TSTP Solution File: LAT027-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LAT027-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n013.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 : Sun Jul 17 05:58:58 EDT 2022
% Result : Unsatisfiable 100.13s 100.31s
% Output : CNFRefutation 100.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 55
% Number of leaves : 94
% Syntax : Number of clauses : 450 ( 244 unt; 0 nHn; 214 RR)
% Number of literals : 748 ( 747 equ; 301 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 1281 ( 96 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(idempotence_of_join,axiom,
join(X,X) = X ).
cnf(commutativity_of_meet,axiom,
meet(X,Y) = meet(Y,X) ).
cnf(commutativity_of_join,axiom,
join(X,Y) = join(Y,X) ).
cnf(wal_1,axiom,
meet(meet(join(X,Y),join(Z,Y)),Y) = Y ).
cnf(wal_2,axiom,
join(join(meet(X,Y),meet(Z,Y)),Y) = Y ).
cnf(absorption,hypothesis,
meet(X,join(Y,join(X,Z))) = X ).
cnf(prove_associativity_of_join,negated_conjecture,
join(join(a,b),c) != join(a,join(b,c)) ).
cnf(refute_0_0,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_1,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_2,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( join(X,Y) != join(Y,X)
| join(Y,X) = join(X,Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(join(X,Y))),bind(Y0,$fot(join(Y,X)))]]) ).
cnf(refute_0_4,plain,
join(Y,X) = join(X,Y),
inference(resolve,[$cnf( $equal(join(X,Y),join(Y,X)) )],[commutativity_of_join,refute_0_3]) ).
cnf(refute_0_5,plain,
join(join(a,b),c) = join(c,join(a,b)),
inference(subst,[],[refute_0_4:[bind(X,$fot(c)),bind(Y,$fot(join(a,b)))]]) ).
cnf(refute_0_6,plain,
( join(c,join(a,b)) != join(a,join(b,c))
| join(join(a,b),c) != join(c,join(a,b))
| join(join(a,b),c) = join(a,join(b,c)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(a,b),c),join(c,join(a,b))) ),[1],$fot(join(a,join(b,c)))]]) ).
cnf(refute_0_7,plain,
( join(c,join(a,b)) != join(a,join(b,c))
| join(join(a,b),c) = join(a,join(b,c)) ),
inference(resolve,[$cnf( $equal(join(join(a,b),c),join(c,join(a,b))) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
join(c,join(a,b)) != join(a,join(b,c)),
inference(resolve,[$cnf( $equal(join(join(a,b),c),join(a,join(b,c))) )],[refute_0_7,prove_associativity_of_join]) ).
cnf(refute_0_9,plain,
join(join(meet(X,Y),meet(Z,Y)),Y) = join(Y,join(meet(X,Y),meet(Z,Y))),
inference(subst,[],[refute_0_4:[bind(X,$fot(Y)),bind(Y,$fot(join(meet(X,Y),meet(Z,Y))))]]) ).
cnf(refute_0_10,plain,
( join(join(meet(X,Y),meet(Z,Y)),Y) != Y
| join(join(meet(X,Y),meet(Z,Y)),Y) != join(Y,join(meet(X,Y),meet(Z,Y)))
| join(Y,join(meet(X,Y),meet(Z,Y))) = Y ),
introduced(tautology,[equality,[$cnf( $equal(join(join(meet(X,Y),meet(Z,Y)),Y),Y) ),[0],$fot(join(Y,join(meet(X,Y),meet(Z,Y))))]]) ).
cnf(refute_0_11,plain,
( join(join(meet(X,Y),meet(Z,Y)),Y) != Y
| join(Y,join(meet(X,Y),meet(Z,Y))) = Y ),
inference(resolve,[$cnf( $equal(join(join(meet(X,Y),meet(Z,Y)),Y),join(Y,join(meet(X,Y),meet(Z,Y)))) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
join(Y,join(meet(X,Y),meet(Z,Y))) = Y,
inference(resolve,[$cnf( $equal(join(join(meet(X,Y),meet(Z,Y)),Y),Y) )],[wal_2,refute_0_11]) ).
cnf(refute_0_13,plain,
join(join(X_7,X_24),join(meet(X_22,join(X_7,X_24)),meet(X_24,join(X_7,X_24)))) = join(X_7,X_24),
inference(subst,[],[refute_0_12:[bind(X,$fot(X_22)),bind(Y,$fot(join(X_7,X_24))),bind(Z,$fot(X_24))]]) ).
cnf(refute_0_14,plain,
meet(X_8,join(X_7,join(X_8,X_8))) = X_8,
inference(subst,[],[absorption:[bind(X,$fot(X_8)),bind(Y,$fot(X_7)),bind(Z,$fot(X_8))]]) ).
cnf(refute_0_15,plain,
join(X_8,X_8) = X_8,
inference(subst,[],[idempotence_of_join:[bind(X,$fot(X_8))]]) ).
cnf(refute_0_16,plain,
( join(X_8,X_8) != X_8
| meet(X_8,join(X_7,join(X_8,X_8))) != X_8
| meet(X_8,join(X_7,X_8)) = X_8 ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_8,join(X_7,join(X_8,X_8))),X_8) ),[0,1,1],$fot(X_8)]]) ).
cnf(refute_0_17,plain,
( meet(X_8,join(X_7,join(X_8,X_8))) != X_8
| meet(X_8,join(X_7,X_8)) = X_8 ),
inference(resolve,[$cnf( $equal(join(X_8,X_8),X_8) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
meet(X_8,join(X_7,X_8)) = X_8,
inference(resolve,[$cnf( $equal(meet(X_8,join(X_7,join(X_8,X_8))),X_8) )],[refute_0_14,refute_0_17]) ).
cnf(refute_0_19,plain,
meet(X_24,join(X_7,X_24)) = X_24,
inference(subst,[],[refute_0_18:[bind(X_8,$fot(X_24))]]) ).
cnf(refute_0_20,plain,
( join(join(X_7,X_24),join(meet(X_22,join(X_7,X_24)),meet(X_24,join(X_7,X_24)))) != join(X_7,X_24)
| meet(X_24,join(X_7,X_24)) != X_24
| join(join(X_7,X_24),join(meet(X_22,join(X_7,X_24)),X_24)) = join(X_7,X_24) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_7,X_24),join(meet(X_22,join(X_7,X_24)),meet(X_24,join(X_7,X_24)))),join(X_7,X_24)) ),[0,1,1],$fot(X_24)]]) ).
cnf(refute_0_21,plain,
( join(join(X_7,X_24),join(meet(X_22,join(X_7,X_24)),meet(X_24,join(X_7,X_24)))) != join(X_7,X_24)
| join(join(X_7,X_24),join(meet(X_22,join(X_7,X_24)),X_24)) = join(X_7,X_24) ),
inference(resolve,[$cnf( $equal(meet(X_24,join(X_7,X_24)),X_24) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
join(join(X_7,X_24),join(meet(X_22,join(X_7,X_24)),X_24)) = join(X_7,X_24),
inference(resolve,[$cnf( $equal(join(join(X_7,X_24),join(meet(X_22,join(X_7,X_24)),meet(X_24,join(X_7,X_24)))),join(X_7,X_24)) )],[refute_0_13,refute_0_21]) ).
cnf(refute_0_23,plain,
join(meet(X_22,join(X_7,X_24)),X_24) = join(X_24,meet(X_22,join(X_7,X_24))),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_24)),bind(Y,$fot(meet(X_22,join(X_7,X_24))))]]) ).
cnf(refute_0_24,plain,
join(join(X_7,X_24),join(meet(X_22,join(X_7,X_24)),X_24)) = join(join(X_7,X_24),join(meet(X_22,join(X_7,X_24)),X_24)),
introduced(tautology,[refl,[$fot(join(join(X_7,X_24),join(meet(X_22,join(X_7,X_24)),X_24)))]]) ).
cnf(refute_0_25,plain,
( join(join(X_7,X_24),join(meet(X_22,join(X_7,X_24)),X_24)) != join(join(X_7,X_24),join(meet(X_22,join(X_7,X_24)),X_24))
| join(meet(X_22,join(X_7,X_24)),X_24) != join(X_24,meet(X_22,join(X_7,X_24)))
| join(join(X_7,X_24),join(meet(X_22,join(X_7,X_24)),X_24)) = join(join(X_7,X_24),join(X_24,meet(X_22,join(X_7,X_24)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_7,X_24),join(meet(X_22,join(X_7,X_24)),X_24)),join(join(X_7,X_24),join(meet(X_22,join(X_7,X_24)),X_24))) ),[1,1],$fot(join(X_24,meet(X_22,join(X_7,X_24))))]]) ).
cnf(refute_0_26,plain,
( join(meet(X_22,join(X_7,X_24)),X_24) != join(X_24,meet(X_22,join(X_7,X_24)))
| join(join(X_7,X_24),join(meet(X_22,join(X_7,X_24)),X_24)) = join(join(X_7,X_24),join(X_24,meet(X_22,join(X_7,X_24)))) ),
inference(resolve,[$cnf( $equal(join(join(X_7,X_24),join(meet(X_22,join(X_7,X_24)),X_24)),join(join(X_7,X_24),join(meet(X_22,join(X_7,X_24)),X_24))) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
join(join(X_7,X_24),join(meet(X_22,join(X_7,X_24)),X_24)) = join(join(X_7,X_24),join(X_24,meet(X_22,join(X_7,X_24)))),
inference(resolve,[$cnf( $equal(join(meet(X_22,join(X_7,X_24)),X_24),join(X_24,meet(X_22,join(X_7,X_24)))) )],[refute_0_23,refute_0_26]) ).
cnf(refute_0_28,plain,
( join(join(X_7,X_24),join(meet(X_22,join(X_7,X_24)),X_24)) != join(X_7,X_24)
| join(join(X_7,X_24),join(meet(X_22,join(X_7,X_24)),X_24)) != join(join(X_7,X_24),join(X_24,meet(X_22,join(X_7,X_24))))
| join(join(X_7,X_24),join(X_24,meet(X_22,join(X_7,X_24)))) = join(X_7,X_24) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_7,X_24),join(meet(X_22,join(X_7,X_24)),X_24)),join(X_7,X_24)) ),[0],$fot(join(join(X_7,X_24),join(X_24,meet(X_22,join(X_7,X_24)))))]]) ).
cnf(refute_0_29,plain,
( join(join(X_7,X_24),join(meet(X_22,join(X_7,X_24)),X_24)) != join(X_7,X_24)
| join(join(X_7,X_24),join(X_24,meet(X_22,join(X_7,X_24)))) = join(X_7,X_24) ),
inference(resolve,[$cnf( $equal(join(join(X_7,X_24),join(meet(X_22,join(X_7,X_24)),X_24)),join(join(X_7,X_24),join(X_24,meet(X_22,join(X_7,X_24))))) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
join(join(X_7,X_24),join(X_24,meet(X_22,join(X_7,X_24)))) = join(X_7,X_24),
inference(resolve,[$cnf( $equal(join(join(X_7,X_24),join(meet(X_22,join(X_7,X_24)),X_24)),join(X_7,X_24)) )],[refute_0_22,refute_0_29]) ).
cnf(refute_0_31,plain,
join(join(join(X_15,X_114),X_115),join(X_115,meet(X_114,join(join(X_15,X_114),X_115)))) = join(join(X_15,X_114),X_115),
inference(subst,[],[refute_0_30:[bind(X_22,$fot(X_114)),bind(X_24,$fot(X_115)),bind(X_7,$fot(join(X_15,X_114)))]]) ).
cnf(refute_0_32,plain,
meet(X_6,join(X_7,join(X_6,X_8))) = X_6,
inference(subst,[],[absorption:[bind(X,$fot(X_6)),bind(Y,$fot(X_7)),bind(Z,$fot(X_8))]]) ).
cnf(refute_0_33,plain,
join(join(X_6,X_8),X_7) = join(X_7,join(X_6,X_8)),
inference(subst,[],[commutativity_of_join:[bind(X,$fot(join(X_6,X_8))),bind(Y,$fot(X_7))]]) ).
cnf(refute_0_34,plain,
( join(join(X_6,X_8),X_7) != join(X_7,join(X_6,X_8))
| join(X_7,join(X_6,X_8)) = join(join(X_6,X_8),X_7) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(join(join(X_6,X_8),X_7))),bind(Y0,$fot(join(X_7,join(X_6,X_8))))]]) ).
cnf(refute_0_35,plain,
join(X_7,join(X_6,X_8)) = join(join(X_6,X_8),X_7),
inference(resolve,[$cnf( $equal(join(join(X_6,X_8),X_7),join(X_7,join(X_6,X_8))) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
( join(X_7,join(X_6,X_8)) != join(join(X_6,X_8),X_7)
| meet(X_6,join(X_7,join(X_6,X_8))) != X_6
| meet(X_6,join(join(X_6,X_8),X_7)) = X_6 ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_6,join(X_7,join(X_6,X_8))),X_6) ),[0,1],$fot(join(join(X_6,X_8),X_7))]]) ).
cnf(refute_0_37,plain,
( meet(X_6,join(X_7,join(X_6,X_8))) != X_6
| meet(X_6,join(join(X_6,X_8),X_7)) = X_6 ),
inference(resolve,[$cnf( $equal(join(X_7,join(X_6,X_8)),join(join(X_6,X_8),X_7)) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
meet(X_6,join(join(X_6,X_8),X_7)) = X_6,
inference(resolve,[$cnf( $equal(meet(X_6,join(X_7,join(X_6,X_8))),X_6) )],[refute_0_32,refute_0_37]) ).
cnf(refute_0_39,plain,
meet(X_13,join(join(X_13,X_15),X_14)) = X_13,
inference(subst,[],[refute_0_38:[bind(X_6,$fot(X_13)),bind(X_7,$fot(X_14)),bind(X_8,$fot(X_15))]]) ).
cnf(refute_0_40,plain,
join(X_15,X_13) = join(X_13,X_15),
inference(subst,[],[commutativity_of_join:[bind(X,$fot(X_15)),bind(Y,$fot(X_13))]]) ).
cnf(refute_0_41,plain,
( join(X_15,X_13) != join(X_13,X_15)
| join(X_13,X_15) = join(X_15,X_13) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(join(X_15,X_13))),bind(Y0,$fot(join(X_13,X_15)))]]) ).
cnf(refute_0_42,plain,
join(X_13,X_15) = join(X_15,X_13),
inference(resolve,[$cnf( $equal(join(X_15,X_13),join(X_13,X_15)) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
( join(X_13,X_15) != join(X_15,X_13)
| meet(X_13,join(join(X_13,X_15),X_14)) != X_13
| meet(X_13,join(join(X_15,X_13),X_14)) = X_13 ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_13,join(join(X_13,X_15),X_14)),X_13) ),[0,1,0],$fot(join(X_15,X_13))]]) ).
cnf(refute_0_44,plain,
( meet(X_13,join(join(X_13,X_15),X_14)) != X_13
| meet(X_13,join(join(X_15,X_13),X_14)) = X_13 ),
inference(resolve,[$cnf( $equal(join(X_13,X_15),join(X_15,X_13)) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
meet(X_13,join(join(X_15,X_13),X_14)) = X_13,
inference(resolve,[$cnf( $equal(meet(X_13,join(join(X_13,X_15),X_14)),X_13) )],[refute_0_39,refute_0_44]) ).
cnf(refute_0_46,plain,
meet(X_114,join(join(X_15,X_114),X_115)) = X_114,
inference(subst,[],[refute_0_45:[bind(X_13,$fot(X_114)),bind(X_14,$fot(X_115))]]) ).
cnf(refute_0_47,plain,
( join(join(join(X_15,X_114),X_115),join(X_115,meet(X_114,join(join(X_15,X_114),X_115)))) != join(join(X_15,X_114),X_115)
| meet(X_114,join(join(X_15,X_114),X_115)) != X_114
| join(join(join(X_15,X_114),X_115),join(X_115,X_114)) = join(join(X_15,X_114),X_115) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(join(X_15,X_114),X_115),join(X_115,meet(X_114,join(join(X_15,X_114),X_115)))),join(join(X_15,X_114),X_115)) ),[0,1,1],$fot(X_114)]]) ).
cnf(refute_0_48,plain,
( join(join(join(X_15,X_114),X_115),join(X_115,meet(X_114,join(join(X_15,X_114),X_115)))) != join(join(X_15,X_114),X_115)
| join(join(join(X_15,X_114),X_115),join(X_115,X_114)) = join(join(X_15,X_114),X_115) ),
inference(resolve,[$cnf( $equal(meet(X_114,join(join(X_15,X_114),X_115)),X_114) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
join(join(join(X_15,X_114),X_115),join(X_115,X_114)) = join(join(X_15,X_114),X_115),
inference(resolve,[$cnf( $equal(join(join(join(X_15,X_114),X_115),join(X_115,meet(X_114,join(join(X_15,X_114),X_115)))),join(join(X_15,X_114),X_115)) )],[refute_0_31,refute_0_48]) ).
cnf(refute_0_50,plain,
join(join(join(X_15,X_114),X_115),join(X_115,X_114)) = join(join(X_115,X_114),join(join(X_15,X_114),X_115)),
inference(subst,[],[refute_0_4:[bind(X,$fot(join(X_115,X_114))),bind(Y,$fot(join(join(X_15,X_114),X_115)))]]) ).
cnf(refute_0_51,plain,
( join(join(join(X_15,X_114),X_115),join(X_115,X_114)) != join(join(X_115,X_114),join(join(X_15,X_114),X_115))
| join(join(join(X_15,X_114),X_115),join(X_115,X_114)) != join(join(X_15,X_114),X_115)
| join(join(X_115,X_114),join(join(X_15,X_114),X_115)) = join(join(X_15,X_114),X_115) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(join(X_15,X_114),X_115),join(X_115,X_114)),join(join(X_15,X_114),X_115)) ),[0],$fot(join(join(X_115,X_114),join(join(X_15,X_114),X_115)))]]) ).
cnf(refute_0_52,plain,
( join(join(join(X_15,X_114),X_115),join(X_115,X_114)) != join(join(X_15,X_114),X_115)
| join(join(X_115,X_114),join(join(X_15,X_114),X_115)) = join(join(X_15,X_114),X_115) ),
inference(resolve,[$cnf( $equal(join(join(join(X_15,X_114),X_115),join(X_115,X_114)),join(join(X_115,X_114),join(join(X_15,X_114),X_115))) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
join(join(X_115,X_114),join(join(X_15,X_114),X_115)) = join(join(X_15,X_114),X_115),
inference(resolve,[$cnf( $equal(join(join(join(X_15,X_114),X_115),join(X_115,X_114)),join(join(X_15,X_114),X_115)) )],[refute_0_49,refute_0_52]) ).
cnf(refute_0_54,plain,
join(join(join(X_359,meet(X_357,X_26)),X_357),join(join(X_359,X_357),join(X_359,meet(X_357,X_26)))) = join(join(X_359,X_357),join(X_359,meet(X_357,X_26))),
inference(subst,[],[refute_0_53:[bind(X_114,$fot(X_357)),bind(X_115,$fot(join(X_359,meet(X_357,X_26)))),bind(X_15,$fot(X_359))]]) ).
cnf(refute_0_55,plain,
join(join(X_24,X_8),join(meet(X_22,join(X_24,X_8)),meet(X_24,join(X_24,X_8)))) = join(X_24,X_8),
inference(subst,[],[refute_0_12:[bind(X,$fot(X_22)),bind(Y,$fot(join(X_24,X_8))),bind(Z,$fot(X_24))]]) ).
cnf(refute_0_56,plain,
meet(X_6,join(join(X_6,X_8),join(X_6,X_8))) = X_6,
inference(subst,[],[absorption:[bind(X,$fot(X_6)),bind(Y,$fot(join(X_6,X_8))),bind(Z,$fot(X_8))]]) ).
cnf(refute_0_57,plain,
join(join(X_6,X_8),join(X_6,X_8)) = join(X_6,X_8),
inference(subst,[],[idempotence_of_join:[bind(X,$fot(join(X_6,X_8)))]]) ).
cnf(refute_0_58,plain,
( join(join(X_6,X_8),join(X_6,X_8)) != join(X_6,X_8)
| meet(X_6,join(join(X_6,X_8),join(X_6,X_8))) != X_6
| meet(X_6,join(X_6,X_8)) = X_6 ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_6,join(join(X_6,X_8),join(X_6,X_8))),X_6) ),[0,1],$fot(join(X_6,X_8))]]) ).
cnf(refute_0_59,plain,
( meet(X_6,join(join(X_6,X_8),join(X_6,X_8))) != X_6
| meet(X_6,join(X_6,X_8)) = X_6 ),
inference(resolve,[$cnf( $equal(join(join(X_6,X_8),join(X_6,X_8)),join(X_6,X_8)) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
meet(X_6,join(X_6,X_8)) = X_6,
inference(resolve,[$cnf( $equal(meet(X_6,join(join(X_6,X_8),join(X_6,X_8))),X_6) )],[refute_0_56,refute_0_59]) ).
cnf(refute_0_61,plain,
meet(X_24,join(X_24,X_8)) = X_24,
inference(subst,[],[refute_0_60:[bind(X_6,$fot(X_24))]]) ).
cnf(refute_0_62,plain,
( join(join(X_24,X_8),join(meet(X_22,join(X_24,X_8)),meet(X_24,join(X_24,X_8)))) != join(X_24,X_8)
| meet(X_24,join(X_24,X_8)) != X_24
| join(join(X_24,X_8),join(meet(X_22,join(X_24,X_8)),X_24)) = join(X_24,X_8) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_24,X_8),join(meet(X_22,join(X_24,X_8)),meet(X_24,join(X_24,X_8)))),join(X_24,X_8)) ),[0,1,1],$fot(X_24)]]) ).
cnf(refute_0_63,plain,
( join(join(X_24,X_8),join(meet(X_22,join(X_24,X_8)),meet(X_24,join(X_24,X_8)))) != join(X_24,X_8)
| join(join(X_24,X_8),join(meet(X_22,join(X_24,X_8)),X_24)) = join(X_24,X_8) ),
inference(resolve,[$cnf( $equal(meet(X_24,join(X_24,X_8)),X_24) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
join(join(X_24,X_8),join(meet(X_22,join(X_24,X_8)),X_24)) = join(X_24,X_8),
inference(resolve,[$cnf( $equal(join(join(X_24,X_8),join(meet(X_22,join(X_24,X_8)),meet(X_24,join(X_24,X_8)))),join(X_24,X_8)) )],[refute_0_55,refute_0_63]) ).
cnf(refute_0_65,plain,
join(meet(X_22,join(X_24,X_8)),X_24) = join(X_24,meet(X_22,join(X_24,X_8))),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_24)),bind(Y,$fot(meet(X_22,join(X_24,X_8))))]]) ).
cnf(refute_0_66,plain,
join(join(X_24,X_8),join(meet(X_22,join(X_24,X_8)),X_24)) = join(join(X_24,X_8),join(meet(X_22,join(X_24,X_8)),X_24)),
introduced(tautology,[refl,[$fot(join(join(X_24,X_8),join(meet(X_22,join(X_24,X_8)),X_24)))]]) ).
cnf(refute_0_67,plain,
( join(join(X_24,X_8),join(meet(X_22,join(X_24,X_8)),X_24)) != join(join(X_24,X_8),join(meet(X_22,join(X_24,X_8)),X_24))
| join(meet(X_22,join(X_24,X_8)),X_24) != join(X_24,meet(X_22,join(X_24,X_8)))
| join(join(X_24,X_8),join(meet(X_22,join(X_24,X_8)),X_24)) = join(join(X_24,X_8),join(X_24,meet(X_22,join(X_24,X_8)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_24,X_8),join(meet(X_22,join(X_24,X_8)),X_24)),join(join(X_24,X_8),join(meet(X_22,join(X_24,X_8)),X_24))) ),[1,1],$fot(join(X_24,meet(X_22,join(X_24,X_8))))]]) ).
cnf(refute_0_68,plain,
( join(meet(X_22,join(X_24,X_8)),X_24) != join(X_24,meet(X_22,join(X_24,X_8)))
| join(join(X_24,X_8),join(meet(X_22,join(X_24,X_8)),X_24)) = join(join(X_24,X_8),join(X_24,meet(X_22,join(X_24,X_8)))) ),
inference(resolve,[$cnf( $equal(join(join(X_24,X_8),join(meet(X_22,join(X_24,X_8)),X_24)),join(join(X_24,X_8),join(meet(X_22,join(X_24,X_8)),X_24))) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
join(join(X_24,X_8),join(meet(X_22,join(X_24,X_8)),X_24)) = join(join(X_24,X_8),join(X_24,meet(X_22,join(X_24,X_8)))),
inference(resolve,[$cnf( $equal(join(meet(X_22,join(X_24,X_8)),X_24),join(X_24,meet(X_22,join(X_24,X_8)))) )],[refute_0_65,refute_0_68]) ).
cnf(refute_0_70,plain,
( join(join(X_24,X_8),join(meet(X_22,join(X_24,X_8)),X_24)) != join(X_24,X_8)
| join(join(X_24,X_8),join(meet(X_22,join(X_24,X_8)),X_24)) != join(join(X_24,X_8),join(X_24,meet(X_22,join(X_24,X_8))))
| join(join(X_24,X_8),join(X_24,meet(X_22,join(X_24,X_8)))) = join(X_24,X_8) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_24,X_8),join(meet(X_22,join(X_24,X_8)),X_24)),join(X_24,X_8)) ),[0],$fot(join(join(X_24,X_8),join(X_24,meet(X_22,join(X_24,X_8)))))]]) ).
cnf(refute_0_71,plain,
( join(join(X_24,X_8),join(meet(X_22,join(X_24,X_8)),X_24)) != join(X_24,X_8)
| join(join(X_24,X_8),join(X_24,meet(X_22,join(X_24,X_8)))) = join(X_24,X_8) ),
inference(resolve,[$cnf( $equal(join(join(X_24,X_8),join(meet(X_22,join(X_24,X_8)),X_24)),join(join(X_24,X_8),join(X_24,meet(X_22,join(X_24,X_8))))) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
join(join(X_24,X_8),join(X_24,meet(X_22,join(X_24,X_8)))) = join(X_24,X_8),
inference(resolve,[$cnf( $equal(join(join(X_24,X_8),join(meet(X_22,join(X_24,X_8)),X_24)),join(X_24,X_8)) )],[refute_0_64,refute_0_71]) ).
cnf(refute_0_73,plain,
join(join(X_69,X_70),join(X_69,meet(meet(X_70,X_26),join(X_69,X_70)))) = join(X_69,X_70),
inference(subst,[],[refute_0_72:[bind(X_22,$fot(meet(X_70,X_26))),bind(X_24,$fot(X_69)),bind(X_8,$fot(X_70))]]) ).
cnf(refute_0_74,plain,
join(X_8,X_6) = join(X_6,X_8),
inference(subst,[],[commutativity_of_join:[bind(X,$fot(X_8)),bind(Y,$fot(X_6))]]) ).
cnf(refute_0_75,plain,
( join(X_8,X_6) != join(X_6,X_8)
| join(X_6,X_8) = join(X_8,X_6) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(join(X_8,X_6))),bind(Y0,$fot(join(X_6,X_8)))]]) ).
cnf(refute_0_76,plain,
join(X_6,X_8) = join(X_8,X_6),
inference(resolve,[$cnf( $equal(join(X_8,X_6),join(X_6,X_8)) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
( join(X_6,X_8) != join(X_8,X_6)
| meet(X_6,join(X_7,join(X_6,X_8))) != X_6
| meet(X_6,join(X_7,join(X_8,X_6))) = X_6 ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_6,join(X_7,join(X_6,X_8))),X_6) ),[0,1,1],$fot(join(X_8,X_6))]]) ).
cnf(refute_0_78,plain,
( meet(X_6,join(X_7,join(X_6,X_8))) != X_6
| meet(X_6,join(X_7,join(X_8,X_6))) = X_6 ),
inference(resolve,[$cnf( $equal(join(X_6,X_8),join(X_8,X_6)) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
meet(X_6,join(X_7,join(X_8,X_6))) = X_6,
inference(resolve,[$cnf( $equal(meet(X_6,join(X_7,join(X_6,X_8))),X_6) )],[refute_0_32,refute_0_78]) ).
cnf(refute_0_80,plain,
meet(meet(X_37,X_26),join(X_36,join(X_37,meet(X_37,X_26)))) = meet(X_37,X_26),
inference(subst,[],[refute_0_79:[bind(X_6,$fot(meet(X_37,X_26))),bind(X_7,$fot(X_36)),bind(X_8,$fot(X_37))]]) ).
cnf(refute_0_81,plain,
join(X_23,join(meet(X_24,X_23),meet(X_24,X_23))) = X_23,
inference(subst,[],[refute_0_12:[bind(X,$fot(X_24)),bind(Y,$fot(X_23)),bind(Z,$fot(X_24))]]) ).
cnf(refute_0_82,plain,
join(meet(X_24,X_23),meet(X_24,X_23)) = meet(X_24,X_23),
inference(subst,[],[idempotence_of_join:[bind(X,$fot(meet(X_24,X_23)))]]) ).
cnf(refute_0_83,plain,
( join(X_23,join(meet(X_24,X_23),meet(X_24,X_23))) != X_23
| join(meet(X_24,X_23),meet(X_24,X_23)) != meet(X_24,X_23)
| join(X_23,meet(X_24,X_23)) = X_23 ),
introduced(tautology,[equality,[$cnf( $equal(join(X_23,join(meet(X_24,X_23),meet(X_24,X_23))),X_23) ),[0,1],$fot(meet(X_24,X_23))]]) ).
cnf(refute_0_84,plain,
( join(X_23,join(meet(X_24,X_23),meet(X_24,X_23))) != X_23
| join(X_23,meet(X_24,X_23)) = X_23 ),
inference(resolve,[$cnf( $equal(join(meet(X_24,X_23),meet(X_24,X_23)),meet(X_24,X_23)) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
join(X_23,meet(X_24,X_23)) = X_23,
inference(resolve,[$cnf( $equal(join(X_23,join(meet(X_24,X_23),meet(X_24,X_23))),X_23) )],[refute_0_81,refute_0_84]) ).
cnf(refute_0_86,plain,
join(X_25,meet(X_26,X_25)) = X_25,
inference(subst,[],[refute_0_85:[bind(X_23,$fot(X_25)),bind(X_24,$fot(X_26))]]) ).
cnf(refute_0_87,plain,
meet(X_25,X_26) = meet(X_26,X_25),
inference(subst,[],[commutativity_of_meet:[bind(X,$fot(X_25)),bind(Y,$fot(X_26))]]) ).
cnf(refute_0_88,plain,
( meet(X_25,X_26) != meet(X_26,X_25)
| meet(X_26,X_25) = meet(X_25,X_26) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(meet(X_25,X_26))),bind(Y0,$fot(meet(X_26,X_25)))]]) ).
cnf(refute_0_89,plain,
meet(X_26,X_25) = meet(X_25,X_26),
inference(resolve,[$cnf( $equal(meet(X_25,X_26),meet(X_26,X_25)) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
( join(X_25,meet(X_26,X_25)) != X_25
| meet(X_26,X_25) != meet(X_25,X_26)
| join(X_25,meet(X_25,X_26)) = X_25 ),
introduced(tautology,[equality,[$cnf( $equal(join(X_25,meet(X_26,X_25)),X_25) ),[0,1],$fot(meet(X_25,X_26))]]) ).
cnf(refute_0_91,plain,
( join(X_25,meet(X_26,X_25)) != X_25
| join(X_25,meet(X_25,X_26)) = X_25 ),
inference(resolve,[$cnf( $equal(meet(X_26,X_25),meet(X_25,X_26)) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
join(X_25,meet(X_25,X_26)) = X_25,
inference(resolve,[$cnf( $equal(join(X_25,meet(X_26,X_25)),X_25) )],[refute_0_86,refute_0_91]) ).
cnf(refute_0_93,plain,
join(X_37,meet(X_37,X_26)) = X_37,
inference(subst,[],[refute_0_92:[bind(X_25,$fot(X_37))]]) ).
cnf(refute_0_94,plain,
( join(X_37,meet(X_37,X_26)) != X_37
| meet(meet(X_37,X_26),join(X_36,join(X_37,meet(X_37,X_26)))) != meet(X_37,X_26)
| meet(meet(X_37,X_26),join(X_36,X_37)) = meet(X_37,X_26) ),
introduced(tautology,[equality,[$cnf( $equal(meet(meet(X_37,X_26),join(X_36,join(X_37,meet(X_37,X_26)))),meet(X_37,X_26)) ),[0,1,1],$fot(X_37)]]) ).
cnf(refute_0_95,plain,
( meet(meet(X_37,X_26),join(X_36,join(X_37,meet(X_37,X_26)))) != meet(X_37,X_26)
| meet(meet(X_37,X_26),join(X_36,X_37)) = meet(X_37,X_26) ),
inference(resolve,[$cnf( $equal(join(X_37,meet(X_37,X_26)),X_37) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
meet(meet(X_37,X_26),join(X_36,X_37)) = meet(X_37,X_26),
inference(resolve,[$cnf( $equal(meet(meet(X_37,X_26),join(X_36,join(X_37,meet(X_37,X_26)))),meet(X_37,X_26)) )],[refute_0_80,refute_0_95]) ).
cnf(refute_0_97,plain,
meet(meet(X_70,X_26),join(X_69,X_70)) = meet(X_70,X_26),
inference(subst,[],[refute_0_96:[bind(X_36,$fot(X_69)),bind(X_37,$fot(X_70))]]) ).
cnf(refute_0_98,plain,
( join(join(X_69,X_70),join(X_69,meet(meet(X_70,X_26),join(X_69,X_70)))) != join(X_69,X_70)
| meet(meet(X_70,X_26),join(X_69,X_70)) != meet(X_70,X_26)
| join(join(X_69,X_70),join(X_69,meet(X_70,X_26))) = join(X_69,X_70) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_69,X_70),join(X_69,meet(meet(X_70,X_26),join(X_69,X_70)))),join(X_69,X_70)) ),[0,1,1],$fot(meet(X_70,X_26))]]) ).
cnf(refute_0_99,plain,
( join(join(X_69,X_70),join(X_69,meet(meet(X_70,X_26),join(X_69,X_70)))) != join(X_69,X_70)
| join(join(X_69,X_70),join(X_69,meet(X_70,X_26))) = join(X_69,X_70) ),
inference(resolve,[$cnf( $equal(meet(meet(X_70,X_26),join(X_69,X_70)),meet(X_70,X_26)) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
join(join(X_69,X_70),join(X_69,meet(X_70,X_26))) = join(X_69,X_70),
inference(resolve,[$cnf( $equal(join(join(X_69,X_70),join(X_69,meet(meet(X_70,X_26),join(X_69,X_70)))),join(X_69,X_70)) )],[refute_0_73,refute_0_99]) ).
cnf(refute_0_101,plain,
join(join(X_359,X_357),join(X_359,meet(X_357,X_26))) = join(X_359,X_357),
inference(subst,[],[refute_0_100:[bind(X_69,$fot(X_359)),bind(X_70,$fot(X_357))]]) ).
cnf(refute_0_102,plain,
( join(join(X_359,X_357),join(X_359,meet(X_357,X_26))) != join(X_359,X_357)
| join(join(join(X_359,meet(X_357,X_26)),X_357),join(join(X_359,X_357),join(X_359,meet(X_357,X_26)))) != join(join(X_359,X_357),join(X_359,meet(X_357,X_26)))
| join(join(join(X_359,meet(X_357,X_26)),X_357),join(X_359,X_357)) = join(join(X_359,X_357),join(X_359,meet(X_357,X_26))) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(join(X_359,meet(X_357,X_26)),X_357),join(join(X_359,X_357),join(X_359,meet(X_357,X_26)))),join(join(X_359,X_357),join(X_359,meet(X_357,X_26)))) ),[0,1],$fot(join(X_359,X_357))]]) ).
cnf(refute_0_103,plain,
( join(join(join(X_359,meet(X_357,X_26)),X_357),join(join(X_359,X_357),join(X_359,meet(X_357,X_26)))) != join(join(X_359,X_357),join(X_359,meet(X_357,X_26)))
| join(join(join(X_359,meet(X_357,X_26)),X_357),join(X_359,X_357)) = join(join(X_359,X_357),join(X_359,meet(X_357,X_26))) ),
inference(resolve,[$cnf( $equal(join(join(X_359,X_357),join(X_359,meet(X_357,X_26))),join(X_359,X_357)) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
join(join(join(X_359,meet(X_357,X_26)),X_357),join(X_359,X_357)) = join(join(X_359,X_357),join(X_359,meet(X_357,X_26))),
inference(resolve,[$cnf( $equal(join(join(join(X_359,meet(X_357,X_26)),X_357),join(join(X_359,X_357),join(X_359,meet(X_357,X_26)))),join(join(X_359,X_357),join(X_359,meet(X_357,X_26)))) )],[refute_0_54,refute_0_103]) ).
cnf(refute_0_105,plain,
join(join(X_69,join(X_68,Z)),join(X_69,meet(X_68,join(X_69,join(X_68,Z))))) = join(X_69,join(X_68,Z)),
inference(subst,[],[refute_0_72:[bind(X_22,$fot(X_68)),bind(X_24,$fot(X_69)),bind(X_8,$fot(join(X_68,Z)))]]) ).
cnf(refute_0_106,plain,
meet(X_68,join(X_69,join(X_68,Z))) = X_68,
inference(subst,[],[absorption:[bind(X,$fot(X_68)),bind(Y,$fot(X_69))]]) ).
cnf(refute_0_107,plain,
( join(join(X_69,join(X_68,Z)),join(X_69,meet(X_68,join(X_69,join(X_68,Z))))) != join(X_69,join(X_68,Z))
| meet(X_68,join(X_69,join(X_68,Z))) != X_68
| join(join(X_69,join(X_68,Z)),join(X_69,X_68)) = join(X_69,join(X_68,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_69,join(X_68,Z)),join(X_69,meet(X_68,join(X_69,join(X_68,Z))))),join(X_69,join(X_68,Z))) ),[0,1,1],$fot(X_68)]]) ).
cnf(refute_0_108,plain,
( join(join(X_69,join(X_68,Z)),join(X_69,meet(X_68,join(X_69,join(X_68,Z))))) != join(X_69,join(X_68,Z))
| join(join(X_69,join(X_68,Z)),join(X_69,X_68)) = join(X_69,join(X_68,Z)) ),
inference(resolve,[$cnf( $equal(meet(X_68,join(X_69,join(X_68,Z))),X_68) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
join(join(X_69,join(X_68,Z)),join(X_69,X_68)) = join(X_69,join(X_68,Z)),
inference(resolve,[$cnf( $equal(join(join(X_69,join(X_68,Z)),join(X_69,meet(X_68,join(X_69,join(X_68,Z))))),join(X_69,join(X_68,Z))) )],[refute_0_105,refute_0_108]) ).
cnf(refute_0_110,plain,
join(join(X_69,join(X_68,Z)),join(X_69,X_68)) = join(join(X_69,X_68),join(X_69,join(X_68,Z))),
inference(subst,[],[refute_0_4:[bind(X,$fot(join(X_69,X_68))),bind(Y,$fot(join(X_69,join(X_68,Z))))]]) ).
cnf(refute_0_111,plain,
( join(join(X_69,join(X_68,Z)),join(X_69,X_68)) != join(X_69,join(X_68,Z))
| join(join(X_69,join(X_68,Z)),join(X_69,X_68)) != join(join(X_69,X_68),join(X_69,join(X_68,Z)))
| join(join(X_69,X_68),join(X_69,join(X_68,Z))) = join(X_69,join(X_68,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_69,join(X_68,Z)),join(X_69,X_68)),join(X_69,join(X_68,Z))) ),[0],$fot(join(join(X_69,X_68),join(X_69,join(X_68,Z))))]]) ).
cnf(refute_0_112,plain,
( join(join(X_69,join(X_68,Z)),join(X_69,X_68)) != join(X_69,join(X_68,Z))
| join(join(X_69,X_68),join(X_69,join(X_68,Z))) = join(X_69,join(X_68,Z)) ),
inference(resolve,[$cnf( $equal(join(join(X_69,join(X_68,Z)),join(X_69,X_68)),join(join(X_69,X_68),join(X_69,join(X_68,Z)))) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
join(join(X_69,X_68),join(X_69,join(X_68,Z))) = join(X_69,join(X_68,Z)),
inference(resolve,[$cnf( $equal(join(join(X_69,join(X_68,Z)),join(X_69,X_68)),join(X_69,join(X_68,Z))) )],[refute_0_109,refute_0_112]) ).
cnf(refute_0_114,plain,
join(join(X_357,X_359),join(X_357,join(X_359,meet(X_357,X_26)))) = join(X_357,join(X_359,meet(X_357,X_26))),
inference(subst,[],[refute_0_113:[bind(Z,$fot(meet(X_357,X_26))),bind(X_68,$fot(X_359)),bind(X_69,$fot(X_357))]]) ).
cnf(refute_0_115,plain,
join(join(X_352,join(X_89,X_90)),join(X_352,meet(join(X_89,X_90),join(X_91,X_89)))) = join(X_352,join(X_89,X_90)),
inference(subst,[],[refute_0_100:[bind(X_26,$fot(join(X_91,X_89))),bind(X_69,$fot(X_352)),bind(X_70,$fot(join(X_89,X_90)))]]) ).
cnf(refute_0_116,plain,
join(meet(join(X_40,X_24),join(X_24,X_42)),meet(X_24,meet(join(X_40,X_24),join(X_24,X_42)))) = meet(join(X_40,X_24),join(X_24,X_42)),
inference(subst,[],[refute_0_85:[bind(X_23,$fot(meet(join(X_40,X_24),join(X_24,X_42))))]]) ).
cnf(refute_0_117,plain,
( meet(X,Y) != meet(Y,X)
| meet(Y,X) = meet(X,Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(meet(X,Y))),bind(Y0,$fot(meet(Y,X)))]]) ).
cnf(refute_0_118,plain,
meet(Y,X) = meet(X,Y),
inference(resolve,[$cnf( $equal(meet(X,Y),meet(Y,X)) )],[commutativity_of_meet,refute_0_117]) ).
cnf(refute_0_119,plain,
meet(meet(join(X,Y),join(Z,Y)),Y) = meet(Y,meet(join(X,Y),join(Z,Y))),
inference(subst,[],[refute_0_118:[bind(X,$fot(Y)),bind(Y,$fot(meet(join(X,Y),join(Z,Y))))]]) ).
cnf(refute_0_120,plain,
( meet(meet(join(X,Y),join(Z,Y)),Y) != Y
| meet(meet(join(X,Y),join(Z,Y)),Y) != meet(Y,meet(join(X,Y),join(Z,Y)))
| meet(Y,meet(join(X,Y),join(Z,Y))) = Y ),
introduced(tautology,[equality,[$cnf( $equal(meet(meet(join(X,Y),join(Z,Y)),Y),Y) ),[0],$fot(meet(Y,meet(join(X,Y),join(Z,Y))))]]) ).
cnf(refute_0_121,plain,
( meet(meet(join(X,Y),join(Z,Y)),Y) != Y
| meet(Y,meet(join(X,Y),join(Z,Y))) = Y ),
inference(resolve,[$cnf( $equal(meet(meet(join(X,Y),join(Z,Y)),Y),meet(Y,meet(join(X,Y),join(Z,Y)))) )],[refute_0_119,refute_0_120]) ).
cnf(refute_0_122,plain,
meet(Y,meet(join(X,Y),join(Z,Y))) = Y,
inference(resolve,[$cnf( $equal(meet(meet(join(X,Y),join(Z,Y)),Y),Y) )],[wal_1,refute_0_121]) ).
cnf(refute_0_123,plain,
meet(X_20,meet(join(X_19,X_20),join(X_21,X_20))) = X_20,
inference(subst,[],[refute_0_122:[bind(X,$fot(X_19)),bind(Y,$fot(X_20)),bind(Z,$fot(X_21))]]) ).
cnf(refute_0_124,plain,
join(X_20,X_21) = join(X_21,X_20),
inference(subst,[],[commutativity_of_join:[bind(X,$fot(X_20)),bind(Y,$fot(X_21))]]) ).
cnf(refute_0_125,plain,
( join(X_20,X_21) != join(X_21,X_20)
| join(X_21,X_20) = join(X_20,X_21) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(join(X_20,X_21))),bind(Y0,$fot(join(X_21,X_20)))]]) ).
cnf(refute_0_126,plain,
join(X_21,X_20) = join(X_20,X_21),
inference(resolve,[$cnf( $equal(join(X_20,X_21),join(X_21,X_20)) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
( join(X_21,X_20) != join(X_20,X_21)
| meet(X_20,meet(join(X_19,X_20),join(X_21,X_20))) != X_20
| meet(X_20,meet(join(X_19,X_20),join(X_20,X_21))) = X_20 ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_20,meet(join(X_19,X_20),join(X_21,X_20))),X_20) ),[0,1,1],$fot(join(X_20,X_21))]]) ).
cnf(refute_0_128,plain,
( meet(X_20,meet(join(X_19,X_20),join(X_21,X_20))) != X_20
| meet(X_20,meet(join(X_19,X_20),join(X_20,X_21))) = X_20 ),
inference(resolve,[$cnf( $equal(join(X_21,X_20),join(X_20,X_21)) )],[refute_0_126,refute_0_127]) ).
cnf(refute_0_129,plain,
meet(X_20,meet(join(X_19,X_20),join(X_20,X_21))) = X_20,
inference(resolve,[$cnf( $equal(meet(X_20,meet(join(X_19,X_20),join(X_21,X_20))),X_20) )],[refute_0_123,refute_0_128]) ).
cnf(refute_0_130,plain,
meet(X_24,meet(join(X_40,X_24),join(X_24,X_42))) = X_24,
inference(subst,[],[refute_0_129:[bind(X_19,$fot(X_40)),bind(X_20,$fot(X_24)),bind(X_21,$fot(X_42))]]) ).
cnf(refute_0_131,plain,
( join(meet(join(X_40,X_24),join(X_24,X_42)),meet(X_24,meet(join(X_40,X_24),join(X_24,X_42)))) != meet(join(X_40,X_24),join(X_24,X_42))
| meet(X_24,meet(join(X_40,X_24),join(X_24,X_42))) != X_24
| join(meet(join(X_40,X_24),join(X_24,X_42)),X_24) = meet(join(X_40,X_24),join(X_24,X_42)) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(join(X_40,X_24),join(X_24,X_42)),meet(X_24,meet(join(X_40,X_24),join(X_24,X_42)))),meet(join(X_40,X_24),join(X_24,X_42))) ),[0,1],$fot(X_24)]]) ).
cnf(refute_0_132,plain,
( join(meet(join(X_40,X_24),join(X_24,X_42)),meet(X_24,meet(join(X_40,X_24),join(X_24,X_42)))) != meet(join(X_40,X_24),join(X_24,X_42))
| join(meet(join(X_40,X_24),join(X_24,X_42)),X_24) = meet(join(X_40,X_24),join(X_24,X_42)) ),
inference(resolve,[$cnf( $equal(meet(X_24,meet(join(X_40,X_24),join(X_24,X_42))),X_24) )],[refute_0_130,refute_0_131]) ).
cnf(refute_0_133,plain,
join(meet(join(X_40,X_24),join(X_24,X_42)),X_24) = meet(join(X_40,X_24),join(X_24,X_42)),
inference(resolve,[$cnf( $equal(join(meet(join(X_40,X_24),join(X_24,X_42)),meet(X_24,meet(join(X_40,X_24),join(X_24,X_42)))),meet(join(X_40,X_24),join(X_24,X_42))) )],[refute_0_116,refute_0_132]) ).
cnf(refute_0_134,plain,
join(meet(join(X_40,X_24),join(X_24,X_42)),X_24) = join(X_24,meet(join(X_40,X_24),join(X_24,X_42))),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_24)),bind(Y,$fot(meet(join(X_40,X_24),join(X_24,X_42))))]]) ).
cnf(refute_0_135,plain,
( join(meet(join(X_40,X_24),join(X_24,X_42)),X_24) != join(X_24,meet(join(X_40,X_24),join(X_24,X_42)))
| join(meet(join(X_40,X_24),join(X_24,X_42)),X_24) != meet(join(X_40,X_24),join(X_24,X_42))
| join(X_24,meet(join(X_40,X_24),join(X_24,X_42))) = meet(join(X_40,X_24),join(X_24,X_42)) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(join(X_40,X_24),join(X_24,X_42)),X_24),meet(join(X_40,X_24),join(X_24,X_42))) ),[0],$fot(join(X_24,meet(join(X_40,X_24),join(X_24,X_42))))]]) ).
cnf(refute_0_136,plain,
( join(meet(join(X_40,X_24),join(X_24,X_42)),X_24) != meet(join(X_40,X_24),join(X_24,X_42))
| join(X_24,meet(join(X_40,X_24),join(X_24,X_42))) = meet(join(X_40,X_24),join(X_24,X_42)) ),
inference(resolve,[$cnf( $equal(join(meet(join(X_40,X_24),join(X_24,X_42)),X_24),join(X_24,meet(join(X_40,X_24),join(X_24,X_42)))) )],[refute_0_134,refute_0_135]) ).
cnf(refute_0_137,plain,
join(X_24,meet(join(X_40,X_24),join(X_24,X_42))) = meet(join(X_40,X_24),join(X_24,X_42)),
inference(resolve,[$cnf( $equal(join(meet(join(X_40,X_24),join(X_24,X_42)),X_24),meet(join(X_40,X_24),join(X_24,X_42))) )],[refute_0_133,refute_0_136]) ).
cnf(refute_0_138,plain,
join(X_89,meet(join(X_90,X_89),join(X_89,X_91))) = meet(join(X_90,X_89),join(X_89,X_91)),
inference(subst,[],[refute_0_137:[bind(X_24,$fot(X_89)),bind(X_40,$fot(X_90)),bind(X_42,$fot(X_91))]]) ).
cnf(refute_0_139,plain,
join(X_89,X_90) = join(X_90,X_89),
inference(subst,[],[commutativity_of_join:[bind(X,$fot(X_89)),bind(Y,$fot(X_90))]]) ).
cnf(refute_0_140,plain,
( join(X_89,X_90) != join(X_90,X_89)
| join(X_90,X_89) = join(X_89,X_90) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(join(X_89,X_90))),bind(Y0,$fot(join(X_90,X_89)))]]) ).
cnf(refute_0_141,plain,
join(X_90,X_89) = join(X_89,X_90),
inference(resolve,[$cnf( $equal(join(X_89,X_90),join(X_90,X_89)) )],[refute_0_139,refute_0_140]) ).
cnf(refute_0_142,plain,
( join(X_89,meet(join(X_90,X_89),join(X_89,X_91))) != meet(join(X_90,X_89),join(X_89,X_91))
| join(X_90,X_89) != join(X_89,X_90)
| join(X_89,meet(join(X_89,X_90),join(X_89,X_91))) = meet(join(X_90,X_89),join(X_89,X_91)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_89,meet(join(X_90,X_89),join(X_89,X_91))),meet(join(X_90,X_89),join(X_89,X_91))) ),[0,1,0],$fot(join(X_89,X_90))]]) ).
cnf(refute_0_143,plain,
( join(X_89,meet(join(X_90,X_89),join(X_89,X_91))) != meet(join(X_90,X_89),join(X_89,X_91))
| join(X_89,meet(join(X_89,X_90),join(X_89,X_91))) = meet(join(X_90,X_89),join(X_89,X_91)) ),
inference(resolve,[$cnf( $equal(join(X_90,X_89),join(X_89,X_90)) )],[refute_0_141,refute_0_142]) ).
cnf(refute_0_144,plain,
join(X_89,meet(join(X_89,X_90),join(X_89,X_91))) = meet(join(X_90,X_89),join(X_89,X_91)),
inference(resolve,[$cnf( $equal(join(X_89,meet(join(X_90,X_89),join(X_89,X_91))),meet(join(X_90,X_89),join(X_89,X_91))) )],[refute_0_138,refute_0_143]) ).
cnf(refute_0_145,plain,
join(meet(join(X_24,X_43),join(X_45,X_24)),meet(X_24,meet(join(X_24,X_43),join(X_45,X_24)))) = meet(join(X_24,X_43),join(X_45,X_24)),
inference(subst,[],[refute_0_85:[bind(X_23,$fot(meet(join(X_24,X_43),join(X_45,X_24))))]]) ).
cnf(refute_0_146,plain,
join(X_20,X_19) = join(X_19,X_20),
inference(subst,[],[commutativity_of_join:[bind(X,$fot(X_20)),bind(Y,$fot(X_19))]]) ).
cnf(refute_0_147,plain,
( join(X_20,X_19) != join(X_19,X_20)
| join(X_19,X_20) = join(X_20,X_19) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(join(X_20,X_19))),bind(Y0,$fot(join(X_19,X_20)))]]) ).
cnf(refute_0_148,plain,
join(X_19,X_20) = join(X_20,X_19),
inference(resolve,[$cnf( $equal(join(X_20,X_19),join(X_19,X_20)) )],[refute_0_146,refute_0_147]) ).
cnf(refute_0_149,plain,
( join(X_19,X_20) != join(X_20,X_19)
| meet(X_20,meet(join(X_19,X_20),join(X_21,X_20))) != X_20
| meet(X_20,meet(join(X_20,X_19),join(X_21,X_20))) = X_20 ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_20,meet(join(X_19,X_20),join(X_21,X_20))),X_20) ),[0,1,0],$fot(join(X_20,X_19))]]) ).
cnf(refute_0_150,plain,
( meet(X_20,meet(join(X_19,X_20),join(X_21,X_20))) != X_20
| meet(X_20,meet(join(X_20,X_19),join(X_21,X_20))) = X_20 ),
inference(resolve,[$cnf( $equal(join(X_19,X_20),join(X_20,X_19)) )],[refute_0_148,refute_0_149]) ).
cnf(refute_0_151,plain,
meet(X_20,meet(join(X_20,X_19),join(X_21,X_20))) = X_20,
inference(resolve,[$cnf( $equal(meet(X_20,meet(join(X_19,X_20),join(X_21,X_20))),X_20) )],[refute_0_123,refute_0_150]) ).
cnf(refute_0_152,plain,
meet(X_24,meet(join(X_24,X_43),join(X_45,X_24))) = X_24,
inference(subst,[],[refute_0_151:[bind(X_19,$fot(X_43)),bind(X_20,$fot(X_24)),bind(X_21,$fot(X_45))]]) ).
cnf(refute_0_153,plain,
( join(meet(join(X_24,X_43),join(X_45,X_24)),meet(X_24,meet(join(X_24,X_43),join(X_45,X_24)))) != meet(join(X_24,X_43),join(X_45,X_24))
| meet(X_24,meet(join(X_24,X_43),join(X_45,X_24))) != X_24
| join(meet(join(X_24,X_43),join(X_45,X_24)),X_24) = meet(join(X_24,X_43),join(X_45,X_24)) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(join(X_24,X_43),join(X_45,X_24)),meet(X_24,meet(join(X_24,X_43),join(X_45,X_24)))),meet(join(X_24,X_43),join(X_45,X_24))) ),[0,1],$fot(X_24)]]) ).
cnf(refute_0_154,plain,
( join(meet(join(X_24,X_43),join(X_45,X_24)),meet(X_24,meet(join(X_24,X_43),join(X_45,X_24)))) != meet(join(X_24,X_43),join(X_45,X_24))
| join(meet(join(X_24,X_43),join(X_45,X_24)),X_24) = meet(join(X_24,X_43),join(X_45,X_24)) ),
inference(resolve,[$cnf( $equal(meet(X_24,meet(join(X_24,X_43),join(X_45,X_24))),X_24) )],[refute_0_152,refute_0_153]) ).
cnf(refute_0_155,plain,
join(meet(join(X_24,X_43),join(X_45,X_24)),X_24) = meet(join(X_24,X_43),join(X_45,X_24)),
inference(resolve,[$cnf( $equal(join(meet(join(X_24,X_43),join(X_45,X_24)),meet(X_24,meet(join(X_24,X_43),join(X_45,X_24)))),meet(join(X_24,X_43),join(X_45,X_24))) )],[refute_0_145,refute_0_154]) ).
cnf(refute_0_156,plain,
join(meet(join(X_24,X_43),join(X_45,X_24)),X_24) = join(X_24,meet(join(X_24,X_43),join(X_45,X_24))),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_24)),bind(Y,$fot(meet(join(X_24,X_43),join(X_45,X_24))))]]) ).
cnf(refute_0_157,plain,
( join(meet(join(X_24,X_43),join(X_45,X_24)),X_24) != join(X_24,meet(join(X_24,X_43),join(X_45,X_24)))
| join(meet(join(X_24,X_43),join(X_45,X_24)),X_24) != meet(join(X_24,X_43),join(X_45,X_24))
| join(X_24,meet(join(X_24,X_43),join(X_45,X_24))) = meet(join(X_24,X_43),join(X_45,X_24)) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(join(X_24,X_43),join(X_45,X_24)),X_24),meet(join(X_24,X_43),join(X_45,X_24))) ),[0],$fot(join(X_24,meet(join(X_24,X_43),join(X_45,X_24))))]]) ).
cnf(refute_0_158,plain,
( join(meet(join(X_24,X_43),join(X_45,X_24)),X_24) != meet(join(X_24,X_43),join(X_45,X_24))
| join(X_24,meet(join(X_24,X_43),join(X_45,X_24))) = meet(join(X_24,X_43),join(X_45,X_24)) ),
inference(resolve,[$cnf( $equal(join(meet(join(X_24,X_43),join(X_45,X_24)),X_24),join(X_24,meet(join(X_24,X_43),join(X_45,X_24)))) )],[refute_0_156,refute_0_157]) ).
cnf(refute_0_159,plain,
join(X_24,meet(join(X_24,X_43),join(X_45,X_24))) = meet(join(X_24,X_43),join(X_45,X_24)),
inference(resolve,[$cnf( $equal(join(meet(join(X_24,X_43),join(X_45,X_24)),X_24),meet(join(X_24,X_43),join(X_45,X_24))) )],[refute_0_155,refute_0_158]) ).
cnf(refute_0_160,plain,
join(X_46,meet(join(X_46,X_47),join(X_48,X_46))) = meet(join(X_46,X_47),join(X_48,X_46)),
inference(subst,[],[refute_0_159:[bind(X_24,$fot(X_46)),bind(X_43,$fot(X_47)),bind(X_45,$fot(X_48))]]) ).
cnf(refute_0_161,plain,
join(X_46,X_48) = join(X_48,X_46),
inference(subst,[],[commutativity_of_join:[bind(X,$fot(X_46)),bind(Y,$fot(X_48))]]) ).
cnf(refute_0_162,plain,
( join(X_46,X_48) != join(X_48,X_46)
| join(X_48,X_46) = join(X_46,X_48) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(join(X_46,X_48))),bind(Y0,$fot(join(X_48,X_46)))]]) ).
cnf(refute_0_163,plain,
join(X_48,X_46) = join(X_46,X_48),
inference(resolve,[$cnf( $equal(join(X_46,X_48),join(X_48,X_46)) )],[refute_0_161,refute_0_162]) ).
cnf(refute_0_164,plain,
( join(X_46,meet(join(X_46,X_47),join(X_48,X_46))) != meet(join(X_46,X_47),join(X_48,X_46))
| join(X_48,X_46) != join(X_46,X_48)
| join(X_46,meet(join(X_46,X_47),join(X_46,X_48))) = meet(join(X_46,X_47),join(X_48,X_46)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_46,meet(join(X_46,X_47),join(X_48,X_46))),meet(join(X_46,X_47),join(X_48,X_46))) ),[0,1,1],$fot(join(X_46,X_48))]]) ).
cnf(refute_0_165,plain,
( join(X_46,meet(join(X_46,X_47),join(X_48,X_46))) != meet(join(X_46,X_47),join(X_48,X_46))
| join(X_46,meet(join(X_46,X_47),join(X_46,X_48))) = meet(join(X_46,X_47),join(X_48,X_46)) ),
inference(resolve,[$cnf( $equal(join(X_48,X_46),join(X_46,X_48)) )],[refute_0_163,refute_0_164]) ).
cnf(refute_0_166,plain,
join(X_46,meet(join(X_46,X_47),join(X_46,X_48))) = meet(join(X_46,X_47),join(X_48,X_46)),
inference(resolve,[$cnf( $equal(join(X_46,meet(join(X_46,X_47),join(X_48,X_46))),meet(join(X_46,X_47),join(X_48,X_46))) )],[refute_0_160,refute_0_165]) ).
cnf(refute_0_167,plain,
join(X_89,meet(join(X_89,X_90),join(X_89,X_91))) = meet(join(X_89,X_90),join(X_91,X_89)),
inference(subst,[],[refute_0_166:[bind(X_46,$fot(X_89)),bind(X_47,$fot(X_90)),bind(X_48,$fot(X_91))]]) ).
cnf(refute_0_168,plain,
( join(X_89,meet(join(X_89,X_90),join(X_89,X_91))) != meet(join(X_89,X_90),join(X_91,X_89))
| join(X_89,meet(join(X_89,X_90),join(X_89,X_91))) != meet(join(X_90,X_89),join(X_89,X_91))
| meet(join(X_89,X_90),join(X_91,X_89)) = meet(join(X_90,X_89),join(X_89,X_91)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_89,meet(join(X_89,X_90),join(X_89,X_91))),meet(join(X_90,X_89),join(X_89,X_91))) ),[0],$fot(meet(join(X_89,X_90),join(X_91,X_89)))]]) ).
cnf(refute_0_169,plain,
( join(X_89,meet(join(X_89,X_90),join(X_89,X_91))) != meet(join(X_90,X_89),join(X_89,X_91))
| meet(join(X_89,X_90),join(X_91,X_89)) = meet(join(X_90,X_89),join(X_89,X_91)) ),
inference(resolve,[$cnf( $equal(join(X_89,meet(join(X_89,X_90),join(X_89,X_91))),meet(join(X_89,X_90),join(X_91,X_89))) )],[refute_0_167,refute_0_168]) ).
cnf(refute_0_170,plain,
meet(join(X_89,X_90),join(X_91,X_89)) = meet(join(X_90,X_89),join(X_89,X_91)),
inference(resolve,[$cnf( $equal(join(X_89,meet(join(X_89,X_90),join(X_89,X_91))),meet(join(X_90,X_89),join(X_89,X_91))) )],[refute_0_144,refute_0_169]) ).
cnf(refute_0_171,plain,
( join(join(X_352,join(X_89,X_90)),join(X_352,meet(join(X_89,X_90),join(X_91,X_89)))) != join(X_352,join(X_89,X_90))
| meet(join(X_89,X_90),join(X_91,X_89)) != meet(join(X_90,X_89),join(X_89,X_91))
| join(join(X_352,join(X_89,X_90)),join(X_352,meet(join(X_90,X_89),join(X_89,X_91)))) = join(X_352,join(X_89,X_90)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_352,join(X_89,X_90)),join(X_352,meet(join(X_89,X_90),join(X_91,X_89)))),join(X_352,join(X_89,X_90))) ),[0,1,1],$fot(meet(join(X_90,X_89),join(X_89,X_91)))]]) ).
cnf(refute_0_172,plain,
( join(join(X_352,join(X_89,X_90)),join(X_352,meet(join(X_89,X_90),join(X_91,X_89)))) != join(X_352,join(X_89,X_90))
| join(join(X_352,join(X_89,X_90)),join(X_352,meet(join(X_90,X_89),join(X_89,X_91)))) = join(X_352,join(X_89,X_90)) ),
inference(resolve,[$cnf( $equal(meet(join(X_89,X_90),join(X_91,X_89)),meet(join(X_90,X_89),join(X_89,X_91))) )],[refute_0_170,refute_0_171]) ).
cnf(refute_0_173,plain,
join(join(X_352,join(X_89,X_90)),join(X_352,meet(join(X_90,X_89),join(X_89,X_91)))) = join(X_352,join(X_89,X_90)),
inference(resolve,[$cnf( $equal(join(join(X_352,join(X_89,X_90)),join(X_352,meet(join(X_89,X_90),join(X_91,X_89)))),join(X_352,join(X_89,X_90))) )],[refute_0_115,refute_0_172]) ).
cnf(refute_0_174,plain,
join(join(X_352,join(X_98,X_96)),join(X_352,meet(join(X_98,X_96),X_351))) = join(X_352,join(X_98,X_96)),
inference(subst,[],[refute_0_100:[bind(X_26,$fot(X_351)),bind(X_69,$fot(X_352)),bind(X_70,$fot(join(X_98,X_96)))]]) ).
cnf(refute_0_175,plain,
join(join(X_36,join(X_37,X_24)),meet(X_24,join(X_36,join(X_37,X_24)))) = join(X_36,join(X_37,X_24)),
inference(subst,[],[refute_0_85:[bind(X_23,$fot(join(X_36,join(X_37,X_24))))]]) ).
cnf(refute_0_176,plain,
meet(X_24,join(X_36,join(X_37,X_24))) = X_24,
inference(subst,[],[refute_0_79:[bind(X_6,$fot(X_24)),bind(X_7,$fot(X_36)),bind(X_8,$fot(X_37))]]) ).
cnf(refute_0_177,plain,
( join(join(X_36,join(X_37,X_24)),meet(X_24,join(X_36,join(X_37,X_24)))) != join(X_36,join(X_37,X_24))
| meet(X_24,join(X_36,join(X_37,X_24))) != X_24
| join(join(X_36,join(X_37,X_24)),X_24) = join(X_36,join(X_37,X_24)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_36,join(X_37,X_24)),meet(X_24,join(X_36,join(X_37,X_24)))),join(X_36,join(X_37,X_24))) ),[0,1],$fot(X_24)]]) ).
cnf(refute_0_178,plain,
( join(join(X_36,join(X_37,X_24)),meet(X_24,join(X_36,join(X_37,X_24)))) != join(X_36,join(X_37,X_24))
| join(join(X_36,join(X_37,X_24)),X_24) = join(X_36,join(X_37,X_24)) ),
inference(resolve,[$cnf( $equal(meet(X_24,join(X_36,join(X_37,X_24))),X_24) )],[refute_0_176,refute_0_177]) ).
cnf(refute_0_179,plain,
join(join(X_36,join(X_37,X_24)),X_24) = join(X_36,join(X_37,X_24)),
inference(resolve,[$cnf( $equal(join(join(X_36,join(X_37,X_24)),meet(X_24,join(X_36,join(X_37,X_24)))),join(X_36,join(X_37,X_24))) )],[refute_0_175,refute_0_178]) ).
cnf(refute_0_180,plain,
join(join(X_36,join(X_37,X_24)),X_24) = join(X_24,join(X_36,join(X_37,X_24))),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_24)),bind(Y,$fot(join(X_36,join(X_37,X_24))))]]) ).
cnf(refute_0_181,plain,
( join(join(X_36,join(X_37,X_24)),X_24) != join(X_24,join(X_36,join(X_37,X_24)))
| join(join(X_36,join(X_37,X_24)),X_24) != join(X_36,join(X_37,X_24))
| join(X_24,join(X_36,join(X_37,X_24))) = join(X_36,join(X_37,X_24)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_36,join(X_37,X_24)),X_24),join(X_36,join(X_37,X_24))) ),[0],$fot(join(X_24,join(X_36,join(X_37,X_24))))]]) ).
cnf(refute_0_182,plain,
( join(join(X_36,join(X_37,X_24)),X_24) != join(X_36,join(X_37,X_24))
| join(X_24,join(X_36,join(X_37,X_24))) = join(X_36,join(X_37,X_24)) ),
inference(resolve,[$cnf( $equal(join(join(X_36,join(X_37,X_24)),X_24),join(X_24,join(X_36,join(X_37,X_24)))) )],[refute_0_180,refute_0_181]) ).
cnf(refute_0_183,plain,
join(X_24,join(X_36,join(X_37,X_24))) = join(X_36,join(X_37,X_24)),
inference(resolve,[$cnf( $equal(join(join(X_36,join(X_37,X_24)),X_24),join(X_36,join(X_37,X_24))) )],[refute_0_179,refute_0_182]) ).
cnf(refute_0_184,plain,
join(X_96,join(X_97,join(X_98,X_96))) = join(X_97,join(X_98,X_96)),
inference(subst,[],[refute_0_183:[bind(X_24,$fot(X_96)),bind(X_36,$fot(X_97)),bind(X_37,$fot(X_98))]]) ).
cnf(refute_0_185,plain,
join(X_96,X_98) = join(X_98,X_96),
inference(subst,[],[commutativity_of_join:[bind(X,$fot(X_96)),bind(Y,$fot(X_98))]]) ).
cnf(refute_0_186,plain,
( join(X_96,X_98) != join(X_98,X_96)
| join(X_98,X_96) = join(X_96,X_98) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(join(X_96,X_98))),bind(Y0,$fot(join(X_98,X_96)))]]) ).
cnf(refute_0_187,plain,
join(X_98,X_96) = join(X_96,X_98),
inference(resolve,[$cnf( $equal(join(X_96,X_98),join(X_98,X_96)) )],[refute_0_185,refute_0_186]) ).
cnf(refute_0_188,plain,
( join(X_96,join(X_97,join(X_98,X_96))) != join(X_97,join(X_98,X_96))
| join(X_98,X_96) != join(X_96,X_98)
| join(X_96,join(X_97,join(X_96,X_98))) = join(X_97,join(X_98,X_96)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_96,join(X_97,join(X_98,X_96))),join(X_97,join(X_98,X_96))) ),[0,1,1],$fot(join(X_96,X_98))]]) ).
cnf(refute_0_189,plain,
( join(X_96,join(X_97,join(X_98,X_96))) != join(X_97,join(X_98,X_96))
| join(X_96,join(X_97,join(X_96,X_98))) = join(X_97,join(X_98,X_96)) ),
inference(resolve,[$cnf( $equal(join(X_98,X_96),join(X_96,X_98)) )],[refute_0_187,refute_0_188]) ).
cnf(refute_0_190,plain,
join(X_96,join(X_97,join(X_96,X_98))) = join(X_97,join(X_98,X_96)),
inference(resolve,[$cnf( $equal(join(X_96,join(X_97,join(X_98,X_96))),join(X_97,join(X_98,X_96))) )],[refute_0_184,refute_0_189]) ).
cnf(refute_0_191,plain,
join(join(Y,join(X_26,Z)),meet(X_26,join(Y,join(X_26,Z)))) = join(Y,join(X_26,Z)),
inference(subst,[],[refute_0_85:[bind(X_23,$fot(join(Y,join(X_26,Z)))),bind(X_24,$fot(X_26))]]) ).
cnf(refute_0_192,plain,
meet(X_26,join(Y,join(X_26,Z))) = X_26,
inference(subst,[],[absorption:[bind(X,$fot(X_26))]]) ).
cnf(refute_0_193,plain,
( join(join(Y,join(X_26,Z)),meet(X_26,join(Y,join(X_26,Z)))) != join(Y,join(X_26,Z))
| meet(X_26,join(Y,join(X_26,Z))) != X_26
| join(join(Y,join(X_26,Z)),X_26) = join(Y,join(X_26,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(Y,join(X_26,Z)),meet(X_26,join(Y,join(X_26,Z)))),join(Y,join(X_26,Z))) ),[0,1],$fot(X_26)]]) ).
cnf(refute_0_194,plain,
( join(join(Y,join(X_26,Z)),meet(X_26,join(Y,join(X_26,Z)))) != join(Y,join(X_26,Z))
| join(join(Y,join(X_26,Z)),X_26) = join(Y,join(X_26,Z)) ),
inference(resolve,[$cnf( $equal(meet(X_26,join(Y,join(X_26,Z))),X_26) )],[refute_0_192,refute_0_193]) ).
cnf(refute_0_195,plain,
join(join(Y,join(X_26,Z)),X_26) = join(Y,join(X_26,Z)),
inference(resolve,[$cnf( $equal(join(join(Y,join(X_26,Z)),meet(X_26,join(Y,join(X_26,Z)))),join(Y,join(X_26,Z))) )],[refute_0_191,refute_0_194]) ).
cnf(refute_0_196,plain,
join(join(Y,join(X_26,Z)),X_26) = join(X_26,join(Y,join(X_26,Z))),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_26)),bind(Y,$fot(join(Y,join(X_26,Z))))]]) ).
cnf(refute_0_197,plain,
( join(join(Y,join(X_26,Z)),X_26) != join(Y,join(X_26,Z))
| join(join(Y,join(X_26,Z)),X_26) != join(X_26,join(Y,join(X_26,Z)))
| join(X_26,join(Y,join(X_26,Z))) = join(Y,join(X_26,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(Y,join(X_26,Z)),X_26),join(Y,join(X_26,Z))) ),[0],$fot(join(X_26,join(Y,join(X_26,Z))))]]) ).
cnf(refute_0_198,plain,
( join(join(Y,join(X_26,Z)),X_26) != join(Y,join(X_26,Z))
| join(X_26,join(Y,join(X_26,Z))) = join(Y,join(X_26,Z)) ),
inference(resolve,[$cnf( $equal(join(join(Y,join(X_26,Z)),X_26),join(X_26,join(Y,join(X_26,Z)))) )],[refute_0_196,refute_0_197]) ).
cnf(refute_0_199,plain,
join(X_26,join(Y,join(X_26,Z))) = join(Y,join(X_26,Z)),
inference(resolve,[$cnf( $equal(join(join(Y,join(X_26,Z)),X_26),join(Y,join(X_26,Z))) )],[refute_0_195,refute_0_198]) ).
cnf(refute_0_200,plain,
join(X_96,join(X_97,join(X_96,X_98))) = join(X_97,join(X_96,X_98)),
inference(subst,[],[refute_0_199:[bind(Y,$fot(X_97)),bind(Z,$fot(X_98)),bind(X_26,$fot(X_96))]]) ).
cnf(refute_0_201,plain,
( join(X_96,join(X_97,join(X_96,X_98))) != join(X_97,join(X_96,X_98))
| join(X_96,join(X_97,join(X_96,X_98))) != join(X_97,join(X_98,X_96))
| join(X_97,join(X_96,X_98)) = join(X_97,join(X_98,X_96)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_96,join(X_97,join(X_96,X_98))),join(X_97,join(X_98,X_96))) ),[0],$fot(join(X_97,join(X_96,X_98)))]]) ).
cnf(refute_0_202,plain,
( join(X_96,join(X_97,join(X_96,X_98))) != join(X_97,join(X_98,X_96))
| join(X_97,join(X_96,X_98)) = join(X_97,join(X_98,X_96)) ),
inference(resolve,[$cnf( $equal(join(X_96,join(X_97,join(X_96,X_98))),join(X_97,join(X_96,X_98))) )],[refute_0_200,refute_0_201]) ).
cnf(refute_0_203,plain,
join(X_97,join(X_96,X_98)) = join(X_97,join(X_98,X_96)),
inference(resolve,[$cnf( $equal(join(X_96,join(X_97,join(X_96,X_98))),join(X_97,join(X_98,X_96))) )],[refute_0_190,refute_0_202]) ).
cnf(refute_0_204,plain,
join(X_352,join(X_96,X_98)) = join(X_352,join(X_98,X_96)),
inference(subst,[],[refute_0_203:[bind(X_97,$fot(X_352))]]) ).
cnf(refute_0_205,plain,
( join(X_352,join(X_96,X_98)) != join(X_352,join(X_98,X_96))
| join(X_352,join(X_98,X_96)) = join(X_352,join(X_96,X_98)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(join(X_352,join(X_96,X_98)))),bind(Y0,$fot(join(X_352,join(X_98,X_96))))]]) ).
cnf(refute_0_206,plain,
join(X_352,join(X_98,X_96)) = join(X_352,join(X_96,X_98)),
inference(resolve,[$cnf( $equal(join(X_352,join(X_96,X_98)),join(X_352,join(X_98,X_96))) )],[refute_0_204,refute_0_205]) ).
cnf(refute_0_207,plain,
( join(X_352,join(X_98,X_96)) != join(X_352,join(X_96,X_98))
| join(join(X_352,join(X_98,X_96)),join(X_352,meet(join(X_98,X_96),X_351))) != join(X_352,join(X_98,X_96))
| join(join(X_352,join(X_96,X_98)),join(X_352,meet(join(X_98,X_96),X_351))) = join(X_352,join(X_98,X_96)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_352,join(X_98,X_96)),join(X_352,meet(join(X_98,X_96),X_351))),join(X_352,join(X_98,X_96))) ),[0,0],$fot(join(X_352,join(X_96,X_98)))]]) ).
cnf(refute_0_208,plain,
( join(join(X_352,join(X_98,X_96)),join(X_352,meet(join(X_98,X_96),X_351))) != join(X_352,join(X_98,X_96))
| join(join(X_352,join(X_96,X_98)),join(X_352,meet(join(X_98,X_96),X_351))) = join(X_352,join(X_98,X_96)) ),
inference(resolve,[$cnf( $equal(join(X_352,join(X_98,X_96)),join(X_352,join(X_96,X_98))) )],[refute_0_206,refute_0_207]) ).
cnf(refute_0_209,plain,
join(join(X_352,join(X_96,X_98)),join(X_352,meet(join(X_98,X_96),X_351))) = join(X_352,join(X_98,X_96)),
inference(resolve,[$cnf( $equal(join(join(X_352,join(X_98,X_96)),join(X_352,meet(join(X_98,X_96),X_351))),join(X_352,join(X_98,X_96))) )],[refute_0_174,refute_0_208]) ).
cnf(refute_0_210,plain,
join(join(X_352,join(X_89,X_90)),join(X_352,meet(join(X_90,X_89),join(X_89,X_91)))) = join(X_352,join(X_90,X_89)),
inference(subst,[],[refute_0_209:[bind(X_351,$fot(join(X_89,X_91))),bind(X_96,$fot(X_89)),bind(X_98,$fot(X_90))]]) ).
cnf(refute_0_211,plain,
( join(join(X_352,join(X_89,X_90)),join(X_352,meet(join(X_90,X_89),join(X_89,X_91)))) != join(X_352,join(X_89,X_90))
| join(join(X_352,join(X_89,X_90)),join(X_352,meet(join(X_90,X_89),join(X_89,X_91)))) != join(X_352,join(X_90,X_89))
| join(X_352,join(X_90,X_89)) = join(X_352,join(X_89,X_90)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_352,join(X_89,X_90)),join(X_352,meet(join(X_90,X_89),join(X_89,X_91)))),join(X_352,join(X_89,X_90))) ),[0],$fot(join(X_352,join(X_90,X_89)))]]) ).
cnf(refute_0_212,plain,
( join(join(X_352,join(X_89,X_90)),join(X_352,meet(join(X_90,X_89),join(X_89,X_91)))) != join(X_352,join(X_89,X_90))
| join(X_352,join(X_90,X_89)) = join(X_352,join(X_89,X_90)) ),
inference(resolve,[$cnf( $equal(join(join(X_352,join(X_89,X_90)),join(X_352,meet(join(X_90,X_89),join(X_89,X_91)))),join(X_352,join(X_90,X_89))) )],[refute_0_210,refute_0_211]) ).
cnf(refute_0_213,plain,
join(X_352,join(X_90,X_89)) = join(X_352,join(X_89,X_90)),
inference(resolve,[$cnf( $equal(join(join(X_352,join(X_89,X_90)),join(X_352,meet(join(X_90,X_89),join(X_89,X_91)))),join(X_352,join(X_89,X_90))) )],[refute_0_173,refute_0_212]) ).
cnf(refute_0_214,plain,
( join(X_352,join(X_90,X_89)) != join(X_352,join(X_89,X_90))
| join(X_352,join(X_89,X_90)) = join(X_352,join(X_90,X_89)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(join(X_352,join(X_90,X_89)))),bind(Y0,$fot(join(X_352,join(X_89,X_90))))]]) ).
cnf(refute_0_215,plain,
join(X_352,join(X_89,X_90)) = join(X_352,join(X_90,X_89)),
inference(resolve,[$cnf( $equal(join(X_352,join(X_90,X_89)),join(X_352,join(X_89,X_90))) )],[refute_0_213,refute_0_214]) ).
cnf(refute_0_216,plain,
join(join(X_357,X_359),join(join(X_359,meet(X_357,X_26)),X_357)) = join(join(X_357,X_359),join(X_357,join(X_359,meet(X_357,X_26)))),
inference(subst,[],[refute_0_215:[bind(X_352,$fot(join(X_357,X_359))),bind(X_89,$fot(join(X_359,meet(X_357,X_26)))),bind(X_90,$fot(X_357))]]) ).
cnf(refute_0_217,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_218,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_2,refute_0_217]) ).
cnf(refute_0_219,plain,
( join(join(X_357,X_359),join(X_357,join(X_359,meet(X_357,X_26)))) != join(X_357,join(X_359,meet(X_357,X_26)))
| join(join(X_357,X_359),join(join(X_359,meet(X_357,X_26)),X_357)) != join(join(X_357,X_359),join(X_357,join(X_359,meet(X_357,X_26))))
| join(join(X_357,X_359),join(join(X_359,meet(X_357,X_26)),X_357)) = join(X_357,join(X_359,meet(X_357,X_26))) ),
inference(subst,[],[refute_0_218:[bind(X0,$fot(join(join(X_357,X_359),join(join(X_359,meet(X_357,X_26)),X_357)))),bind(Y0,$fot(join(join(X_357,X_359),join(X_357,join(X_359,meet(X_357,X_26)))))),bind(Z0,$fot(join(X_357,join(X_359,meet(X_357,X_26)))))]]) ).
cnf(refute_0_220,plain,
( join(join(X_357,X_359),join(X_357,join(X_359,meet(X_357,X_26)))) != join(X_357,join(X_359,meet(X_357,X_26)))
| join(join(X_357,X_359),join(join(X_359,meet(X_357,X_26)),X_357)) = join(X_357,join(X_359,meet(X_357,X_26))) ),
inference(resolve,[$cnf( $equal(join(join(X_357,X_359),join(join(X_359,meet(X_357,X_26)),X_357)),join(join(X_357,X_359),join(X_357,join(X_359,meet(X_357,X_26))))) )],[refute_0_216,refute_0_219]) ).
cnf(refute_0_221,plain,
join(join(X_357,X_359),join(join(X_359,meet(X_357,X_26)),X_357)) = join(X_357,join(X_359,meet(X_357,X_26))),
inference(resolve,[$cnf( $equal(join(join(X_357,X_359),join(X_357,join(X_359,meet(X_357,X_26)))),join(X_357,join(X_359,meet(X_357,X_26)))) )],[refute_0_114,refute_0_220]) ).
cnf(refute_0_222,plain,
join(X,join(X_317,X_315)) = join(join(X_317,X_315),X),
inference(subst,[],[commutativity_of_join:[bind(Y,$fot(join(X_317,X_315)))]]) ).
cnf(refute_0_223,plain,
join(join(join(X_26,X_8),X_7),meet(X_26,join(join(X_26,X_8),X_7))) = join(join(X_26,X_8),X_7),
inference(subst,[],[refute_0_85:[bind(X_23,$fot(join(join(X_26,X_8),X_7))),bind(X_24,$fot(X_26))]]) ).
cnf(refute_0_224,plain,
meet(X_26,join(join(X_26,X_8),X_7)) = X_26,
inference(subst,[],[refute_0_38:[bind(X_6,$fot(X_26))]]) ).
cnf(refute_0_225,plain,
( join(join(join(X_26,X_8),X_7),meet(X_26,join(join(X_26,X_8),X_7))) != join(join(X_26,X_8),X_7)
| meet(X_26,join(join(X_26,X_8),X_7)) != X_26
| join(join(join(X_26,X_8),X_7),X_26) = join(join(X_26,X_8),X_7) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(join(X_26,X_8),X_7),meet(X_26,join(join(X_26,X_8),X_7))),join(join(X_26,X_8),X_7)) ),[0,1],$fot(X_26)]]) ).
cnf(refute_0_226,plain,
( join(join(join(X_26,X_8),X_7),meet(X_26,join(join(X_26,X_8),X_7))) != join(join(X_26,X_8),X_7)
| join(join(join(X_26,X_8),X_7),X_26) = join(join(X_26,X_8),X_7) ),
inference(resolve,[$cnf( $equal(meet(X_26,join(join(X_26,X_8),X_7)),X_26) )],[refute_0_224,refute_0_225]) ).
cnf(refute_0_227,plain,
join(join(join(X_26,X_8),X_7),X_26) = join(join(X_26,X_8),X_7),
inference(resolve,[$cnf( $equal(join(join(join(X_26,X_8),X_7),meet(X_26,join(join(X_26,X_8),X_7))),join(join(X_26,X_8),X_7)) )],[refute_0_223,refute_0_226]) ).
cnf(refute_0_228,plain,
join(join(join(X_26,X_8),X_7),X_26) = join(X_26,join(join(X_26,X_8),X_7)),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_26)),bind(Y,$fot(join(join(X_26,X_8),X_7)))]]) ).
cnf(refute_0_229,plain,
( join(join(join(X_26,X_8),X_7),X_26) != join(X_26,join(join(X_26,X_8),X_7))
| join(join(join(X_26,X_8),X_7),X_26) != join(join(X_26,X_8),X_7)
| join(X_26,join(join(X_26,X_8),X_7)) = join(join(X_26,X_8),X_7) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(join(X_26,X_8),X_7),X_26),join(join(X_26,X_8),X_7)) ),[0],$fot(join(X_26,join(join(X_26,X_8),X_7)))]]) ).
cnf(refute_0_230,plain,
( join(join(join(X_26,X_8),X_7),X_26) != join(join(X_26,X_8),X_7)
| join(X_26,join(join(X_26,X_8),X_7)) = join(join(X_26,X_8),X_7) ),
inference(resolve,[$cnf( $equal(join(join(join(X_26,X_8),X_7),X_26),join(X_26,join(join(X_26,X_8),X_7))) )],[refute_0_228,refute_0_229]) ).
cnf(refute_0_231,plain,
join(X_26,join(join(X_26,X_8),X_7)) = join(join(X_26,X_8),X_7),
inference(resolve,[$cnf( $equal(join(join(join(X_26,X_8),X_7),X_26),join(join(X_26,X_8),X_7)) )],[refute_0_227,refute_0_230]) ).
cnf(refute_0_232,plain,
join(X_145,join(join(X_145,X_147),X_146)) = join(join(X_145,X_147),X_146),
inference(subst,[],[refute_0_231:[bind(X_26,$fot(X_145)),bind(X_7,$fot(X_146)),bind(X_8,$fot(X_147))]]) ).
cnf(refute_0_233,plain,
join(X_147,X_145) = join(X_145,X_147),
inference(subst,[],[commutativity_of_join:[bind(X,$fot(X_147)),bind(Y,$fot(X_145))]]) ).
cnf(refute_0_234,plain,
( join(X_147,X_145) != join(X_145,X_147)
| join(X_145,X_147) = join(X_147,X_145) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(join(X_147,X_145))),bind(Y0,$fot(join(X_145,X_147)))]]) ).
cnf(refute_0_235,plain,
join(X_145,X_147) = join(X_147,X_145),
inference(resolve,[$cnf( $equal(join(X_147,X_145),join(X_145,X_147)) )],[refute_0_233,refute_0_234]) ).
cnf(refute_0_236,plain,
( join(X_145,X_147) != join(X_147,X_145)
| join(X_145,join(join(X_145,X_147),X_146)) != join(join(X_145,X_147),X_146)
| join(X_145,join(join(X_147,X_145),X_146)) = join(join(X_145,X_147),X_146) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_145,join(join(X_145,X_147),X_146)),join(join(X_145,X_147),X_146)) ),[0,1,0],$fot(join(X_147,X_145))]]) ).
cnf(refute_0_237,plain,
( join(X_145,join(join(X_145,X_147),X_146)) != join(join(X_145,X_147),X_146)
| join(X_145,join(join(X_147,X_145),X_146)) = join(join(X_145,X_147),X_146) ),
inference(resolve,[$cnf( $equal(join(X_145,X_147),join(X_147,X_145)) )],[refute_0_235,refute_0_236]) ).
cnf(refute_0_238,plain,
join(X_145,join(join(X_147,X_145),X_146)) = join(join(X_145,X_147),X_146),
inference(resolve,[$cnf( $equal(join(X_145,join(join(X_145,X_147),X_146)),join(join(X_145,X_147),X_146)) )],[refute_0_232,refute_0_237]) ).
cnf(refute_0_239,plain,
join(join(join(X_15,X_26),X_14),meet(X_26,join(join(X_15,X_26),X_14))) = join(join(X_15,X_26),X_14),
inference(subst,[],[refute_0_85:[bind(X_23,$fot(join(join(X_15,X_26),X_14))),bind(X_24,$fot(X_26))]]) ).
cnf(refute_0_240,plain,
meet(X_26,join(join(X_15,X_26),X_14)) = X_26,
inference(subst,[],[refute_0_45:[bind(X_13,$fot(X_26))]]) ).
cnf(refute_0_241,plain,
( join(join(join(X_15,X_26),X_14),meet(X_26,join(join(X_15,X_26),X_14))) != join(join(X_15,X_26),X_14)
| meet(X_26,join(join(X_15,X_26),X_14)) != X_26
| join(join(join(X_15,X_26),X_14),X_26) = join(join(X_15,X_26),X_14) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(join(X_15,X_26),X_14),meet(X_26,join(join(X_15,X_26),X_14))),join(join(X_15,X_26),X_14)) ),[0,1],$fot(X_26)]]) ).
cnf(refute_0_242,plain,
( join(join(join(X_15,X_26),X_14),meet(X_26,join(join(X_15,X_26),X_14))) != join(join(X_15,X_26),X_14)
| join(join(join(X_15,X_26),X_14),X_26) = join(join(X_15,X_26),X_14) ),
inference(resolve,[$cnf( $equal(meet(X_26,join(join(X_15,X_26),X_14)),X_26) )],[refute_0_240,refute_0_241]) ).
cnf(refute_0_243,plain,
join(join(join(X_15,X_26),X_14),X_26) = join(join(X_15,X_26),X_14),
inference(resolve,[$cnf( $equal(join(join(join(X_15,X_26),X_14),meet(X_26,join(join(X_15,X_26),X_14))),join(join(X_15,X_26),X_14)) )],[refute_0_239,refute_0_242]) ).
cnf(refute_0_244,plain,
join(join(join(X_15,X_26),X_14),X_26) = join(X_26,join(join(X_15,X_26),X_14)),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_26)),bind(Y,$fot(join(join(X_15,X_26),X_14)))]]) ).
cnf(refute_0_245,plain,
( join(join(join(X_15,X_26),X_14),X_26) != join(X_26,join(join(X_15,X_26),X_14))
| join(join(join(X_15,X_26),X_14),X_26) != join(join(X_15,X_26),X_14)
| join(X_26,join(join(X_15,X_26),X_14)) = join(join(X_15,X_26),X_14) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(join(X_15,X_26),X_14),X_26),join(join(X_15,X_26),X_14)) ),[0],$fot(join(X_26,join(join(X_15,X_26),X_14)))]]) ).
cnf(refute_0_246,plain,
( join(join(join(X_15,X_26),X_14),X_26) != join(join(X_15,X_26),X_14)
| join(X_26,join(join(X_15,X_26),X_14)) = join(join(X_15,X_26),X_14) ),
inference(resolve,[$cnf( $equal(join(join(join(X_15,X_26),X_14),X_26),join(X_26,join(join(X_15,X_26),X_14))) )],[refute_0_244,refute_0_245]) ).
cnf(refute_0_247,plain,
join(X_26,join(join(X_15,X_26),X_14)) = join(join(X_15,X_26),X_14),
inference(resolve,[$cnf( $equal(join(join(join(X_15,X_26),X_14),X_26),join(join(X_15,X_26),X_14)) )],[refute_0_243,refute_0_246]) ).
cnf(refute_0_248,plain,
join(X_145,join(join(X_147,X_145),X_146)) = join(join(X_147,X_145),X_146),
inference(subst,[],[refute_0_247:[bind(X_14,$fot(X_146)),bind(X_15,$fot(X_147)),bind(X_26,$fot(X_145))]]) ).
cnf(refute_0_249,plain,
( join(X_145,join(join(X_147,X_145),X_146)) != join(join(X_145,X_147),X_146)
| join(X_145,join(join(X_147,X_145),X_146)) != join(join(X_147,X_145),X_146)
| join(join(X_147,X_145),X_146) = join(join(X_145,X_147),X_146) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_145,join(join(X_147,X_145),X_146)),join(join(X_145,X_147),X_146)) ),[0],$fot(join(join(X_147,X_145),X_146))]]) ).
cnf(refute_0_250,plain,
( join(X_145,join(join(X_147,X_145),X_146)) != join(join(X_145,X_147),X_146)
| join(join(X_147,X_145),X_146) = join(join(X_145,X_147),X_146) ),
inference(resolve,[$cnf( $equal(join(X_145,join(join(X_147,X_145),X_146)),join(join(X_147,X_145),X_146)) )],[refute_0_248,refute_0_249]) ).
cnf(refute_0_251,plain,
join(join(X_147,X_145),X_146) = join(join(X_145,X_147),X_146),
inference(resolve,[$cnf( $equal(join(X_145,join(join(X_147,X_145),X_146)),join(join(X_145,X_147),X_146)) )],[refute_0_238,refute_0_250]) ).
cnf(refute_0_252,plain,
join(join(X_317,X_315),X) = join(join(X_315,X_317),X),
inference(subst,[],[refute_0_251:[bind(X_145,$fot(X_315)),bind(X_146,$fot(X)),bind(X_147,$fot(X_317))]]) ).
cnf(refute_0_253,plain,
( join(X,join(X_317,X_315)) != join(join(X_317,X_315),X)
| join(join(X_317,X_315),X) != join(join(X_315,X_317),X)
| join(X,join(X_317,X_315)) = join(join(X_315,X_317),X) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X,join(X_317,X_315)),join(join(X_315,X_317),X)) ),[0],$fot(join(join(X_317,X_315),X))]]) ).
cnf(refute_0_254,plain,
( join(X,join(X_317,X_315)) != join(join(X_317,X_315),X)
| join(X,join(X_317,X_315)) = join(join(X_315,X_317),X) ),
inference(resolve,[$cnf( $equal(join(join(X_317,X_315),X),join(join(X_315,X_317),X)) )],[refute_0_252,refute_0_253]) ).
cnf(refute_0_255,plain,
join(X,join(X_317,X_315)) = join(join(X_315,X_317),X),
inference(resolve,[$cnf( $equal(join(X,join(X_317,X_315)),join(join(X_317,X_315),X)) )],[refute_0_222,refute_0_254]) ).
cnf(refute_0_256,plain,
join(join(join(X_359,meet(X_357,X_26)),X_357),join(X_359,X_357)) = join(join(X_357,X_359),join(join(X_359,meet(X_357,X_26)),X_357)),
inference(subst,[],[refute_0_255:[bind(X,$fot(join(join(X_359,meet(X_357,X_26)),X_357))),bind(X_315,$fot(X_357)),bind(X_317,$fot(X_359))]]) ).
cnf(refute_0_257,plain,
( join(join(X_357,X_359),join(join(X_359,meet(X_357,X_26)),X_357)) != join(X_357,join(X_359,meet(X_357,X_26)))
| join(join(join(X_359,meet(X_357,X_26)),X_357),join(X_359,X_357)) != join(join(X_357,X_359),join(join(X_359,meet(X_357,X_26)),X_357))
| join(join(join(X_359,meet(X_357,X_26)),X_357),join(X_359,X_357)) = join(X_357,join(X_359,meet(X_357,X_26))) ),
inference(subst,[],[refute_0_218:[bind(X0,$fot(join(join(join(X_359,meet(X_357,X_26)),X_357),join(X_359,X_357)))),bind(Y0,$fot(join(join(X_357,X_359),join(join(X_359,meet(X_357,X_26)),X_357)))),bind(Z0,$fot(join(X_357,join(X_359,meet(X_357,X_26)))))]]) ).
cnf(refute_0_258,plain,
( join(join(X_357,X_359),join(join(X_359,meet(X_357,X_26)),X_357)) != join(X_357,join(X_359,meet(X_357,X_26)))
| join(join(join(X_359,meet(X_357,X_26)),X_357),join(X_359,X_357)) = join(X_357,join(X_359,meet(X_357,X_26))) ),
inference(resolve,[$cnf( $equal(join(join(join(X_359,meet(X_357,X_26)),X_357),join(X_359,X_357)),join(join(X_357,X_359),join(join(X_359,meet(X_357,X_26)),X_357))) )],[refute_0_256,refute_0_257]) ).
cnf(refute_0_259,plain,
join(join(join(X_359,meet(X_357,X_26)),X_357),join(X_359,X_357)) = join(X_357,join(X_359,meet(X_357,X_26))),
inference(resolve,[$cnf( $equal(join(join(X_357,X_359),join(join(X_359,meet(X_357,X_26)),X_357)),join(X_357,join(X_359,meet(X_357,X_26)))) )],[refute_0_221,refute_0_258]) ).
cnf(refute_0_260,plain,
( join(join(join(X_359,meet(X_357,X_26)),X_357),join(X_359,X_357)) != join(X_357,join(X_359,meet(X_357,X_26)))
| join(join(join(X_359,meet(X_357,X_26)),X_357),join(X_359,X_357)) != join(join(X_359,X_357),join(X_359,meet(X_357,X_26)))
| join(X_357,join(X_359,meet(X_357,X_26))) = join(join(X_359,X_357),join(X_359,meet(X_357,X_26))) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(join(X_359,meet(X_357,X_26)),X_357),join(X_359,X_357)),join(join(X_359,X_357),join(X_359,meet(X_357,X_26)))) ),[0],$fot(join(X_357,join(X_359,meet(X_357,X_26))))]]) ).
cnf(refute_0_261,plain,
( join(join(join(X_359,meet(X_357,X_26)),X_357),join(X_359,X_357)) != join(join(X_359,X_357),join(X_359,meet(X_357,X_26)))
| join(X_357,join(X_359,meet(X_357,X_26))) = join(join(X_359,X_357),join(X_359,meet(X_357,X_26))) ),
inference(resolve,[$cnf( $equal(join(join(join(X_359,meet(X_357,X_26)),X_357),join(X_359,X_357)),join(X_357,join(X_359,meet(X_357,X_26)))) )],[refute_0_259,refute_0_260]) ).
cnf(refute_0_262,plain,
( join(X_357,join(X_359,meet(X_357,X_26))) != join(join(X_359,X_357),join(X_359,meet(X_357,X_26)))
| join(join(X_359,X_357),join(X_359,meet(X_357,X_26))) != join(X_359,X_357)
| join(X_357,join(X_359,meet(X_357,X_26))) = join(X_359,X_357) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_357,join(X_359,meet(X_357,X_26))),join(X_359,X_357)) ),[0],$fot(join(join(X_359,X_357),join(X_359,meet(X_357,X_26))))]]) ).
cnf(refute_0_263,plain,
( join(X_357,join(X_359,meet(X_357,X_26))) != join(join(X_359,X_357),join(X_359,meet(X_357,X_26)))
| join(X_357,join(X_359,meet(X_357,X_26))) = join(X_359,X_357) ),
inference(resolve,[$cnf( $equal(join(join(X_359,X_357),join(X_359,meet(X_357,X_26))),join(X_359,X_357)) )],[refute_0_101,refute_0_262]) ).
cnf(refute_0_264,plain,
( join(join(join(X_359,meet(X_357,X_26)),X_357),join(X_359,X_357)) != join(join(X_359,X_357),join(X_359,meet(X_357,X_26)))
| join(X_357,join(X_359,meet(X_357,X_26))) = join(X_359,X_357) ),
inference(resolve,[$cnf( $equal(join(X_357,join(X_359,meet(X_357,X_26))),join(join(X_359,X_357),join(X_359,meet(X_357,X_26)))) )],[refute_0_261,refute_0_263]) ).
cnf(refute_0_265,plain,
join(X_357,join(X_359,meet(X_357,X_26))) = join(X_359,X_357),
inference(resolve,[$cnf( $equal(join(join(join(X_359,meet(X_357,X_26)),X_357),join(X_359,X_357)),join(join(X_359,X_357),join(X_359,meet(X_357,X_26)))) )],[refute_0_104,refute_0_264]) ).
cnf(refute_0_266,plain,
join(join(X_105,X_106),join(X_362,meet(join(X_105,X_106),join(X_107,X_105)))) = join(X_362,join(X_105,X_106)),
inference(subst,[],[refute_0_265:[bind(X_26,$fot(join(X_107,X_105))),bind(X_357,$fot(join(X_105,X_106))),bind(X_359,$fot(X_362))]]) ).
cnf(refute_0_267,plain,
join(X_105,meet(join(X_105,X_106),join(X_105,X_107))) = meet(join(X_105,X_106),join(X_107,X_105)),
inference(subst,[],[refute_0_166:[bind(X_46,$fot(X_105)),bind(X_47,$fot(X_106)),bind(X_48,$fot(X_107))]]) ).
cnf(refute_0_268,plain,
meet(join(X_105,X_107),join(X_105,X_106)) = meet(join(X_105,X_106),join(X_105,X_107)),
inference(subst,[],[commutativity_of_meet:[bind(X,$fot(join(X_105,X_107))),bind(Y,$fot(join(X_105,X_106)))]]) ).
cnf(refute_0_269,plain,
( meet(join(X_105,X_107),join(X_105,X_106)) != meet(join(X_105,X_106),join(X_105,X_107))
| meet(join(X_105,X_106),join(X_105,X_107)) = meet(join(X_105,X_107),join(X_105,X_106)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(meet(join(X_105,X_107),join(X_105,X_106)))),bind(Y0,$fot(meet(join(X_105,X_106),join(X_105,X_107))))]]) ).
cnf(refute_0_270,plain,
meet(join(X_105,X_106),join(X_105,X_107)) = meet(join(X_105,X_107),join(X_105,X_106)),
inference(resolve,[$cnf( $equal(meet(join(X_105,X_107),join(X_105,X_106)),meet(join(X_105,X_106),join(X_105,X_107))) )],[refute_0_268,refute_0_269]) ).
cnf(refute_0_271,plain,
( join(X_105,meet(join(X_105,X_106),join(X_105,X_107))) != meet(join(X_105,X_106),join(X_107,X_105))
| meet(join(X_105,X_106),join(X_105,X_107)) != meet(join(X_105,X_107),join(X_105,X_106))
| join(X_105,meet(join(X_105,X_107),join(X_105,X_106))) = meet(join(X_105,X_106),join(X_107,X_105)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_105,meet(join(X_105,X_106),join(X_105,X_107))),meet(join(X_105,X_106),join(X_107,X_105))) ),[0,1],$fot(meet(join(X_105,X_107),join(X_105,X_106)))]]) ).
cnf(refute_0_272,plain,
( join(X_105,meet(join(X_105,X_106),join(X_105,X_107))) != meet(join(X_105,X_106),join(X_107,X_105))
| join(X_105,meet(join(X_105,X_107),join(X_105,X_106))) = meet(join(X_105,X_106),join(X_107,X_105)) ),
inference(resolve,[$cnf( $equal(meet(join(X_105,X_106),join(X_105,X_107)),meet(join(X_105,X_107),join(X_105,X_106))) )],[refute_0_270,refute_0_271]) ).
cnf(refute_0_273,plain,
join(X_105,meet(join(X_105,X_107),join(X_105,X_106))) = meet(join(X_105,X_106),join(X_107,X_105)),
inference(resolve,[$cnf( $equal(join(X_105,meet(join(X_105,X_106),join(X_105,X_107))),meet(join(X_105,X_106),join(X_107,X_105))) )],[refute_0_267,refute_0_272]) ).
cnf(refute_0_274,plain,
join(X_105,meet(join(X_105,X_107),join(X_105,X_106))) = meet(join(X_105,X_107),join(X_106,X_105)),
inference(subst,[],[refute_0_166:[bind(X_46,$fot(X_105)),bind(X_47,$fot(X_107)),bind(X_48,$fot(X_106))]]) ).
cnf(refute_0_275,plain,
( join(X_105,meet(join(X_105,X_107),join(X_105,X_106))) != meet(join(X_105,X_106),join(X_107,X_105))
| join(X_105,meet(join(X_105,X_107),join(X_105,X_106))) != meet(join(X_105,X_107),join(X_106,X_105))
| meet(join(X_105,X_107),join(X_106,X_105)) = meet(join(X_105,X_106),join(X_107,X_105)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_105,meet(join(X_105,X_107),join(X_105,X_106))),meet(join(X_105,X_106),join(X_107,X_105))) ),[0],$fot(meet(join(X_105,X_107),join(X_106,X_105)))]]) ).
cnf(refute_0_276,plain,
( join(X_105,meet(join(X_105,X_107),join(X_105,X_106))) != meet(join(X_105,X_106),join(X_107,X_105))
| meet(join(X_105,X_107),join(X_106,X_105)) = meet(join(X_105,X_106),join(X_107,X_105)) ),
inference(resolve,[$cnf( $equal(join(X_105,meet(join(X_105,X_107),join(X_105,X_106))),meet(join(X_105,X_107),join(X_106,X_105))) )],[refute_0_274,refute_0_275]) ).
cnf(refute_0_277,plain,
meet(join(X_105,X_107),join(X_106,X_105)) = meet(join(X_105,X_106),join(X_107,X_105)),
inference(resolve,[$cnf( $equal(join(X_105,meet(join(X_105,X_107),join(X_105,X_106))),meet(join(X_105,X_106),join(X_107,X_105))) )],[refute_0_273,refute_0_276]) ).
cnf(refute_0_278,plain,
( meet(join(X_105,X_107),join(X_106,X_105)) != meet(join(X_105,X_106),join(X_107,X_105))
| meet(join(X_105,X_106),join(X_107,X_105)) = meet(join(X_105,X_107),join(X_106,X_105)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(meet(join(X_105,X_107),join(X_106,X_105)))),bind(Y0,$fot(meet(join(X_105,X_106),join(X_107,X_105))))]]) ).
cnf(refute_0_279,plain,
meet(join(X_105,X_106),join(X_107,X_105)) = meet(join(X_105,X_107),join(X_106,X_105)),
inference(resolve,[$cnf( $equal(meet(join(X_105,X_107),join(X_106,X_105)),meet(join(X_105,X_106),join(X_107,X_105))) )],[refute_0_277,refute_0_278]) ).
cnf(refute_0_280,plain,
( join(join(X_105,X_106),join(X_362,meet(join(X_105,X_106),join(X_107,X_105)))) != join(X_362,join(X_105,X_106))
| meet(join(X_105,X_106),join(X_107,X_105)) != meet(join(X_105,X_107),join(X_106,X_105))
| join(join(X_105,X_106),join(X_362,meet(join(X_105,X_107),join(X_106,X_105)))) = join(X_362,join(X_105,X_106)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_105,X_106),join(X_362,meet(join(X_105,X_106),join(X_107,X_105)))),join(X_362,join(X_105,X_106))) ),[0,1,1],$fot(meet(join(X_105,X_107),join(X_106,X_105)))]]) ).
cnf(refute_0_281,plain,
( join(join(X_105,X_106),join(X_362,meet(join(X_105,X_106),join(X_107,X_105)))) != join(X_362,join(X_105,X_106))
| join(join(X_105,X_106),join(X_362,meet(join(X_105,X_107),join(X_106,X_105)))) = join(X_362,join(X_105,X_106)) ),
inference(resolve,[$cnf( $equal(meet(join(X_105,X_106),join(X_107,X_105)),meet(join(X_105,X_107),join(X_106,X_105))) )],[refute_0_279,refute_0_280]) ).
cnf(refute_0_282,plain,
join(join(X_105,X_106),join(X_362,meet(join(X_105,X_107),join(X_106,X_105)))) = join(X_362,join(X_105,X_106)),
inference(resolve,[$cnf( $equal(join(join(X_105,X_106),join(X_362,meet(join(X_105,X_106),join(X_107,X_105)))),join(X_362,join(X_105,X_106))) )],[refute_0_266,refute_0_281]) ).
cnf(refute_0_283,plain,
join(join(X_56,X_57),meet(meet(X_55,X_57),join(X_56,X_57))) = join(X_56,X_57),
inference(subst,[],[refute_0_85:[bind(X_23,$fot(join(X_56,X_57))),bind(X_24,$fot(meet(X_55,X_57)))]]) ).
cnf(refute_0_284,plain,
meet(meet(X_24,X_37),join(X_36,join(X_37,meet(X_24,X_37)))) = meet(X_24,X_37),
inference(subst,[],[refute_0_79:[bind(X_6,$fot(meet(X_24,X_37))),bind(X_7,$fot(X_36)),bind(X_8,$fot(X_37))]]) ).
cnf(refute_0_285,plain,
join(X_37,meet(X_24,X_37)) = X_37,
inference(subst,[],[refute_0_85:[bind(X_23,$fot(X_37))]]) ).
cnf(refute_0_286,plain,
( join(X_37,meet(X_24,X_37)) != X_37
| meet(meet(X_24,X_37),join(X_36,join(X_37,meet(X_24,X_37)))) != meet(X_24,X_37)
| meet(meet(X_24,X_37),join(X_36,X_37)) = meet(X_24,X_37) ),
introduced(tautology,[equality,[$cnf( $equal(meet(meet(X_24,X_37),join(X_36,join(X_37,meet(X_24,X_37)))),meet(X_24,X_37)) ),[0,1,1],$fot(X_37)]]) ).
cnf(refute_0_287,plain,
( meet(meet(X_24,X_37),join(X_36,join(X_37,meet(X_24,X_37)))) != meet(X_24,X_37)
| meet(meet(X_24,X_37),join(X_36,X_37)) = meet(X_24,X_37) ),
inference(resolve,[$cnf( $equal(join(X_37,meet(X_24,X_37)),X_37) )],[refute_0_285,refute_0_286]) ).
cnf(refute_0_288,plain,
meet(meet(X_24,X_37),join(X_36,X_37)) = meet(X_24,X_37),
inference(resolve,[$cnf( $equal(meet(meet(X_24,X_37),join(X_36,join(X_37,meet(X_24,X_37)))),meet(X_24,X_37)) )],[refute_0_284,refute_0_287]) ).
cnf(refute_0_289,plain,
meet(meet(X_55,X_57),join(X_56,X_57)) = meet(X_55,X_57),
inference(subst,[],[refute_0_288:[bind(X_24,$fot(X_55)),bind(X_36,$fot(X_56)),bind(X_37,$fot(X_57))]]) ).
cnf(refute_0_290,plain,
( join(join(X_56,X_57),meet(meet(X_55,X_57),join(X_56,X_57))) != join(X_56,X_57)
| meet(meet(X_55,X_57),join(X_56,X_57)) != meet(X_55,X_57)
| join(join(X_56,X_57),meet(X_55,X_57)) = join(X_56,X_57) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_56,X_57),meet(meet(X_55,X_57),join(X_56,X_57))),join(X_56,X_57)) ),[0,1],$fot(meet(X_55,X_57))]]) ).
cnf(refute_0_291,plain,
( join(join(X_56,X_57),meet(meet(X_55,X_57),join(X_56,X_57))) != join(X_56,X_57)
| join(join(X_56,X_57),meet(X_55,X_57)) = join(X_56,X_57) ),
inference(resolve,[$cnf( $equal(meet(meet(X_55,X_57),join(X_56,X_57)),meet(X_55,X_57)) )],[refute_0_289,refute_0_290]) ).
cnf(refute_0_292,plain,
join(join(X_56,X_57),meet(X_55,X_57)) = join(X_56,X_57),
inference(resolve,[$cnf( $equal(join(join(X_56,X_57),meet(meet(X_55,X_57),join(X_56,X_57))),join(X_56,X_57)) )],[refute_0_283,refute_0_291]) ).
cnf(refute_0_293,plain,
join(join(X_121,X_122),meet(X_120,X_122)) = join(X_121,X_122),
inference(subst,[],[refute_0_292:[bind(X_55,$fot(X_120)),bind(X_56,$fot(X_121)),bind(X_57,$fot(X_122))]]) ).
cnf(refute_0_294,plain,
join(X_122,X_121) = join(X_121,X_122),
inference(subst,[],[commutativity_of_join:[bind(X,$fot(X_122)),bind(Y,$fot(X_121))]]) ).
cnf(refute_0_295,plain,
( join(X_122,X_121) != join(X_121,X_122)
| join(X_121,X_122) = join(X_122,X_121) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(join(X_122,X_121))),bind(Y0,$fot(join(X_121,X_122)))]]) ).
cnf(refute_0_296,plain,
join(X_121,X_122) = join(X_122,X_121),
inference(resolve,[$cnf( $equal(join(X_122,X_121),join(X_121,X_122)) )],[refute_0_294,refute_0_295]) ).
cnf(refute_0_297,plain,
( join(X_121,X_122) != join(X_122,X_121)
| join(join(X_121,X_122),meet(X_120,X_122)) != join(X_121,X_122)
| join(join(X_122,X_121),meet(X_120,X_122)) = join(X_121,X_122) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_121,X_122),meet(X_120,X_122)),join(X_121,X_122)) ),[0,0],$fot(join(X_122,X_121))]]) ).
cnf(refute_0_298,plain,
( join(join(X_121,X_122),meet(X_120,X_122)) != join(X_121,X_122)
| join(join(X_122,X_121),meet(X_120,X_122)) = join(X_121,X_122) ),
inference(resolve,[$cnf( $equal(join(X_121,X_122),join(X_122,X_121)) )],[refute_0_296,refute_0_297]) ).
cnf(refute_0_299,plain,
join(join(X_122,X_121),meet(X_120,X_122)) = join(X_121,X_122),
inference(resolve,[$cnf( $equal(join(join(X_121,X_122),meet(X_120,X_122)),join(X_121,X_122)) )],[refute_0_293,refute_0_298]) ).
cnf(refute_0_300,plain,
join(join(join(X_317,X_315),X_121),meet(X_120,join(X_317,X_315))) = join(X_121,join(X_317,X_315)),
inference(subst,[],[refute_0_299:[bind(X_122,$fot(join(X_317,X_315)))]]) ).
cnf(refute_0_301,plain,
join(join(X_317,X_315),X_121) = join(join(X_315,X_317),X_121),
inference(subst,[],[refute_0_251:[bind(X_145,$fot(X_315)),bind(X_146,$fot(X_121)),bind(X_147,$fot(X_317))]]) ).
cnf(refute_0_302,plain,
( join(join(X_317,X_315),X_121) != join(join(X_315,X_317),X_121)
| join(join(join(X_317,X_315),X_121),meet(X_120,join(X_317,X_315))) != join(X_121,join(X_317,X_315))
| join(join(join(X_315,X_317),X_121),meet(X_120,join(X_317,X_315))) = join(X_121,join(X_317,X_315)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(join(X_317,X_315),X_121),meet(X_120,join(X_317,X_315))),join(X_121,join(X_317,X_315))) ),[0,0],$fot(join(join(X_315,X_317),X_121))]]) ).
cnf(refute_0_303,plain,
( join(join(join(X_317,X_315),X_121),meet(X_120,join(X_317,X_315))) != join(X_121,join(X_317,X_315))
| join(join(join(X_315,X_317),X_121),meet(X_120,join(X_317,X_315))) = join(X_121,join(X_317,X_315)) ),
inference(resolve,[$cnf( $equal(join(join(X_317,X_315),X_121),join(join(X_315,X_317),X_121)) )],[refute_0_301,refute_0_302]) ).
cnf(refute_0_304,plain,
join(join(join(X_315,X_317),X_121),meet(X_120,join(X_317,X_315))) = join(X_121,join(X_317,X_315)),
inference(resolve,[$cnf( $equal(join(join(join(X_317,X_315),X_121),meet(X_120,join(X_317,X_315))),join(X_121,join(X_317,X_315))) )],[refute_0_300,refute_0_303]) ).
cnf(refute_0_305,plain,
join(X_68,join(join(X_69,X_68),Z)) = join(join(X_69,X_68),Z),
inference(subst,[],[refute_0_247:[bind(X_14,$fot(Z)),bind(X_15,$fot(X_69)),bind(X_26,$fot(X_68))]]) ).
cnf(refute_0_306,plain,
join(join(X_291,X_8),join(X_362,meet(join(X_291,X_8),join(X_362,X_8)))) = join(X_362,join(X_291,X_8)),
inference(subst,[],[refute_0_265:[bind(X_26,$fot(join(X_362,X_8))),bind(X_357,$fot(join(X_291,X_8))),bind(X_359,$fot(X_362))]]) ).
cnf(refute_0_307,plain,
join(join(X_24,X_8),join(X_24,meet(join(X_8,X_291),join(X_24,X_8)))) = join(X_24,X_8),
inference(subst,[],[refute_0_72:[bind(X_22,$fot(join(X_8,X_291)))]]) ).
cnf(refute_0_308,plain,
join(X_47,X_46) = join(X_46,X_47),
inference(subst,[],[commutativity_of_join:[bind(X,$fot(X_47)),bind(Y,$fot(X_46))]]) ).
cnf(refute_0_309,plain,
( join(X_47,X_46) != join(X_46,X_47)
| join(X_46,X_47) = join(X_47,X_46) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(join(X_47,X_46))),bind(Y0,$fot(join(X_46,X_47)))]]) ).
cnf(refute_0_310,plain,
join(X_46,X_47) = join(X_47,X_46),
inference(resolve,[$cnf( $equal(join(X_47,X_46),join(X_46,X_47)) )],[refute_0_308,refute_0_309]) ).
cnf(refute_0_311,plain,
( join(X_46,X_47) != join(X_47,X_46)
| join(X_46,meet(join(X_46,X_47),join(X_48,X_46))) != meet(join(X_46,X_47),join(X_48,X_46))
| join(X_46,meet(join(X_47,X_46),join(X_48,X_46))) = meet(join(X_46,X_47),join(X_48,X_46)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_46,meet(join(X_46,X_47),join(X_48,X_46))),meet(join(X_46,X_47),join(X_48,X_46))) ),[0,1,0],$fot(join(X_47,X_46))]]) ).
cnf(refute_0_312,plain,
( join(X_46,meet(join(X_46,X_47),join(X_48,X_46))) != meet(join(X_46,X_47),join(X_48,X_46))
| join(X_46,meet(join(X_47,X_46),join(X_48,X_46))) = meet(join(X_46,X_47),join(X_48,X_46)) ),
inference(resolve,[$cnf( $equal(join(X_46,X_47),join(X_47,X_46)) )],[refute_0_310,refute_0_311]) ).
cnf(refute_0_313,plain,
join(X_46,meet(join(X_47,X_46),join(X_48,X_46))) = meet(join(X_46,X_47),join(X_48,X_46)),
inference(resolve,[$cnf( $equal(join(X_46,meet(join(X_46,X_47),join(X_48,X_46))),meet(join(X_46,X_47),join(X_48,X_46))) )],[refute_0_160,refute_0_312]) ).
cnf(refute_0_314,plain,
join(meet(join(X,X_26),join(Z,X_26)),meet(X_26,meet(join(X,X_26),join(Z,X_26)))) = meet(join(X,X_26),join(Z,X_26)),
inference(subst,[],[refute_0_85:[bind(X_23,$fot(meet(join(X,X_26),join(Z,X_26)))),bind(X_24,$fot(X_26))]]) ).
cnf(refute_0_315,plain,
meet(X_26,meet(join(X,X_26),join(Z,X_26))) = X_26,
inference(subst,[],[refute_0_122:[bind(Y,$fot(X_26))]]) ).
cnf(refute_0_316,plain,
( join(meet(join(X,X_26),join(Z,X_26)),meet(X_26,meet(join(X,X_26),join(Z,X_26)))) != meet(join(X,X_26),join(Z,X_26))
| meet(X_26,meet(join(X,X_26),join(Z,X_26))) != X_26
| join(meet(join(X,X_26),join(Z,X_26)),X_26) = meet(join(X,X_26),join(Z,X_26)) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(join(X,X_26),join(Z,X_26)),meet(X_26,meet(join(X,X_26),join(Z,X_26)))),meet(join(X,X_26),join(Z,X_26))) ),[0,1],$fot(X_26)]]) ).
cnf(refute_0_317,plain,
( join(meet(join(X,X_26),join(Z,X_26)),meet(X_26,meet(join(X,X_26),join(Z,X_26)))) != meet(join(X,X_26),join(Z,X_26))
| join(meet(join(X,X_26),join(Z,X_26)),X_26) = meet(join(X,X_26),join(Z,X_26)) ),
inference(resolve,[$cnf( $equal(meet(X_26,meet(join(X,X_26),join(Z,X_26))),X_26) )],[refute_0_315,refute_0_316]) ).
cnf(refute_0_318,plain,
join(meet(join(X,X_26),join(Z,X_26)),X_26) = meet(join(X,X_26),join(Z,X_26)),
inference(resolve,[$cnf( $equal(join(meet(join(X,X_26),join(Z,X_26)),meet(X_26,meet(join(X,X_26),join(Z,X_26)))),meet(join(X,X_26),join(Z,X_26))) )],[refute_0_314,refute_0_317]) ).
cnf(refute_0_319,plain,
join(meet(join(X,X_26),join(Z,X_26)),X_26) = join(X_26,meet(join(X,X_26),join(Z,X_26))),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_26)),bind(Y,$fot(meet(join(X,X_26),join(Z,X_26))))]]) ).
cnf(refute_0_320,plain,
( join(meet(join(X,X_26),join(Z,X_26)),X_26) != join(X_26,meet(join(X,X_26),join(Z,X_26)))
| join(meet(join(X,X_26),join(Z,X_26)),X_26) != meet(join(X,X_26),join(Z,X_26))
| join(X_26,meet(join(X,X_26),join(Z,X_26))) = meet(join(X,X_26),join(Z,X_26)) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(join(X,X_26),join(Z,X_26)),X_26),meet(join(X,X_26),join(Z,X_26))) ),[0],$fot(join(X_26,meet(join(X,X_26),join(Z,X_26))))]]) ).
cnf(refute_0_321,plain,
( join(meet(join(X,X_26),join(Z,X_26)),X_26) != meet(join(X,X_26),join(Z,X_26))
| join(X_26,meet(join(X,X_26),join(Z,X_26))) = meet(join(X,X_26),join(Z,X_26)) ),
inference(resolve,[$cnf( $equal(join(meet(join(X,X_26),join(Z,X_26)),X_26),join(X_26,meet(join(X,X_26),join(Z,X_26)))) )],[refute_0_319,refute_0_320]) ).
cnf(refute_0_322,plain,
join(X_26,meet(join(X,X_26),join(Z,X_26))) = meet(join(X,X_26),join(Z,X_26)),
inference(resolve,[$cnf( $equal(join(meet(join(X,X_26),join(Z,X_26)),X_26),meet(join(X,X_26),join(Z,X_26))) )],[refute_0_318,refute_0_321]) ).
cnf(refute_0_323,plain,
join(X_46,meet(join(X_47,X_46),join(X_48,X_46))) = meet(join(X_47,X_46),join(X_48,X_46)),
inference(subst,[],[refute_0_322:[bind(X,$fot(X_47)),bind(Z,$fot(X_48)),bind(X_26,$fot(X_46))]]) ).
cnf(refute_0_324,plain,
( join(X_46,meet(join(X_47,X_46),join(X_48,X_46))) != meet(join(X_46,X_47),join(X_48,X_46))
| join(X_46,meet(join(X_47,X_46),join(X_48,X_46))) != meet(join(X_47,X_46),join(X_48,X_46))
| meet(join(X_47,X_46),join(X_48,X_46)) = meet(join(X_46,X_47),join(X_48,X_46)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_46,meet(join(X_47,X_46),join(X_48,X_46))),meet(join(X_46,X_47),join(X_48,X_46))) ),[0],$fot(meet(join(X_47,X_46),join(X_48,X_46)))]]) ).
cnf(refute_0_325,plain,
( join(X_46,meet(join(X_47,X_46),join(X_48,X_46))) != meet(join(X_46,X_47),join(X_48,X_46))
| meet(join(X_47,X_46),join(X_48,X_46)) = meet(join(X_46,X_47),join(X_48,X_46)) ),
inference(resolve,[$cnf( $equal(join(X_46,meet(join(X_47,X_46),join(X_48,X_46))),meet(join(X_47,X_46),join(X_48,X_46))) )],[refute_0_323,refute_0_324]) ).
cnf(refute_0_326,plain,
meet(join(X_47,X_46),join(X_48,X_46)) = meet(join(X_46,X_47),join(X_48,X_46)),
inference(resolve,[$cnf( $equal(join(X_46,meet(join(X_47,X_46),join(X_48,X_46))),meet(join(X_46,X_47),join(X_48,X_46))) )],[refute_0_313,refute_0_325]) ).
cnf(refute_0_327,plain,
meet(join(X_291,X_8),join(X_24,X_8)) = meet(join(X_8,X_291),join(X_24,X_8)),
inference(subst,[],[refute_0_326:[bind(X_46,$fot(X_8)),bind(X_47,$fot(X_291)),bind(X_48,$fot(X_24))]]) ).
cnf(refute_0_328,plain,
( meet(join(X_291,X_8),join(X_24,X_8)) != meet(join(X_8,X_291),join(X_24,X_8))
| meet(join(X_8,X_291),join(X_24,X_8)) = meet(join(X_291,X_8),join(X_24,X_8)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(meet(join(X_291,X_8),join(X_24,X_8)))),bind(Y0,$fot(meet(join(X_8,X_291),join(X_24,X_8))))]]) ).
cnf(refute_0_329,plain,
meet(join(X_8,X_291),join(X_24,X_8)) = meet(join(X_291,X_8),join(X_24,X_8)),
inference(resolve,[$cnf( $equal(meet(join(X_291,X_8),join(X_24,X_8)),meet(join(X_8,X_291),join(X_24,X_8))) )],[refute_0_327,refute_0_328]) ).
cnf(refute_0_330,plain,
( join(join(X_24,X_8),join(X_24,meet(join(X_8,X_291),join(X_24,X_8)))) != join(X_24,X_8)
| meet(join(X_8,X_291),join(X_24,X_8)) != meet(join(X_291,X_8),join(X_24,X_8))
| join(join(X_24,X_8),join(X_24,meet(join(X_291,X_8),join(X_24,X_8)))) = join(X_24,X_8) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_24,X_8),join(X_24,meet(join(X_8,X_291),join(X_24,X_8)))),join(X_24,X_8)) ),[0,1,1],$fot(meet(join(X_291,X_8),join(X_24,X_8)))]]) ).
cnf(refute_0_331,plain,
( join(join(X_24,X_8),join(X_24,meet(join(X_8,X_291),join(X_24,X_8)))) != join(X_24,X_8)
| join(join(X_24,X_8),join(X_24,meet(join(X_291,X_8),join(X_24,X_8)))) = join(X_24,X_8) ),
inference(resolve,[$cnf( $equal(meet(join(X_8,X_291),join(X_24,X_8)),meet(join(X_291,X_8),join(X_24,X_8))) )],[refute_0_329,refute_0_330]) ).
cnf(refute_0_332,plain,
join(join(X_24,X_8),join(X_24,meet(join(X_291,X_8),join(X_24,X_8)))) = join(X_24,X_8),
inference(resolve,[$cnf( $equal(join(join(X_24,X_8),join(X_24,meet(join(X_8,X_291),join(X_24,X_8)))),join(X_24,X_8)) )],[refute_0_307,refute_0_331]) ).
cnf(refute_0_333,plain,
join(join(X_69,X_68),join(X_69,join(X_68,meet(join(X_174,X_68),join(X_175,X_68))))) = join(X_69,join(X_68,meet(join(X_174,X_68),join(X_175,X_68)))),
inference(subst,[],[refute_0_113:[bind(Z,$fot(meet(join(X_174,X_68),join(X_175,X_68))))]]) ).
cnf(refute_0_334,plain,
join(X_68,meet(join(X_174,X_68),join(X_175,X_68))) = meet(join(X_174,X_68),join(X_175,X_68)),
inference(subst,[],[refute_0_322:[bind(X,$fot(X_174)),bind(Z,$fot(X_175)),bind(X_26,$fot(X_68))]]) ).
cnf(refute_0_335,plain,
( join(X_68,meet(join(X_174,X_68),join(X_175,X_68))) != meet(join(X_174,X_68),join(X_175,X_68))
| join(join(X_69,X_68),join(X_69,join(X_68,meet(join(X_174,X_68),join(X_175,X_68))))) != join(X_69,join(X_68,meet(join(X_174,X_68),join(X_175,X_68))))
| join(join(X_69,X_68),join(X_69,meet(join(X_174,X_68),join(X_175,X_68)))) = join(X_69,join(X_68,meet(join(X_174,X_68),join(X_175,X_68)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_69,X_68),join(X_69,join(X_68,meet(join(X_174,X_68),join(X_175,X_68))))),join(X_69,join(X_68,meet(join(X_174,X_68),join(X_175,X_68))))) ),[0,1,1],$fot(meet(join(X_174,X_68),join(X_175,X_68)))]]) ).
cnf(refute_0_336,plain,
( join(join(X_69,X_68),join(X_69,join(X_68,meet(join(X_174,X_68),join(X_175,X_68))))) != join(X_69,join(X_68,meet(join(X_174,X_68),join(X_175,X_68))))
| join(join(X_69,X_68),join(X_69,meet(join(X_174,X_68),join(X_175,X_68)))) = join(X_69,join(X_68,meet(join(X_174,X_68),join(X_175,X_68)))) ),
inference(resolve,[$cnf( $equal(join(X_68,meet(join(X_174,X_68),join(X_175,X_68))),meet(join(X_174,X_68),join(X_175,X_68))) )],[refute_0_334,refute_0_335]) ).
cnf(refute_0_337,plain,
join(join(X_69,X_68),join(X_69,meet(join(X_174,X_68),join(X_175,X_68)))) = join(X_69,join(X_68,meet(join(X_174,X_68),join(X_175,X_68)))),
inference(resolve,[$cnf( $equal(join(join(X_69,X_68),join(X_69,join(X_68,meet(join(X_174,X_68),join(X_175,X_68))))),join(X_69,join(X_68,meet(join(X_174,X_68),join(X_175,X_68))))) )],[refute_0_333,refute_0_336]) ).
cnf(refute_0_338,plain,
join(X_69,join(X_68,meet(join(X_174,X_68),join(X_175,X_68)))) = join(X_69,join(X_68,meet(join(X_174,X_68),join(X_175,X_68)))),
introduced(tautology,[refl,[$fot(join(X_69,join(X_68,meet(join(X_174,X_68),join(X_175,X_68)))))]]) ).
cnf(refute_0_339,plain,
( join(X_68,meet(join(X_174,X_68),join(X_175,X_68))) != meet(join(X_174,X_68),join(X_175,X_68))
| join(X_69,join(X_68,meet(join(X_174,X_68),join(X_175,X_68)))) != join(X_69,join(X_68,meet(join(X_174,X_68),join(X_175,X_68))))
| join(X_69,join(X_68,meet(join(X_174,X_68),join(X_175,X_68)))) = join(X_69,meet(join(X_174,X_68),join(X_175,X_68))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_69,join(X_68,meet(join(X_174,X_68),join(X_175,X_68)))),join(X_69,join(X_68,meet(join(X_174,X_68),join(X_175,X_68))))) ),[1,1],$fot(meet(join(X_174,X_68),join(X_175,X_68)))]]) ).
cnf(refute_0_340,plain,
( join(X_68,meet(join(X_174,X_68),join(X_175,X_68))) != meet(join(X_174,X_68),join(X_175,X_68))
| join(X_69,join(X_68,meet(join(X_174,X_68),join(X_175,X_68)))) = join(X_69,meet(join(X_174,X_68),join(X_175,X_68))) ),
inference(resolve,[$cnf( $equal(join(X_69,join(X_68,meet(join(X_174,X_68),join(X_175,X_68)))),join(X_69,join(X_68,meet(join(X_174,X_68),join(X_175,X_68))))) )],[refute_0_338,refute_0_339]) ).
cnf(refute_0_341,plain,
join(X_69,join(X_68,meet(join(X_174,X_68),join(X_175,X_68)))) = join(X_69,meet(join(X_174,X_68),join(X_175,X_68))),
inference(resolve,[$cnf( $equal(join(X_68,meet(join(X_174,X_68),join(X_175,X_68))),meet(join(X_174,X_68),join(X_175,X_68))) )],[refute_0_334,refute_0_340]) ).
cnf(refute_0_342,plain,
( join(X_69,join(X_68,meet(join(X_174,X_68),join(X_175,X_68)))) != join(X_69,meet(join(X_174,X_68),join(X_175,X_68)))
| join(join(X_69,X_68),join(X_69,meet(join(X_174,X_68),join(X_175,X_68)))) != join(X_69,join(X_68,meet(join(X_174,X_68),join(X_175,X_68))))
| join(join(X_69,X_68),join(X_69,meet(join(X_174,X_68),join(X_175,X_68)))) = join(X_69,meet(join(X_174,X_68),join(X_175,X_68))) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_69,X_68),join(X_69,meet(join(X_174,X_68),join(X_175,X_68)))),join(X_69,join(X_68,meet(join(X_174,X_68),join(X_175,X_68))))) ),[1],$fot(join(X_69,meet(join(X_174,X_68),join(X_175,X_68))))]]) ).
cnf(refute_0_343,plain,
( join(join(X_69,X_68),join(X_69,meet(join(X_174,X_68),join(X_175,X_68)))) != join(X_69,join(X_68,meet(join(X_174,X_68),join(X_175,X_68))))
| join(join(X_69,X_68),join(X_69,meet(join(X_174,X_68),join(X_175,X_68)))) = join(X_69,meet(join(X_174,X_68),join(X_175,X_68))) ),
inference(resolve,[$cnf( $equal(join(X_69,join(X_68,meet(join(X_174,X_68),join(X_175,X_68)))),join(X_69,meet(join(X_174,X_68),join(X_175,X_68)))) )],[refute_0_341,refute_0_342]) ).
cnf(refute_0_344,plain,
join(join(X_69,X_68),join(X_69,meet(join(X_174,X_68),join(X_175,X_68)))) = join(X_69,meet(join(X_174,X_68),join(X_175,X_68))),
inference(resolve,[$cnf( $equal(join(join(X_69,X_68),join(X_69,meet(join(X_174,X_68),join(X_175,X_68)))),join(X_69,join(X_68,meet(join(X_174,X_68),join(X_175,X_68))))) )],[refute_0_337,refute_0_343]) ).
cnf(refute_0_345,plain,
join(join(X_24,X_8),join(X_24,meet(join(X_291,X_8),join(X_24,X_8)))) = join(X_24,meet(join(X_291,X_8),join(X_24,X_8))),
inference(subst,[],[refute_0_344:[bind(X_174,$fot(X_291)),bind(X_175,$fot(X_24)),bind(X_68,$fot(X_8)),bind(X_69,$fot(X_24))]]) ).
cnf(refute_0_346,plain,
( join(join(X_24,X_8),join(X_24,meet(join(X_291,X_8),join(X_24,X_8)))) != join(X_24,X_8)
| join(join(X_24,X_8),join(X_24,meet(join(X_291,X_8),join(X_24,X_8)))) != join(X_24,meet(join(X_291,X_8),join(X_24,X_8)))
| join(X_24,meet(join(X_291,X_8),join(X_24,X_8))) = join(X_24,X_8) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_24,X_8),join(X_24,meet(join(X_291,X_8),join(X_24,X_8)))),join(X_24,X_8)) ),[0],$fot(join(X_24,meet(join(X_291,X_8),join(X_24,X_8))))]]) ).
cnf(refute_0_347,plain,
( join(join(X_24,X_8),join(X_24,meet(join(X_291,X_8),join(X_24,X_8)))) != join(X_24,X_8)
| join(X_24,meet(join(X_291,X_8),join(X_24,X_8))) = join(X_24,X_8) ),
inference(resolve,[$cnf( $equal(join(join(X_24,X_8),join(X_24,meet(join(X_291,X_8),join(X_24,X_8)))),join(X_24,meet(join(X_291,X_8),join(X_24,X_8)))) )],[refute_0_345,refute_0_346]) ).
cnf(refute_0_348,plain,
join(X_24,meet(join(X_291,X_8),join(X_24,X_8))) = join(X_24,X_8),
inference(resolve,[$cnf( $equal(join(join(X_24,X_8),join(X_24,meet(join(X_291,X_8),join(X_24,X_8)))),join(X_24,X_8)) )],[refute_0_332,refute_0_347]) ).
cnf(refute_0_349,plain,
join(X_362,meet(join(X_291,X_8),join(X_362,X_8))) = join(X_362,X_8),
inference(subst,[],[refute_0_348:[bind(X_24,$fot(X_362))]]) ).
cnf(refute_0_350,plain,
( join(X_362,meet(join(X_291,X_8),join(X_362,X_8))) != join(X_362,X_8)
| join(join(X_291,X_8),join(X_362,meet(join(X_291,X_8),join(X_362,X_8)))) != join(X_362,join(X_291,X_8))
| join(join(X_291,X_8),join(X_362,X_8)) = join(X_362,join(X_291,X_8)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_291,X_8),join(X_362,meet(join(X_291,X_8),join(X_362,X_8)))),join(X_362,join(X_291,X_8))) ),[0,1],$fot(join(X_362,X_8))]]) ).
cnf(refute_0_351,plain,
( join(join(X_291,X_8),join(X_362,meet(join(X_291,X_8),join(X_362,X_8)))) != join(X_362,join(X_291,X_8))
| join(join(X_291,X_8),join(X_362,X_8)) = join(X_362,join(X_291,X_8)) ),
inference(resolve,[$cnf( $equal(join(X_362,meet(join(X_291,X_8),join(X_362,X_8))),join(X_362,X_8)) )],[refute_0_349,refute_0_350]) ).
cnf(refute_0_352,plain,
join(join(X_291,X_8),join(X_362,X_8)) = join(X_362,join(X_291,X_8)),
inference(resolve,[$cnf( $equal(join(join(X_291,X_8),join(X_362,meet(join(X_291,X_8),join(X_362,X_8)))),join(X_362,join(X_291,X_8))) )],[refute_0_306,refute_0_351]) ).
cnf(refute_0_353,plain,
join(join(X_69,join(X_8,X_68)),join(X_69,meet(X_68,join(X_69,join(X_8,X_68))))) = join(X_69,join(X_8,X_68)),
inference(subst,[],[refute_0_72:[bind(X_22,$fot(X_68)),bind(X_24,$fot(X_69)),bind(X_8,$fot(join(X_8,X_68)))]]) ).
cnf(refute_0_354,plain,
meet(X_68,join(X_69,join(X_8,X_68))) = X_68,
inference(subst,[],[refute_0_79:[bind(X_6,$fot(X_68)),bind(X_7,$fot(X_69))]]) ).
cnf(refute_0_355,plain,
( join(join(X_69,join(X_8,X_68)),join(X_69,meet(X_68,join(X_69,join(X_8,X_68))))) != join(X_69,join(X_8,X_68))
| meet(X_68,join(X_69,join(X_8,X_68))) != X_68
| join(join(X_69,join(X_8,X_68)),join(X_69,X_68)) = join(X_69,join(X_8,X_68)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_69,join(X_8,X_68)),join(X_69,meet(X_68,join(X_69,join(X_8,X_68))))),join(X_69,join(X_8,X_68))) ),[0,1,1],$fot(X_68)]]) ).
cnf(refute_0_356,plain,
( join(join(X_69,join(X_8,X_68)),join(X_69,meet(X_68,join(X_69,join(X_8,X_68))))) != join(X_69,join(X_8,X_68))
| join(join(X_69,join(X_8,X_68)),join(X_69,X_68)) = join(X_69,join(X_8,X_68)) ),
inference(resolve,[$cnf( $equal(meet(X_68,join(X_69,join(X_8,X_68))),X_68) )],[refute_0_354,refute_0_355]) ).
cnf(refute_0_357,plain,
join(join(X_69,join(X_8,X_68)),join(X_69,X_68)) = join(X_69,join(X_8,X_68)),
inference(resolve,[$cnf( $equal(join(join(X_69,join(X_8,X_68)),join(X_69,meet(X_68,join(X_69,join(X_8,X_68))))),join(X_69,join(X_8,X_68))) )],[refute_0_353,refute_0_356]) ).
cnf(refute_0_358,plain,
join(join(X_69,join(X_8,X_68)),join(X_69,X_68)) = join(join(X_69,X_68),join(X_69,join(X_8,X_68))),
inference(subst,[],[refute_0_4:[bind(X,$fot(join(X_69,X_68))),bind(Y,$fot(join(X_69,join(X_8,X_68))))]]) ).
cnf(refute_0_359,plain,
( join(join(X_69,join(X_8,X_68)),join(X_69,X_68)) != join(X_69,join(X_8,X_68))
| join(join(X_69,join(X_8,X_68)),join(X_69,X_68)) != join(join(X_69,X_68),join(X_69,join(X_8,X_68)))
| join(join(X_69,X_68),join(X_69,join(X_8,X_68))) = join(X_69,join(X_8,X_68)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_69,join(X_8,X_68)),join(X_69,X_68)),join(X_69,join(X_8,X_68))) ),[0],$fot(join(join(X_69,X_68),join(X_69,join(X_8,X_68))))]]) ).
cnf(refute_0_360,plain,
( join(join(X_69,join(X_8,X_68)),join(X_69,X_68)) != join(X_69,join(X_8,X_68))
| join(join(X_69,X_68),join(X_69,join(X_8,X_68))) = join(X_69,join(X_8,X_68)) ),
inference(resolve,[$cnf( $equal(join(join(X_69,join(X_8,X_68)),join(X_69,X_68)),join(join(X_69,X_68),join(X_69,join(X_8,X_68)))) )],[refute_0_358,refute_0_359]) ).
cnf(refute_0_361,plain,
join(join(X_69,X_68),join(X_69,join(X_8,X_68))) = join(X_69,join(X_8,X_68)),
inference(resolve,[$cnf( $equal(join(join(X_69,join(X_8,X_68)),join(X_69,X_68)),join(X_69,join(X_8,X_68))) )],[refute_0_357,refute_0_360]) ).
cnf(refute_0_362,plain,
join(join(join(X_8,X_303),join(X_305,X_303)),join(join(X_8,X_303),join(X_8,join(X_305,X_303)))) = join(join(X_8,X_303),join(X_8,join(X_305,X_303))),
inference(subst,[],[refute_0_361:[bind(X_68,$fot(join(X_305,X_303))),bind(X_69,$fot(join(X_8,X_303)))]]) ).
cnf(refute_0_363,plain,
join(join(X_8,X_303),join(X_8,join(X_305,X_303))) = join(X_8,join(X_305,X_303)),
inference(subst,[],[refute_0_361:[bind(X_68,$fot(X_303)),bind(X_69,$fot(X_8)),bind(X_8,$fot(X_305))]]) ).
cnf(refute_0_364,plain,
( join(join(X_8,X_303),join(X_8,join(X_305,X_303))) != join(X_8,join(X_305,X_303))
| join(join(join(X_8,X_303),join(X_305,X_303)),join(join(X_8,X_303),join(X_8,join(X_305,X_303)))) != join(join(X_8,X_303),join(X_8,join(X_305,X_303)))
| join(join(join(X_8,X_303),join(X_305,X_303)),join(X_8,join(X_305,X_303))) = join(join(X_8,X_303),join(X_8,join(X_305,X_303))) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(join(X_8,X_303),join(X_305,X_303)),join(join(X_8,X_303),join(X_8,join(X_305,X_303)))),join(join(X_8,X_303),join(X_8,join(X_305,X_303)))) ),[0,1],$fot(join(X_8,join(X_305,X_303)))]]) ).
cnf(refute_0_365,plain,
( join(join(join(X_8,X_303),join(X_305,X_303)),join(join(X_8,X_303),join(X_8,join(X_305,X_303)))) != join(join(X_8,X_303),join(X_8,join(X_305,X_303)))
| join(join(join(X_8,X_303),join(X_305,X_303)),join(X_8,join(X_305,X_303))) = join(join(X_8,X_303),join(X_8,join(X_305,X_303))) ),
inference(resolve,[$cnf( $equal(join(join(X_8,X_303),join(X_8,join(X_305,X_303))),join(X_8,join(X_305,X_303))) )],[refute_0_363,refute_0_364]) ).
cnf(refute_0_366,plain,
join(join(join(X_8,X_303),join(X_305,X_303)),join(X_8,join(X_305,X_303))) = join(join(X_8,X_303),join(X_8,join(X_305,X_303))),
inference(resolve,[$cnf( $equal(join(join(join(X_8,X_303),join(X_305,X_303)),join(join(X_8,X_303),join(X_8,join(X_305,X_303)))),join(join(X_8,X_303),join(X_8,join(X_305,X_303)))) )],[refute_0_362,refute_0_365]) ).
cnf(refute_0_367,plain,
join(join(join(X_114,X_8),X_115),join(X_115,meet(X_114,join(join(X_114,X_8),X_115)))) = join(join(X_114,X_8),X_115),
inference(subst,[],[refute_0_30:[bind(X_22,$fot(X_114)),bind(X_24,$fot(X_115)),bind(X_7,$fot(join(X_114,X_8)))]]) ).
cnf(refute_0_368,plain,
meet(X_114,join(join(X_114,X_8),X_115)) = X_114,
inference(subst,[],[refute_0_38:[bind(X_6,$fot(X_114)),bind(X_7,$fot(X_115))]]) ).
cnf(refute_0_369,plain,
( join(join(join(X_114,X_8),X_115),join(X_115,meet(X_114,join(join(X_114,X_8),X_115)))) != join(join(X_114,X_8),X_115)
| meet(X_114,join(join(X_114,X_8),X_115)) != X_114
| join(join(join(X_114,X_8),X_115),join(X_115,X_114)) = join(join(X_114,X_8),X_115) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(join(X_114,X_8),X_115),join(X_115,meet(X_114,join(join(X_114,X_8),X_115)))),join(join(X_114,X_8),X_115)) ),[0,1,1],$fot(X_114)]]) ).
cnf(refute_0_370,plain,
( join(join(join(X_114,X_8),X_115),join(X_115,meet(X_114,join(join(X_114,X_8),X_115)))) != join(join(X_114,X_8),X_115)
| join(join(join(X_114,X_8),X_115),join(X_115,X_114)) = join(join(X_114,X_8),X_115) ),
inference(resolve,[$cnf( $equal(meet(X_114,join(join(X_114,X_8),X_115)),X_114) )],[refute_0_368,refute_0_369]) ).
cnf(refute_0_371,plain,
join(join(join(X_114,X_8),X_115),join(X_115,X_114)) = join(join(X_114,X_8),X_115),
inference(resolve,[$cnf( $equal(join(join(join(X_114,X_8),X_115),join(X_115,meet(X_114,join(join(X_114,X_8),X_115)))),join(join(X_114,X_8),X_115)) )],[refute_0_367,refute_0_370]) ).
cnf(refute_0_372,plain,
join(join(join(X_114,X_8),X_115),join(X_115,X_114)) = join(join(X_115,X_114),join(join(X_114,X_8),X_115)),
inference(subst,[],[refute_0_4:[bind(X,$fot(join(X_115,X_114))),bind(Y,$fot(join(join(X_114,X_8),X_115)))]]) ).
cnf(refute_0_373,plain,
( join(join(join(X_114,X_8),X_115),join(X_115,X_114)) != join(join(X_114,X_8),X_115)
| join(join(join(X_114,X_8),X_115),join(X_115,X_114)) != join(join(X_115,X_114),join(join(X_114,X_8),X_115))
| join(join(X_115,X_114),join(join(X_114,X_8),X_115)) = join(join(X_114,X_8),X_115) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(join(X_114,X_8),X_115),join(X_115,X_114)),join(join(X_114,X_8),X_115)) ),[0],$fot(join(join(X_115,X_114),join(join(X_114,X_8),X_115)))]]) ).
cnf(refute_0_374,plain,
( join(join(join(X_114,X_8),X_115),join(X_115,X_114)) != join(join(X_114,X_8),X_115)
| join(join(X_115,X_114),join(join(X_114,X_8),X_115)) = join(join(X_114,X_8),X_115) ),
inference(resolve,[$cnf( $equal(join(join(join(X_114,X_8),X_115),join(X_115,X_114)),join(join(X_115,X_114),join(join(X_114,X_8),X_115))) )],[refute_0_372,refute_0_373]) ).
cnf(refute_0_375,plain,
join(join(X_115,X_114),join(join(X_114,X_8),X_115)) = join(join(X_114,X_8),X_115),
inference(resolve,[$cnf( $equal(join(join(join(X_114,X_8),X_115),join(X_115,X_114)),join(join(X_114,X_8),X_115)) )],[refute_0_371,refute_0_374]) ).
cnf(refute_0_376,plain,
join(join(join(X_305,X_303),X_8),join(join(X_8,X_303),join(X_305,X_303))) = join(join(X_8,X_303),join(X_305,X_303)),
inference(subst,[],[refute_0_375:[bind(X_114,$fot(X_8)),bind(X_115,$fot(join(X_305,X_303))),bind(X_8,$fot(X_303))]]) ).
cnf(refute_0_377,plain,
join(join(X_264,X_266),Y) = join(Y,join(X_264,X_266)),
inference(subst,[],[commutativity_of_join:[bind(X,$fot(join(X_264,X_266)))]]) ).
cnf(refute_0_378,plain,
join(Y,join(X_264,X_266)) = join(Y,join(X_266,X_264)),
inference(subst,[],[refute_0_203:[bind(X_96,$fot(X_264)),bind(X_97,$fot(Y)),bind(X_98,$fot(X_266))]]) ).
cnf(refute_0_379,plain,
( join(Y,join(X_264,X_266)) != join(Y,join(X_266,X_264))
| join(join(X_264,X_266),Y) != join(Y,join(X_264,X_266))
| join(join(X_264,X_266),Y) = join(Y,join(X_266,X_264)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_264,X_266),Y),join(Y,join(X_264,X_266))) ),[1],$fot(join(Y,join(X_266,X_264)))]]) ).
cnf(refute_0_380,plain,
( join(join(X_264,X_266),Y) != join(Y,join(X_264,X_266))
| join(join(X_264,X_266),Y) = join(Y,join(X_266,X_264)) ),
inference(resolve,[$cnf( $equal(join(Y,join(X_264,X_266)),join(Y,join(X_266,X_264))) )],[refute_0_378,refute_0_379]) ).
cnf(refute_0_381,plain,
join(join(X_264,X_266),Y) = join(Y,join(X_266,X_264)),
inference(resolve,[$cnf( $equal(join(join(X_264,X_266),Y),join(Y,join(X_264,X_266))) )],[refute_0_377,refute_0_380]) ).
cnf(refute_0_382,plain,
( join(join(X_264,X_266),Y) != join(Y,join(X_266,X_264))
| join(Y,join(X_266,X_264)) = join(join(X_264,X_266),Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(join(join(X_264,X_266),Y))),bind(Y0,$fot(join(Y,join(X_266,X_264))))]]) ).
cnf(refute_0_383,plain,
join(Y,join(X_266,X_264)) = join(join(X_264,X_266),Y),
inference(resolve,[$cnf( $equal(join(join(X_264,X_266),Y),join(Y,join(X_266,X_264))) )],[refute_0_381,refute_0_382]) ).
cnf(refute_0_384,plain,
join(join(join(X_8,X_303),join(X_305,X_303)),join(X_8,join(X_305,X_303))) = join(join(join(X_305,X_303),X_8),join(join(X_8,X_303),join(X_305,X_303))),
inference(subst,[],[refute_0_383:[bind(Y,$fot(join(join(X_8,X_303),join(X_305,X_303)))),bind(X_264,$fot(join(X_305,X_303))),bind(X_266,$fot(X_8))]]) ).
cnf(refute_0_385,plain,
( join(join(join(X_305,X_303),X_8),join(join(X_8,X_303),join(X_305,X_303))) != join(join(X_8,X_303),join(X_305,X_303))
| join(join(join(X_8,X_303),join(X_305,X_303)),join(X_8,join(X_305,X_303))) != join(join(join(X_305,X_303),X_8),join(join(X_8,X_303),join(X_305,X_303)))
| join(join(join(X_8,X_303),join(X_305,X_303)),join(X_8,join(X_305,X_303))) = join(join(X_8,X_303),join(X_305,X_303)) ),
inference(subst,[],[refute_0_218:[bind(X0,$fot(join(join(join(X_8,X_303),join(X_305,X_303)),join(X_8,join(X_305,X_303))))),bind(Y0,$fot(join(join(join(X_305,X_303),X_8),join(join(X_8,X_303),join(X_305,X_303))))),bind(Z0,$fot(join(join(X_8,X_303),join(X_305,X_303))))]]) ).
cnf(refute_0_386,plain,
( join(join(join(X_305,X_303),X_8),join(join(X_8,X_303),join(X_305,X_303))) != join(join(X_8,X_303),join(X_305,X_303))
| join(join(join(X_8,X_303),join(X_305,X_303)),join(X_8,join(X_305,X_303))) = join(join(X_8,X_303),join(X_305,X_303)) ),
inference(resolve,[$cnf( $equal(join(join(join(X_8,X_303),join(X_305,X_303)),join(X_8,join(X_305,X_303))),join(join(join(X_305,X_303),X_8),join(join(X_8,X_303),join(X_305,X_303)))) )],[refute_0_384,refute_0_385]) ).
cnf(refute_0_387,plain,
join(join(join(X_8,X_303),join(X_305,X_303)),join(X_8,join(X_305,X_303))) = join(join(X_8,X_303),join(X_305,X_303)),
inference(resolve,[$cnf( $equal(join(join(join(X_305,X_303),X_8),join(join(X_8,X_303),join(X_305,X_303))),join(join(X_8,X_303),join(X_305,X_303))) )],[refute_0_376,refute_0_386]) ).
cnf(refute_0_388,plain,
( join(join(join(X_8,X_303),join(X_305,X_303)),join(X_8,join(X_305,X_303))) != join(join(X_8,X_303),join(X_305,X_303))
| join(join(join(X_8,X_303),join(X_305,X_303)),join(X_8,join(X_305,X_303))) != join(join(X_8,X_303),join(X_8,join(X_305,X_303)))
| join(join(X_8,X_303),join(X_305,X_303)) = join(join(X_8,X_303),join(X_8,join(X_305,X_303))) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(join(X_8,X_303),join(X_305,X_303)),join(X_8,join(X_305,X_303))),join(join(X_8,X_303),join(X_8,join(X_305,X_303)))) ),[0],$fot(join(join(X_8,X_303),join(X_305,X_303)))]]) ).
cnf(refute_0_389,plain,
( join(join(join(X_8,X_303),join(X_305,X_303)),join(X_8,join(X_305,X_303))) != join(join(X_8,X_303),join(X_8,join(X_305,X_303)))
| join(join(X_8,X_303),join(X_305,X_303)) = join(join(X_8,X_303),join(X_8,join(X_305,X_303))) ),
inference(resolve,[$cnf( $equal(join(join(join(X_8,X_303),join(X_305,X_303)),join(X_8,join(X_305,X_303))),join(join(X_8,X_303),join(X_305,X_303))) )],[refute_0_387,refute_0_388]) ).
cnf(refute_0_390,plain,
( join(join(X_8,X_303),join(X_305,X_303)) != join(join(X_8,X_303),join(X_8,join(X_305,X_303)))
| join(join(X_8,X_303),join(X_8,join(X_305,X_303))) != join(X_8,join(X_305,X_303))
| join(join(X_8,X_303),join(X_305,X_303)) = join(X_8,join(X_305,X_303)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(join(X_8,X_303),join(X_305,X_303)),join(X_8,join(X_305,X_303))) ),[0],$fot(join(join(X_8,X_303),join(X_8,join(X_305,X_303))))]]) ).
cnf(refute_0_391,plain,
( join(join(X_8,X_303),join(X_305,X_303)) != join(join(X_8,X_303),join(X_8,join(X_305,X_303)))
| join(join(X_8,X_303),join(X_305,X_303)) = join(X_8,join(X_305,X_303)) ),
inference(resolve,[$cnf( $equal(join(join(X_8,X_303),join(X_8,join(X_305,X_303))),join(X_8,join(X_305,X_303))) )],[refute_0_363,refute_0_390]) ).
cnf(refute_0_392,plain,
( join(join(join(X_8,X_303),join(X_305,X_303)),join(X_8,join(X_305,X_303))) != join(join(X_8,X_303),join(X_8,join(X_305,X_303)))
| join(join(X_8,X_303),join(X_305,X_303)) = join(X_8,join(X_305,X_303)) ),
inference(resolve,[$cnf( $equal(join(join(X_8,X_303),join(X_305,X_303)),join(join(X_8,X_303),join(X_8,join(X_305,X_303)))) )],[refute_0_389,refute_0_391]) ).
cnf(refute_0_393,plain,
join(join(X_8,X_303),join(X_305,X_303)) = join(X_8,join(X_305,X_303)),
inference(resolve,[$cnf( $equal(join(join(join(X_8,X_303),join(X_305,X_303)),join(X_8,join(X_305,X_303))),join(join(X_8,X_303),join(X_8,join(X_305,X_303)))) )],[refute_0_366,refute_0_392]) ).
cnf(refute_0_394,plain,
join(join(X_291,X_8),join(X_362,X_8)) = join(X_291,join(X_362,X_8)),
inference(subst,[],[refute_0_393:[bind(X_303,$fot(X_8)),bind(X_305,$fot(X_362)),bind(X_8,$fot(X_291))]]) ).
cnf(refute_0_395,plain,
( join(join(X_291,X_8),join(X_362,X_8)) != join(X_291,join(X_362,X_8))
| join(join(X_291,X_8),join(X_362,X_8)) != join(X_362,join(X_291,X_8))
| join(X_291,join(X_362,X_8)) = join(X_362,join(X_291,X_8)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_291,X_8),join(X_362,X_8)),join(X_362,join(X_291,X_8))) ),[0],$fot(join(X_291,join(X_362,X_8)))]]) ).
cnf(refute_0_396,plain,
( join(join(X_291,X_8),join(X_362,X_8)) != join(X_362,join(X_291,X_8))
| join(X_291,join(X_362,X_8)) = join(X_362,join(X_291,X_8)) ),
inference(resolve,[$cnf( $equal(join(join(X_291,X_8),join(X_362,X_8)),join(X_291,join(X_362,X_8))) )],[refute_0_394,refute_0_395]) ).
cnf(refute_0_397,plain,
join(X_291,join(X_362,X_8)) = join(X_362,join(X_291,X_8)),
inference(resolve,[$cnf( $equal(join(join(X_291,X_8),join(X_362,X_8)),join(X_362,join(X_291,X_8))) )],[refute_0_352,refute_0_396]) ).
cnf(refute_0_398,plain,
( join(X_291,join(X_362,X_8)) != join(X_362,join(X_291,X_8))
| join(X_362,join(X_291,X_8)) = join(X_291,join(X_362,X_8)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(join(X_291,join(X_362,X_8)))),bind(Y0,$fot(join(X_362,join(X_291,X_8))))]]) ).
cnf(refute_0_399,plain,
join(X_362,join(X_291,X_8)) = join(X_291,join(X_362,X_8)),
inference(resolve,[$cnf( $equal(join(X_291,join(X_362,X_8)),join(X_362,join(X_291,X_8))) )],[refute_0_397,refute_0_398]) ).
cnf(refute_0_400,plain,
join(join(X_69,X_68),join(X_68,Z)) = join(X_68,join(join(X_69,X_68),Z)),
inference(subst,[],[refute_0_399:[bind(X_291,$fot(X_68)),bind(X_362,$fot(join(X_69,X_68))),bind(X_8,$fot(Z))]]) ).
cnf(refute_0_401,plain,
( join(X_68,join(join(X_69,X_68),Z)) != join(join(X_69,X_68),Z)
| join(join(X_69,X_68),join(X_68,Z)) != join(X_68,join(join(X_69,X_68),Z))
| join(join(X_69,X_68),join(X_68,Z)) = join(join(X_69,X_68),Z) ),
inference(subst,[],[refute_0_218:[bind(X0,$fot(join(join(X_69,X_68),join(X_68,Z)))),bind(Y0,$fot(join(X_68,join(join(X_69,X_68),Z)))),bind(Z0,$fot(join(join(X_69,X_68),Z)))]]) ).
cnf(refute_0_402,plain,
( join(X_68,join(join(X_69,X_68),Z)) != join(join(X_69,X_68),Z)
| join(join(X_69,X_68),join(X_68,Z)) = join(join(X_69,X_68),Z) ),
inference(resolve,[$cnf( $equal(join(join(X_69,X_68),join(X_68,Z)),join(X_68,join(join(X_69,X_68),Z))) )],[refute_0_400,refute_0_401]) ).
cnf(refute_0_403,plain,
join(join(X_69,X_68),join(X_68,Z)) = join(join(X_69,X_68),Z),
inference(resolve,[$cnf( $equal(join(X_68,join(join(X_69,X_68),Z)),join(join(X_69,X_68),Z)) )],[refute_0_305,refute_0_402]) ).
cnf(refute_0_404,plain,
join(X_69,join(join(X_69,X_68),join(X_68,Z))) = join(join(X_69,X_68),join(X_68,Z)),
inference(subst,[],[refute_0_231:[bind(X_26,$fot(X_69)),bind(X_7,$fot(join(X_68,Z))),bind(X_8,$fot(X_68))]]) ).
cnf(refute_0_405,plain,
( join(X_69,join(join(X_69,X_68),join(X_68,Z))) != join(join(X_69,X_68),join(X_68,Z))
| join(join(X_69,X_68),join(X_68,Z)) != join(join(X_69,X_68),Z)
| join(X_69,join(join(X_69,X_68),join(X_68,Z))) = join(join(X_69,X_68),Z) ),
inference(subst,[],[refute_0_218:[bind(X0,$fot(join(X_69,join(join(X_69,X_68),join(X_68,Z))))),bind(Y0,$fot(join(join(X_69,X_68),join(X_68,Z)))),bind(Z0,$fot(join(join(X_69,X_68),Z)))]]) ).
cnf(refute_0_406,plain,
( join(join(X_69,X_68),join(X_68,Z)) != join(join(X_69,X_68),Z)
| join(X_69,join(join(X_69,X_68),join(X_68,Z))) = join(join(X_69,X_68),Z) ),
inference(resolve,[$cnf( $equal(join(X_69,join(join(X_69,X_68),join(X_68,Z))),join(join(X_69,X_68),join(X_68,Z))) )],[refute_0_404,refute_0_405]) ).
cnf(refute_0_407,plain,
join(X_69,join(join(X_69,X_68),join(X_68,Z))) = join(join(X_69,X_68),Z),
inference(resolve,[$cnf( $equal(join(join(X_69,X_68),join(X_68,Z)),join(join(X_69,X_68),Z)) )],[refute_0_403,refute_0_406]) ).
cnf(refute_0_408,plain,
join(join(X_69,X_68),join(X_69,join(X_68,Z))) = join(X_69,join(join(X_69,X_68),join(X_68,Z))),
inference(subst,[],[refute_0_399:[bind(X_291,$fot(X_69)),bind(X_362,$fot(join(X_69,X_68))),bind(X_8,$fot(join(X_68,Z)))]]) ).
cnf(refute_0_409,plain,
( join(X_69,join(join(X_69,X_68),join(X_68,Z))) != join(join(X_69,X_68),Z)
| join(join(X_69,X_68),join(X_69,join(X_68,Z))) != join(X_69,join(join(X_69,X_68),join(X_68,Z)))
| join(join(X_69,X_68),join(X_69,join(X_68,Z))) = join(join(X_69,X_68),Z) ),
inference(subst,[],[refute_0_218:[bind(X0,$fot(join(join(X_69,X_68),join(X_69,join(X_68,Z))))),bind(Y0,$fot(join(X_69,join(join(X_69,X_68),join(X_68,Z))))),bind(Z0,$fot(join(join(X_69,X_68),Z)))]]) ).
cnf(refute_0_410,plain,
( join(X_69,join(join(X_69,X_68),join(X_68,Z))) != join(join(X_69,X_68),Z)
| join(join(X_69,X_68),join(X_69,join(X_68,Z))) = join(join(X_69,X_68),Z) ),
inference(resolve,[$cnf( $equal(join(join(X_69,X_68),join(X_69,join(X_68,Z))),join(X_69,join(join(X_69,X_68),join(X_68,Z)))) )],[refute_0_408,refute_0_409]) ).
cnf(refute_0_411,plain,
join(join(X_69,X_68),join(X_69,join(X_68,Z))) = join(join(X_69,X_68),Z),
inference(resolve,[$cnf( $equal(join(X_69,join(join(X_69,X_68),join(X_68,Z))),join(join(X_69,X_68),Z)) )],[refute_0_407,refute_0_410]) ).
cnf(refute_0_412,plain,
( join(join(X_69,X_68),join(X_69,join(X_68,Z))) != join(X_69,join(X_68,Z))
| join(join(X_69,X_68),join(X_69,join(X_68,Z))) != join(join(X_69,X_68),Z)
| join(join(X_69,X_68),Z) = join(X_69,join(X_68,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_69,X_68),join(X_69,join(X_68,Z))),join(X_69,join(X_68,Z))) ),[0],$fot(join(join(X_69,X_68),Z))]]) ).
cnf(refute_0_413,plain,
( join(join(X_69,X_68),join(X_69,join(X_68,Z))) != join(X_69,join(X_68,Z))
| join(join(X_69,X_68),Z) = join(X_69,join(X_68,Z)) ),
inference(resolve,[$cnf( $equal(join(join(X_69,X_68),join(X_69,join(X_68,Z))),join(join(X_69,X_68),Z)) )],[refute_0_411,refute_0_412]) ).
cnf(refute_0_414,plain,
join(join(X_69,X_68),Z) = join(X_69,join(X_68,Z)),
inference(resolve,[$cnf( $equal(join(join(X_69,X_68),join(X_69,join(X_68,Z))),join(X_69,join(X_68,Z))) )],[refute_0_113,refute_0_413]) ).
cnf(refute_0_415,plain,
join(join(X_315,X_317),join(X_121,meet(X_120,join(X_317,X_315)))) = join(X_315,join(X_317,join(X_121,meet(X_120,join(X_317,X_315))))),
inference(subst,[],[refute_0_414:[bind(Z,$fot(join(X_121,meet(X_120,join(X_317,X_315))))),bind(X_68,$fot(X_317)),bind(X_69,$fot(X_315))]]) ).
cnf(refute_0_416,plain,
join(join(join(X_315,X_317),X_121),meet(X_120,join(X_317,X_315))) = join(join(X_315,X_317),join(X_121,meet(X_120,join(X_317,X_315)))),
inference(subst,[],[refute_0_414:[bind(Z,$fot(meet(X_120,join(X_317,X_315)))),bind(X_68,$fot(X_121)),bind(X_69,$fot(join(X_315,X_317)))]]) ).
cnf(refute_0_417,plain,
( join(join(X_315,X_317),join(X_121,meet(X_120,join(X_317,X_315)))) != join(X_315,join(X_317,join(X_121,meet(X_120,join(X_317,X_315)))))
| join(join(join(X_315,X_317),X_121),meet(X_120,join(X_317,X_315))) != join(join(X_315,X_317),join(X_121,meet(X_120,join(X_317,X_315))))
| join(join(join(X_315,X_317),X_121),meet(X_120,join(X_317,X_315))) = join(X_315,join(X_317,join(X_121,meet(X_120,join(X_317,X_315))))) ),
inference(subst,[],[refute_0_218:[bind(X0,$fot(join(join(join(X_315,X_317),X_121),meet(X_120,join(X_317,X_315))))),bind(Y0,$fot(join(join(X_315,X_317),join(X_121,meet(X_120,join(X_317,X_315)))))),bind(Z0,$fot(join(X_315,join(X_317,join(X_121,meet(X_120,join(X_317,X_315)))))))]]) ).
cnf(refute_0_418,plain,
( join(join(X_315,X_317),join(X_121,meet(X_120,join(X_317,X_315)))) != join(X_315,join(X_317,join(X_121,meet(X_120,join(X_317,X_315)))))
| join(join(join(X_315,X_317),X_121),meet(X_120,join(X_317,X_315))) = join(X_315,join(X_317,join(X_121,meet(X_120,join(X_317,X_315))))) ),
inference(resolve,[$cnf( $equal(join(join(join(X_315,X_317),X_121),meet(X_120,join(X_317,X_315))),join(join(X_315,X_317),join(X_121,meet(X_120,join(X_317,X_315))))) )],[refute_0_416,refute_0_417]) ).
cnf(refute_0_419,plain,
join(join(join(X_315,X_317),X_121),meet(X_120,join(X_317,X_315))) = join(X_315,join(X_317,join(X_121,meet(X_120,join(X_317,X_315))))),
inference(resolve,[$cnf( $equal(join(join(X_315,X_317),join(X_121,meet(X_120,join(X_317,X_315)))),join(X_315,join(X_317,join(X_121,meet(X_120,join(X_317,X_315)))))) )],[refute_0_415,refute_0_418]) ).
cnf(refute_0_420,plain,
( join(join(join(X_315,X_317),X_121),meet(X_120,join(X_317,X_315))) != join(X_121,join(X_317,X_315))
| join(join(join(X_315,X_317),X_121),meet(X_120,join(X_317,X_315))) != join(X_315,join(X_317,join(X_121,meet(X_120,join(X_317,X_315)))))
| join(X_315,join(X_317,join(X_121,meet(X_120,join(X_317,X_315))))) = join(X_121,join(X_317,X_315)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(join(X_315,X_317),X_121),meet(X_120,join(X_317,X_315))),join(X_121,join(X_317,X_315))) ),[0],$fot(join(X_315,join(X_317,join(X_121,meet(X_120,join(X_317,X_315))))))]]) ).
cnf(refute_0_421,plain,
( join(join(join(X_315,X_317),X_121),meet(X_120,join(X_317,X_315))) != join(X_121,join(X_317,X_315))
| join(X_315,join(X_317,join(X_121,meet(X_120,join(X_317,X_315))))) = join(X_121,join(X_317,X_315)) ),
inference(resolve,[$cnf( $equal(join(join(join(X_315,X_317),X_121),meet(X_120,join(X_317,X_315))),join(X_315,join(X_317,join(X_121,meet(X_120,join(X_317,X_315)))))) )],[refute_0_419,refute_0_420]) ).
cnf(refute_0_422,plain,
join(X_315,join(X_317,join(X_121,meet(X_120,join(X_317,X_315))))) = join(X_121,join(X_317,X_315)),
inference(resolve,[$cnf( $equal(join(join(join(X_315,X_317),X_121),meet(X_120,join(X_317,X_315))),join(X_121,join(X_317,X_315))) )],[refute_0_304,refute_0_421]) ).
cnf(refute_0_423,plain,
join(X_105,join(X_106,join(X_362,meet(join(X_105,X_107),join(X_106,X_105))))) = join(X_362,join(X_106,X_105)),
inference(subst,[],[refute_0_422:[bind(X_120,$fot(join(X_105,X_107))),bind(X_121,$fot(X_362)),bind(X_315,$fot(X_105)),bind(X_317,$fot(X_106))]]) ).
cnf(refute_0_424,plain,
join(join(X_105,X_106),join(X_362,meet(join(X_105,X_107),join(X_106,X_105)))) = join(X_105,join(X_106,join(X_362,meet(join(X_105,X_107),join(X_106,X_105))))),
inference(subst,[],[refute_0_414:[bind(Z,$fot(join(X_362,meet(join(X_105,X_107),join(X_106,X_105))))),bind(X_68,$fot(X_106)),bind(X_69,$fot(X_105))]]) ).
cnf(refute_0_425,plain,
( join(X_105,join(X_106,join(X_362,meet(join(X_105,X_107),join(X_106,X_105))))) != join(X_362,join(X_106,X_105))
| join(join(X_105,X_106),join(X_362,meet(join(X_105,X_107),join(X_106,X_105)))) != join(X_105,join(X_106,join(X_362,meet(join(X_105,X_107),join(X_106,X_105)))))
| join(join(X_105,X_106),join(X_362,meet(join(X_105,X_107),join(X_106,X_105)))) = join(X_362,join(X_106,X_105)) ),
inference(subst,[],[refute_0_218:[bind(X0,$fot(join(join(X_105,X_106),join(X_362,meet(join(X_105,X_107),join(X_106,X_105)))))),bind(Y0,$fot(join(X_105,join(X_106,join(X_362,meet(join(X_105,X_107),join(X_106,X_105))))))),bind(Z0,$fot(join(X_362,join(X_106,X_105))))]]) ).
cnf(refute_0_426,plain,
( join(X_105,join(X_106,join(X_362,meet(join(X_105,X_107),join(X_106,X_105))))) != join(X_362,join(X_106,X_105))
| join(join(X_105,X_106),join(X_362,meet(join(X_105,X_107),join(X_106,X_105)))) = join(X_362,join(X_106,X_105)) ),
inference(resolve,[$cnf( $equal(join(join(X_105,X_106),join(X_362,meet(join(X_105,X_107),join(X_106,X_105)))),join(X_105,join(X_106,join(X_362,meet(join(X_105,X_107),join(X_106,X_105)))))) )],[refute_0_424,refute_0_425]) ).
cnf(refute_0_427,plain,
join(join(X_105,X_106),join(X_362,meet(join(X_105,X_107),join(X_106,X_105)))) = join(X_362,join(X_106,X_105)),
inference(resolve,[$cnf( $equal(join(X_105,join(X_106,join(X_362,meet(join(X_105,X_107),join(X_106,X_105))))),join(X_362,join(X_106,X_105))) )],[refute_0_423,refute_0_426]) ).
cnf(refute_0_428,plain,
( join(join(X_105,X_106),join(X_362,meet(join(X_105,X_107),join(X_106,X_105)))) != join(X_362,join(X_105,X_106))
| join(join(X_105,X_106),join(X_362,meet(join(X_105,X_107),join(X_106,X_105)))) != join(X_362,join(X_106,X_105))
| join(X_362,join(X_106,X_105)) = join(X_362,join(X_105,X_106)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_105,X_106),join(X_362,meet(join(X_105,X_107),join(X_106,X_105)))),join(X_362,join(X_105,X_106))) ),[0],$fot(join(X_362,join(X_106,X_105)))]]) ).
cnf(refute_0_429,plain,
( join(join(X_105,X_106),join(X_362,meet(join(X_105,X_107),join(X_106,X_105)))) != join(X_362,join(X_105,X_106))
| join(X_362,join(X_106,X_105)) = join(X_362,join(X_105,X_106)) ),
inference(resolve,[$cnf( $equal(join(join(X_105,X_106),join(X_362,meet(join(X_105,X_107),join(X_106,X_105)))),join(X_362,join(X_106,X_105))) )],[refute_0_427,refute_0_428]) ).
cnf(refute_0_430,plain,
join(X_362,join(X_106,X_105)) = join(X_362,join(X_105,X_106)),
inference(resolve,[$cnf( $equal(join(join(X_105,X_106),join(X_362,meet(join(X_105,X_107),join(X_106,X_105)))),join(X_362,join(X_105,X_106))) )],[refute_0_282,refute_0_429]) ).
cnf(refute_0_431,plain,
( join(X_362,join(X_106,X_105)) != join(X_362,join(X_105,X_106))
| join(X_362,join(X_105,X_106)) = join(X_362,join(X_106,X_105)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(join(X_362,join(X_106,X_105)))),bind(Y0,$fot(join(X_362,join(X_105,X_106))))]]) ).
cnf(refute_0_432,plain,
join(X_362,join(X_105,X_106)) = join(X_362,join(X_106,X_105)),
inference(resolve,[$cnf( $equal(join(X_362,join(X_106,X_105)),join(X_362,join(X_105,X_106))) )],[refute_0_430,refute_0_431]) ).
cnf(refute_0_433,plain,
join(a,join(c,b)) = join(a,join(b,c)),
inference(subst,[],[refute_0_432:[bind(X_105,$fot(c)),bind(X_106,$fot(b)),bind(X_362,$fot(a))]]) ).
cnf(refute_0_434,plain,
join(c,join(a,b)) = join(a,join(c,b)),
inference(subst,[],[refute_0_399:[bind(X_291,$fot(a)),bind(X_362,$fot(c)),bind(X_8,$fot(b))]]) ).
cnf(refute_0_435,plain,
( join(a,join(c,b)) != join(a,join(b,c))
| join(c,join(a,b)) != join(a,join(c,b))
| join(c,join(a,b)) = join(a,join(b,c)) ),
inference(subst,[],[refute_0_218:[bind(X0,$fot(join(c,join(a,b)))),bind(Y0,$fot(join(a,join(c,b)))),bind(Z0,$fot(join(a,join(b,c))))]]) ).
cnf(refute_0_436,plain,
( join(a,join(c,b)) != join(a,join(b,c))
| join(c,join(a,b)) = join(a,join(b,c)) ),
inference(resolve,[$cnf( $equal(join(c,join(a,b)),join(a,join(c,b))) )],[refute_0_434,refute_0_435]) ).
cnf(refute_0_437,plain,
join(c,join(a,b)) = join(a,join(b,c)),
inference(resolve,[$cnf( $equal(join(a,join(c,b)),join(a,join(b,c))) )],[refute_0_433,refute_0_436]) ).
cnf(refute_0_438,plain,
( join(a,join(b,c)) != join(a,join(b,c))
| join(c,join(a,b)) != join(a,join(b,c))
| join(c,join(a,b)) = join(a,join(b,c)) ),
introduced(tautology,[equality,[$cnf( $equal(join(c,join(a,b)),join(a,join(b,c))) ),[1],$fot(join(a,join(b,c)))]]) ).
cnf(refute_0_439,plain,
( join(a,join(b,c)) != join(a,join(b,c))
| join(c,join(a,b)) = join(a,join(b,c)) ),
inference(resolve,[$cnf( $equal(join(c,join(a,b)),join(a,join(b,c))) )],[refute_0_437,refute_0_438]) ).
cnf(refute_0_440,plain,
join(a,join(b,c)) != join(a,join(b,c)),
inference(resolve,[$cnf( $equal(join(c,join(a,b)),join(a,join(b,c))) )],[refute_0_439,refute_0_8]) ).
cnf(refute_0_441,plain,
join(a,join(b,c)) = join(a,join(b,c)),
introduced(tautology,[refl,[$fot(join(a,join(b,c)))]]) ).
cnf(refute_0_442,plain,
$false,
inference(resolve,[$cnf( $equal(join(a,join(b,c)),join(a,join(b,c))) )],[refute_0_441,refute_0_440]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : LAT027-1 : TPTP v8.1.0. Released v2.2.0.
% 0.04/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.35 % Computer : n013.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Wed Jun 29 03:54:44 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 100.13/100.31 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 100.13/100.31
% 100.13/100.31 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 100.21/100.35
%------------------------------------------------------------------------------