TSTP Solution File: LAT032-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LAT032-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 05:59:01 EDT 2022
% Result : Unsatisfiable 3.34s 3.52s
% Output : CNFRefutation 3.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 47
% Syntax : Number of clauses : 182 ( 102 unt; 0 nHn; 84 RR)
% Number of literals : 299 ( 298 equ; 119 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 : 456 ( 19 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(idempotence_of_meet,axiom,
meet(X,X) = X ).
cnf(absorption1,axiom,
meet(X,join(X,Y)) = X ).
cnf(absorption2,axiom,
join(X,meet(X,Y)) = X ).
cnf(commutativity_of_meet,axiom,
meet(X,Y) = meet(Y,X) ).
cnf(commutativity_of_join,axiom,
join(X,Y) = join(Y,X) ).
cnf(associativity_of_meet,axiom,
meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ).
cnf(associativity_of_join,axiom,
join(join(X,Y),Z) = join(X,join(Y,Z)) ).
cnf(dist_join,hypothesis,
join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)) ).
cnf(dist_meet,negated_conjecture,
meet(xx,join(yy,zz)) != join(meet(xx,yy),meet(xx,zz)) ).
cnf(refute_0_0,plain,
( join(X,meet(X,Y)) != X
| meet(X,Y) != meet(Y,X)
| join(X,meet(Y,X)) = X ),
introduced(tautology,[equality,[$cnf( $equal(join(X,meet(X,Y)),X) ),[0,1],$fot(meet(Y,X))]]) ).
cnf(refute_0_1,plain,
( join(X,meet(X,Y)) != X
| join(X,meet(Y,X)) = X ),
inference(resolve,[$cnf( $equal(meet(X,Y),meet(Y,X)) )],[commutativity_of_meet,refute_0_0]) ).
cnf(refute_0_2,plain,
join(X,meet(Y,X)) = X,
inference(resolve,[$cnf( $equal(join(X,meet(X,Y)),X) )],[absorption2,refute_0_1]) ).
cnf(refute_0_3,plain,
join(join(X_15,Y),meet(X_15,join(X_15,Y))) = join(X_15,Y),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_15,Y))),bind(Y,$fot(X_15))]]) ).
cnf(refute_0_4,plain,
meet(X_15,join(X_15,Y)) = X_15,
inference(subst,[],[absorption1:[bind(X,$fot(X_15))]]) ).
cnf(refute_0_5,plain,
( join(join(X_15,Y),meet(X_15,join(X_15,Y))) != join(X_15,Y)
| meet(X_15,join(X_15,Y)) != X_15
| join(join(X_15,Y),X_15) = join(X_15,Y) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_15,Y),meet(X_15,join(X_15,Y))),join(X_15,Y)) ),[0,1],$fot(X_15)]]) ).
cnf(refute_0_6,plain,
( join(join(X_15,Y),meet(X_15,join(X_15,Y))) != join(X_15,Y)
| join(join(X_15,Y),X_15) = join(X_15,Y) ),
inference(resolve,[$cnf( $equal(meet(X_15,join(X_15,Y)),X_15) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
join(join(X_15,Y),X_15) = join(X_15,Y),
inference(resolve,[$cnf( $equal(join(join(X_15,Y),meet(X_15,join(X_15,Y))),join(X_15,Y)) )],[refute_0_3,refute_0_6]) ).
cnf(refute_0_8,plain,
join(join(X_15,Y),X_15) = join(X_15,join(Y,X_15)),
inference(subst,[],[associativity_of_join:[bind(X,$fot(X_15)),bind(Z,$fot(X_15))]]) ).
cnf(refute_0_9,plain,
( join(join(X_15,Y),X_15) != join(X_15,Y)
| join(join(X_15,Y),X_15) != join(X_15,join(Y,X_15))
| join(X_15,join(Y,X_15)) = join(X_15,Y) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_15,Y),X_15),join(X_15,Y)) ),[0],$fot(join(X_15,join(Y,X_15)))]]) ).
cnf(refute_0_10,plain,
( join(join(X_15,Y),X_15) != join(X_15,Y)
| join(X_15,join(Y,X_15)) = join(X_15,Y) ),
inference(resolve,[$cnf( $equal(join(join(X_15,Y),X_15),join(X_15,join(Y,X_15))) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
join(X_15,join(Y,X_15)) = join(X_15,Y),
inference(resolve,[$cnf( $equal(join(join(X_15,Y),X_15),join(X_15,Y)) )],[refute_0_7,refute_0_10]) ).
cnf(refute_0_12,plain,
join(meet(X_93,X_92),join(Y,meet(X_93,X_92))) = join(meet(X_93,X_92),Y),
inference(subst,[],[refute_0_11:[bind(X_15,$fot(meet(X_93,X_92)))]]) ).
cnf(refute_0_13,plain,
meet(join(X_31,X_33),join(X_31,X_32)) = meet(join(X_31,X_32),join(X_31,X_33)),
inference(subst,[],[commutativity_of_meet:[bind(X,$fot(join(X_31,X_33))),bind(Y,$fot(join(X_31,X_32)))]]) ).
cnf(refute_0_14,plain,
join(X_31,meet(X_32,X_33)) = meet(join(X_31,X_32),join(X_31,X_33)),
inference(subst,[],[dist_join:[bind(X,$fot(X_31)),bind(Y,$fot(X_32)),bind(Z,$fot(X_33))]]) ).
cnf(refute_0_15,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_16,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_17,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
( join(X_31,meet(X_32,X_33)) != meet(join(X_31,X_32),join(X_31,X_33))
| meet(join(X_31,X_32),join(X_31,X_33)) = join(X_31,meet(X_32,X_33)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(join(X_31,meet(X_32,X_33)))),bind(Y0,$fot(meet(join(X_31,X_32),join(X_31,X_33))))]]) ).
cnf(refute_0_19,plain,
meet(join(X_31,X_32),join(X_31,X_33)) = join(X_31,meet(X_32,X_33)),
inference(resolve,[$cnf( $equal(join(X_31,meet(X_32,X_33)),meet(join(X_31,X_32),join(X_31,X_33))) )],[refute_0_14,refute_0_18]) ).
cnf(refute_0_20,plain,
( meet(join(X_31,X_32),join(X_31,X_33)) != join(X_31,meet(X_32,X_33))
| meet(join(X_31,X_33),join(X_31,X_32)) != meet(join(X_31,X_32),join(X_31,X_33))
| meet(join(X_31,X_33),join(X_31,X_32)) = join(X_31,meet(X_32,X_33)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(X_31,X_33),join(X_31,X_32)),meet(join(X_31,X_32),join(X_31,X_33))) ),[1],$fot(join(X_31,meet(X_32,X_33)))]]) ).
cnf(refute_0_21,plain,
( meet(join(X_31,X_33),join(X_31,X_32)) != meet(join(X_31,X_32),join(X_31,X_33))
| meet(join(X_31,X_33),join(X_31,X_32)) = join(X_31,meet(X_32,X_33)) ),
inference(resolve,[$cnf( $equal(meet(join(X_31,X_32),join(X_31,X_33)),join(X_31,meet(X_32,X_33))) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
meet(join(X_31,X_33),join(X_31,X_32)) = join(X_31,meet(X_32,X_33)),
inference(resolve,[$cnf( $equal(meet(join(X_31,X_33),join(X_31,X_32)),meet(join(X_31,X_32),join(X_31,X_33))) )],[refute_0_13,refute_0_21]) ).
cnf(refute_0_23,plain,
( join(X,meet(Y,Z)) != meet(join(X,Y),join(X,Z))
| meet(join(X,Y),join(X,Z)) = join(X,meet(Y,Z)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(join(X,meet(Y,Z)))),bind(Y0,$fot(meet(join(X,Y),join(X,Z))))]]) ).
cnf(refute_0_24,plain,
meet(join(X,Y),join(X,Z)) = join(X,meet(Y,Z)),
inference(resolve,[$cnf( $equal(join(X,meet(Y,Z)),meet(join(X,Y),join(X,Z))) )],[dist_join,refute_0_23]) ).
cnf(refute_0_25,plain,
meet(join(X_31,X_33),join(X_31,X_32)) = join(X_31,meet(X_33,X_32)),
inference(subst,[],[refute_0_24:[bind(X,$fot(X_31)),bind(Y,$fot(X_33)),bind(Z,$fot(X_32))]]) ).
cnf(refute_0_26,plain,
( meet(join(X_31,X_33),join(X_31,X_32)) != join(X_31,meet(X_32,X_33))
| meet(join(X_31,X_33),join(X_31,X_32)) != join(X_31,meet(X_33,X_32))
| join(X_31,meet(X_33,X_32)) = join(X_31,meet(X_32,X_33)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(X_31,X_33),join(X_31,X_32)),join(X_31,meet(X_32,X_33))) ),[0],$fot(join(X_31,meet(X_33,X_32)))]]) ).
cnf(refute_0_27,plain,
( meet(join(X_31,X_33),join(X_31,X_32)) != join(X_31,meet(X_32,X_33))
| join(X_31,meet(X_33,X_32)) = join(X_31,meet(X_32,X_33)) ),
inference(resolve,[$cnf( $equal(meet(join(X_31,X_33),join(X_31,X_32)),join(X_31,meet(X_33,X_32))) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
join(X_31,meet(X_33,X_32)) = join(X_31,meet(X_32,X_33)),
inference(resolve,[$cnf( $equal(meet(join(X_31,X_33),join(X_31,X_32)),join(X_31,meet(X_32,X_33))) )],[refute_0_22,refute_0_27]) ).
cnf(refute_0_29,plain,
join(Y,meet(X_93,X_92)) = join(Y,meet(X_92,X_93)),
inference(subst,[],[refute_0_28:[bind(X_31,$fot(Y)),bind(X_32,$fot(X_92)),bind(X_33,$fot(X_93))]]) ).
cnf(refute_0_30,plain,
( join(Y,meet(X_93,X_92)) != join(Y,meet(X_92,X_93))
| join(meet(X_93,X_92),join(Y,meet(X_93,X_92))) != join(meet(X_93,X_92),Y)
| join(meet(X_93,X_92),join(Y,meet(X_92,X_93))) = join(meet(X_93,X_92),Y) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_93,X_92),join(Y,meet(X_93,X_92))),join(meet(X_93,X_92),Y)) ),[0,1],$fot(join(Y,meet(X_92,X_93)))]]) ).
cnf(refute_0_31,plain,
( join(meet(X_93,X_92),join(Y,meet(X_93,X_92))) != join(meet(X_93,X_92),Y)
| join(meet(X_93,X_92),join(Y,meet(X_92,X_93))) = join(meet(X_93,X_92),Y) ),
inference(resolve,[$cnf( $equal(join(Y,meet(X_93,X_92)),join(Y,meet(X_92,X_93))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
join(meet(X_93,X_92),join(Y,meet(X_92,X_93))) = join(meet(X_93,X_92),Y),
inference(resolve,[$cnf( $equal(join(meet(X_93,X_92),join(Y,meet(X_93,X_92))),join(meet(X_93,X_92),Y)) )],[refute_0_12,refute_0_31]) ).
cnf(refute_0_33,plain,
join(join(X,meet(X_34,X_35)),meet(X_35,X_34)) = join(X,join(meet(X_34,X_35),meet(X_35,X_34))),
inference(subst,[],[associativity_of_join:[bind(Y,$fot(meet(X_34,X_35))),bind(Z,$fot(meet(X_35,X_34)))]]) ).
cnf(refute_0_34,plain,
join(meet(Y,X_15),meet(X_15,meet(Y,X_15))) = meet(Y,X_15),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(Y,X_15))),bind(Y,$fot(X_15))]]) ).
cnf(refute_0_35,plain,
meet(X_6,join(X_6,X_7)) = X_6,
inference(subst,[],[absorption1:[bind(X,$fot(X_6)),bind(Y,$fot(X_7))]]) ).
cnf(refute_0_36,plain,
join(X_7,X_6) = join(X_6,X_7),
inference(subst,[],[commutativity_of_join:[bind(X,$fot(X_7)),bind(Y,$fot(X_6))]]) ).
cnf(refute_0_37,plain,
( join(X_7,X_6) != join(X_6,X_7)
| join(X_6,X_7) = join(X_7,X_6) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(join(X_7,X_6))),bind(Y0,$fot(join(X_6,X_7)))]]) ).
cnf(refute_0_38,plain,
join(X_6,X_7) = join(X_7,X_6),
inference(resolve,[$cnf( $equal(join(X_7,X_6),join(X_6,X_7)) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
( join(X_6,X_7) != join(X_7,X_6)
| meet(X_6,join(X_6,X_7)) != X_6
| meet(X_6,join(X_7,X_6)) = X_6 ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_6,join(X_6,X_7)),X_6) ),[0,1],$fot(join(X_7,X_6))]]) ).
cnf(refute_0_40,plain,
( meet(X_6,join(X_6,X_7)) != X_6
| meet(X_6,join(X_7,X_6)) = X_6 ),
inference(resolve,[$cnf( $equal(join(X_6,X_7),join(X_7,X_6)) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
meet(X_6,join(X_7,X_6)) = X_6,
inference(resolve,[$cnf( $equal(meet(X_6,join(X_6,X_7)),X_6) )],[refute_0_35,refute_0_40]) ).
cnf(refute_0_42,plain,
meet(meet(X_9,Y),join(X_9,meet(X_9,Y))) = meet(X_9,Y),
inference(subst,[],[refute_0_41:[bind(X_6,$fot(meet(X_9,Y))),bind(X_7,$fot(X_9))]]) ).
cnf(refute_0_43,plain,
join(X_9,meet(X_9,Y)) = X_9,
inference(subst,[],[absorption2:[bind(X,$fot(X_9))]]) ).
cnf(refute_0_44,plain,
( join(X_9,meet(X_9,Y)) != X_9
| meet(meet(X_9,Y),join(X_9,meet(X_9,Y))) != meet(X_9,Y)
| meet(meet(X_9,Y),X_9) = meet(X_9,Y) ),
introduced(tautology,[equality,[$cnf( $equal(meet(meet(X_9,Y),join(X_9,meet(X_9,Y))),meet(X_9,Y)) ),[0,1],$fot(X_9)]]) ).
cnf(refute_0_45,plain,
( meet(meet(X_9,Y),join(X_9,meet(X_9,Y))) != meet(X_9,Y)
| meet(meet(X_9,Y),X_9) = meet(X_9,Y) ),
inference(resolve,[$cnf( $equal(join(X_9,meet(X_9,Y)),X_9) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
meet(meet(X_9,Y),X_9) = meet(X_9,Y),
inference(resolve,[$cnf( $equal(meet(meet(X_9,Y),join(X_9,meet(X_9,Y))),meet(X_9,Y)) )],[refute_0_42,refute_0_45]) ).
cnf(refute_0_47,plain,
meet(meet(X_9,Y),X_9) = meet(X_9,meet(Y,X_9)),
inference(subst,[],[associativity_of_meet:[bind(X,$fot(X_9)),bind(Z,$fot(X_9))]]) ).
cnf(refute_0_48,plain,
( meet(meet(X_9,Y),X_9) != meet(X_9,Y)
| meet(meet(X_9,Y),X_9) != meet(X_9,meet(Y,X_9))
| meet(X_9,meet(Y,X_9)) = meet(X_9,Y) ),
introduced(tautology,[equality,[$cnf( $equal(meet(meet(X_9,Y),X_9),meet(X_9,Y)) ),[0],$fot(meet(X_9,meet(Y,X_9)))]]) ).
cnf(refute_0_49,plain,
( meet(meet(X_9,Y),X_9) != meet(X_9,Y)
| meet(X_9,meet(Y,X_9)) = meet(X_9,Y) ),
inference(resolve,[$cnf( $equal(meet(meet(X_9,Y),X_9),meet(X_9,meet(Y,X_9))) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
meet(X_9,meet(Y,X_9)) = meet(X_9,Y),
inference(resolve,[$cnf( $equal(meet(meet(X_9,Y),X_9),meet(X_9,Y)) )],[refute_0_46,refute_0_49]) ).
cnf(refute_0_51,plain,
meet(X_15,meet(Y,X_15)) = meet(X_15,Y),
inference(subst,[],[refute_0_50:[bind(X_9,$fot(X_15))]]) ).
cnf(refute_0_52,plain,
( join(meet(Y,X_15),meet(X_15,meet(Y,X_15))) != meet(Y,X_15)
| meet(X_15,meet(Y,X_15)) != meet(X_15,Y)
| join(meet(Y,X_15),meet(X_15,Y)) = meet(Y,X_15) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(Y,X_15),meet(X_15,meet(Y,X_15))),meet(Y,X_15)) ),[0,1],$fot(meet(X_15,Y))]]) ).
cnf(refute_0_53,plain,
( join(meet(Y,X_15),meet(X_15,meet(Y,X_15))) != meet(Y,X_15)
| join(meet(Y,X_15),meet(X_15,Y)) = meet(Y,X_15) ),
inference(resolve,[$cnf( $equal(meet(X_15,meet(Y,X_15)),meet(X_15,Y)) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
join(meet(Y,X_15),meet(X_15,Y)) = meet(Y,X_15),
inference(resolve,[$cnf( $equal(join(meet(Y,X_15),meet(X_15,meet(Y,X_15))),meet(Y,X_15)) )],[refute_0_34,refute_0_53]) ).
cnf(refute_0_55,plain,
join(meet(X_34,X_35),meet(X_35,X_34)) = meet(X_34,X_35),
inference(subst,[],[refute_0_54:[bind(Y,$fot(X_34)),bind(X_15,$fot(X_35))]]) ).
cnf(refute_0_56,plain,
( join(join(X,meet(X_34,X_35)),meet(X_35,X_34)) != join(X,join(meet(X_34,X_35),meet(X_35,X_34)))
| join(meet(X_34,X_35),meet(X_35,X_34)) != meet(X_34,X_35)
| join(join(X,meet(X_34,X_35)),meet(X_35,X_34)) = join(X,meet(X_34,X_35)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X,meet(X_34,X_35)),meet(X_35,X_34)),join(X,join(meet(X_34,X_35),meet(X_35,X_34)))) ),[1,1],$fot(meet(X_34,X_35))]]) ).
cnf(refute_0_57,plain,
( join(join(X,meet(X_34,X_35)),meet(X_35,X_34)) != join(X,join(meet(X_34,X_35),meet(X_35,X_34)))
| join(join(X,meet(X_34,X_35)),meet(X_35,X_34)) = join(X,meet(X_34,X_35)) ),
inference(resolve,[$cnf( $equal(join(meet(X_34,X_35),meet(X_35,X_34)),meet(X_34,X_35)) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
join(join(X,meet(X_34,X_35)),meet(X_35,X_34)) = join(X,meet(X_34,X_35)),
inference(resolve,[$cnf( $equal(join(join(X,meet(X_34,X_35)),meet(X_35,X_34)),join(X,join(meet(X_34,X_35),meet(X_35,X_34)))) )],[refute_0_33,refute_0_57]) ).
cnf(refute_0_59,plain,
meet(join(X_18,X_7),join(X_7,join(X_18,X_7))) = join(X_18,X_7),
inference(subst,[],[refute_0_41:[bind(X_6,$fot(join(X_18,X_7)))]]) ).
cnf(refute_0_60,plain,
join(X_7,join(X_18,X_7)) = join(X_7,X_18),
inference(subst,[],[refute_0_11:[bind(Y,$fot(X_18)),bind(X_15,$fot(X_7))]]) ).
cnf(refute_0_61,plain,
( join(X_7,join(X_18,X_7)) != join(X_7,X_18)
| meet(join(X_18,X_7),join(X_7,join(X_18,X_7))) != join(X_18,X_7)
| meet(join(X_18,X_7),join(X_7,X_18)) = join(X_18,X_7) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(X_18,X_7),join(X_7,join(X_18,X_7))),join(X_18,X_7)) ),[0,1],$fot(join(X_7,X_18))]]) ).
cnf(refute_0_62,plain,
( meet(join(X_18,X_7),join(X_7,join(X_18,X_7))) != join(X_18,X_7)
| meet(join(X_18,X_7),join(X_7,X_18)) = join(X_18,X_7) ),
inference(resolve,[$cnf( $equal(join(X_7,join(X_18,X_7)),join(X_7,X_18)) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
meet(join(X_18,X_7),join(X_7,X_18)) = join(X_18,X_7),
inference(resolve,[$cnf( $equal(meet(join(X_18,X_7),join(X_7,join(X_18,X_7))),join(X_18,X_7)) )],[refute_0_59,refute_0_62]) ).
cnf(refute_0_64,plain,
meet(X_18,X_18) = X_18,
inference(subst,[],[idempotence_of_meet:[bind(X,$fot(X_18))]]) ).
cnf(refute_0_65,plain,
join(X_7,meet(X_18,X_18)) = join(X_7,meet(X_18,X_18)),
introduced(tautology,[refl,[$fot(join(X_7,meet(X_18,X_18)))]]) ).
cnf(refute_0_66,plain,
( join(X_7,meet(X_18,X_18)) != join(X_7,meet(X_18,X_18))
| meet(X_18,X_18) != X_18
| join(X_7,meet(X_18,X_18)) = join(X_7,X_18) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_7,meet(X_18,X_18)),join(X_7,meet(X_18,X_18))) ),[1,1],$fot(X_18)]]) ).
cnf(refute_0_67,plain,
( meet(X_18,X_18) != X_18
| join(X_7,meet(X_18,X_18)) = join(X_7,X_18) ),
inference(resolve,[$cnf( $equal(join(X_7,meet(X_18,X_18)),join(X_7,meet(X_18,X_18))) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
join(X_7,meet(X_18,X_18)) = join(X_7,X_18),
inference(resolve,[$cnf( $equal(meet(X_18,X_18),X_18) )],[refute_0_64,refute_0_67]) ).
cnf(refute_0_69,plain,
join(X_32,X_31) = join(X_31,X_32),
inference(subst,[],[commutativity_of_join:[bind(X,$fot(X_32)),bind(Y,$fot(X_31))]]) ).
cnf(refute_0_70,plain,
( join(X_32,X_31) != join(X_31,X_32)
| join(X_31,X_32) = join(X_32,X_31) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(join(X_32,X_31))),bind(Y0,$fot(join(X_31,X_32)))]]) ).
cnf(refute_0_71,plain,
join(X_31,X_32) = join(X_32,X_31),
inference(resolve,[$cnf( $equal(join(X_32,X_31),join(X_31,X_32)) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
( join(X_31,X_32) != join(X_32,X_31)
| join(X_31,meet(X_32,X_33)) != meet(join(X_31,X_32),join(X_31,X_33))
| join(X_31,meet(X_32,X_33)) = meet(join(X_32,X_31),join(X_31,X_33)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_31,meet(X_32,X_33)),meet(join(X_31,X_32),join(X_31,X_33))) ),[1,0],$fot(join(X_32,X_31))]]) ).
cnf(refute_0_73,plain,
( join(X_31,meet(X_32,X_33)) != meet(join(X_31,X_32),join(X_31,X_33))
| join(X_31,meet(X_32,X_33)) = meet(join(X_32,X_31),join(X_31,X_33)) ),
inference(resolve,[$cnf( $equal(join(X_31,X_32),join(X_32,X_31)) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
join(X_31,meet(X_32,X_33)) = meet(join(X_32,X_31),join(X_31,X_33)),
inference(resolve,[$cnf( $equal(join(X_31,meet(X_32,X_33)),meet(join(X_31,X_32),join(X_31,X_33))) )],[refute_0_14,refute_0_73]) ).
cnf(refute_0_75,plain,
( join(X_31,meet(X_32,X_33)) != meet(join(X_32,X_31),join(X_31,X_33))
| meet(join(X_32,X_31),join(X_31,X_33)) = join(X_31,meet(X_32,X_33)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(join(X_31,meet(X_32,X_33)))),bind(Y0,$fot(meet(join(X_32,X_31),join(X_31,X_33))))]]) ).
cnf(refute_0_76,plain,
meet(join(X_32,X_31),join(X_31,X_33)) = join(X_31,meet(X_32,X_33)),
inference(resolve,[$cnf( $equal(join(X_31,meet(X_32,X_33)),meet(join(X_32,X_31),join(X_31,X_33))) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
meet(join(X_18,X_7),join(X_7,X_18)) = join(X_7,meet(X_18,X_18)),
inference(subst,[],[refute_0_76:[bind(X_31,$fot(X_7)),bind(X_32,$fot(X_18)),bind(X_33,$fot(X_18))]]) ).
cnf(refute_0_78,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_79,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_17,refute_0_78]) ).
cnf(refute_0_80,plain,
( join(X_7,meet(X_18,X_18)) != join(X_7,X_18)
| meet(join(X_18,X_7),join(X_7,X_18)) != join(X_7,meet(X_18,X_18))
| meet(join(X_18,X_7),join(X_7,X_18)) = join(X_7,X_18) ),
inference(subst,[],[refute_0_79:[bind(X0,$fot(meet(join(X_18,X_7),join(X_7,X_18)))),bind(Y0,$fot(join(X_7,meet(X_18,X_18)))),bind(Z0,$fot(join(X_7,X_18)))]]) ).
cnf(refute_0_81,plain,
( join(X_7,meet(X_18,X_18)) != join(X_7,X_18)
| meet(join(X_18,X_7),join(X_7,X_18)) = join(X_7,X_18) ),
inference(resolve,[$cnf( $equal(meet(join(X_18,X_7),join(X_7,X_18)),join(X_7,meet(X_18,X_18))) )],[refute_0_77,refute_0_80]) ).
cnf(refute_0_82,plain,
meet(join(X_18,X_7),join(X_7,X_18)) = join(X_7,X_18),
inference(resolve,[$cnf( $equal(join(X_7,meet(X_18,X_18)),join(X_7,X_18)) )],[refute_0_68,refute_0_81]) ).
cnf(refute_0_83,plain,
( meet(join(X_18,X_7),join(X_7,X_18)) != join(X_18,X_7)
| meet(join(X_18,X_7),join(X_7,X_18)) != join(X_7,X_18)
| join(X_7,X_18) = join(X_18,X_7) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(X_18,X_7),join(X_7,X_18)),join(X_18,X_7)) ),[0],$fot(join(X_7,X_18))]]) ).
cnf(refute_0_84,plain,
( meet(join(X_18,X_7),join(X_7,X_18)) != join(X_18,X_7)
| join(X_7,X_18) = join(X_18,X_7) ),
inference(resolve,[$cnf( $equal(meet(join(X_18,X_7),join(X_7,X_18)),join(X_7,X_18)) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
join(X_7,X_18) = join(X_18,X_7),
inference(resolve,[$cnf( $equal(meet(join(X_18,X_7),join(X_7,X_18)),join(X_18,X_7)) )],[refute_0_63,refute_0_84]) ).
cnf(refute_0_86,plain,
( join(X_7,X_18) != join(X_18,X_7)
| join(X_18,X_7) = join(X_7,X_18) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(join(X_7,X_18))),bind(Y0,$fot(join(X_18,X_7)))]]) ).
cnf(refute_0_87,plain,
join(X_18,X_7) = join(X_7,X_18),
inference(resolve,[$cnf( $equal(join(X_7,X_18),join(X_18,X_7)) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
join(join(X,meet(X_34,X_35)),meet(X_35,X_34)) = join(meet(X_35,X_34),join(X,meet(X_34,X_35))),
inference(subst,[],[refute_0_87:[bind(X_18,$fot(join(X,meet(X_34,X_35)))),bind(X_7,$fot(meet(X_35,X_34)))]]) ).
cnf(refute_0_89,plain,
( join(join(X,meet(X_34,X_35)),meet(X_35,X_34)) != join(X,meet(X_34,X_35))
| join(join(X,meet(X_34,X_35)),meet(X_35,X_34)) != join(meet(X_35,X_34),join(X,meet(X_34,X_35)))
| join(meet(X_35,X_34),join(X,meet(X_34,X_35))) = join(X,meet(X_34,X_35)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X,meet(X_34,X_35)),meet(X_35,X_34)),join(X,meet(X_34,X_35))) ),[0],$fot(join(meet(X_35,X_34),join(X,meet(X_34,X_35))))]]) ).
cnf(refute_0_90,plain,
( join(join(X,meet(X_34,X_35)),meet(X_35,X_34)) != join(X,meet(X_34,X_35))
| join(meet(X_35,X_34),join(X,meet(X_34,X_35))) = join(X,meet(X_34,X_35)) ),
inference(resolve,[$cnf( $equal(join(join(X,meet(X_34,X_35)),meet(X_35,X_34)),join(meet(X_35,X_34),join(X,meet(X_34,X_35)))) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
join(meet(X_35,X_34),join(X,meet(X_34,X_35))) = join(X,meet(X_34,X_35)),
inference(resolve,[$cnf( $equal(join(join(X,meet(X_34,X_35)),meet(X_35,X_34)),join(X,meet(X_34,X_35))) )],[refute_0_58,refute_0_90]) ).
cnf(refute_0_92,plain,
join(meet(X_93,X_92),join(Y,meet(X_92,X_93))) = join(Y,meet(X_92,X_93)),
inference(subst,[],[refute_0_91:[bind(X,$fot(Y)),bind(X_34,$fot(X_92)),bind(X_35,$fot(X_93))]]) ).
cnf(refute_0_93,plain,
( join(meet(X_93,X_92),join(Y,meet(X_92,X_93))) != join(Y,meet(X_92,X_93))
| join(meet(X_93,X_92),join(Y,meet(X_92,X_93))) != join(meet(X_93,X_92),Y)
| join(Y,meet(X_92,X_93)) = join(meet(X_93,X_92),Y) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_93,X_92),join(Y,meet(X_92,X_93))),join(meet(X_93,X_92),Y)) ),[0],$fot(join(Y,meet(X_92,X_93)))]]) ).
cnf(refute_0_94,plain,
( join(meet(X_93,X_92),join(Y,meet(X_92,X_93))) != join(meet(X_93,X_92),Y)
| join(Y,meet(X_92,X_93)) = join(meet(X_93,X_92),Y) ),
inference(resolve,[$cnf( $equal(join(meet(X_93,X_92),join(Y,meet(X_92,X_93))),join(Y,meet(X_92,X_93))) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
join(Y,meet(X_92,X_93)) = join(meet(X_93,X_92),Y),
inference(resolve,[$cnf( $equal(join(meet(X_93,X_92),join(Y,meet(X_92,X_93))),join(meet(X_93,X_92),Y)) )],[refute_0_32,refute_0_94]) ).
cnf(refute_0_96,plain,
join(meet(X_92,X_114),meet(X_92,X_93)) = join(meet(X_93,X_92),meet(X_92,X_114)),
inference(subst,[],[refute_0_95:[bind(Y,$fot(meet(X_92,X_114)))]]) ).
cnf(refute_0_97,plain,
meet(meet(X_22,X_23),join(X_7,meet(X_22,X_23))) = meet(X_22,X_23),
inference(subst,[],[refute_0_41:[bind(X_6,$fot(meet(X_22,X_23)))]]) ).
cnf(refute_0_98,plain,
meet(meet(X_22,X_23),join(X_7,meet(X_22,X_23))) = meet(X_22,meet(X_23,join(X_7,meet(X_22,X_23)))),
inference(subst,[],[associativity_of_meet:[bind(X,$fot(X_22)),bind(Y,$fot(X_23)),bind(Z,$fot(join(X_7,meet(X_22,X_23))))]]) ).
cnf(refute_0_99,plain,
( meet(meet(X_22,X_23),join(X_7,meet(X_22,X_23))) != meet(X_22,X_23)
| meet(meet(X_22,X_23),join(X_7,meet(X_22,X_23))) != meet(X_22,meet(X_23,join(X_7,meet(X_22,X_23))))
| meet(X_22,meet(X_23,join(X_7,meet(X_22,X_23)))) = meet(X_22,X_23) ),
introduced(tautology,[equality,[$cnf( $equal(meet(meet(X_22,X_23),join(X_7,meet(X_22,X_23))),meet(X_22,X_23)) ),[0],$fot(meet(X_22,meet(X_23,join(X_7,meet(X_22,X_23)))))]]) ).
cnf(refute_0_100,plain,
( meet(meet(X_22,X_23),join(X_7,meet(X_22,X_23))) != meet(X_22,X_23)
| meet(X_22,meet(X_23,join(X_7,meet(X_22,X_23)))) = meet(X_22,X_23) ),
inference(resolve,[$cnf( $equal(meet(meet(X_22,X_23),join(X_7,meet(X_22,X_23))),meet(X_22,meet(X_23,join(X_7,meet(X_22,X_23))))) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
meet(X_22,meet(X_23,join(X_7,meet(X_22,X_23)))) = meet(X_22,X_23),
inference(resolve,[$cnf( $equal(meet(meet(X_22,X_23),join(X_7,meet(X_22,X_23))),meet(X_22,X_23)) )],[refute_0_97,refute_0_100]) ).
cnf(refute_0_102,plain,
meet(X_51,meet(join(X_53,Y),join(X_53,meet(X_51,join(X_53,Y))))) = meet(X_51,join(X_53,Y)),
inference(subst,[],[refute_0_101:[bind(X_22,$fot(X_51)),bind(X_23,$fot(join(X_53,Y))),bind(X_7,$fot(X_53))]]) ).
cnf(refute_0_103,plain,
join(X_53,meet(Y,meet(X_51,join(X_53,Y)))) = meet(join(X_53,Y),join(X_53,meet(X_51,join(X_53,Y)))),
inference(subst,[],[dist_join:[bind(X,$fot(X_53)),bind(Z,$fot(meet(X_51,join(X_53,Y))))]]) ).
cnf(refute_0_104,plain,
( join(X_53,meet(Y,meet(X_51,join(X_53,Y)))) != meet(join(X_53,Y),join(X_53,meet(X_51,join(X_53,Y))))
| meet(join(X_53,Y),join(X_53,meet(X_51,join(X_53,Y)))) = join(X_53,meet(Y,meet(X_51,join(X_53,Y)))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(join(X_53,meet(Y,meet(X_51,join(X_53,Y)))))),bind(Y0,$fot(meet(join(X_53,Y),join(X_53,meet(X_51,join(X_53,Y))))))]]) ).
cnf(refute_0_105,plain,
meet(join(X_53,Y),join(X_53,meet(X_51,join(X_53,Y)))) = join(X_53,meet(Y,meet(X_51,join(X_53,Y)))),
inference(resolve,[$cnf( $equal(join(X_53,meet(Y,meet(X_51,join(X_53,Y)))),meet(join(X_53,Y),join(X_53,meet(X_51,join(X_53,Y))))) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
( meet(X_51,meet(join(X_53,Y),join(X_53,meet(X_51,join(X_53,Y))))) != meet(X_51,join(X_53,Y))
| meet(join(X_53,Y),join(X_53,meet(X_51,join(X_53,Y)))) != join(X_53,meet(Y,meet(X_51,join(X_53,Y))))
| meet(X_51,join(X_53,meet(Y,meet(X_51,join(X_53,Y))))) = meet(X_51,join(X_53,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_51,meet(join(X_53,Y),join(X_53,meet(X_51,join(X_53,Y))))),meet(X_51,join(X_53,Y))) ),[0,1],$fot(join(X_53,meet(Y,meet(X_51,join(X_53,Y)))))]]) ).
cnf(refute_0_107,plain,
( meet(X_51,meet(join(X_53,Y),join(X_53,meet(X_51,join(X_53,Y))))) != meet(X_51,join(X_53,Y))
| meet(X_51,join(X_53,meet(Y,meet(X_51,join(X_53,Y))))) = meet(X_51,join(X_53,Y)) ),
inference(resolve,[$cnf( $equal(meet(join(X_53,Y),join(X_53,meet(X_51,join(X_53,Y)))),join(X_53,meet(Y,meet(X_51,join(X_53,Y))))) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
meet(X_51,join(X_53,meet(Y,meet(X_51,join(X_53,Y))))) = meet(X_51,join(X_53,Y)),
inference(resolve,[$cnf( $equal(meet(X_51,meet(join(X_53,Y),join(X_53,meet(X_51,join(X_53,Y))))),meet(X_51,join(X_53,Y))) )],[refute_0_102,refute_0_107]) ).
cnf(refute_0_109,plain,
join(meet(X_52,join(X_53,meet(Y,X_52))),meet(Y,meet(X_52,join(X_53,meet(Y,X_52))))) = meet(X_52,join(X_53,meet(Y,X_52))),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(X_52,join(X_53,meet(Y,X_52)))))]]) ).
cnf(refute_0_110,plain,
meet(Y,meet(X_52,join(X_53,meet(Y,X_52)))) = meet(Y,X_52),
inference(subst,[],[refute_0_101:[bind(X_22,$fot(Y)),bind(X_23,$fot(X_52)),bind(X_7,$fot(X_53))]]) ).
cnf(refute_0_111,plain,
( join(meet(X_52,join(X_53,meet(Y,X_52))),meet(Y,meet(X_52,join(X_53,meet(Y,X_52))))) != meet(X_52,join(X_53,meet(Y,X_52)))
| meet(Y,meet(X_52,join(X_53,meet(Y,X_52)))) != meet(Y,X_52)
| join(meet(X_52,join(X_53,meet(Y,X_52))),meet(Y,X_52)) = meet(X_52,join(X_53,meet(Y,X_52))) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_52,join(X_53,meet(Y,X_52))),meet(Y,meet(X_52,join(X_53,meet(Y,X_52))))),meet(X_52,join(X_53,meet(Y,X_52)))) ),[0,1],$fot(meet(Y,X_52))]]) ).
cnf(refute_0_112,plain,
( join(meet(X_52,join(X_53,meet(Y,X_52))),meet(Y,meet(X_52,join(X_53,meet(Y,X_52))))) != meet(X_52,join(X_53,meet(Y,X_52)))
| join(meet(X_52,join(X_53,meet(Y,X_52))),meet(Y,X_52)) = meet(X_52,join(X_53,meet(Y,X_52))) ),
inference(resolve,[$cnf( $equal(meet(Y,meet(X_52,join(X_53,meet(Y,X_52)))),meet(Y,X_52)) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
join(meet(X_52,join(X_53,meet(Y,X_52))),meet(Y,X_52)) = meet(X_52,join(X_53,meet(Y,X_52))),
inference(resolve,[$cnf( $equal(join(meet(X_52,join(X_53,meet(Y,X_52))),meet(Y,meet(X_52,join(X_53,meet(Y,X_52))))),meet(X_52,join(X_53,meet(Y,X_52)))) )],[refute_0_109,refute_0_112]) ).
cnf(refute_0_114,plain,
join(X_31,meet(X_32,join(Y,X_31))) = meet(join(X_31,X_32),join(X_31,join(Y,X_31))),
inference(subst,[],[dist_join:[bind(X,$fot(X_31)),bind(Y,$fot(X_32)),bind(Z,$fot(join(Y,X_31)))]]) ).
cnf(refute_0_115,plain,
join(X_31,join(Y,X_31)) = join(X_31,Y),
inference(subst,[],[refute_0_11:[bind(X_15,$fot(X_31))]]) ).
cnf(refute_0_116,plain,
( join(X_31,join(Y,X_31)) != join(X_31,Y)
| join(X_31,meet(X_32,join(Y,X_31))) != meet(join(X_31,X_32),join(X_31,join(Y,X_31)))
| join(X_31,meet(X_32,join(Y,X_31))) = meet(join(X_31,X_32),join(X_31,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_31,meet(X_32,join(Y,X_31))),meet(join(X_31,X_32),join(X_31,join(Y,X_31)))) ),[1,1],$fot(join(X_31,Y))]]) ).
cnf(refute_0_117,plain,
( join(X_31,meet(X_32,join(Y,X_31))) != meet(join(X_31,X_32),join(X_31,join(Y,X_31)))
| join(X_31,meet(X_32,join(Y,X_31))) = meet(join(X_31,X_32),join(X_31,Y)) ),
inference(resolve,[$cnf( $equal(join(X_31,join(Y,X_31)),join(X_31,Y)) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
join(X_31,meet(X_32,join(Y,X_31))) = meet(join(X_31,X_32),join(X_31,Y)),
inference(resolve,[$cnf( $equal(join(X_31,meet(X_32,join(Y,X_31))),meet(join(X_31,X_32),join(X_31,join(Y,X_31)))) )],[refute_0_114,refute_0_117]) ).
cnf(refute_0_119,plain,
meet(join(X_31,X_32),join(X_31,Y)) = join(X_31,meet(X_32,Y)),
inference(subst,[],[refute_0_24:[bind(X,$fot(X_31)),bind(Y,$fot(X_32)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_120,plain,
( join(X_31,meet(X_32,join(Y,X_31))) != meet(join(X_31,X_32),join(X_31,Y))
| meet(join(X_31,X_32),join(X_31,Y)) != join(X_31,meet(X_32,Y))
| join(X_31,meet(X_32,join(Y,X_31))) = join(X_31,meet(X_32,Y)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_31,meet(X_32,join(Y,X_31))),join(X_31,meet(X_32,Y))) ),[0],$fot(meet(join(X_31,X_32),join(X_31,Y)))]]) ).
cnf(refute_0_121,plain,
( join(X_31,meet(X_32,join(Y,X_31))) != meet(join(X_31,X_32),join(X_31,Y))
| join(X_31,meet(X_32,join(Y,X_31))) = join(X_31,meet(X_32,Y)) ),
inference(resolve,[$cnf( $equal(meet(join(X_31,X_32),join(X_31,Y)),join(X_31,meet(X_32,Y))) )],[refute_0_119,refute_0_120]) ).
cnf(refute_0_122,plain,
join(X_31,meet(X_32,join(Y,X_31))) = join(X_31,meet(X_32,Y)),
inference(resolve,[$cnf( $equal(join(X_31,meet(X_32,join(Y,X_31))),meet(join(X_31,X_32),join(X_31,Y))) )],[refute_0_118,refute_0_121]) ).
cnf(refute_0_123,plain,
join(meet(Y,X_52),meet(X_52,join(X_53,meet(Y,X_52)))) = join(meet(Y,X_52),meet(X_52,X_53)),
inference(subst,[],[refute_0_122:[bind(Y,$fot(X_53)),bind(X_31,$fot(meet(Y,X_52))),bind(X_32,$fot(X_52))]]) ).
cnf(refute_0_124,plain,
join(meet(X_52,join(X_53,meet(Y,X_52))),meet(Y,X_52)) = join(meet(Y,X_52),meet(X_52,join(X_53,meet(Y,X_52)))),
inference(subst,[],[refute_0_87:[bind(X_18,$fot(meet(X_52,join(X_53,meet(Y,X_52))))),bind(X_7,$fot(meet(Y,X_52)))]]) ).
cnf(refute_0_125,plain,
( join(meet(Y,X_52),meet(X_52,join(X_53,meet(Y,X_52)))) != join(meet(Y,X_52),meet(X_52,X_53))
| join(meet(X_52,join(X_53,meet(Y,X_52))),meet(Y,X_52)) != join(meet(Y,X_52),meet(X_52,join(X_53,meet(Y,X_52))))
| join(meet(X_52,join(X_53,meet(Y,X_52))),meet(Y,X_52)) = join(meet(Y,X_52),meet(X_52,X_53)) ),
inference(subst,[],[refute_0_79:[bind(X0,$fot(join(meet(X_52,join(X_53,meet(Y,X_52))),meet(Y,X_52)))),bind(Y0,$fot(join(meet(Y,X_52),meet(X_52,join(X_53,meet(Y,X_52)))))),bind(Z0,$fot(join(meet(Y,X_52),meet(X_52,X_53))))]]) ).
cnf(refute_0_126,plain,
( join(meet(Y,X_52),meet(X_52,join(X_53,meet(Y,X_52)))) != join(meet(Y,X_52),meet(X_52,X_53))
| join(meet(X_52,join(X_53,meet(Y,X_52))),meet(Y,X_52)) = join(meet(Y,X_52),meet(X_52,X_53)) ),
inference(resolve,[$cnf( $equal(join(meet(X_52,join(X_53,meet(Y,X_52))),meet(Y,X_52)),join(meet(Y,X_52),meet(X_52,join(X_53,meet(Y,X_52))))) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
join(meet(X_52,join(X_53,meet(Y,X_52))),meet(Y,X_52)) = join(meet(Y,X_52),meet(X_52,X_53)),
inference(resolve,[$cnf( $equal(join(meet(Y,X_52),meet(X_52,join(X_53,meet(Y,X_52)))),join(meet(Y,X_52),meet(X_52,X_53))) )],[refute_0_123,refute_0_126]) ).
cnf(refute_0_128,plain,
( join(meet(X_52,join(X_53,meet(Y,X_52))),meet(Y,X_52)) != join(meet(Y,X_52),meet(X_52,X_53))
| join(meet(X_52,join(X_53,meet(Y,X_52))),meet(Y,X_52)) != meet(X_52,join(X_53,meet(Y,X_52)))
| join(meet(Y,X_52),meet(X_52,X_53)) = meet(X_52,join(X_53,meet(Y,X_52))) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_52,join(X_53,meet(Y,X_52))),meet(Y,X_52)),meet(X_52,join(X_53,meet(Y,X_52)))) ),[0],$fot(join(meet(Y,X_52),meet(X_52,X_53)))]]) ).
cnf(refute_0_129,plain,
( join(meet(X_52,join(X_53,meet(Y,X_52))),meet(Y,X_52)) != meet(X_52,join(X_53,meet(Y,X_52)))
| join(meet(Y,X_52),meet(X_52,X_53)) = meet(X_52,join(X_53,meet(Y,X_52))) ),
inference(resolve,[$cnf( $equal(join(meet(X_52,join(X_53,meet(Y,X_52))),meet(Y,X_52)),join(meet(Y,X_52),meet(X_52,X_53))) )],[refute_0_127,refute_0_128]) ).
cnf(refute_0_130,plain,
join(meet(Y,X_52),meet(X_52,X_53)) = meet(X_52,join(X_53,meet(Y,X_52))),
inference(resolve,[$cnf( $equal(join(meet(X_52,join(X_53,meet(Y,X_52))),meet(Y,X_52)),meet(X_52,join(X_53,meet(Y,X_52)))) )],[refute_0_113,refute_0_129]) ).
cnf(refute_0_131,plain,
( join(meet(Y,X_52),meet(X_52,X_53)) != meet(X_52,join(X_53,meet(Y,X_52)))
| meet(X_52,join(X_53,meet(Y,X_52))) = join(meet(Y,X_52),meet(X_52,X_53)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(join(meet(Y,X_52),meet(X_52,X_53)))),bind(Y0,$fot(meet(X_52,join(X_53,meet(Y,X_52)))))]]) ).
cnf(refute_0_132,plain,
meet(X_52,join(X_53,meet(Y,X_52))) = join(meet(Y,X_52),meet(X_52,X_53)),
inference(resolve,[$cnf( $equal(join(meet(Y,X_52),meet(X_52,X_53)),meet(X_52,join(X_53,meet(Y,X_52)))) )],[refute_0_130,refute_0_131]) ).
cnf(refute_0_133,plain,
meet(X_51,join(X_53,meet(Y,X_51))) = join(meet(Y,X_51),meet(X_51,X_53)),
inference(subst,[],[refute_0_132:[bind(X_52,$fot(X_51))]]) ).
cnf(refute_0_134,plain,
meet(X_6,join(join(X_25,X_26),X_6)) = X_6,
inference(subst,[],[refute_0_41:[bind(X_7,$fot(join(X_25,X_26)))]]) ).
cnf(refute_0_135,plain,
join(join(X_25,X_26),X_6) = join(X_25,join(X_26,X_6)),
inference(subst,[],[associativity_of_join:[bind(X,$fot(X_25)),bind(Y,$fot(X_26)),bind(Z,$fot(X_6))]]) ).
cnf(refute_0_136,plain,
( join(join(X_25,X_26),X_6) != join(X_25,join(X_26,X_6))
| meet(X_6,join(join(X_25,X_26),X_6)) != X_6
| meet(X_6,join(X_25,join(X_26,X_6))) = X_6 ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_6,join(join(X_25,X_26),X_6)),X_6) ),[0,1],$fot(join(X_25,join(X_26,X_6)))]]) ).
cnf(refute_0_137,plain,
( meet(X_6,join(join(X_25,X_26),X_6)) != X_6
| meet(X_6,join(X_25,join(X_26,X_6))) = X_6 ),
inference(resolve,[$cnf( $equal(join(join(X_25,X_26),X_6),join(X_25,join(X_26,X_6))) )],[refute_0_135,refute_0_136]) ).
cnf(refute_0_138,plain,
meet(X_6,join(X_25,join(X_26,X_6))) = X_6,
inference(resolve,[$cnf( $equal(meet(X_6,join(join(X_25,X_26),X_6)),X_6) )],[refute_0_134,refute_0_137]) ).
cnf(refute_0_139,plain,
meet(meet(X_29,Y),join(X_28,join(X_29,meet(X_29,Y)))) = meet(X_29,Y),
inference(subst,[],[refute_0_138:[bind(X_25,$fot(X_28)),bind(X_26,$fot(X_29)),bind(X_6,$fot(meet(X_29,Y)))]]) ).
cnf(refute_0_140,plain,
join(X_29,meet(X_29,Y)) = X_29,
inference(subst,[],[absorption2:[bind(X,$fot(X_29))]]) ).
cnf(refute_0_141,plain,
( join(X_29,meet(X_29,Y)) != X_29
| meet(meet(X_29,Y),join(X_28,join(X_29,meet(X_29,Y)))) != meet(X_29,Y)
| meet(meet(X_29,Y),join(X_28,X_29)) = meet(X_29,Y) ),
introduced(tautology,[equality,[$cnf( $equal(meet(meet(X_29,Y),join(X_28,join(X_29,meet(X_29,Y)))),meet(X_29,Y)) ),[0,1,1],$fot(X_29)]]) ).
cnf(refute_0_142,plain,
( meet(meet(X_29,Y),join(X_28,join(X_29,meet(X_29,Y)))) != meet(X_29,Y)
| meet(meet(X_29,Y),join(X_28,X_29)) = meet(X_29,Y) ),
inference(resolve,[$cnf( $equal(join(X_29,meet(X_29,Y)),X_29) )],[refute_0_140,refute_0_141]) ).
cnf(refute_0_143,plain,
meet(meet(X_29,Y),join(X_28,X_29)) = meet(X_29,Y),
inference(resolve,[$cnf( $equal(meet(meet(X_29,Y),join(X_28,join(X_29,meet(X_29,Y)))),meet(X_29,Y)) )],[refute_0_139,refute_0_142]) ).
cnf(refute_0_144,plain,
meet(meet(X_29,Y),join(X_28,X_29)) = meet(X_29,meet(Y,join(X_28,X_29))),
inference(subst,[],[associativity_of_meet:[bind(X,$fot(X_29)),bind(Z,$fot(join(X_28,X_29)))]]) ).
cnf(refute_0_145,plain,
( meet(meet(X_29,Y),join(X_28,X_29)) != meet(X_29,Y)
| meet(meet(X_29,Y),join(X_28,X_29)) != meet(X_29,meet(Y,join(X_28,X_29)))
| meet(X_29,meet(Y,join(X_28,X_29))) = meet(X_29,Y) ),
introduced(tautology,[equality,[$cnf( $equal(meet(meet(X_29,Y),join(X_28,X_29)),meet(X_29,Y)) ),[0],$fot(meet(X_29,meet(Y,join(X_28,X_29))))]]) ).
cnf(refute_0_146,plain,
( meet(meet(X_29,Y),join(X_28,X_29)) != meet(X_29,Y)
| meet(X_29,meet(Y,join(X_28,X_29))) = meet(X_29,Y) ),
inference(resolve,[$cnf( $equal(meet(meet(X_29,Y),join(X_28,X_29)),meet(X_29,meet(Y,join(X_28,X_29)))) )],[refute_0_144,refute_0_145]) ).
cnf(refute_0_147,plain,
meet(X_29,meet(Y,join(X_28,X_29))) = meet(X_29,Y),
inference(resolve,[$cnf( $equal(meet(meet(X_29,Y),join(X_28,X_29)),meet(X_29,Y)) )],[refute_0_143,refute_0_146]) ).
cnf(refute_0_148,plain,
meet(Y,meet(X_51,join(X_53,Y))) = meet(Y,X_51),
inference(subst,[],[refute_0_147:[bind(Y,$fot(X_51)),bind(X_28,$fot(X_53)),bind(X_29,$fot(Y))]]) ).
cnf(refute_0_149,plain,
join(X_53,meet(Y,meet(X_51,join(X_53,Y)))) = join(X_53,meet(Y,meet(X_51,join(X_53,Y)))),
introduced(tautology,[refl,[$fot(join(X_53,meet(Y,meet(X_51,join(X_53,Y)))))]]) ).
cnf(refute_0_150,plain,
( join(X_53,meet(Y,meet(X_51,join(X_53,Y)))) != join(X_53,meet(Y,meet(X_51,join(X_53,Y))))
| meet(Y,meet(X_51,join(X_53,Y))) != meet(Y,X_51)
| join(X_53,meet(Y,meet(X_51,join(X_53,Y)))) = join(X_53,meet(Y,X_51)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_53,meet(Y,meet(X_51,join(X_53,Y)))),join(X_53,meet(Y,meet(X_51,join(X_53,Y))))) ),[1,1],$fot(meet(Y,X_51))]]) ).
cnf(refute_0_151,plain,
( meet(Y,meet(X_51,join(X_53,Y))) != meet(Y,X_51)
| join(X_53,meet(Y,meet(X_51,join(X_53,Y)))) = join(X_53,meet(Y,X_51)) ),
inference(resolve,[$cnf( $equal(join(X_53,meet(Y,meet(X_51,join(X_53,Y)))),join(X_53,meet(Y,meet(X_51,join(X_53,Y))))) )],[refute_0_149,refute_0_150]) ).
cnf(refute_0_152,plain,
join(X_53,meet(Y,meet(X_51,join(X_53,Y)))) = join(X_53,meet(Y,X_51)),
inference(resolve,[$cnf( $equal(meet(Y,meet(X_51,join(X_53,Y))),meet(Y,X_51)) )],[refute_0_148,refute_0_151]) ).
cnf(refute_0_153,plain,
meet(X_51,join(X_53,meet(Y,meet(X_51,join(X_53,Y))))) = meet(X_51,join(X_53,meet(Y,meet(X_51,join(X_53,Y))))),
introduced(tautology,[refl,[$fot(meet(X_51,join(X_53,meet(Y,meet(X_51,join(X_53,Y))))))]]) ).
cnf(refute_0_154,plain,
( join(X_53,meet(Y,meet(X_51,join(X_53,Y)))) != join(X_53,meet(Y,X_51))
| meet(X_51,join(X_53,meet(Y,meet(X_51,join(X_53,Y))))) != meet(X_51,join(X_53,meet(Y,meet(X_51,join(X_53,Y)))))
| meet(X_51,join(X_53,meet(Y,meet(X_51,join(X_53,Y))))) = meet(X_51,join(X_53,meet(Y,X_51))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_51,join(X_53,meet(Y,meet(X_51,join(X_53,Y))))),meet(X_51,join(X_53,meet(Y,meet(X_51,join(X_53,Y)))))) ),[1,1],$fot(join(X_53,meet(Y,X_51)))]]) ).
cnf(refute_0_155,plain,
( join(X_53,meet(Y,meet(X_51,join(X_53,Y)))) != join(X_53,meet(Y,X_51))
| meet(X_51,join(X_53,meet(Y,meet(X_51,join(X_53,Y))))) = meet(X_51,join(X_53,meet(Y,X_51))) ),
inference(resolve,[$cnf( $equal(meet(X_51,join(X_53,meet(Y,meet(X_51,join(X_53,Y))))),meet(X_51,join(X_53,meet(Y,meet(X_51,join(X_53,Y)))))) )],[refute_0_153,refute_0_154]) ).
cnf(refute_0_156,plain,
meet(X_51,join(X_53,meet(Y,meet(X_51,join(X_53,Y))))) = meet(X_51,join(X_53,meet(Y,X_51))),
inference(resolve,[$cnf( $equal(join(X_53,meet(Y,meet(X_51,join(X_53,Y)))),join(X_53,meet(Y,X_51))) )],[refute_0_152,refute_0_155]) ).
cnf(refute_0_157,plain,
( meet(X_51,join(X_53,meet(Y,X_51))) != join(meet(Y,X_51),meet(X_51,X_53))
| meet(X_51,join(X_53,meet(Y,meet(X_51,join(X_53,Y))))) != meet(X_51,join(X_53,meet(Y,X_51)))
| meet(X_51,join(X_53,meet(Y,meet(X_51,join(X_53,Y))))) = join(meet(Y,X_51),meet(X_51,X_53)) ),
inference(subst,[],[refute_0_79:[bind(X0,$fot(meet(X_51,join(X_53,meet(Y,meet(X_51,join(X_53,Y))))))),bind(Y0,$fot(meet(X_51,join(X_53,meet(Y,X_51))))),bind(Z0,$fot(join(meet(Y,X_51),meet(X_51,X_53))))]]) ).
cnf(refute_0_158,plain,
( meet(X_51,join(X_53,meet(Y,X_51))) != join(meet(Y,X_51),meet(X_51,X_53))
| meet(X_51,join(X_53,meet(Y,meet(X_51,join(X_53,Y))))) = join(meet(Y,X_51),meet(X_51,X_53)) ),
inference(resolve,[$cnf( $equal(meet(X_51,join(X_53,meet(Y,meet(X_51,join(X_53,Y))))),meet(X_51,join(X_53,meet(Y,X_51)))) )],[refute_0_156,refute_0_157]) ).
cnf(refute_0_159,plain,
meet(X_51,join(X_53,meet(Y,meet(X_51,join(X_53,Y))))) = join(meet(Y,X_51),meet(X_51,X_53)),
inference(resolve,[$cnf( $equal(meet(X_51,join(X_53,meet(Y,X_51))),join(meet(Y,X_51),meet(X_51,X_53))) )],[refute_0_133,refute_0_158]) ).
cnf(refute_0_160,plain,
( meet(X_51,join(X_53,meet(Y,meet(X_51,join(X_53,Y))))) != join(meet(Y,X_51),meet(X_51,X_53))
| meet(X_51,join(X_53,meet(Y,meet(X_51,join(X_53,Y))))) != meet(X_51,join(X_53,Y))
| join(meet(Y,X_51),meet(X_51,X_53)) = meet(X_51,join(X_53,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_51,join(X_53,meet(Y,meet(X_51,join(X_53,Y))))),meet(X_51,join(X_53,Y))) ),[0],$fot(join(meet(Y,X_51),meet(X_51,X_53)))]]) ).
cnf(refute_0_161,plain,
( meet(X_51,join(X_53,meet(Y,meet(X_51,join(X_53,Y))))) != meet(X_51,join(X_53,Y))
| join(meet(Y,X_51),meet(X_51,X_53)) = meet(X_51,join(X_53,Y)) ),
inference(resolve,[$cnf( $equal(meet(X_51,join(X_53,meet(Y,meet(X_51,join(X_53,Y))))),join(meet(Y,X_51),meet(X_51,X_53))) )],[refute_0_159,refute_0_160]) ).
cnf(refute_0_162,plain,
join(meet(Y,X_51),meet(X_51,X_53)) = meet(X_51,join(X_53,Y)),
inference(resolve,[$cnf( $equal(meet(X_51,join(X_53,meet(Y,meet(X_51,join(X_53,Y))))),meet(X_51,join(X_53,Y))) )],[refute_0_108,refute_0_161]) ).
cnf(refute_0_163,plain,
join(meet(X_93,X_92),meet(X_92,X_114)) = meet(X_92,join(X_114,X_93)),
inference(subst,[],[refute_0_162:[bind(Y,$fot(X_93)),bind(X_51,$fot(X_92)),bind(X_53,$fot(X_114))]]) ).
cnf(refute_0_164,plain,
( join(meet(X_92,X_114),meet(X_92,X_93)) != join(meet(X_93,X_92),meet(X_92,X_114))
| join(meet(X_93,X_92),meet(X_92,X_114)) != meet(X_92,join(X_114,X_93))
| join(meet(X_92,X_114),meet(X_92,X_93)) = meet(X_92,join(X_114,X_93)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(meet(X_92,X_114),meet(X_92,X_93)),meet(X_92,join(X_114,X_93))) ),[0],$fot(join(meet(X_93,X_92),meet(X_92,X_114)))]]) ).
cnf(refute_0_165,plain,
( join(meet(X_92,X_114),meet(X_92,X_93)) != join(meet(X_93,X_92),meet(X_92,X_114))
| join(meet(X_92,X_114),meet(X_92,X_93)) = meet(X_92,join(X_114,X_93)) ),
inference(resolve,[$cnf( $equal(join(meet(X_93,X_92),meet(X_92,X_114)),meet(X_92,join(X_114,X_93))) )],[refute_0_163,refute_0_164]) ).
cnf(refute_0_166,plain,
join(meet(X_92,X_114),meet(X_92,X_93)) = meet(X_92,join(X_114,X_93)),
inference(resolve,[$cnf( $equal(join(meet(X_92,X_114),meet(X_92,X_93)),join(meet(X_93,X_92),meet(X_92,X_114))) )],[refute_0_96,refute_0_165]) ).
cnf(refute_0_167,plain,
join(meet(xx,yy),meet(xx,zz)) = meet(xx,join(yy,zz)),
inference(subst,[],[refute_0_166:[bind(X_114,$fot(yy)),bind(X_92,$fot(xx)),bind(X_93,$fot(zz))]]) ).
cnf(refute_0_168,plain,
( join(meet(xx,yy),meet(xx,zz)) != meet(xx,join(yy,zz))
| meet(xx,join(yy,zz)) != meet(xx,join(yy,zz))
| meet(xx,join(yy,zz)) = join(meet(xx,yy),meet(xx,zz)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(meet(xx,join(yy,zz)),join(meet(xx,yy),meet(xx,zz))) ),[1],$fot(meet(xx,join(yy,zz)))]]) ).
cnf(refute_0_169,plain,
( meet(xx,join(yy,zz)) != meet(xx,join(yy,zz))
| meet(xx,join(yy,zz)) = join(meet(xx,yy),meet(xx,zz)) ),
inference(resolve,[$cnf( $equal(join(meet(xx,yy),meet(xx,zz)),meet(xx,join(yy,zz))) )],[refute_0_167,refute_0_168]) ).
cnf(refute_0_170,plain,
meet(xx,join(yy,zz)) != meet(xx,join(yy,zz)),
inference(resolve,[$cnf( $equal(meet(xx,join(yy,zz)),join(meet(xx,yy),meet(xx,zz))) )],[refute_0_169,dist_meet]) ).
cnf(refute_0_171,plain,
meet(xx,join(yy,zz)) = meet(xx,join(yy,zz)),
introduced(tautology,[refl,[$fot(meet(xx,join(yy,zz)))]]) ).
cnf(refute_0_172,plain,
$false,
inference(resolve,[$cnf( $equal(meet(xx,join(yy,zz)),meet(xx,join(yy,zz))) )],[refute_0_171,refute_0_170]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LAT032-1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jun 29 23:45:41 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 3.34/3.52 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.34/3.52
% 3.34/3.52 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.37/3.53
%------------------------------------------------------------------------------