X1)),complement(meet(top,X1))) != meet(complement(meet(top,X1)),join(zero,complement(X1)))
| join(zero,meet(join(zero,complement(X1)),complement(meet(top,X1)))) = join(zero,meet(complement(meet(top,X1)),join(zero,complement(X1)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,meet(join(zero,complement(X1)),complement(meet(top,X1)))),join(zero,meet(join(zero,complement(X1)),complement(meet(top,X1))))) ),[1,1],$fot(meet(complement(meet(top,X1)),join(zero,complement(X1))))]]) ).
cnf(refute_0_224,plain,
( meet(join(zero,complement(X1)),complement(meet(top,X1))) != meet(complement(meet(top,X1)),join(zero,complement(X1)))
| join(zero,meet(join(zero,complement(X1)),complement(meet(top,X1)))) = join(zero,meet(complement(meet(top,X1)),join(zero,complement(X1)))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(join(zero,complement(X1)),complement(meet(top,X1)))),join(zero,meet(join(zero,complement(X1)),complement(meet(top,X1))))) )],[refute_0_222,refute_0_223]) ).
cnf(refute_0_225,plain,
join(zero,meet(join(zero,complement(X1)),complement(meet(top,X1)))) = join(zero,meet(complement(meet(top,X1)),join(zero,complement(X1)))),
inference(resolve,[$cnf( $equal(meet(join(zero,complement(X1)),complement(meet(top,X1))),meet(complement(meet(top,X1)),join(zero,complement(X1)))) )],[refute_0_221,refute_0_224]) ).
cnf(refute_0_226,plain,
( join(zero,complement(X1)) != join(zero,meet(join(zero,complement(X1)),complement(meet(top,X1))))
| join(zero,meet(join(zero,complement(X1)),complement(meet(top,X1)))) != join(zero,meet(complement(meet(top,X1)),join(zero,complement(X1))))
| join(zero,complement(X1)) = join(zero,meet(complement(meet(top,X1)),join(zero,complement(X1)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(zero,complement(X1)),join(zero,meet(complement(meet(top,X1)),join(zero,complement(X1))))) ),[0],$fot(join(zero,meet(join(zero,complement(X1)),complement(meet(top,X1)))))]]) ).
cnf(refute_0_227,plain,
( join(zero,complement(X1)) != join(zero,meet(join(zero,complement(X1)),complement(meet(top,X1))))
| join(zero,complement(X1)) = join(zero,meet(complement(meet(top,X1)),join(zero,complement(X1)))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(join(zero,complement(X1)),complement(meet(top,X1)))),join(zero,meet(complement(meet(top,X1)),join(zero,complement(X1))))) )],[refute_0_225,refute_0_226]) ).
cnf(refute_0_228,plain,
join(zero,complement(X1)) = join(zero,meet(complement(meet(top,X1)),join(zero,complement(X1)))),
inference(resolve,[$cnf( $equal(join(zero,complement(X1)),join(zero,meet(join(zero,complement(X1)),complement(meet(top,X1))))) )],[refute_0_220,refute_0_227]) ).
cnf(refute_0_229,plain,
( join(zero,complement(X1)) != join(zero,meet(complement(meet(top,X1)),join(zero,complement(X1))))
| join(zero,meet(complement(meet(top,X1)),join(zero,complement(X1)))) = join(zero,complement(X1)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(join(zero,complement(X1)))),bind(Y,$fot(join(zero,meet(complement(meet(top,X1)),join(zero,complement(X1))))))]]) ).
cnf(refute_0_230,plain,
join(zero,meet(complement(meet(top,X1)),join(zero,complement(X1)))) = join(zero,complement(X1)),
inference(resolve,[$cnf( $equal(join(zero,complement(X1)),join(zero,meet(complement(meet(top,X1)),join(zero,complement(X1))))) )],[refute_0_228,refute_0_229]) ).
cnf(refute_0_231,plain,
join(zero,meet(complement(meet(top,X_9)),join(zero,complement(X_9)))) = join(zero,complement(X_9)),
inference(subst,[],[refute_0_230:[bind(X1,$fot(X_9))]]) ).
cnf(refute_0_232,plain,
meet(join(zero,complement(X_9)),complement(meet(top,X_9))) = meet(complement(meet(top,X_9)),join(zero,complement(X_9))),
inference(subst,[],[refute_0_171:[bind(X_6,$fot(complement(meet(top,X_9)))),bind(X_7,$fot(join(zero,complement(X_9))))]]) ).
cnf(refute_0_233,plain,
meet(join(zero,complement(X_9)),meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))) = meet(join(zero,complement(X_9)),meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),
introduced(tautology,[refl,[$fot(meet(join(zero,complement(X_9)),meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))))]]) ).
cnf(refute_0_234,plain,
( meet(join(zero,complement(X_9)),meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))) != meet(join(zero,complement(X_9)),meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9)))))
| meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9)))) != complement(meet(top,X_9))
| meet(join(zero,complement(X_9)),meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))) = meet(join(zero,complement(X_9)),complement(meet(top,X_9))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(zero,complement(X_9)),meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(join(zero,complement(X_9)),meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9)))))) ),[1,1],$fot(complement(meet(top,X_9)))]]) ).
cnf(refute_0_235,plain,
( meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9)))) != complement(meet(top,X_9))
| meet(join(zero,complement(X_9)),meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))) = meet(join(zero,complement(X_9)),complement(meet(top,X_9))) ),
inference(resolve,[$cnf( $equal(meet(join(zero,complement(X_9)),meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(join(zero,complement(X_9)),meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9)))))) )],[refute_0_233,refute_0_234]) ).
cnf(refute_0_236,plain,
meet(join(zero,complement(X_9)),meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))) = meet(join(zero,complement(X_9)),complement(meet(top,X_9))),
inference(resolve,[$cnf( $equal(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9)))),complement(meet(top,X_9))) )],[refute_0_194,refute_0_235]) ).
cnf(refute_0_237,plain,
( meet(join(zero,complement(X_9)),complement(meet(top,X_9))) != meet(complement(meet(top,X_9)),join(zero,complement(X_9)))
| meet(join(zero,complement(X_9)),meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))) != meet(join(zero,complement(X_9)),complement(meet(top,X_9)))
| meet(join(zero,complement(X_9)),meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))) = meet(complement(meet(top,X_9)),join(zero,complement(X_9))) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(meet(join(zero,complement(X_9)),meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))))),bind(Y,$fot(meet(join(zero,complement(X_9)),complement(meet(top,X_9))))),bind(Z,$fot(meet(complement(meet(top,X_9)),join(zero,complement(X_9)))))]]) ).
cnf(refute_0_238,plain,
( meet(join(zero,complement(X_9)),complement(meet(top,X_9))) != meet(complement(meet(top,X_9)),join(zero,complement(X_9)))
| meet(join(zero,complement(X_9)),meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))) = meet(complement(meet(top,X_9)),join(zero,complement(X_9))) ),
inference(resolve,[$cnf( $equal(meet(join(zero,complement(X_9)),meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(join(zero,complement(X_9)),complement(meet(top,X_9)))) )],[refute_0_236,refute_0_237]) ).
cnf(refute_0_239,plain,
meet(join(zero,complement(X_9)),meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))) = meet(complement(meet(top,X_9)),join(zero,complement(X_9))),
inference(resolve,[$cnf( $equal(meet(join(zero,complement(X_9)),complement(meet(top,X_9))),meet(complement(meet(top,X_9)),join(zero,complement(X_9)))) )],[refute_0_232,refute_0_238]) ).
cnf(refute_0_240,plain,
meet(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9)))),join(zero,complement(X_9))) = meet(join(zero,complement(X_9)),meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),
inference(subst,[],[refute_0_171:[bind(X_6,$fot(join(zero,complement(X_9)))),bind(X_7,$fot(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))))]]) ).
cnf(refute_0_241,plain,
meet(X0,join(zero,complement(X_9))) = complement(join(complement(X0),complement(join(zero,complement(X_9))))),
inference(subst,[],[refute_0_94:[bind(X1,$fot(join(zero,complement(X_9))))]]) ).
cnf(refute_0_242,plain,
( complement(join(zero,complement(X_9))) != meet(top,X_9)
| meet(X0,join(zero,complement(X_9))) != complement(join(complement(X0),complement(join(zero,complement(X_9)))))
| meet(X0,join(zero,complement(X_9))) = complement(join(complement(X0),meet(top,X_9))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X0,join(zero,complement(X_9))),complement(join(complement(X0),complement(join(zero,complement(X_9)))))) ),[1,0,1],$fot(meet(top,X_9))]]) ).
cnf(refute_0_243,plain,
( meet(X0,join(zero,complement(X_9))) != complement(join(complement(X0),complement(join(zero,complement(X_9)))))
| meet(X0,join(zero,complement(X_9))) = complement(join(complement(X0),meet(top,X_9))) ),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(X_9))),meet(top,X_9)) )],[refute_0_156,refute_0_242]) ).
cnf(refute_0_244,plain,
meet(X0,join(zero,complement(X_9))) = complement(join(complement(X0),meet(top,X_9))),
inference(resolve,[$cnf( $equal(meet(X0,join(zero,complement(X_9))),complement(join(complement(X0),complement(join(zero,complement(X_9)))))) )],[refute_0_241,refute_0_243]) ).
cnf(refute_0_245,plain,
( meet(X0,join(zero,complement(X_9))) != complement(join(complement(X0),meet(top,X_9)))
| complement(join(complement(X0),meet(top,X_9))) = meet(X0,join(zero,complement(X_9))) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(meet(X0,join(zero,complement(X_9))))),bind(Y,$fot(complement(join(complement(X0),meet(top,X_9)))))]]) ).
cnf(refute_0_246,plain,
complement(join(complement(X0),meet(top,X_9))) = meet(X0,join(zero,complement(X_9))),
inference(resolve,[$cnf( $equal(meet(X0,join(zero,complement(X_9))),complement(join(complement(X0),meet(top,X_9)))) )],[refute_0_244,refute_0_245]) ).
cnf(refute_0_247,plain,
complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(top,X_9))) = meet(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9)))),join(zero,complement(X_9))),
inference(subst,[],[refute_0_246:[bind(X0,$fot(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))))]]) ).
cnf(refute_0_248,plain,
( complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(top,X_9))) != meet(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9)))),join(zero,complement(X_9)))
| meet(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9)))),join(zero,complement(X_9))) != meet(join(zero,complement(X_9)),meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9)))))
| complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(top,X_9))) = meet(join(zero,complement(X_9)),meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(top,X_9))))),bind(Y,$fot(meet(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9)))),join(zero,complement(X_9))))),bind(Z,$fot(meet(join(zero,complement(X_9)),meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9)))))))]]) ).
cnf(refute_0_249,plain,
( meet(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9)))),join(zero,complement(X_9))) != meet(join(zero,complement(X_9)),meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9)))))
| complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(top,X_9))) = meet(join(zero,complement(X_9)),meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(top,X_9))),meet(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9)))),join(zero,complement(X_9)))) )],[refute_0_247,refute_0_248]) ).
cnf(refute_0_250,plain,
complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(top,X_9))) = meet(join(zero,complement(X_9)),meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),
inference(resolve,[$cnf( $equal(meet(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9)))),join(zero,complement(X_9))),meet(join(zero,complement(X_9)),meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9)))))) )],[refute_0_240,refute_0_249]) ).
cnf(refute_0_251,plain,
( complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(top,X_9))) != meet(join(zero,complement(X_9)),meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9)))))
| meet(join(zero,complement(X_9)),meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))) != meet(complement(meet(top,X_9)),join(zero,complement(X_9)))
| complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(top,X_9))) = meet(complement(meet(top,X_9)),join(zero,complement(X_9))) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(top,X_9))))),bind(Y,$fot(meet(join(zero,complement(X_9)),meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))))),bind(Z,$fot(meet(complement(meet(top,X_9)),join(zero,complement(X_9)))))]]) ).
cnf(refute_0_252,plain,
( meet(join(zero,complement(X_9)),meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))) != meet(complement(meet(top,X_9)),join(zero,complement(X_9)))
| complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(top,X_9))) = meet(complement(meet(top,X_9)),join(zero,complement(X_9))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(top,X_9))),meet(join(zero,complement(X_9)),meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9)))))) )],[refute_0_250,refute_0_251]) ).
cnf(refute_0_253,plain,
complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(top,X_9))) = meet(complement(meet(top,X_9)),join(zero,complement(X_9))),
inference(resolve,[$cnf( $equal(meet(join(zero,complement(X_9)),meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(complement(meet(top,X_9)),join(zero,complement(X_9)))) )],[refute_0_239,refute_0_252]) ).
cnf(refute_0_254,plain,
join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(top,X_9)))) = join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(top,X_9)))),
introduced(tautology,[refl,[$fot(join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(top,X_9)))))]]) ).
cnf(refute_0_255,plain,
( complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(top,X_9))) != meet(complement(meet(top,X_9)),join(zero,complement(X_9)))
| join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(top,X_9)))) != join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(top,X_9))))
| join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(top,X_9)))) = join(zero,meet(complement(meet(top,X_9)),join(zero,complement(X_9)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(top,X_9)))),join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(top,X_9))))) ),[1,1],$fot(meet(complement(meet(top,X_9)),join(zero,complement(X_9))))]]) ).
cnf(refute_0_256,plain,
( complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(top,X_9))) != meet(complement(meet(top,X_9)),join(zero,complement(X_9)))
| join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(top,X_9)))) = join(zero,meet(complement(meet(top,X_9)),join(zero,complement(X_9)))) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(top,X_9)))),join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(top,X_9))))) )],[refute_0_254,refute_0_255]) ).
cnf(refute_0_257,plain,
join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(top,X_9)))) = join(zero,meet(complement(meet(top,X_9)),join(zero,complement(X_9)))),
inference(resolve,[$cnf( $equal(complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(top,X_9))),meet(complement(meet(top,X_9)),join(zero,complement(X_9)))) )],[refute_0_253,refute_0_256]) ).
cnf(refute_0_258,plain,
( join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(top,X_9)))) != join(zero,meet(complement(meet(top,X_9)),join(zero,complement(X_9))))
| join(zero,meet(complement(meet(top,X_9)),join(zero,complement(X_9)))) != join(zero,complement(X_9))
| join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(top,X_9)))) = join(zero,complement(X_9)) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(top,X_9)))))),bind(Y,$fot(join(zero,meet(complement(meet(top,X_9)),join(zero,complement(X_9)))))),bind(Z,$fot(join(zero,complement(X_9))))]]) ).
cnf(refute_0_259,plain,
( join(zero,meet(complement(meet(top,X_9)),join(zero,complement(X_9)))) != join(zero,complement(X_9))
| join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(top,X_9)))) = join(zero,complement(X_9)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(top,X_9)))),join(zero,meet(complement(meet(top,X_9)),join(zero,complement(X_9))))) )],[refute_0_257,refute_0_258]) ).
cnf(refute_0_260,plain,
join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(top,X_9)))) = join(zero,complement(X_9)),
inference(resolve,[$cnf( $equal(join(zero,meet(complement(meet(top,X_9)),join(zero,complement(X_9)))),join(zero,complement(X_9))) )],[refute_0_231,refute_0_259]) ).
cnf(refute_0_261,plain,
( complement(meet(top,X_9)) != join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(top,X_9))))
| join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(top,X_9)))) != join(zero,complement(X_9))
| complement(meet(top,X_9)) = join(zero,complement(X_9)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(meet(top,X_9)),join(zero,complement(X_9))) ),[0],$fot(join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(top,X_9)))))]]) ).
cnf(refute_0_262,plain,
( complement(meet(top,X_9)) != join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(top,X_9))))
| complement(meet(top,X_9)) = join(zero,complement(X_9)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(top,X_9)))),join(zero,complement(X_9))) )],[refute_0_260,refute_0_261]) ).
cnf(refute_0_263,plain,
( meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9)))) != join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(top,X_9))))
| complement(meet(top,X_9)) = join(zero,complement(X_9)) ),
inference(resolve,[$cnf( $equal(complement(meet(top,X_9)),join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(top,X_9))))) )],[refute_0_196,refute_0_262]) ).
cnf(refute_0_264,plain,
complement(meet(top,X_9)) = join(zero,complement(X_9)),
inference(resolve,[$cnf( $equal(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9)))),join(zero,complement(join(complement(meet(top,join(complement(meet(top,X_9)),join(zero,complement(X_9))))),meet(top,X_9))))) )],[refute_0_186,refute_0_263]) ).
cnf(refute_0_265,plain,
( complement(meet(top,X_9)) != join(zero,complement(X_9))
| join(zero,complement(X_9)) = complement(meet(top,X_9)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(complement(meet(top,X_9)))),bind(Y,$fot(join(zero,complement(X_9))))]]) ).
cnf(refute_0_266,plain,
join(zero,complement(X_9)) = complement(meet(top,X_9)),
inference(resolve,[$cnf( $equal(complement(meet(top,X_9)),join(zero,complement(X_9))) )],[refute_0_264,refute_0_265]) ).
cnf(refute_0_267,plain,
join(zero,complement(complement(X_37))) = complement(meet(top,complement(X_37))),
inference(subst,[],[refute_0_266:[bind(X_9,$fot(complement(X_37)))]]) ).
cnf(refute_0_268,plain,
join(complement(complement(X_37)),zero) = join(zero,complement(complement(X_37))),
inference(subst,[],[refute_0_6:[bind(X0,$fot(zero)),bind(X1,$fot(complement(complement(X_37))))]]) ).
cnf(refute_0_269,plain,
( join(complement(complement(X_37)),zero) != join(zero,complement(complement(X_37)))
| join(zero,complement(complement(X_37))) != complement(meet(top,complement(X_37)))
| join(complement(complement(X_37)),zero) = complement(meet(top,complement(X_37))) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(complement(complement(X_37)),zero))),bind(Y,$fot(join(zero,complement(complement(X_37))))),bind(Z,$fot(complement(meet(top,complement(X_37)))))]]) ).
cnf(refute_0_270,plain,
( join(zero,complement(complement(X_37))) != complement(meet(top,complement(X_37)))
| join(complement(complement(X_37)),zero) = complement(meet(top,complement(X_37))) ),
inference(resolve,[$cnf( $equal(join(complement(complement(X_37)),zero),join(zero,complement(complement(X_37)))) )],[refute_0_268,refute_0_269]) ).
cnf(refute_0_271,plain,
join(complement(complement(X_37)),zero) = complement(meet(top,complement(X_37))),
inference(resolve,[$cnf( $equal(join(zero,complement(complement(X_37))),complement(meet(top,complement(X_37)))) )],[refute_0_267,refute_0_270]) ).
cnf(refute_0_272,plain,
( zero != meet(X0,complement(X0))
| meet(X0,complement(X0)) = zero ),
inference(subst,[],[refute_0_4:[bind(X,$fot(zero)),bind(Y,$fot(meet(X0,complement(X0))))]]) ).
cnf(refute_0_273,plain,
meet(X0,complement(X0)) = zero,
inference(resolve,[$cnf( $equal(zero,meet(X0,complement(X0))) )],[refute_0_120,refute_0_272]) ).
cnf(refute_0_274,plain,
meet(X_37,complement(X_37)) = zero,
inference(subst,[],[refute_0_273:[bind(X0,$fot(X_37))]]) ).
cnf(refute_0_275,plain,
join(complement(complement(X_37)),meet(X_37,complement(X_37))) = join(complement(complement(X_37)),meet(X_37,complement(X_37))),
introduced(tautology,[refl,[$fot(join(complement(complement(X_37)),meet(X_37,complement(X_37))))]]) ).
cnf(refute_0_276,plain,
( join(complement(complement(X_37)),meet(X_37,complement(X_37))) != join(complement(complement(X_37)),meet(X_37,complement(X_37)))
| meet(X_37,complement(X_37)) != zero
| join(complement(complement(X_37)),meet(X_37,complement(X_37))) = join(complement(complement(X_37)),zero) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(complement(X_37)),meet(X_37,complement(X_37))),join(complement(complement(X_37)),meet(X_37,complement(X_37)))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_277,plain,
( meet(X_37,complement(X_37)) != zero
| join(complement(complement(X_37)),meet(X_37,complement(X_37))) = join(complement(complement(X_37)),zero) ),
inference(resolve,[$cnf( $equal(join(complement(complement(X_37)),meet(X_37,complement(X_37))),join(complement(complement(X_37)),meet(X_37,complement(X_37)))) )],[refute_0_275,refute_0_276]) ).
cnf(refute_0_278,plain,
join(complement(complement(X_37)),meet(X_37,complement(X_37))) = join(complement(complement(X_37)),zero),
inference(resolve,[$cnf( $equal(meet(X_37,complement(X_37)),zero) )],[refute_0_274,refute_0_277]) ).
cnf(refute_0_279,plain,
( join(complement(complement(X_37)),meet(X_37,complement(X_37))) != join(complement(complement(X_37)),zero)
| join(complement(complement(X_37)),zero) != complement(meet(top,complement(X_37)))
| join(complement(complement(X_37)),meet(X_37,complement(X_37))) = complement(meet(top,complement(X_37))) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(complement(complement(X_37)),meet(X_37,complement(X_37))))),bind(Y,$fot(join(complement(complement(X_37)),zero))),bind(Z,$fot(complement(meet(top,complement(X_37)))))]]) ).
cnf(refute_0_280,plain,
( join(complement(complement(X_37)),zero) != complement(meet(top,complement(X_37)))
| join(complement(complement(X_37)),meet(X_37,complement(X_37))) = complement(meet(top,complement(X_37))) ),
inference(resolve,[$cnf( $equal(join(complement(complement(X_37)),meet(X_37,complement(X_37))),join(complement(complement(X_37)),zero)) )],[refute_0_278,refute_0_279]) ).
cnf(refute_0_281,plain,
join(complement(complement(X_37)),meet(X_37,complement(X_37))) = complement(meet(top,complement(X_37))),
inference(resolve,[$cnf( $equal(join(complement(complement(X_37)),zero),complement(meet(top,complement(X_37)))) )],[refute_0_271,refute_0_280]) ).
cnf(refute_0_282,plain,
join(meet(X_37,complement(X_37)),complement(complement(X_37))) = join(complement(complement(X_37)),meet(X_37,complement(X_37))),
inference(subst,[],[refute_0_6:[bind(X0,$fot(complement(complement(X_37)))),bind(X1,$fot(meet(X_37,complement(X_37))))]]) ).
cnf(refute_0_283,plain,
( join(complement(complement(X_37)),meet(X_37,complement(X_37))) != complement(meet(top,complement(X_37)))
| join(meet(X_37,complement(X_37)),complement(complement(X_37))) != join(complement(complement(X_37)),meet(X_37,complement(X_37)))
| join(meet(X_37,complement(X_37)),complement(complement(X_37))) = complement(meet(top,complement(X_37))) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(meet(X_37,complement(X_37)),complement(complement(X_37))))),bind(Y,$fot(join(complement(complement(X_37)),meet(X_37,complement(X_37))))),bind(Z,$fot(complement(meet(top,complement(X_37)))))]]) ).
cnf(refute_0_284,plain,
( join(complement(complement(X_37)),meet(X_37,complement(X_37))) != complement(meet(top,complement(X_37)))
| join(meet(X_37,complement(X_37)),complement(complement(X_37))) = complement(meet(top,complement(X_37))) ),
inference(resolve,[$cnf( $equal(join(meet(X_37,complement(X_37)),complement(complement(X_37))),join(complement(complement(X_37)),meet(X_37,complement(X_37)))) )],[refute_0_282,refute_0_283]) ).
cnf(refute_0_285,plain,
join(meet(X_37,complement(X_37)),complement(complement(X_37))) = complement(meet(top,complement(X_37))),
inference(resolve,[$cnf( $equal(join(complement(complement(X_37)),meet(X_37,complement(X_37))),complement(meet(top,complement(X_37)))) )],[refute_0_281,refute_0_284]) ).
cnf(refute_0_286,plain,
( X_37 != join(meet(X_37,complement(X_37)),complement(complement(X_37)))
| join(meet(X_37,complement(X_37)),complement(complement(X_37))) != complement(meet(top,complement(X_37)))
| X_37 = complement(meet(top,complement(X_37))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_37,complement(meet(top,complement(X_37)))) ),[0],$fot(join(meet(X_37,complement(X_37)),complement(complement(X_37))))]]) ).
cnf(refute_0_287,plain,
( X_37 != join(meet(X_37,complement(X_37)),complement(complement(X_37)))
| X_37 = complement(meet(top,complement(X_37))) ),
inference(resolve,[$cnf( $equal(join(meet(X_37,complement(X_37)),complement(complement(X_37))),complement(meet(top,complement(X_37)))) )],[refute_0_285,refute_0_286]) ).
cnf(refute_0_288,plain,
X_37 = complement(meet(top,complement(X_37))),
inference(resolve,[$cnf( $equal(X_37,join(meet(X_37,complement(X_37)),complement(complement(X_37)))) )],[refute_0_118,refute_0_287]) ).
cnf(refute_0_289,plain,
X_69 = complement(meet(top,complement(X_69))),
inference(subst,[],[refute_0_288:[bind(X_37,$fot(X_69))]]) ).
cnf(refute_0_290,plain,
( X_69 != complement(meet(top,complement(X_69)))
| complement(meet(top,complement(X_69))) = X_69 ),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_69)),bind(Y,$fot(complement(meet(top,complement(X_69)))))]]) ).
cnf(refute_0_291,plain,
complement(meet(top,complement(X_69))) = X_69,
inference(resolve,[$cnf( $equal(X_69,complement(meet(top,complement(X_69)))) )],[refute_0_289,refute_0_290]) ).
cnf(refute_0_292,plain,
( complement(meet(top,complement(X_69))) != X_69
| join(complement(meet(top,complement(X_69))),complement(meet(top,complement(X_69)))) != complement(meet(top,complement(X_69)))
| join(X_69,complement(meet(top,complement(X_69)))) = complement(meet(top,complement(X_69))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(meet(top,complement(X_69))),complement(meet(top,complement(X_69)))),complement(meet(top,complement(X_69)))) ),[0,0],$fot(X_69)]]) ).
cnf(refute_0_293,plain,
( join(complement(meet(top,complement(X_69))),complement(meet(top,complement(X_69)))) != complement(meet(top,complement(X_69)))
| join(X_69,complement(meet(top,complement(X_69)))) = complement(meet(top,complement(X_69))) ),
inference(resolve,[$cnf( $equal(complement(meet(top,complement(X_69))),X_69) )],[refute_0_291,refute_0_292]) ).
cnf(refute_0_294,plain,
join(X_69,complement(meet(top,complement(X_69)))) = complement(meet(top,complement(X_69))),
inference(resolve,[$cnf( $equal(join(complement(meet(top,complement(X_69))),complement(meet(top,complement(X_69)))),complement(meet(top,complement(X_69)))) )],[refute_0_87,refute_0_293]) ).
cnf(refute_0_295,plain,
join(X_69,complement(meet(top,complement(X_69)))) = join(X_69,complement(meet(top,complement(X_69)))),
introduced(tautology,[refl,[$fot(join(X_69,complement(meet(top,complement(X_69)))))]]) ).
cnf(refute_0_296,plain,
( complement(meet(top,complement(X_69))) != X_69
| join(X_69,complement(meet(top,complement(X_69)))) != join(X_69,complement(meet(top,complement(X_69))))
| join(X_69,complement(meet(top,complement(X_69)))) = join(X_69,X_69) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_69,complement(meet(top,complement(X_69)))),join(X_69,complement(meet(top,complement(X_69))))) ),[1,1],$fot(X_69)]]) ).
cnf(refute_0_297,plain,
( complement(meet(top,complement(X_69))) != X_69
| join(X_69,complement(meet(top,complement(X_69)))) = join(X_69,X_69) ),
inference(resolve,[$cnf( $equal(join(X_69,complement(meet(top,complement(X_69)))),join(X_69,complement(meet(top,complement(X_69))))) )],[refute_0_295,refute_0_296]) ).
cnf(refute_0_298,plain,
join(X_69,complement(meet(top,complement(X_69)))) = join(X_69,X_69),
inference(resolve,[$cnf( $equal(complement(meet(top,complement(X_69))),X_69) )],[refute_0_291,refute_0_297]) ).
cnf(refute_0_299,plain,
( join(X_69,complement(meet(top,complement(X_69)))) != complement(meet(top,complement(X_69)))
| join(X_69,complement(meet(top,complement(X_69)))) != join(X_69,X_69)
| join(X_69,X_69) = complement(meet(top,complement(X_69))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_69,complement(meet(top,complement(X_69)))),complement(meet(top,complement(X_69)))) ),[0],$fot(join(X_69,X_69))]]) ).
cnf(refute_0_300,plain,
( join(X_69,complement(meet(top,complement(X_69)))) != complement(meet(top,complement(X_69)))
| join(X_69,X_69) = complement(meet(top,complement(X_69))) ),
inference(resolve,[$cnf( $equal(join(X_69,complement(meet(top,complement(X_69)))),join(X_69,X_69)) )],[refute_0_298,refute_0_299]) ).
cnf(refute_0_301,plain,
( complement(meet(top,complement(X_69))) != X_69
| join(X_69,X_69) != complement(meet(top,complement(X_69)))
| join(X_69,X_69) = X_69 ),
introduced(tautology,[equality,[$cnf( $equal(join(X_69,X_69),complement(meet(top,complement(X_69)))) ),[1],$fot(X_69)]]) ).
cnf(refute_0_302,plain,
( join(X_69,X_69) != complement(meet(top,complement(X_69)))
| join(X_69,X_69) = X_69 ),
inference(resolve,[$cnf( $equal(complement(meet(top,complement(X_69))),X_69) )],[refute_0_291,refute_0_301]) ).
cnf(refute_0_303,plain,
( join(X_69,complement(meet(top,complement(X_69)))) != complement(meet(top,complement(X_69)))
| join(X_69,X_69) = X_69 ),
inference(resolve,[$cnf( $equal(join(X_69,X_69),complement(meet(top,complement(X_69)))) )],[refute_0_300,refute_0_302]) ).
cnf(refute_0_304,plain,
join(X_69,X_69) = X_69,
inference(resolve,[$cnf( $equal(join(X_69,complement(meet(top,complement(X_69)))),complement(meet(top,complement(X_69)))) )],[refute_0_294,refute_0_303]) ).
cnf(refute_0_305,plain,
join(X_95,X_95) = X_95,
inference(subst,[],[refute_0_304:[bind(X_69,$fot(X_95))]]) ).
cnf(refute_0_306,plain,
( join(X_95,X_95) != X_95
| join(X_95,join(X_95,X_96)) != join(join(X_95,X_95),X_96)
| join(X_95,join(X_95,X_96)) = join(X_95,X_96) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_95,join(X_95,X_96)),join(join(X_95,X_95),X_96)) ),[1,0],$fot(X_95)]]) ).
cnf(refute_0_307,plain,
( join(X_95,join(X_95,X_96)) != join(join(X_95,X_95),X_96)
| join(X_95,join(X_95,X_96)) = join(X_95,X_96) ),
inference(resolve,[$cnf( $equal(join(X_95,X_95),X_95) )],[refute_0_305,refute_0_306]) ).
cnf(refute_0_308,plain,
join(X_95,join(X_95,X_96)) = join(X_95,X_96),
inference(resolve,[$cnf( $equal(join(X_95,join(X_95,X_96)),join(join(X_95,X_95),X_96)) )],[refute_0_25,refute_0_307]) ).
cnf(refute_0_309,plain,
join(meet(X_156,X_155),join(meet(X_156,X_155),meet(X_156,complement(X_155)))) = join(meet(X_156,X_155),meet(X_156,complement(X_155))),
inference(subst,[],[refute_0_308:[bind(X_95,$fot(meet(X_156,X_155))),bind(X_96,$fot(meet(X_156,complement(X_155))))]]) ).
cnf(refute_0_310,plain,
X_37 = join(meet(X_37,complement(X1)),complement(join(complement(X_37),complement(X1)))),
inference(subst,[],[refute_0_106:[bind(X0,$fot(X_37)),bind(X1,$fot(complement(X1)))]]) ).
cnf(refute_0_311,plain,
meet(X_37,X1) = complement(join(complement(X_37),complement(X1))),
inference(subst,[],[refute_0_94:[bind(X0,$fot(X_37))]]) ).
cnf(refute_0_312,plain,
( meet(X_37,X1) != complement(join(complement(X_37),complement(X1)))
| complement(join(complement(X_37),complement(X1))) = meet(X_37,X1) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(meet(X_37,X1))),bind(Y,$fot(complement(join(complement(X_37),complement(X1)))))]]) ).
cnf(refute_0_313,plain,
complement(join(complement(X_37),complement(X1))) = meet(X_37,X1),
inference(resolve,[$cnf( $equal(meet(X_37,X1),complement(join(complement(X_37),complement(X1)))) )],[refute_0_311,refute_0_312]) ).
cnf(refute_0_314,plain,
( X_37 != join(meet(X_37,complement(X1)),complement(join(complement(X_37),complement(X1))))
| complement(join(complement(X_37),complement(X1))) != meet(X_37,X1)
| X_37 = join(meet(X_37,complement(X1)),meet(X_37,X1)) ),
introduced(tautology,[equality,[$cnf( $equal(X_37,join(meet(X_37,complement(X1)),complement(join(complement(X_37),complement(X1))))) ),[1,1],$fot(meet(X_37,X1))]]) ).
cnf(refute_0_315,plain,
( X_37 != join(meet(X_37,complement(X1)),complement(join(complement(X_37),complement(X1))))
| X_37 = join(meet(X_37,complement(X1)),meet(X_37,X1)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_37),complement(X1))),meet(X_37,X1)) )],[refute_0_313,refute_0_314]) ).
cnf(refute_0_316,plain,
X_37 = join(meet(X_37,complement(X1)),meet(X_37,X1)),
inference(resolve,[$cnf( $equal(X_37,join(meet(X_37,complement(X1)),complement(join(complement(X_37),complement(X1))))) )],[refute_0_310,refute_0_315]) ).
cnf(refute_0_317,plain,
join(meet(X_37,complement(X1)),meet(X_37,X1)) = join(meet(X_37,X1),meet(X_37,complement(X1))),
inference(subst,[],[refute_0_6:[bind(X0,$fot(meet(X_37,X1))),bind(X1,$fot(meet(X_37,complement(X1))))]]) ).
cnf(refute_0_318,plain,
( X_37 != join(meet(X_37,complement(X1)),meet(X_37,X1))
| join(meet(X_37,complement(X1)),meet(X_37,X1)) != join(meet(X_37,X1),meet(X_37,complement(X1)))
| X_37 = join(meet(X_37,X1),meet(X_37,complement(X1))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_37,join(meet(X_37,X1),meet(X_37,complement(X1)))) ),[0],$fot(join(meet(X_37,complement(X1)),meet(X_37,X1)))]]) ).
cnf(refute_0_319,plain,
( X_37 != join(meet(X_37,complement(X1)),meet(X_37,X1))
| X_37 = join(meet(X_37,X1),meet(X_37,complement(X1))) ),
inference(resolve,[$cnf( $equal(join(meet(X_37,complement(X1)),meet(X_37,X1)),join(meet(X_37,X1),meet(X_37,complement(X1)))) )],[refute_0_317,refute_0_318]) ).
cnf(refute_0_320,plain,
X_37 = join(meet(X_37,X1),meet(X_37,complement(X1))),
inference(resolve,[$cnf( $equal(X_37,join(meet(X_37,complement(X1)),meet(X_37,X1))) )],[refute_0_316,refute_0_319]) ).
cnf(refute_0_321,plain,
X_156 = join(meet(X_156,X_155),meet(X_156,complement(X_155))),
inference(subst,[],[refute_0_320:[bind(X1,$fot(X_155)),bind(X_37,$fot(X_156))]]) ).
cnf(refute_0_322,plain,
( X_156 != join(meet(X_156,X_155),meet(X_156,complement(X_155)))
| join(meet(X_156,X_155),meet(X_156,complement(X_155))) = X_156 ),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_156)),bind(Y,$fot(join(meet(X_156,X_155),meet(X_156,complement(X_155)))))]]) ).
cnf(refute_0_323,plain,
join(meet(X_156,X_155),meet(X_156,complement(X_155))) = X_156,
inference(resolve,[$cnf( $equal(X_156,join(meet(X_156,X_155),meet(X_156,complement(X_155)))) )],[refute_0_321,refute_0_322]) ).
cnf(refute_0_324,plain,
( join(meet(X_156,X_155),join(meet(X_156,X_155),meet(X_156,complement(X_155)))) != join(meet(X_156,X_155),meet(X_156,complement(X_155)))
| join(meet(X_156,X_155),meet(X_156,complement(X_155))) != X_156
| join(meet(X_156,X_155),X_156) = join(meet(X_156,X_155),meet(X_156,complement(X_155))) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_156,X_155),join(meet(X_156,X_155),meet(X_156,complement(X_155)))),join(meet(X_156,X_155),meet(X_156,complement(X_155)))) ),[0,1],$fot(X_156)]]) ).
cnf(refute_0_325,plain,
( join(meet(X_156,X_155),join(meet(X_156,X_155),meet(X_156,complement(X_155)))) != join(meet(X_156,X_155),meet(X_156,complement(X_155)))
| join(meet(X_156,X_155),X_156) = join(meet(X_156,X_155),meet(X_156,complement(X_155))) ),
inference(resolve,[$cnf( $equal(join(meet(X_156,X_155),meet(X_156,complement(X_155))),X_156) )],[refute_0_323,refute_0_324]) ).
cnf(refute_0_326,plain,
join(meet(X_156,X_155),X_156) = join(meet(X_156,X_155),meet(X_156,complement(X_155))),
inference(resolve,[$cnf( $equal(join(meet(X_156,X_155),join(meet(X_156,X_155),meet(X_156,complement(X_155)))),join(meet(X_156,X_155),meet(X_156,complement(X_155)))) )],[refute_0_309,refute_0_325]) ).
cnf(refute_0_327,plain,
join(meet(X_156,X_155),X_156) = join(X_156,meet(X_156,X_155)),
inference(subst,[],[refute_0_6:[bind(X0,$fot(X_156)),bind(X1,$fot(meet(X_156,X_155)))]]) ).
cnf(refute_0_328,plain,
( join(meet(X_156,X_155),X_156) != join(X_156,meet(X_156,X_155))
| join(meet(X_156,X_155),X_156) != join(meet(X_156,X_155),meet(X_156,complement(X_155)))
| join(X_156,meet(X_156,X_155)) = join(meet(X_156,X_155),meet(X_156,complement(X_155))) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_156,X_155),X_156),join(meet(X_156,X_155),meet(X_156,complement(X_155)))) ),[0],$fot(join(X_156,meet(X_156,X_155)))]]) ).
cnf(refute_0_329,plain,
( join(meet(X_156,X_155),X_156) != join(meet(X_156,X_155),meet(X_156,complement(X_155)))
| join(X_156,meet(X_156,X_155)) = join(meet(X_156,X_155),meet(X_156,complement(X_155))) ),
inference(resolve,[$cnf( $equal(join(meet(X_156,X_155),X_156),join(X_156,meet(X_156,X_155))) )],[refute_0_327,refute_0_328]) ).
cnf(refute_0_330,plain,
( join(X_156,meet(X_156,X_155)) != join(meet(X_156,X_155),meet(X_156,complement(X_155)))
| join(meet(X_156,X_155),meet(X_156,complement(X_155))) != X_156
| join(X_156,meet(X_156,X_155)) = X_156 ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_156,meet(X_156,X_155)),X_156) ),[0],$fot(join(meet(X_156,X_155),meet(X_156,complement(X_155))))]]) ).
cnf(refute_0_331,plain,
( join(X_156,meet(X_156,X_155)) != join(meet(X_156,X_155),meet(X_156,complement(X_155)))
| join(X_156,meet(X_156,X_155)) = X_156 ),
inference(resolve,[$cnf( $equal(join(meet(X_156,X_155),meet(X_156,complement(X_155))),X_156) )],[refute_0_323,refute_0_330]) ).
cnf(refute_0_332,plain,
( join(meet(X_156,X_155),X_156) != join(meet(X_156,X_155),meet(X_156,complement(X_155)))
| join(X_156,meet(X_156,X_155)) = X_156 ),
inference(resolve,[$cnf( $equal(join(X_156,meet(X_156,X_155)),join(meet(X_156,X_155),meet(X_156,complement(X_155)))) )],[refute_0_329,refute_0_331]) ).
cnf(refute_0_333,plain,
join(X_156,meet(X_156,X_155)) = X_156,
inference(resolve,[$cnf( $equal(join(meet(X_156,X_155),X_156),join(meet(X_156,X_155),meet(X_156,complement(X_155)))) )],[refute_0_326,refute_0_332]) ).
cnf(refute_0_334,plain,
join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1))) = skolemFOFtoCNF_X0,
inference(subst,[],[refute_0_333:[bind(X_155,$fot(converse(skolemFOFtoCNF_X1))),bind(X_156,$fot(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_335,plain,
composition(join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1))),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)) = composition(join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1))),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),
introduced(tautology,[refl,[$fot(composition(join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1))),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)))]]) ).
cnf(refute_0_336,plain,
( composition(join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1))),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)) != composition(join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1))),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2))
| join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1))) != skolemFOFtoCNF_X0
| composition(join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1))),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)) = composition(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1))),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),composition(join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1))),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2))) ),[1,0],$fot(skolemFOFtoCNF_X0)]]) ).
cnf(refute_0_337,plain,
( join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1))) != skolemFOFtoCNF_X0
| composition(join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1))),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)) = composition(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)) ),
inference(resolve,[$cnf( $equal(composition(join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1))),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),composition(join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1))),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2))) )],[refute_0_335,refute_0_336]) ).
cnf(refute_0_338,plain,
composition(join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1))),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)) = composition(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),
inference(resolve,[$cnf( $equal(join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1))),skolemFOFtoCNF_X0) )],[refute_0_334,refute_0_337]) ).
cnf(refute_0_339,plain,
( composition(join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1))),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)) != composition(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2))
| composition(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)) != composition(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2))
| composition(join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1))),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)) = composition(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1))),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),composition(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2))) ),[0],$fot(composition(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)))]]) ).
cnf(refute_0_340,plain,
( composition(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)) != composition(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2))
| composition(join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1))),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)) = composition(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)) ),
inference(resolve,[$cnf( $equal(composition(join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1))),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),composition(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2))) )],[refute_0_338,refute_0_339]) ).
cnf(refute_0_341,plain,
composition(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)) != composition(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),
inference(resolve,[$cnf( $equal(composition(join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X0,converse(skolemFOFtoCNF_X1))),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),composition(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2))) )],[refute_0_340,refute_0_23]) ).
cnf(refute_0_342,plain,
composition(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)) = composition(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),
introduced(tautology,[refl,[$fot(composition(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)))]]) ).
cnf(refute_0_343,plain,
$false,
inference(resolve,[$cnf( $equal(composition(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),composition(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2))) )],[refute_0_342,refute_0_341]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : REL023+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n012.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Fri Jul 8 09:13:29 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.89/1.08 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.89/1.08
% 0.89/1.08 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.95/1.12
%------------------------------------------------------------------------------