TSTP Solution File: LAT042-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LAT042-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n029.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 05:59:05 EDT 2022
% Result : Unsatisfiable 20.65s 20.83s
% Output : CNFRefutation 20.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 57
% Syntax : Number of clauses : 249 ( 134 unt; 0 nHn; 123 RR)
% Number of literals : 414 ( 413 equ; 168 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 : 656 ( 19 sgn)
% Comments :
%------------------------------------------------------------------------------
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(distributivity,axiom,
meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)) ).
cnf(prove_modular_law,negated_conjecture,
join(a,meet(b,join(a,c))) != meet(join(a,b),join(a,c)) ).
cnf(refute_0_0,plain,
join(join(X_46,meet(Y,X_46)),X_48) = join(X_46,join(meet(Y,X_46),X_48)),
inference(subst,[],[associativity_of_join:[bind(X,$fot(X_46)),bind(Y,$fot(meet(Y,X_46))),bind(Z,$fot(X_48))]]) ).
cnf(refute_0_1,plain,
( join(X,meet(X,Y)) != X
| meet(X,Y) != meet(Y,X)
| join(X,meet(Y,X)) = X ),
introduced(tautology,[equality,[$cnf( $equal(join(X,meet(X,Y)),X) ),[0,1],$fot(meet(Y,X))]]) ).
cnf(refute_0_2,plain,
( join(X,meet(X,Y)) != X
| join(X,meet(Y,X)) = X ),
inference(resolve,[$cnf( $equal(meet(X,Y),meet(Y,X)) )],[commutativity_of_meet,refute_0_1]) ).
cnf(refute_0_3,plain,
join(X,meet(Y,X)) = X,
inference(resolve,[$cnf( $equal(join(X,meet(X,Y)),X) )],[absorption2,refute_0_2]) ).
cnf(refute_0_4,plain,
join(X_46,meet(Y,X_46)) = X_46,
inference(subst,[],[refute_0_3:[bind(X,$fot(X_46))]]) ).
cnf(refute_0_5,plain,
( join(X_46,meet(Y,X_46)) != X_46
| join(join(X_46,meet(Y,X_46)),X_48) != join(X_46,join(meet(Y,X_46),X_48))
| join(X_46,X_48) = join(X_46,join(meet(Y,X_46),X_48)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_46,meet(Y,X_46)),X_48),join(X_46,join(meet(Y,X_46),X_48))) ),[0,0],$fot(X_46)]]) ).
cnf(refute_0_6,plain,
( join(join(X_46,meet(Y,X_46)),X_48) != join(X_46,join(meet(Y,X_46),X_48))
| join(X_46,X_48) = join(X_46,join(meet(Y,X_46),X_48)) ),
inference(resolve,[$cnf( $equal(join(X_46,meet(Y,X_46)),X_46) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
join(X_46,X_48) = join(X_46,join(meet(Y,X_46),X_48)),
inference(resolve,[$cnf( $equal(join(join(X_46,meet(Y,X_46)),X_48),join(X_46,join(meet(Y,X_46),X_48))) )],[refute_0_0,refute_0_6]) ).
cnf(refute_0_8,plain,
join(X_66,meet(X_65,Z)) = join(X_66,join(meet(X_65,X_66),meet(X_65,Z))),
inference(subst,[],[refute_0_7:[bind(Y,$fot(X_65)),bind(X_46,$fot(X_66)),bind(X_48,$fot(meet(X_65,Z)))]]) ).
cnf(refute_0_9,plain,
meet(X_65,join(X_66,Z)) = join(meet(X_65,X_66),meet(X_65,Z)),
inference(subst,[],[distributivity:[bind(X,$fot(X_65)),bind(Y,$fot(X_66))]]) ).
cnf(refute_0_10,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_11,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_12,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( meet(X_65,join(X_66,Z)) != join(meet(X_65,X_66),meet(X_65,Z))
| join(meet(X_65,X_66),meet(X_65,Z)) = meet(X_65,join(X_66,Z)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(meet(X_65,join(X_66,Z)))),bind(Y0,$fot(join(meet(X_65,X_66),meet(X_65,Z))))]]) ).
cnf(refute_0_14,plain,
join(meet(X_65,X_66),meet(X_65,Z)) = meet(X_65,join(X_66,Z)),
inference(resolve,[$cnf( $equal(meet(X_65,join(X_66,Z)),join(meet(X_65,X_66),meet(X_65,Z))) )],[refute_0_9,refute_0_13]) ).
cnf(refute_0_15,plain,
( join(X_66,meet(X_65,Z)) != join(X_66,join(meet(X_65,X_66),meet(X_65,Z)))
| join(meet(X_65,X_66),meet(X_65,Z)) != meet(X_65,join(X_66,Z))
| join(X_66,meet(X_65,Z)) = join(X_66,meet(X_65,join(X_66,Z))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_66,meet(X_65,Z)),join(X_66,join(meet(X_65,X_66),meet(X_65,Z)))) ),[1,1],$fot(meet(X_65,join(X_66,Z)))]]) ).
cnf(refute_0_16,plain,
( join(X_66,meet(X_65,Z)) != join(X_66,join(meet(X_65,X_66),meet(X_65,Z)))
| join(X_66,meet(X_65,Z)) = join(X_66,meet(X_65,join(X_66,Z))) ),
inference(resolve,[$cnf( $equal(join(meet(X_65,X_66),meet(X_65,Z)),meet(X_65,join(X_66,Z))) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
join(X_66,meet(X_65,Z)) = join(X_66,meet(X_65,join(X_66,Z))),
inference(resolve,[$cnf( $equal(join(X_66,meet(X_65,Z)),join(X_66,join(meet(X_65,X_66),meet(X_65,Z)))) )],[refute_0_8,refute_0_16]) ).
cnf(refute_0_18,plain,
( join(X_66,meet(X_65,Z)) != join(X_66,meet(X_65,join(X_66,Z)))
| join(X_66,meet(X_65,join(X_66,Z))) = join(X_66,meet(X_65,Z)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(join(X_66,meet(X_65,Z)))),bind(Y0,$fot(join(X_66,meet(X_65,join(X_66,Z)))))]]) ).
cnf(refute_0_19,plain,
join(X_66,meet(X_65,join(X_66,Z))) = join(X_66,meet(X_65,Z)),
inference(resolve,[$cnf( $equal(join(X_66,meet(X_65,Z)),join(X_66,meet(X_65,join(X_66,Z)))) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
join(a,meet(b,join(a,c))) = join(a,meet(b,c)),
inference(subst,[],[refute_0_19:[bind(Z,$fot(c)),bind(X_65,$fot(b)),bind(X_66,$fot(a))]]) ).
cnf(refute_0_21,plain,
( join(a,meet(b,c)) != meet(join(a,b),join(a,c))
| join(a,meet(b,join(a,c))) != join(a,meet(b,c))
| join(a,meet(b,join(a,c))) = meet(join(a,b),join(a,c)) ),
introduced(tautology,[equality,[$cnf( $equal(join(a,meet(b,join(a,c))),join(a,meet(b,c))) ),[1],$fot(meet(join(a,b),join(a,c)))]]) ).
cnf(refute_0_22,plain,
( join(a,meet(b,c)) != meet(join(a,b),join(a,c))
| join(a,meet(b,join(a,c))) = meet(join(a,b),join(a,c)) ),
inference(resolve,[$cnf( $equal(join(a,meet(b,join(a,c))),join(a,meet(b,c))) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
join(a,meet(b,c)) != meet(join(a,b),join(a,c)),
inference(resolve,[$cnf( $equal(join(a,meet(b,join(a,c))),meet(join(a,b),join(a,c))) )],[refute_0_22,prove_modular_law]) ).
cnf(refute_0_24,plain,
join(join(X_46,X_47),meet(join(X_46,X_47),Y)) = join(X_46,X_47),
inference(subst,[],[absorption2:[bind(X,$fot(join(X_46,X_47)))]]) ).
cnf(refute_0_25,plain,
join(join(X_46,X_47),meet(join(X_46,X_47),Y)) = join(X_46,join(X_47,meet(join(X_46,X_47),Y))),
inference(subst,[],[associativity_of_join:[bind(X,$fot(X_46)),bind(Y,$fot(X_47)),bind(Z,$fot(meet(join(X_46,X_47),Y)))]]) ).
cnf(refute_0_26,plain,
( join(join(X_46,X_47),meet(join(X_46,X_47),Y)) != join(X_46,X_47)
| join(join(X_46,X_47),meet(join(X_46,X_47),Y)) != join(X_46,join(X_47,meet(join(X_46,X_47),Y)))
| join(X_46,join(X_47,meet(join(X_46,X_47),Y))) = join(X_46,X_47) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_46,X_47),meet(join(X_46,X_47),Y)),join(X_46,X_47)) ),[0],$fot(join(X_46,join(X_47,meet(join(X_46,X_47),Y))))]]) ).
cnf(refute_0_27,plain,
( join(join(X_46,X_47),meet(join(X_46,X_47),Y)) != join(X_46,X_47)
| join(X_46,join(X_47,meet(join(X_46,X_47),Y))) = join(X_46,X_47) ),
inference(resolve,[$cnf( $equal(join(join(X_46,X_47),meet(join(X_46,X_47),Y)),join(X_46,join(X_47,meet(join(X_46,X_47),Y)))) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
join(X_46,join(X_47,meet(join(X_46,X_47),Y))) = join(X_46,X_47),
inference(resolve,[$cnf( $equal(join(join(X_46,X_47),meet(join(X_46,X_47),Y)),join(X_46,X_47)) )],[refute_0_24,refute_0_27]) ).
cnf(refute_0_29,plain,
join(X_46,join(meet(X_328,Y),meet(join(X_46,meet(X_328,Y)),Y))) = join(X_46,meet(X_328,Y)),
inference(subst,[],[refute_0_28:[bind(X_47,$fot(meet(X_328,Y)))]]) ).
cnf(refute_0_30,plain,
meet(X_55,join(X_56,X_57)) = join(meet(X_55,X_56),meet(X_55,X_57)),
inference(subst,[],[distributivity:[bind(X,$fot(X_55)),bind(Y,$fot(X_56)),bind(Z,$fot(X_57))]]) ).
cnf(refute_0_31,plain,
meet(X_57,X_55) = meet(X_55,X_57),
inference(subst,[],[commutativity_of_meet:[bind(X,$fot(X_57)),bind(Y,$fot(X_55))]]) ).
cnf(refute_0_32,plain,
( meet(X_57,X_55) != meet(X_55,X_57)
| meet(X_55,X_57) = meet(X_57,X_55) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(meet(X_57,X_55))),bind(Y0,$fot(meet(X_55,X_57)))]]) ).
cnf(refute_0_33,plain,
meet(X_55,X_57) = meet(X_57,X_55),
inference(resolve,[$cnf( $equal(meet(X_57,X_55),meet(X_55,X_57)) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
( meet(X_55,X_57) != meet(X_57,X_55)
| meet(X_55,join(X_56,X_57)) != join(meet(X_55,X_56),meet(X_55,X_57))
| meet(X_55,join(X_56,X_57)) = join(meet(X_55,X_56),meet(X_57,X_55)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_55,join(X_56,X_57)),join(meet(X_55,X_56),meet(X_55,X_57))) ),[1,1],$fot(meet(X_57,X_55))]]) ).
cnf(refute_0_35,plain,
( meet(X_55,join(X_56,X_57)) != join(meet(X_55,X_56),meet(X_55,X_57))
| meet(X_55,join(X_56,X_57)) = join(meet(X_55,X_56),meet(X_57,X_55)) ),
inference(resolve,[$cnf( $equal(meet(X_55,X_57),meet(X_57,X_55)) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
meet(X_55,join(X_56,X_57)) = join(meet(X_55,X_56),meet(X_57,X_55)),
inference(resolve,[$cnf( $equal(meet(X_55,join(X_56,X_57)),join(meet(X_55,X_56),meet(X_55,X_57))) )],[refute_0_30,refute_0_35]) ).
cnf(refute_0_37,plain,
meet(X_136,join(X_137,X_138)) = join(meet(X_136,X_137),meet(X_138,X_136)),
inference(subst,[],[refute_0_36:[bind(X_55,$fot(X_136)),bind(X_56,$fot(X_137)),bind(X_57,$fot(X_138))]]) ).
cnf(refute_0_38,plain,
meet(X_137,X_136) = meet(X_136,X_137),
inference(subst,[],[commutativity_of_meet:[bind(X,$fot(X_137)),bind(Y,$fot(X_136))]]) ).
cnf(refute_0_39,plain,
( meet(X_137,X_136) != meet(X_136,X_137)
| meet(X_136,X_137) = meet(X_137,X_136) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(meet(X_137,X_136))),bind(Y0,$fot(meet(X_136,X_137)))]]) ).
cnf(refute_0_40,plain,
meet(X_136,X_137) = meet(X_137,X_136),
inference(resolve,[$cnf( $equal(meet(X_137,X_136),meet(X_136,X_137)) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
( meet(X_136,X_137) != meet(X_137,X_136)
| meet(X_136,join(X_137,X_138)) != join(meet(X_136,X_137),meet(X_138,X_136))
| meet(X_136,join(X_137,X_138)) = join(meet(X_137,X_136),meet(X_138,X_136)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_136,join(X_137,X_138)),join(meet(X_136,X_137),meet(X_138,X_136))) ),[1,0],$fot(meet(X_137,X_136))]]) ).
cnf(refute_0_42,plain,
( meet(X_136,join(X_137,X_138)) != join(meet(X_136,X_137),meet(X_138,X_136))
| meet(X_136,join(X_137,X_138)) = join(meet(X_137,X_136),meet(X_138,X_136)) ),
inference(resolve,[$cnf( $equal(meet(X_136,X_137),meet(X_137,X_136)) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
meet(X_136,join(X_137,X_138)) = join(meet(X_137,X_136),meet(X_138,X_136)),
inference(resolve,[$cnf( $equal(meet(X_136,join(X_137,X_138)),join(meet(X_136,X_137),meet(X_138,X_136))) )],[refute_0_37,refute_0_42]) ).
cnf(refute_0_44,plain,
meet(Y,join(X_328,join(X_46,meet(X_328,Y)))) = join(meet(X_328,Y),meet(join(X_46,meet(X_328,Y)),Y)),
inference(subst,[],[refute_0_43:[bind(X_136,$fot(Y)),bind(X_137,$fot(X_328)),bind(X_138,$fot(join(X_46,meet(X_328,Y))))]]) ).
cnf(refute_0_45,plain,
( meet(Y,join(X_328,join(X_46,meet(X_328,Y)))) != join(meet(X_328,Y),meet(join(X_46,meet(X_328,Y)),Y))
| join(meet(X_328,Y),meet(join(X_46,meet(X_328,Y)),Y)) = meet(Y,join(X_328,join(X_46,meet(X_328,Y)))) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(meet(Y,join(X_328,join(X_46,meet(X_328,Y)))))),bind(Y0,$fot(join(meet(X_328,Y),meet(join(X_46,meet(X_328,Y)),Y))))]]) ).
cnf(refute_0_46,plain,
join(meet(X_328,Y),meet(join(X_46,meet(X_328,Y)),Y)) = meet(Y,join(X_328,join(X_46,meet(X_328,Y)))),
inference(resolve,[$cnf( $equal(meet(Y,join(X_328,join(X_46,meet(X_328,Y)))),join(meet(X_328,Y),meet(join(X_46,meet(X_328,Y)),Y))) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
( join(X_46,join(meet(X_328,Y),meet(join(X_46,meet(X_328,Y)),Y))) != join(X_46,meet(X_328,Y))
| join(meet(X_328,Y),meet(join(X_46,meet(X_328,Y)),Y)) != meet(Y,join(X_328,join(X_46,meet(X_328,Y))))
| join(X_46,meet(Y,join(X_328,join(X_46,meet(X_328,Y))))) = join(X_46,meet(X_328,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_46,join(meet(X_328,Y),meet(join(X_46,meet(X_328,Y)),Y))),join(X_46,meet(X_328,Y))) ),[0,1],$fot(meet(Y,join(X_328,join(X_46,meet(X_328,Y)))))]]) ).
cnf(refute_0_48,plain,
( join(X_46,join(meet(X_328,Y),meet(join(X_46,meet(X_328,Y)),Y))) != join(X_46,meet(X_328,Y))
| join(X_46,meet(Y,join(X_328,join(X_46,meet(X_328,Y))))) = join(X_46,meet(X_328,Y)) ),
inference(resolve,[$cnf( $equal(join(meet(X_328,Y),meet(join(X_46,meet(X_328,Y)),Y)),meet(Y,join(X_328,join(X_46,meet(X_328,Y))))) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
join(X_46,meet(Y,join(X_328,join(X_46,meet(X_328,Y))))) = join(X_46,meet(X_328,Y)),
inference(resolve,[$cnf( $equal(join(X_46,join(meet(X_328,Y),meet(join(X_46,meet(X_328,Y)),Y))),join(X_46,meet(X_328,Y))) )],[refute_0_29,refute_0_48]) ).
cnf(refute_0_50,plain,
join(join(X_46,X_47),meet(Y,join(X_46,X_47))) = join(X_46,X_47),
inference(subst,[],[refute_0_3:[bind(X,$fot(join(X_46,X_47)))]]) ).
cnf(refute_0_51,plain,
join(join(X_46,X_47),meet(Y,join(X_46,X_47))) = join(X_46,join(X_47,meet(Y,join(X_46,X_47)))),
inference(subst,[],[associativity_of_join:[bind(X,$fot(X_46)),bind(Y,$fot(X_47)),bind(Z,$fot(meet(Y,join(X_46,X_47))))]]) ).
cnf(refute_0_52,plain,
( join(join(X_46,X_47),meet(Y,join(X_46,X_47))) != join(X_46,X_47)
| join(join(X_46,X_47),meet(Y,join(X_46,X_47))) != join(X_46,join(X_47,meet(Y,join(X_46,X_47))))
| join(X_46,join(X_47,meet(Y,join(X_46,X_47)))) = join(X_46,X_47) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_46,X_47),meet(Y,join(X_46,X_47))),join(X_46,X_47)) ),[0],$fot(join(X_46,join(X_47,meet(Y,join(X_46,X_47)))))]]) ).
cnf(refute_0_53,plain,
( join(join(X_46,X_47),meet(Y,join(X_46,X_47))) != join(X_46,X_47)
| join(X_46,join(X_47,meet(Y,join(X_46,X_47)))) = join(X_46,X_47) ),
inference(resolve,[$cnf( $equal(join(join(X_46,X_47),meet(Y,join(X_46,X_47))),join(X_46,join(X_47,meet(Y,join(X_46,X_47))))) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
join(X_46,join(X_47,meet(Y,join(X_46,X_47)))) = join(X_46,X_47),
inference(resolve,[$cnf( $equal(join(join(X_46,X_47),meet(Y,join(X_46,X_47))),join(X_46,X_47)) )],[refute_0_50,refute_0_53]) ).
cnf(refute_0_55,plain,
join(X_108,join(meet(X_107,Y),meet(X_107,join(X_108,meet(X_107,Y))))) = join(X_108,meet(X_107,Y)),
inference(subst,[],[refute_0_54:[bind(Y,$fot(X_107)),bind(X_46,$fot(X_108)),bind(X_47,$fot(meet(X_107,Y)))]]) ).
cnf(refute_0_56,plain,
meet(X_107,join(Y,join(X_108,meet(X_107,Y)))) = join(meet(X_107,Y),meet(X_107,join(X_108,meet(X_107,Y)))),
inference(subst,[],[distributivity:[bind(X,$fot(X_107)),bind(Z,$fot(join(X_108,meet(X_107,Y))))]]) ).
cnf(refute_0_57,plain,
( meet(X_107,join(Y,join(X_108,meet(X_107,Y)))) != join(meet(X_107,Y),meet(X_107,join(X_108,meet(X_107,Y))))
| join(meet(X_107,Y),meet(X_107,join(X_108,meet(X_107,Y)))) = meet(X_107,join(Y,join(X_108,meet(X_107,Y)))) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(meet(X_107,join(Y,join(X_108,meet(X_107,Y)))))),bind(Y0,$fot(join(meet(X_107,Y),meet(X_107,join(X_108,meet(X_107,Y))))))]]) ).
cnf(refute_0_58,plain,
join(meet(X_107,Y),meet(X_107,join(X_108,meet(X_107,Y)))) = meet(X_107,join(Y,join(X_108,meet(X_107,Y)))),
inference(resolve,[$cnf( $equal(meet(X_107,join(Y,join(X_108,meet(X_107,Y)))),join(meet(X_107,Y),meet(X_107,join(X_108,meet(X_107,Y))))) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
( join(X_108,join(meet(X_107,Y),meet(X_107,join(X_108,meet(X_107,Y))))) != join(X_108,meet(X_107,Y))
| join(meet(X_107,Y),meet(X_107,join(X_108,meet(X_107,Y)))) != meet(X_107,join(Y,join(X_108,meet(X_107,Y))))
| join(X_108,meet(X_107,join(Y,join(X_108,meet(X_107,Y))))) = join(X_108,meet(X_107,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_108,join(meet(X_107,Y),meet(X_107,join(X_108,meet(X_107,Y))))),join(X_108,meet(X_107,Y))) ),[0,1],$fot(meet(X_107,join(Y,join(X_108,meet(X_107,Y)))))]]) ).
cnf(refute_0_60,plain,
( join(X_108,join(meet(X_107,Y),meet(X_107,join(X_108,meet(X_107,Y))))) != join(X_108,meet(X_107,Y))
| join(X_108,meet(X_107,join(Y,join(X_108,meet(X_107,Y))))) = join(X_108,meet(X_107,Y)) ),
inference(resolve,[$cnf( $equal(join(meet(X_107,Y),meet(X_107,join(X_108,meet(X_107,Y)))),meet(X_107,join(Y,join(X_108,meet(X_107,Y))))) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
join(X_108,meet(X_107,join(Y,join(X_108,meet(X_107,Y))))) = join(X_108,meet(X_107,Y)),
inference(resolve,[$cnf( $equal(join(X_108,join(meet(X_107,Y),meet(X_107,join(X_108,meet(X_107,Y))))),join(X_108,meet(X_107,Y))) )],[refute_0_55,refute_0_60]) ).
cnf(refute_0_62,plain,
join(join(X_24,Y),meet(X_24,join(X_24,Y))) = join(X_24,Y),
inference(subst,[],[refute_0_3:[bind(X,$fot(join(X_24,Y))),bind(Y,$fot(X_24))]]) ).
cnf(refute_0_63,plain,
meet(X_24,join(X_24,Y)) = X_24,
inference(subst,[],[absorption1:[bind(X,$fot(X_24))]]) ).
cnf(refute_0_64,plain,
( join(join(X_24,Y),meet(X_24,join(X_24,Y))) != join(X_24,Y)
| meet(X_24,join(X_24,Y)) != X_24
| join(join(X_24,Y),X_24) = join(X_24,Y) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_24,Y),meet(X_24,join(X_24,Y))),join(X_24,Y)) ),[0,1],$fot(X_24)]]) ).
cnf(refute_0_65,plain,
( join(join(X_24,Y),meet(X_24,join(X_24,Y))) != join(X_24,Y)
| join(join(X_24,Y),X_24) = join(X_24,Y) ),
inference(resolve,[$cnf( $equal(meet(X_24,join(X_24,Y)),X_24) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
join(join(X_24,Y),X_24) = join(X_24,Y),
inference(resolve,[$cnf( $equal(join(join(X_24,Y),meet(X_24,join(X_24,Y))),join(X_24,Y)) )],[refute_0_62,refute_0_65]) ).
cnf(refute_0_67,plain,
join(join(X_24,Y),X_24) = join(X_24,join(Y,X_24)),
inference(subst,[],[associativity_of_join:[bind(X,$fot(X_24)),bind(Z,$fot(X_24))]]) ).
cnf(refute_0_68,plain,
( join(join(X_24,Y),X_24) != join(X_24,Y)
| join(join(X_24,Y),X_24) != join(X_24,join(Y,X_24))
| join(X_24,join(Y,X_24)) = join(X_24,Y) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_24,Y),X_24),join(X_24,Y)) ),[0],$fot(join(X_24,join(Y,X_24)))]]) ).
cnf(refute_0_69,plain,
( join(join(X_24,Y),X_24) != join(X_24,Y)
| join(X_24,join(Y,X_24)) = join(X_24,Y) ),
inference(resolve,[$cnf( $equal(join(join(X_24,Y),X_24),join(X_24,join(Y,X_24))) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
join(X_24,join(Y,X_24)) = join(X_24,Y),
inference(resolve,[$cnf( $equal(join(join(X_24,Y),X_24),join(X_24,Y)) )],[refute_0_66,refute_0_69]) ).
cnf(refute_0_71,plain,
join(join(meet(X_65,Y),X_67),join(Y,join(meet(X_65,Y),X_67))) = join(join(meet(X_65,Y),X_67),Y),
inference(subst,[],[refute_0_70:[bind(X_24,$fot(join(meet(X_65,Y),X_67)))]]) ).
cnf(refute_0_72,plain,
join(Y,X_67) = join(Y,join(meet(X_65,Y),X_67)),
inference(subst,[],[refute_0_7:[bind(Y,$fot(X_65)),bind(X_46,$fot(Y)),bind(X_48,$fot(X_67))]]) ).
cnf(refute_0_73,plain,
( join(Y,X_67) != join(Y,join(meet(X_65,Y),X_67))
| join(Y,join(meet(X_65,Y),X_67)) = join(Y,X_67) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(join(Y,X_67))),bind(Y0,$fot(join(Y,join(meet(X_65,Y),X_67))))]]) ).
cnf(refute_0_74,plain,
join(Y,join(meet(X_65,Y),X_67)) = join(Y,X_67),
inference(resolve,[$cnf( $equal(join(Y,X_67),join(Y,join(meet(X_65,Y),X_67))) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
( join(Y,join(meet(X_65,Y),X_67)) != join(Y,X_67)
| join(join(meet(X_65,Y),X_67),join(Y,join(meet(X_65,Y),X_67))) != join(join(meet(X_65,Y),X_67),Y)
| join(join(meet(X_65,Y),X_67),join(Y,X_67)) = join(join(meet(X_65,Y),X_67),Y) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(meet(X_65,Y),X_67),join(Y,join(meet(X_65,Y),X_67))),join(join(meet(X_65,Y),X_67),Y)) ),[0,1],$fot(join(Y,X_67))]]) ).
cnf(refute_0_76,plain,
( join(join(meet(X_65,Y),X_67),join(Y,join(meet(X_65,Y),X_67))) != join(join(meet(X_65,Y),X_67),Y)
| join(join(meet(X_65,Y),X_67),join(Y,X_67)) = join(join(meet(X_65,Y),X_67),Y) ),
inference(resolve,[$cnf( $equal(join(Y,join(meet(X_65,Y),X_67)),join(Y,X_67)) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
join(join(meet(X_65,Y),X_67),join(Y,X_67)) = join(join(meet(X_65,Y),X_67),Y),
inference(resolve,[$cnf( $equal(join(join(meet(X_65,Y),X_67),join(Y,join(meet(X_65,Y),X_67))),join(join(meet(X_65,Y),X_67),Y)) )],[refute_0_71,refute_0_76]) ).
cnf(refute_0_78,plain,
join(X_67,join(meet(X_65,Y),X_67)) = join(X_67,meet(X_65,Y)),
inference(subst,[],[refute_0_70:[bind(Y,$fot(meet(X_65,Y))),bind(X_24,$fot(X_67))]]) ).
cnf(refute_0_79,plain,
join(Y,join(X_67,join(meet(X_65,Y),X_67))) = join(Y,join(X_67,join(meet(X_65,Y),X_67))),
introduced(tautology,[refl,[$fot(join(Y,join(X_67,join(meet(X_65,Y),X_67))))]]) ).
cnf(refute_0_80,plain,
( join(Y,join(X_67,join(meet(X_65,Y),X_67))) != join(Y,join(X_67,join(meet(X_65,Y),X_67)))
| join(X_67,join(meet(X_65,Y),X_67)) != join(X_67,meet(X_65,Y))
| join(Y,join(X_67,join(meet(X_65,Y),X_67))) = join(Y,join(X_67,meet(X_65,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(join(Y,join(X_67,join(meet(X_65,Y),X_67))),join(Y,join(X_67,join(meet(X_65,Y),X_67)))) ),[1,1],$fot(join(X_67,meet(X_65,Y)))]]) ).
cnf(refute_0_81,plain,
( join(X_67,join(meet(X_65,Y),X_67)) != join(X_67,meet(X_65,Y))
| join(Y,join(X_67,join(meet(X_65,Y),X_67))) = join(Y,join(X_67,meet(X_65,Y))) ),
inference(resolve,[$cnf( $equal(join(Y,join(X_67,join(meet(X_65,Y),X_67))),join(Y,join(X_67,join(meet(X_65,Y),X_67)))) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
join(Y,join(X_67,join(meet(X_65,Y),X_67))) = join(Y,join(X_67,meet(X_65,Y))),
inference(resolve,[$cnf( $equal(join(X_67,join(meet(X_65,Y),X_67)),join(X_67,meet(X_65,Y))) )],[refute_0_78,refute_0_81]) ).
cnf(refute_0_83,plain,
join(join(X_46,X_47),X_48) = join(X_46,join(X_47,X_48)),
inference(subst,[],[associativity_of_join:[bind(X,$fot(X_46)),bind(Y,$fot(X_47)),bind(Z,$fot(X_48))]]) ).
cnf(refute_0_84,plain,
join(X_48,X_47) = join(X_47,X_48),
inference(subst,[],[commutativity_of_join:[bind(X,$fot(X_48)),bind(Y,$fot(X_47))]]) ).
cnf(refute_0_85,plain,
( join(X_48,X_47) != join(X_47,X_48)
| join(X_47,X_48) = join(X_48,X_47) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(join(X_48,X_47))),bind(Y0,$fot(join(X_47,X_48)))]]) ).
cnf(refute_0_86,plain,
join(X_47,X_48) = join(X_48,X_47),
inference(resolve,[$cnf( $equal(join(X_48,X_47),join(X_47,X_48)) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
( join(X_47,X_48) != join(X_48,X_47)
| join(join(X_46,X_47),X_48) != join(X_46,join(X_47,X_48))
| join(join(X_46,X_47),X_48) = join(X_46,join(X_48,X_47)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_46,X_47),X_48),join(X_46,join(X_47,X_48))) ),[1,1],$fot(join(X_48,X_47))]]) ).
cnf(refute_0_88,plain,
( join(join(X_46,X_47),X_48) != join(X_46,join(X_47,X_48))
| join(join(X_46,X_47),X_48) = join(X_46,join(X_48,X_47)) ),
inference(resolve,[$cnf( $equal(join(X_47,X_48),join(X_48,X_47)) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
join(join(X_46,X_47),X_48) = join(X_46,join(X_48,X_47)),
inference(resolve,[$cnf( $equal(join(join(X_46,X_47),X_48),join(X_46,join(X_47,X_48))) )],[refute_0_83,refute_0_88]) ).
cnf(refute_0_90,plain,
( join(join(X_46,X_47),X_48) != join(X_46,join(X_47,X_48))
| join(join(X_46,X_47),X_48) != join(X_46,join(X_48,X_47))
| join(X_46,join(X_47,X_48)) = join(X_46,join(X_48,X_47)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_46,X_47),X_48),join(X_46,join(X_48,X_47))) ),[0],$fot(join(X_46,join(X_47,X_48)))]]) ).
cnf(refute_0_91,plain,
( join(join(X_46,X_47),X_48) != join(X_46,join(X_48,X_47))
| join(X_46,join(X_47,X_48)) = join(X_46,join(X_48,X_47)) ),
inference(resolve,[$cnf( $equal(join(join(X_46,X_47),X_48),join(X_46,join(X_47,X_48))) )],[refute_0_83,refute_0_90]) ).
cnf(refute_0_92,plain,
join(X_46,join(X_47,X_48)) = join(X_46,join(X_48,X_47)),
inference(resolve,[$cnf( $equal(join(join(X_46,X_47),X_48),join(X_46,join(X_48,X_47))) )],[refute_0_89,refute_0_91]) ).
cnf(refute_0_93,plain,
( join(X_46,join(X_47,X_48)) != join(X_46,join(X_48,X_47))
| join(X_46,join(X_48,X_47)) = join(X_46,join(X_47,X_48)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(join(X_46,join(X_47,X_48)))),bind(Y0,$fot(join(X_46,join(X_48,X_47))))]]) ).
cnf(refute_0_94,plain,
join(X_46,join(X_48,X_47)) = join(X_46,join(X_47,X_48)),
inference(resolve,[$cnf( $equal(join(X_46,join(X_47,X_48)),join(X_46,join(X_48,X_47))) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
join(Y,join(join(meet(X_65,Y),X_67),X_67)) = join(Y,join(X_67,join(meet(X_65,Y),X_67))),
inference(subst,[],[refute_0_94:[bind(X_46,$fot(Y)),bind(X_47,$fot(X_67)),bind(X_48,$fot(join(meet(X_65,Y),X_67)))]]) ).
cnf(refute_0_96,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_97,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_12:[bind(X0,$fot(join(X_47,X_46))),bind(Y0,$fot(join(X_46,X_47)))]]) ).
cnf(refute_0_98,plain,
join(X_46,X_47) = join(X_47,X_46),
inference(resolve,[$cnf( $equal(join(X_47,X_46),join(X_46,X_47)) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
( join(X_46,X_47) != join(X_47,X_46)
| join(join(X_46,X_47),X_48) != join(X_46,join(X_47,X_48))
| join(join(X_47,X_46),X_48) = join(X_46,join(X_47,X_48)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_46,X_47),X_48),join(X_46,join(X_47,X_48))) ),[0,0],$fot(join(X_47,X_46))]]) ).
cnf(refute_0_100,plain,
( join(join(X_46,X_47),X_48) != join(X_46,join(X_47,X_48))
| join(join(X_47,X_46),X_48) = join(X_46,join(X_47,X_48)) ),
inference(resolve,[$cnf( $equal(join(X_46,X_47),join(X_47,X_46)) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
join(join(X_47,X_46),X_48) = join(X_46,join(X_47,X_48)),
inference(resolve,[$cnf( $equal(join(join(X_46,X_47),X_48),join(X_46,join(X_47,X_48))) )],[refute_0_83,refute_0_100]) ).
cnf(refute_0_102,plain,
join(join(X_47,X_46),X_48) = join(X_47,join(X_46,X_48)),
inference(subst,[],[associativity_of_join:[bind(X,$fot(X_47)),bind(Y,$fot(X_46)),bind(Z,$fot(X_48))]]) ).
cnf(refute_0_103,plain,
( join(join(X_47,X_46),X_48) != join(X_46,join(X_47,X_48))
| join(join(X_47,X_46),X_48) != join(X_47,join(X_46,X_48))
| join(X_47,join(X_46,X_48)) = join(X_46,join(X_47,X_48)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_47,X_46),X_48),join(X_46,join(X_47,X_48))) ),[0],$fot(join(X_47,join(X_46,X_48)))]]) ).
cnf(refute_0_104,plain,
( join(join(X_47,X_46),X_48) != join(X_46,join(X_47,X_48))
| join(X_47,join(X_46,X_48)) = join(X_46,join(X_47,X_48)) ),
inference(resolve,[$cnf( $equal(join(join(X_47,X_46),X_48),join(X_47,join(X_46,X_48))) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
join(X_47,join(X_46,X_48)) = join(X_46,join(X_47,X_48)),
inference(resolve,[$cnf( $equal(join(join(X_47,X_46),X_48),join(X_46,join(X_47,X_48))) )],[refute_0_101,refute_0_104]) ).
cnf(refute_0_106,plain,
( join(X_47,join(X_46,X_48)) != join(X_46,join(X_47,X_48))
| join(X_46,join(X_47,X_48)) = join(X_47,join(X_46,X_48)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(join(X_47,join(X_46,X_48)))),bind(Y0,$fot(join(X_46,join(X_47,X_48))))]]) ).
cnf(refute_0_107,plain,
join(X_46,join(X_47,X_48)) = join(X_47,join(X_46,X_48)),
inference(resolve,[$cnf( $equal(join(X_47,join(X_46,X_48)),join(X_46,join(X_47,X_48))) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
join(join(meet(X_65,Y),X_67),join(Y,X_67)) = join(Y,join(join(meet(X_65,Y),X_67),X_67)),
inference(subst,[],[refute_0_107:[bind(X_46,$fot(join(meet(X_65,Y),X_67))),bind(X_47,$fot(Y)),bind(X_48,$fot(X_67))]]) ).
cnf(refute_0_109,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_110,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_12,refute_0_109]) ).
cnf(refute_0_111,plain,
( join(Y,join(join(meet(X_65,Y),X_67),X_67)) != join(Y,join(X_67,join(meet(X_65,Y),X_67)))
| join(join(meet(X_65,Y),X_67),join(Y,X_67)) != join(Y,join(join(meet(X_65,Y),X_67),X_67))
| join(join(meet(X_65,Y),X_67),join(Y,X_67)) = join(Y,join(X_67,join(meet(X_65,Y),X_67))) ),
inference(subst,[],[refute_0_110:[bind(X0,$fot(join(join(meet(X_65,Y),X_67),join(Y,X_67)))),bind(Y0,$fot(join(Y,join(join(meet(X_65,Y),X_67),X_67)))),bind(Z0,$fot(join(Y,join(X_67,join(meet(X_65,Y),X_67)))))]]) ).
cnf(refute_0_112,plain,
( join(Y,join(join(meet(X_65,Y),X_67),X_67)) != join(Y,join(X_67,join(meet(X_65,Y),X_67)))
| join(join(meet(X_65,Y),X_67),join(Y,X_67)) = join(Y,join(X_67,join(meet(X_65,Y),X_67))) ),
inference(resolve,[$cnf( $equal(join(join(meet(X_65,Y),X_67),join(Y,X_67)),join(Y,join(join(meet(X_65,Y),X_67),X_67))) )],[refute_0_108,refute_0_111]) ).
cnf(refute_0_113,plain,
join(join(meet(X_65,Y),X_67),join(Y,X_67)) = join(Y,join(X_67,join(meet(X_65,Y),X_67))),
inference(resolve,[$cnf( $equal(join(Y,join(join(meet(X_65,Y),X_67),X_67)),join(Y,join(X_67,join(meet(X_65,Y),X_67)))) )],[refute_0_95,refute_0_112]) ).
cnf(refute_0_114,plain,
( join(Y,join(X_67,join(meet(X_65,Y),X_67))) != join(Y,join(X_67,meet(X_65,Y)))
| join(join(meet(X_65,Y),X_67),join(Y,X_67)) != join(Y,join(X_67,join(meet(X_65,Y),X_67)))
| join(join(meet(X_65,Y),X_67),join(Y,X_67)) = join(Y,join(X_67,meet(X_65,Y))) ),
inference(subst,[],[refute_0_110:[bind(X0,$fot(join(join(meet(X_65,Y),X_67),join(Y,X_67)))),bind(Y0,$fot(join(Y,join(X_67,join(meet(X_65,Y),X_67))))),bind(Z0,$fot(join(Y,join(X_67,meet(X_65,Y)))))]]) ).
cnf(refute_0_115,plain,
( join(Y,join(X_67,join(meet(X_65,Y),X_67))) != join(Y,join(X_67,meet(X_65,Y)))
| join(join(meet(X_65,Y),X_67),join(Y,X_67)) = join(Y,join(X_67,meet(X_65,Y))) ),
inference(resolve,[$cnf( $equal(join(join(meet(X_65,Y),X_67),join(Y,X_67)),join(Y,join(X_67,join(meet(X_65,Y),X_67)))) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
join(join(meet(X_65,Y),X_67),join(Y,X_67)) = join(Y,join(X_67,meet(X_65,Y))),
inference(resolve,[$cnf( $equal(join(Y,join(X_67,join(meet(X_65,Y),X_67))),join(Y,join(X_67,meet(X_65,Y)))) )],[refute_0_82,refute_0_115]) ).
cnf(refute_0_117,plain,
( join(join(meet(X_65,Y),X_67),join(Y,X_67)) != join(Y,join(X_67,meet(X_65,Y)))
| join(join(meet(X_65,Y),X_67),join(Y,X_67)) != join(join(meet(X_65,Y),X_67),Y)
| join(Y,join(X_67,meet(X_65,Y))) = join(join(meet(X_65,Y),X_67),Y) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(meet(X_65,Y),X_67),join(Y,X_67)),join(join(meet(X_65,Y),X_67),Y)) ),[0],$fot(join(Y,join(X_67,meet(X_65,Y))))]]) ).
cnf(refute_0_118,plain,
( join(join(meet(X_65,Y),X_67),join(Y,X_67)) != join(join(meet(X_65,Y),X_67),Y)
| join(Y,join(X_67,meet(X_65,Y))) = join(join(meet(X_65,Y),X_67),Y) ),
inference(resolve,[$cnf( $equal(join(join(meet(X_65,Y),X_67),join(Y,X_67)),join(Y,join(X_67,meet(X_65,Y)))) )],[refute_0_116,refute_0_117]) ).
cnf(refute_0_119,plain,
join(X,join(X_46,X_47)) = join(join(X_46,X_47),X),
inference(subst,[],[commutativity_of_join:[bind(Y,$fot(join(X_46,X_47)))]]) ).
cnf(refute_0_120,plain,
join(join(X_46,X_47),X) = join(X_46,join(X_47,X)),
inference(subst,[],[associativity_of_join:[bind(X,$fot(X_46)),bind(Y,$fot(X_47)),bind(Z,$fot(X))]]) ).
cnf(refute_0_121,plain,
( join(X,join(X_46,X_47)) != join(join(X_46,X_47),X)
| join(join(X_46,X_47),X) != join(X_46,join(X_47,X))
| join(X,join(X_46,X_47)) = join(X_46,join(X_47,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X,join(X_46,X_47)),join(X_46,join(X_47,X))) ),[0],$fot(join(join(X_46,X_47),X))]]) ).
cnf(refute_0_122,plain,
( join(X,join(X_46,X_47)) != join(join(X_46,X_47),X)
| join(X,join(X_46,X_47)) = join(X_46,join(X_47,X)) ),
inference(resolve,[$cnf( $equal(join(join(X_46,X_47),X),join(X_46,join(X_47,X))) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
join(X,join(X_46,X_47)) = join(X_46,join(X_47,X)),
inference(resolve,[$cnf( $equal(join(X,join(X_46,X_47)),join(join(X_46,X_47),X)) )],[refute_0_119,refute_0_122]) ).
cnf(refute_0_124,plain,
( join(X,join(X_46,X_47)) != join(X_46,join(X_47,X))
| join(X_46,join(X_47,X)) = join(X,join(X_46,X_47)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(join(X,join(X_46,X_47)))),bind(Y0,$fot(join(X_46,join(X_47,X))))]]) ).
cnf(refute_0_125,plain,
join(X_46,join(X_47,X)) = join(X,join(X_46,X_47)),
inference(resolve,[$cnf( $equal(join(X,join(X_46,X_47)),join(X_46,join(X_47,X))) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
join(meet(X_65,Y),join(X_67,Y)) = join(Y,join(meet(X_65,Y),X_67)),
inference(subst,[],[refute_0_125:[bind(X,$fot(Y)),bind(X_46,$fot(meet(X_65,Y))),bind(X_47,$fot(X_67))]]) ).
cnf(refute_0_127,plain,
( join(Y,join(meet(X_65,Y),X_67)) != join(Y,X_67)
| join(meet(X_65,Y),join(X_67,Y)) != join(Y,join(meet(X_65,Y),X_67))
| join(meet(X_65,Y),join(X_67,Y)) = join(Y,X_67) ),
inference(subst,[],[refute_0_110:[bind(X0,$fot(join(meet(X_65,Y),join(X_67,Y)))),bind(Y0,$fot(join(Y,join(meet(X_65,Y),X_67)))),bind(Z0,$fot(join(Y,X_67)))]]) ).
cnf(refute_0_128,plain,
( join(Y,join(meet(X_65,Y),X_67)) != join(Y,X_67)
| join(meet(X_65,Y),join(X_67,Y)) = join(Y,X_67) ),
inference(resolve,[$cnf( $equal(join(meet(X_65,Y),join(X_67,Y)),join(Y,join(meet(X_65,Y),X_67))) )],[refute_0_126,refute_0_127]) ).
cnf(refute_0_129,plain,
join(meet(X_65,Y),join(X_67,Y)) = join(Y,X_67),
inference(resolve,[$cnf( $equal(join(Y,join(meet(X_65,Y),X_67)),join(Y,X_67)) )],[refute_0_74,refute_0_128]) ).
cnf(refute_0_130,plain,
join(join(meet(X_65,Y),X_67),Y) = join(meet(X_65,Y),join(X_67,Y)),
inference(subst,[],[associativity_of_join:[bind(X,$fot(meet(X_65,Y))),bind(Y,$fot(X_67)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_131,plain,
( join(join(meet(X_65,Y),X_67),Y) != join(meet(X_65,Y),join(X_67,Y))
| join(meet(X_65,Y),join(X_67,Y)) != join(Y,X_67)
| join(join(meet(X_65,Y),X_67),Y) = join(Y,X_67) ),
inference(subst,[],[refute_0_110:[bind(X0,$fot(join(join(meet(X_65,Y),X_67),Y))),bind(Y0,$fot(join(meet(X_65,Y),join(X_67,Y)))),bind(Z0,$fot(join(Y,X_67)))]]) ).
cnf(refute_0_132,plain,
( join(meet(X_65,Y),join(X_67,Y)) != join(Y,X_67)
| join(join(meet(X_65,Y),X_67),Y) = join(Y,X_67) ),
inference(resolve,[$cnf( $equal(join(join(meet(X_65,Y),X_67),Y),join(meet(X_65,Y),join(X_67,Y))) )],[refute_0_130,refute_0_131]) ).
cnf(refute_0_133,plain,
join(join(meet(X_65,Y),X_67),Y) = join(Y,X_67),
inference(resolve,[$cnf( $equal(join(meet(X_65,Y),join(X_67,Y)),join(Y,X_67)) )],[refute_0_129,refute_0_132]) ).
cnf(refute_0_134,plain,
( join(Y,join(X_67,meet(X_65,Y))) != join(join(meet(X_65,Y),X_67),Y)
| join(join(meet(X_65,Y),X_67),Y) != join(Y,X_67)
| join(Y,join(X_67,meet(X_65,Y))) = join(Y,X_67) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(Y,join(X_67,meet(X_65,Y))),join(Y,X_67)) ),[0],$fot(join(join(meet(X_65,Y),X_67),Y))]]) ).
cnf(refute_0_135,plain,
( join(Y,join(X_67,meet(X_65,Y))) != join(join(meet(X_65,Y),X_67),Y)
| join(Y,join(X_67,meet(X_65,Y))) = join(Y,X_67) ),
inference(resolve,[$cnf( $equal(join(join(meet(X_65,Y),X_67),Y),join(Y,X_67)) )],[refute_0_133,refute_0_134]) ).
cnf(refute_0_136,plain,
( join(join(meet(X_65,Y),X_67),join(Y,X_67)) != join(join(meet(X_65,Y),X_67),Y)
| join(Y,join(X_67,meet(X_65,Y))) = join(Y,X_67) ),
inference(resolve,[$cnf( $equal(join(Y,join(X_67,meet(X_65,Y))),join(join(meet(X_65,Y),X_67),Y)) )],[refute_0_118,refute_0_135]) ).
cnf(refute_0_137,plain,
join(Y,join(X_67,meet(X_65,Y))) = join(Y,X_67),
inference(resolve,[$cnf( $equal(join(join(meet(X_65,Y),X_67),join(Y,X_67)),join(join(meet(X_65,Y),X_67),Y)) )],[refute_0_77,refute_0_136]) ).
cnf(refute_0_138,plain,
join(Y,join(X_108,meet(X_107,Y))) = join(Y,X_108),
inference(subst,[],[refute_0_137:[bind(X_65,$fot(X_107)),bind(X_67,$fot(X_108))]]) ).
cnf(refute_0_139,plain,
meet(X_107,join(Y,join(X_108,meet(X_107,Y)))) = meet(X_107,join(Y,join(X_108,meet(X_107,Y)))),
introduced(tautology,[refl,[$fot(meet(X_107,join(Y,join(X_108,meet(X_107,Y)))))]]) ).
cnf(refute_0_140,plain,
( join(Y,join(X_108,meet(X_107,Y))) != join(Y,X_108)
| meet(X_107,join(Y,join(X_108,meet(X_107,Y)))) != meet(X_107,join(Y,join(X_108,meet(X_107,Y))))
| meet(X_107,join(Y,join(X_108,meet(X_107,Y)))) = meet(X_107,join(Y,X_108)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_107,join(Y,join(X_108,meet(X_107,Y)))),meet(X_107,join(Y,join(X_108,meet(X_107,Y))))) ),[1,1],$fot(join(Y,X_108))]]) ).
cnf(refute_0_141,plain,
( join(Y,join(X_108,meet(X_107,Y))) != join(Y,X_108)
| meet(X_107,join(Y,join(X_108,meet(X_107,Y)))) = meet(X_107,join(Y,X_108)) ),
inference(resolve,[$cnf( $equal(meet(X_107,join(Y,join(X_108,meet(X_107,Y)))),meet(X_107,join(Y,join(X_108,meet(X_107,Y))))) )],[refute_0_139,refute_0_140]) ).
cnf(refute_0_142,plain,
meet(X_107,join(Y,join(X_108,meet(X_107,Y)))) = meet(X_107,join(Y,X_108)),
inference(resolve,[$cnf( $equal(join(Y,join(X_108,meet(X_107,Y))),join(Y,X_108)) )],[refute_0_138,refute_0_141]) ).
cnf(refute_0_143,plain,
join(X_108,meet(X_107,join(Y,join(X_108,meet(X_107,Y))))) = join(X_108,meet(X_107,join(Y,join(X_108,meet(X_107,Y))))),
introduced(tautology,[refl,[$fot(join(X_108,meet(X_107,join(Y,join(X_108,meet(X_107,Y))))))]]) ).
cnf(refute_0_144,plain,
( join(X_108,meet(X_107,join(Y,join(X_108,meet(X_107,Y))))) != join(X_108,meet(X_107,join(Y,join(X_108,meet(X_107,Y)))))
| meet(X_107,join(Y,join(X_108,meet(X_107,Y)))) != meet(X_107,join(Y,X_108))
| join(X_108,meet(X_107,join(Y,join(X_108,meet(X_107,Y))))) = join(X_108,meet(X_107,join(Y,X_108))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_108,meet(X_107,join(Y,join(X_108,meet(X_107,Y))))),join(X_108,meet(X_107,join(Y,join(X_108,meet(X_107,Y)))))) ),[1,1],$fot(meet(X_107,join(Y,X_108)))]]) ).
cnf(refute_0_145,plain,
( meet(X_107,join(Y,join(X_108,meet(X_107,Y)))) != meet(X_107,join(Y,X_108))
| join(X_108,meet(X_107,join(Y,join(X_108,meet(X_107,Y))))) = join(X_108,meet(X_107,join(Y,X_108))) ),
inference(resolve,[$cnf( $equal(join(X_108,meet(X_107,join(Y,join(X_108,meet(X_107,Y))))),join(X_108,meet(X_107,join(Y,join(X_108,meet(X_107,Y)))))) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
join(X_108,meet(X_107,join(Y,join(X_108,meet(X_107,Y))))) = join(X_108,meet(X_107,join(Y,X_108))),
inference(resolve,[$cnf( $equal(meet(X_107,join(Y,join(X_108,meet(X_107,Y)))),meet(X_107,join(Y,X_108))) )],[refute_0_142,refute_0_145]) ).
cnf(refute_0_147,plain,
( join(X_108,meet(X_107,join(Y,join(X_108,meet(X_107,Y))))) != join(X_108,meet(X_107,Y))
| join(X_108,meet(X_107,join(Y,join(X_108,meet(X_107,Y))))) != join(X_108,meet(X_107,join(Y,X_108)))
| join(X_108,meet(X_107,join(Y,X_108))) = join(X_108,meet(X_107,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_108,meet(X_107,join(Y,join(X_108,meet(X_107,Y))))),join(X_108,meet(X_107,Y))) ),[0],$fot(join(X_108,meet(X_107,join(Y,X_108))))]]) ).
cnf(refute_0_148,plain,
( join(X_108,meet(X_107,join(Y,join(X_108,meet(X_107,Y))))) != join(X_108,meet(X_107,Y))
| join(X_108,meet(X_107,join(Y,X_108))) = join(X_108,meet(X_107,Y)) ),
inference(resolve,[$cnf( $equal(join(X_108,meet(X_107,join(Y,join(X_108,meet(X_107,Y))))),join(X_108,meet(X_107,join(Y,X_108)))) )],[refute_0_146,refute_0_147]) ).
cnf(refute_0_149,plain,
join(X_108,meet(X_107,join(Y,X_108))) = join(X_108,meet(X_107,Y)),
inference(resolve,[$cnf( $equal(join(X_108,meet(X_107,join(Y,join(X_108,meet(X_107,Y))))),join(X_108,meet(X_107,Y))) )],[refute_0_61,refute_0_148]) ).
cnf(refute_0_150,plain,
join(X_46,meet(Y,join(X_328,X_46))) = join(X_46,meet(Y,X_328)),
inference(subst,[],[refute_0_149:[bind(Y,$fot(X_328)),bind(X_107,$fot(Y)),bind(X_108,$fot(X_46))]]) ).
cnf(refute_0_151,plain,
join(X_328,join(X_46,X_328)) = join(X_328,X_46),
inference(subst,[],[refute_0_70:[bind(Y,$fot(X_46)),bind(X_24,$fot(X_328))]]) ).
cnf(refute_0_152,plain,
meet(Y,join(X_328,join(X_46,X_328))) = meet(Y,join(X_328,join(X_46,X_328))),
introduced(tautology,[refl,[$fot(meet(Y,join(X_328,join(X_46,X_328))))]]) ).
cnf(refute_0_153,plain,
( join(X_328,join(X_46,X_328)) != join(X_328,X_46)
| meet(Y,join(X_328,join(X_46,X_328))) != meet(Y,join(X_328,join(X_46,X_328)))
| meet(Y,join(X_328,join(X_46,X_328))) = meet(Y,join(X_328,X_46)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(Y,join(X_328,join(X_46,X_328))),meet(Y,join(X_328,join(X_46,X_328)))) ),[1,1],$fot(join(X_328,X_46))]]) ).
cnf(refute_0_154,plain,
( join(X_328,join(X_46,X_328)) != join(X_328,X_46)
| meet(Y,join(X_328,join(X_46,X_328))) = meet(Y,join(X_328,X_46)) ),
inference(resolve,[$cnf( $equal(meet(Y,join(X_328,join(X_46,X_328))),meet(Y,join(X_328,join(X_46,X_328)))) )],[refute_0_152,refute_0_153]) ).
cnf(refute_0_155,plain,
meet(Y,join(X_328,join(X_46,X_328))) = meet(Y,join(X_328,X_46)),
inference(resolve,[$cnf( $equal(join(X_328,join(X_46,X_328)),join(X_328,X_46)) )],[refute_0_151,refute_0_154]) ).
cnf(refute_0_156,plain,
meet(X_55,join(X_56,meet(X_55,X_27))) = join(meet(X_55,X_56),meet(X_55,meet(X_55,X_27))),
inference(subst,[],[distributivity:[bind(X,$fot(X_55)),bind(Y,$fot(X_56)),bind(Z,$fot(meet(X_55,X_27)))]]) ).
cnf(refute_0_157,plain,
( join(X,Y) != join(Y,X)
| meet(X,join(X,Y)) != X
| meet(X,join(Y,X)) = X ),
introduced(tautology,[equality,[$cnf( $equal(meet(X,join(X,Y)),X) ),[0,1],$fot(join(Y,X))]]) ).
cnf(refute_0_158,plain,
( meet(X,join(X,Y)) != X
| meet(X,join(Y,X)) = X ),
inference(resolve,[$cnf( $equal(join(X,Y),join(Y,X)) )],[commutativity_of_join,refute_0_157]) ).
cnf(refute_0_159,plain,
meet(X,join(Y,X)) = X,
inference(resolve,[$cnf( $equal(meet(X,join(X,Y)),X) )],[absorption1,refute_0_158]) ).
cnf(refute_0_160,plain,
meet(meet(X_22,Y),join(X_22,meet(X_22,Y))) = meet(X_22,Y),
inference(subst,[],[refute_0_159:[bind(X,$fot(meet(X_22,Y))),bind(Y,$fot(X_22))]]) ).
cnf(refute_0_161,plain,
join(X_22,meet(X_22,Y)) = X_22,
inference(subst,[],[absorption2:[bind(X,$fot(X_22))]]) ).
cnf(refute_0_162,plain,
( join(X_22,meet(X_22,Y)) != X_22
| meet(meet(X_22,Y),join(X_22,meet(X_22,Y))) != meet(X_22,Y)
| meet(meet(X_22,Y),X_22) = meet(X_22,Y) ),
introduced(tautology,[equality,[$cnf( $equal(meet(meet(X_22,Y),join(X_22,meet(X_22,Y))),meet(X_22,Y)) ),[0,1],$fot(X_22)]]) ).
cnf(refute_0_163,plain,
( meet(meet(X_22,Y),join(X_22,meet(X_22,Y))) != meet(X_22,Y)
| meet(meet(X_22,Y),X_22) = meet(X_22,Y) ),
inference(resolve,[$cnf( $equal(join(X_22,meet(X_22,Y)),X_22) )],[refute_0_161,refute_0_162]) ).
cnf(refute_0_164,plain,
meet(meet(X_22,Y),X_22) = meet(X_22,Y),
inference(resolve,[$cnf( $equal(meet(meet(X_22,Y),join(X_22,meet(X_22,Y))),meet(X_22,Y)) )],[refute_0_160,refute_0_163]) ).
cnf(refute_0_165,plain,
meet(meet(X_22,Y),X_22) = meet(X_22,meet(Y,X_22)),
inference(subst,[],[associativity_of_meet:[bind(X,$fot(X_22)),bind(Z,$fot(X_22))]]) ).
cnf(refute_0_166,plain,
( meet(meet(X_22,Y),X_22) != meet(X_22,Y)
| meet(meet(X_22,Y),X_22) != meet(X_22,meet(Y,X_22))
| meet(X_22,meet(Y,X_22)) = meet(X_22,Y) ),
introduced(tautology,[equality,[$cnf( $equal(meet(meet(X_22,Y),X_22),meet(X_22,Y)) ),[0],$fot(meet(X_22,meet(Y,X_22)))]]) ).
cnf(refute_0_167,plain,
( meet(meet(X_22,Y),X_22) != meet(X_22,Y)
| meet(X_22,meet(Y,X_22)) = meet(X_22,Y) ),
inference(resolve,[$cnf( $equal(meet(meet(X_22,Y),X_22),meet(X_22,meet(Y,X_22))) )],[refute_0_165,refute_0_166]) ).
cnf(refute_0_168,plain,
meet(X_22,meet(Y,X_22)) = meet(X_22,Y),
inference(resolve,[$cnf( $equal(meet(meet(X_22,Y),X_22),meet(X_22,Y)) )],[refute_0_164,refute_0_167]) ).
cnf(refute_0_169,plain,
meet(X_28,meet(X_27,X_28)) = meet(X_28,X_27),
inference(subst,[],[refute_0_168:[bind(Y,$fot(X_27)),bind(X_22,$fot(X_28))]]) ).
cnf(refute_0_170,plain,
meet(X_28,X_27) = meet(X_27,X_28),
inference(subst,[],[commutativity_of_meet:[bind(X,$fot(X_28)),bind(Y,$fot(X_27))]]) ).
cnf(refute_0_171,plain,
( meet(X_28,X_27) != meet(X_27,X_28)
| meet(X_27,X_28) = meet(X_28,X_27) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(meet(X_28,X_27))),bind(Y0,$fot(meet(X_27,X_28)))]]) ).
cnf(refute_0_172,plain,
meet(X_27,X_28) = meet(X_28,X_27),
inference(resolve,[$cnf( $equal(meet(X_28,X_27),meet(X_27,X_28)) )],[refute_0_170,refute_0_171]) ).
cnf(refute_0_173,plain,
( meet(X_27,X_28) != meet(X_28,X_27)
| meet(X_28,meet(X_27,X_28)) != meet(X_28,X_27)
| meet(X_28,meet(X_28,X_27)) = meet(X_28,X_27) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_28,meet(X_27,X_28)),meet(X_28,X_27)) ),[0,1],$fot(meet(X_28,X_27))]]) ).
cnf(refute_0_174,plain,
( meet(X_28,meet(X_27,X_28)) != meet(X_28,X_27)
| meet(X_28,meet(X_28,X_27)) = meet(X_28,X_27) ),
inference(resolve,[$cnf( $equal(meet(X_27,X_28),meet(X_28,X_27)) )],[refute_0_172,refute_0_173]) ).
cnf(refute_0_175,plain,
meet(X_28,meet(X_28,X_27)) = meet(X_28,X_27),
inference(resolve,[$cnf( $equal(meet(X_28,meet(X_27,X_28)),meet(X_28,X_27)) )],[refute_0_169,refute_0_174]) ).
cnf(refute_0_176,plain,
meet(X_55,meet(X_55,X_27)) = meet(X_55,X_27),
inference(subst,[],[refute_0_175:[bind(X_28,$fot(X_55))]]) ).
cnf(refute_0_177,plain,
( meet(X_55,join(X_56,meet(X_55,X_27))) != join(meet(X_55,X_56),meet(X_55,meet(X_55,X_27)))
| meet(X_55,meet(X_55,X_27)) != meet(X_55,X_27)
| meet(X_55,join(X_56,meet(X_55,X_27))) = join(meet(X_55,X_56),meet(X_55,X_27)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_55,join(X_56,meet(X_55,X_27))),join(meet(X_55,X_56),meet(X_55,meet(X_55,X_27)))) ),[1,1],$fot(meet(X_55,X_27))]]) ).
cnf(refute_0_178,plain,
( meet(X_55,join(X_56,meet(X_55,X_27))) != join(meet(X_55,X_56),meet(X_55,meet(X_55,X_27)))
| meet(X_55,join(X_56,meet(X_55,X_27))) = join(meet(X_55,X_56),meet(X_55,X_27)) ),
inference(resolve,[$cnf( $equal(meet(X_55,meet(X_55,X_27)),meet(X_55,X_27)) )],[refute_0_176,refute_0_177]) ).
cnf(refute_0_179,plain,
meet(X_55,join(X_56,meet(X_55,X_27))) = join(meet(X_55,X_56),meet(X_55,X_27)),
inference(resolve,[$cnf( $equal(meet(X_55,join(X_56,meet(X_55,X_27))),join(meet(X_55,X_56),meet(X_55,meet(X_55,X_27)))) )],[refute_0_156,refute_0_178]) ).
cnf(refute_0_180,plain,
( meet(X,join(Y,Z)) != join(meet(X,Y),meet(X,Z))
| join(meet(X,Y),meet(X,Z)) = meet(X,join(Y,Z)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(meet(X,join(Y,Z)))),bind(Y0,$fot(join(meet(X,Y),meet(X,Z))))]]) ).
cnf(refute_0_181,plain,
join(meet(X,Y),meet(X,Z)) = meet(X,join(Y,Z)),
inference(resolve,[$cnf( $equal(meet(X,join(Y,Z)),join(meet(X,Y),meet(X,Z))) )],[distributivity,refute_0_180]) ).
cnf(refute_0_182,plain,
join(meet(X_55,X_56),meet(X_55,X_27)) = meet(X_55,join(X_56,X_27)),
inference(subst,[],[refute_0_181:[bind(X,$fot(X_55)),bind(Y,$fot(X_56)),bind(Z,$fot(X_27))]]) ).
cnf(refute_0_183,plain,
( join(meet(X_55,X_56),meet(X_55,X_27)) != meet(X_55,join(X_56,X_27))
| meet(X_55,join(X_56,meet(X_55,X_27))) != join(meet(X_55,X_56),meet(X_55,X_27))
| meet(X_55,join(X_56,meet(X_55,X_27))) = meet(X_55,join(X_56,X_27)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_55,join(X_56,meet(X_55,X_27))),join(meet(X_55,X_56),meet(X_55,X_27))) ),[1],$fot(meet(X_55,join(X_56,X_27)))]]) ).
cnf(refute_0_184,plain,
( meet(X_55,join(X_56,meet(X_55,X_27))) != join(meet(X_55,X_56),meet(X_55,X_27))
| meet(X_55,join(X_56,meet(X_55,X_27))) = meet(X_55,join(X_56,X_27)) ),
inference(resolve,[$cnf( $equal(join(meet(X_55,X_56),meet(X_55,X_27)),meet(X_55,join(X_56,X_27))) )],[refute_0_182,refute_0_183]) ).
cnf(refute_0_185,plain,
meet(X_55,join(X_56,meet(X_55,X_27))) = meet(X_55,join(X_56,X_27)),
inference(resolve,[$cnf( $equal(meet(X_55,join(X_56,meet(X_55,X_27))),join(meet(X_55,X_56),meet(X_55,X_27))) )],[refute_0_179,refute_0_184]) ).
cnf(refute_0_186,plain,
meet(X_55,join(X_56,meet(X_55,join(X_264,meet(X_262,X_55))))) = meet(X_55,join(X_56,join(X_264,meet(X_262,X_55)))),
inference(subst,[],[refute_0_185:[bind(X_27,$fot(join(X_264,meet(X_262,X_55))))]]) ).
cnf(refute_0_187,plain,
meet(X_55,join(X_56,meet(Y,X_55))) = join(meet(X_55,X_56),meet(X_55,meet(Y,X_55))),
inference(subst,[],[distributivity:[bind(X,$fot(X_55)),bind(Y,$fot(X_56)),bind(Z,$fot(meet(Y,X_55)))]]) ).
cnf(refute_0_188,plain,
meet(X_55,meet(Y,X_55)) = meet(X_55,Y),
inference(subst,[],[refute_0_168:[bind(X_22,$fot(X_55))]]) ).
cnf(refute_0_189,plain,
( meet(X_55,join(X_56,meet(Y,X_55))) != join(meet(X_55,X_56),meet(X_55,meet(Y,X_55)))
| meet(X_55,meet(Y,X_55)) != meet(X_55,Y)
| meet(X_55,join(X_56,meet(Y,X_55))) = join(meet(X_55,X_56),meet(X_55,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_55,join(X_56,meet(Y,X_55))),join(meet(X_55,X_56),meet(X_55,meet(Y,X_55)))) ),[1,1],$fot(meet(X_55,Y))]]) ).
cnf(refute_0_190,plain,
( meet(X_55,join(X_56,meet(Y,X_55))) != join(meet(X_55,X_56),meet(X_55,meet(Y,X_55)))
| meet(X_55,join(X_56,meet(Y,X_55))) = join(meet(X_55,X_56),meet(X_55,Y)) ),
inference(resolve,[$cnf( $equal(meet(X_55,meet(Y,X_55)),meet(X_55,Y)) )],[refute_0_188,refute_0_189]) ).
cnf(refute_0_191,plain,
meet(X_55,join(X_56,meet(Y,X_55))) = join(meet(X_55,X_56),meet(X_55,Y)),
inference(resolve,[$cnf( $equal(meet(X_55,join(X_56,meet(Y,X_55))),join(meet(X_55,X_56),meet(X_55,meet(Y,X_55)))) )],[refute_0_187,refute_0_190]) ).
cnf(refute_0_192,plain,
join(meet(X_55,X_56),meet(X_55,Y)) = meet(X_55,join(X_56,Y)),
inference(subst,[],[refute_0_181:[bind(X,$fot(X_55)),bind(Y,$fot(X_56)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_193,plain,
( join(meet(X_55,X_56),meet(X_55,Y)) != meet(X_55,join(X_56,Y))
| meet(X_55,join(X_56,meet(Y,X_55))) != join(meet(X_55,X_56),meet(X_55,Y))
| meet(X_55,join(X_56,meet(Y,X_55))) = meet(X_55,join(X_56,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_55,join(X_56,meet(Y,X_55))),join(meet(X_55,X_56),meet(X_55,Y))) ),[1],$fot(meet(X_55,join(X_56,Y)))]]) ).
cnf(refute_0_194,plain,
( meet(X_55,join(X_56,meet(Y,X_55))) != join(meet(X_55,X_56),meet(X_55,Y))
| meet(X_55,join(X_56,meet(Y,X_55))) = meet(X_55,join(X_56,Y)) ),
inference(resolve,[$cnf( $equal(join(meet(X_55,X_56),meet(X_55,Y)),meet(X_55,join(X_56,Y))) )],[refute_0_192,refute_0_193]) ).
cnf(refute_0_195,plain,
meet(X_55,join(X_56,meet(Y,X_55))) = meet(X_55,join(X_56,Y)),
inference(resolve,[$cnf( $equal(meet(X_55,join(X_56,meet(Y,X_55))),join(meet(X_55,X_56),meet(X_55,Y))) )],[refute_0_191,refute_0_194]) ).
cnf(refute_0_196,plain,
meet(X_55,join(X_264,meet(X_262,X_55))) = meet(X_55,join(X_264,X_262)),
inference(subst,[],[refute_0_195:[bind(Y,$fot(X_262)),bind(X_56,$fot(X_264))]]) ).
cnf(refute_0_197,plain,
( meet(X_55,join(X_264,meet(X_262,X_55))) != meet(X_55,join(X_264,X_262))
| meet(X_55,join(X_56,meet(X_55,join(X_264,meet(X_262,X_55))))) != meet(X_55,join(X_56,join(X_264,meet(X_262,X_55))))
| meet(X_55,join(X_56,meet(X_55,join(X_264,X_262)))) = meet(X_55,join(X_56,join(X_264,meet(X_262,X_55)))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_55,join(X_56,meet(X_55,join(X_264,meet(X_262,X_55))))),meet(X_55,join(X_56,join(X_264,meet(X_262,X_55))))) ),[0,1,1],$fot(meet(X_55,join(X_264,X_262)))]]) ).
cnf(refute_0_198,plain,
( meet(X_55,join(X_56,meet(X_55,join(X_264,meet(X_262,X_55))))) != meet(X_55,join(X_56,join(X_264,meet(X_262,X_55))))
| meet(X_55,join(X_56,meet(X_55,join(X_264,X_262)))) = meet(X_55,join(X_56,join(X_264,meet(X_262,X_55)))) ),
inference(resolve,[$cnf( $equal(meet(X_55,join(X_264,meet(X_262,X_55))),meet(X_55,join(X_264,X_262))) )],[refute_0_196,refute_0_197]) ).
cnf(refute_0_199,plain,
meet(X_55,join(X_56,meet(X_55,join(X_264,X_262)))) = meet(X_55,join(X_56,join(X_264,meet(X_262,X_55)))),
inference(resolve,[$cnf( $equal(meet(X_55,join(X_56,meet(X_55,join(X_264,meet(X_262,X_55))))),meet(X_55,join(X_56,join(X_264,meet(X_262,X_55))))) )],[refute_0_186,refute_0_198]) ).
cnf(refute_0_200,plain,
meet(X_55,join(X_56,meet(X_55,join(X_264,X_262)))) = meet(X_55,join(X_56,join(X_264,X_262))),
inference(subst,[],[refute_0_185:[bind(X_27,$fot(join(X_264,X_262)))]]) ).
cnf(refute_0_201,plain,
( meet(X_55,join(X_56,meet(X_55,join(X_264,X_262)))) != meet(X_55,join(X_56,join(X_264,X_262)))
| meet(X_55,join(X_56,meet(X_55,join(X_264,X_262)))) != meet(X_55,join(X_56,join(X_264,meet(X_262,X_55))))
| meet(X_55,join(X_56,join(X_264,X_262))) = meet(X_55,join(X_56,join(X_264,meet(X_262,X_55)))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_55,join(X_56,meet(X_55,join(X_264,X_262)))),meet(X_55,join(X_56,join(X_264,meet(X_262,X_55))))) ),[0],$fot(meet(X_55,join(X_56,join(X_264,X_262))))]]) ).
cnf(refute_0_202,plain,
( meet(X_55,join(X_56,meet(X_55,join(X_264,X_262)))) != meet(X_55,join(X_56,join(X_264,meet(X_262,X_55))))
| meet(X_55,join(X_56,join(X_264,X_262))) = meet(X_55,join(X_56,join(X_264,meet(X_262,X_55)))) ),
inference(resolve,[$cnf( $equal(meet(X_55,join(X_56,meet(X_55,join(X_264,X_262)))),meet(X_55,join(X_56,join(X_264,X_262)))) )],[refute_0_200,refute_0_201]) ).
cnf(refute_0_203,plain,
meet(X_55,join(X_56,join(X_264,X_262))) = meet(X_55,join(X_56,join(X_264,meet(X_262,X_55)))),
inference(resolve,[$cnf( $equal(meet(X_55,join(X_56,meet(X_55,join(X_264,X_262)))),meet(X_55,join(X_56,join(X_264,meet(X_262,X_55))))) )],[refute_0_199,refute_0_202]) ).
cnf(refute_0_204,plain,
( meet(X_55,join(X_56,join(X_264,X_262))) != meet(X_55,join(X_56,join(X_264,meet(X_262,X_55))))
| meet(X_55,join(X_56,join(X_264,meet(X_262,X_55)))) = meet(X_55,join(X_56,join(X_264,X_262))) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(meet(X_55,join(X_56,join(X_264,X_262))))),bind(Y0,$fot(meet(X_55,join(X_56,join(X_264,meet(X_262,X_55))))))]]) ).
cnf(refute_0_205,plain,
meet(X_55,join(X_56,join(X_264,meet(X_262,X_55)))) = meet(X_55,join(X_56,join(X_264,X_262))),
inference(resolve,[$cnf( $equal(meet(X_55,join(X_56,join(X_264,X_262))),meet(X_55,join(X_56,join(X_264,meet(X_262,X_55))))) )],[refute_0_203,refute_0_204]) ).
cnf(refute_0_206,plain,
meet(Y,join(X_328,join(X_46,meet(X_328,Y)))) = meet(Y,join(X_328,join(X_46,X_328))),
inference(subst,[],[refute_0_205:[bind(X_262,$fot(X_328)),bind(X_264,$fot(X_46)),bind(X_55,$fot(Y)),bind(X_56,$fot(X_328))]]) ).
cnf(refute_0_207,plain,
( meet(Y,join(X_328,join(X_46,X_328))) != meet(Y,join(X_328,X_46))
| meet(Y,join(X_328,join(X_46,meet(X_328,Y)))) != meet(Y,join(X_328,join(X_46,X_328)))
| meet(Y,join(X_328,join(X_46,meet(X_328,Y)))) = meet(Y,join(X_328,X_46)) ),
inference(subst,[],[refute_0_110:[bind(X0,$fot(meet(Y,join(X_328,join(X_46,meet(X_328,Y)))))),bind(Y0,$fot(meet(Y,join(X_328,join(X_46,X_328))))),bind(Z0,$fot(meet(Y,join(X_328,X_46))))]]) ).
cnf(refute_0_208,plain,
( meet(Y,join(X_328,join(X_46,X_328))) != meet(Y,join(X_328,X_46))
| meet(Y,join(X_328,join(X_46,meet(X_328,Y)))) = meet(Y,join(X_328,X_46)) ),
inference(resolve,[$cnf( $equal(meet(Y,join(X_328,join(X_46,meet(X_328,Y)))),meet(Y,join(X_328,join(X_46,X_328)))) )],[refute_0_206,refute_0_207]) ).
cnf(refute_0_209,plain,
meet(Y,join(X_328,join(X_46,meet(X_328,Y)))) = meet(Y,join(X_328,X_46)),
inference(resolve,[$cnf( $equal(meet(Y,join(X_328,join(X_46,X_328))),meet(Y,join(X_328,X_46))) )],[refute_0_155,refute_0_208]) ).
cnf(refute_0_210,plain,
join(X_46,meet(Y,join(X_328,join(X_46,meet(X_328,Y))))) = join(X_46,meet(Y,join(X_328,join(X_46,meet(X_328,Y))))),
introduced(tautology,[refl,[$fot(join(X_46,meet(Y,join(X_328,join(X_46,meet(X_328,Y))))))]]) ).
cnf(refute_0_211,plain,
( join(X_46,meet(Y,join(X_328,join(X_46,meet(X_328,Y))))) != join(X_46,meet(Y,join(X_328,join(X_46,meet(X_328,Y)))))
| meet(Y,join(X_328,join(X_46,meet(X_328,Y)))) != meet(Y,join(X_328,X_46))
| join(X_46,meet(Y,join(X_328,join(X_46,meet(X_328,Y))))) = join(X_46,meet(Y,join(X_328,X_46))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_46,meet(Y,join(X_328,join(X_46,meet(X_328,Y))))),join(X_46,meet(Y,join(X_328,join(X_46,meet(X_328,Y)))))) ),[1,1],$fot(meet(Y,join(X_328,X_46)))]]) ).
cnf(refute_0_212,plain,
( meet(Y,join(X_328,join(X_46,meet(X_328,Y)))) != meet(Y,join(X_328,X_46))
| join(X_46,meet(Y,join(X_328,join(X_46,meet(X_328,Y))))) = join(X_46,meet(Y,join(X_328,X_46))) ),
inference(resolve,[$cnf( $equal(join(X_46,meet(Y,join(X_328,join(X_46,meet(X_328,Y))))),join(X_46,meet(Y,join(X_328,join(X_46,meet(X_328,Y)))))) )],[refute_0_210,refute_0_211]) ).
cnf(refute_0_213,plain,
join(X_46,meet(Y,join(X_328,join(X_46,meet(X_328,Y))))) = join(X_46,meet(Y,join(X_328,X_46))),
inference(resolve,[$cnf( $equal(meet(Y,join(X_328,join(X_46,meet(X_328,Y)))),meet(Y,join(X_328,X_46))) )],[refute_0_209,refute_0_212]) ).
cnf(refute_0_214,plain,
( join(X_46,meet(Y,join(X_328,X_46))) != join(X_46,meet(Y,X_328))
| join(X_46,meet(Y,join(X_328,join(X_46,meet(X_328,Y))))) != join(X_46,meet(Y,join(X_328,X_46)))
| join(X_46,meet(Y,join(X_328,join(X_46,meet(X_328,Y))))) = join(X_46,meet(Y,X_328)) ),
inference(subst,[],[refute_0_110:[bind(X0,$fot(join(X_46,meet(Y,join(X_328,join(X_46,meet(X_328,Y))))))),bind(Y0,$fot(join(X_46,meet(Y,join(X_328,X_46))))),bind(Z0,$fot(join(X_46,meet(Y,X_328))))]]) ).
cnf(refute_0_215,plain,
( join(X_46,meet(Y,join(X_328,X_46))) != join(X_46,meet(Y,X_328))
| join(X_46,meet(Y,join(X_328,join(X_46,meet(X_328,Y))))) = join(X_46,meet(Y,X_328)) ),
inference(resolve,[$cnf( $equal(join(X_46,meet(Y,join(X_328,join(X_46,meet(X_328,Y))))),join(X_46,meet(Y,join(X_328,X_46)))) )],[refute_0_213,refute_0_214]) ).
cnf(refute_0_216,plain,
join(X_46,meet(Y,join(X_328,join(X_46,meet(X_328,Y))))) = join(X_46,meet(Y,X_328)),
inference(resolve,[$cnf( $equal(join(X_46,meet(Y,join(X_328,X_46))),join(X_46,meet(Y,X_328))) )],[refute_0_150,refute_0_215]) ).
cnf(refute_0_217,plain,
( join(X_46,meet(Y,join(X_328,join(X_46,meet(X_328,Y))))) != join(X_46,meet(Y,X_328))
| join(X_46,meet(Y,join(X_328,join(X_46,meet(X_328,Y))))) != join(X_46,meet(X_328,Y))
| join(X_46,meet(Y,X_328)) = join(X_46,meet(X_328,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_46,meet(Y,join(X_328,join(X_46,meet(X_328,Y))))),join(X_46,meet(X_328,Y))) ),[0],$fot(join(X_46,meet(Y,X_328)))]]) ).
cnf(refute_0_218,plain,
( join(X_46,meet(Y,join(X_328,join(X_46,meet(X_328,Y))))) != join(X_46,meet(X_328,Y))
| join(X_46,meet(Y,X_328)) = join(X_46,meet(X_328,Y)) ),
inference(resolve,[$cnf( $equal(join(X_46,meet(Y,join(X_328,join(X_46,meet(X_328,Y))))),join(X_46,meet(Y,X_328))) )],[refute_0_216,refute_0_217]) ).
cnf(refute_0_219,plain,
join(X_46,meet(Y,X_328)) = join(X_46,meet(X_328,Y)),
inference(resolve,[$cnf( $equal(join(X_46,meet(Y,join(X_328,join(X_46,meet(X_328,Y))))),join(X_46,meet(X_328,Y))) )],[refute_0_49,refute_0_218]) ).
cnf(refute_0_220,plain,
( join(X_46,meet(Y,X_328)) != join(X_46,meet(X_328,Y))
| join(X_46,meet(X_328,Y)) = join(X_46,meet(Y,X_328)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(join(X_46,meet(Y,X_328)))),bind(Y0,$fot(join(X_46,meet(X_328,Y))))]]) ).
cnf(refute_0_221,plain,
join(X_46,meet(X_328,Y)) = join(X_46,meet(Y,X_328)),
inference(resolve,[$cnf( $equal(join(X_46,meet(Y,X_328)),join(X_46,meet(X_328,Y))) )],[refute_0_219,refute_0_220]) ).
cnf(refute_0_222,plain,
join(a,meet(c,b)) = join(a,meet(b,c)),
inference(subst,[],[refute_0_221:[bind(Y,$fot(b)),bind(X_328,$fot(c)),bind(X_46,$fot(a))]]) ).
cnf(refute_0_223,plain,
meet(join(X_328,Y),join(X_328,X_329)) = join(meet(X_328,join(X_328,Y)),meet(X_329,join(X_328,Y))),
inference(subst,[],[refute_0_43:[bind(X_136,$fot(join(X_328,Y))),bind(X_137,$fot(X_328)),bind(X_138,$fot(X_329))]]) ).
cnf(refute_0_224,plain,
meet(X_328,join(X_328,Y)) = X_328,
inference(subst,[],[absorption1:[bind(X,$fot(X_328))]]) ).
cnf(refute_0_225,plain,
( meet(X_328,join(X_328,Y)) != X_328
| meet(join(X_328,Y),join(X_328,X_329)) != join(meet(X_328,join(X_328,Y)),meet(X_329,join(X_328,Y)))
| meet(join(X_328,Y),join(X_328,X_329)) = join(X_328,meet(X_329,join(X_328,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(X_328,Y),join(X_328,X_329)),join(meet(X_328,join(X_328,Y)),meet(X_329,join(X_328,Y)))) ),[1,0],$fot(X_328)]]) ).
cnf(refute_0_226,plain,
( meet(join(X_328,Y),join(X_328,X_329)) != join(meet(X_328,join(X_328,Y)),meet(X_329,join(X_328,Y)))
| meet(join(X_328,Y),join(X_328,X_329)) = join(X_328,meet(X_329,join(X_328,Y))) ),
inference(resolve,[$cnf( $equal(meet(X_328,join(X_328,Y)),X_328) )],[refute_0_224,refute_0_225]) ).
cnf(refute_0_227,plain,
meet(join(X_328,Y),join(X_328,X_329)) = join(X_328,meet(X_329,join(X_328,Y))),
inference(resolve,[$cnf( $equal(meet(join(X_328,Y),join(X_328,X_329)),join(meet(X_328,join(X_328,Y)),meet(X_329,join(X_328,Y)))) )],[refute_0_223,refute_0_226]) ).
cnf(refute_0_228,plain,
join(X_328,meet(X_329,join(X_328,Y))) = join(X_328,meet(X_329,Y)),
inference(subst,[],[refute_0_19:[bind(Z,$fot(Y)),bind(X_65,$fot(X_329)),bind(X_66,$fot(X_328))]]) ).
cnf(refute_0_229,plain,
( join(X_328,meet(X_329,join(X_328,Y))) != join(X_328,meet(X_329,Y))
| meet(join(X_328,Y),join(X_328,X_329)) != join(X_328,meet(X_329,join(X_328,Y)))
| meet(join(X_328,Y),join(X_328,X_329)) = join(X_328,meet(X_329,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(X_328,Y),join(X_328,X_329)),join(X_328,meet(X_329,join(X_328,Y)))) ),[1],$fot(join(X_328,meet(X_329,Y)))]]) ).
cnf(refute_0_230,plain,
( meet(join(X_328,Y),join(X_328,X_329)) != join(X_328,meet(X_329,join(X_328,Y)))
| meet(join(X_328,Y),join(X_328,X_329)) = join(X_328,meet(X_329,Y)) ),
inference(resolve,[$cnf( $equal(join(X_328,meet(X_329,join(X_328,Y))),join(X_328,meet(X_329,Y))) )],[refute_0_228,refute_0_229]) ).
cnf(refute_0_231,plain,
meet(join(X_328,Y),join(X_328,X_329)) = join(X_328,meet(X_329,Y)),
inference(resolve,[$cnf( $equal(meet(join(X_328,Y),join(X_328,X_329)),join(X_328,meet(X_329,join(X_328,Y)))) )],[refute_0_227,refute_0_230]) ).
cnf(refute_0_232,plain,
meet(join(a,b),join(a,c)) = join(a,meet(c,b)),
inference(subst,[],[refute_0_231:[bind(Y,$fot(b)),bind(X_328,$fot(a)),bind(X_329,$fot(c))]]) ).
cnf(refute_0_233,plain,
( join(a,meet(c,b)) != join(a,meet(b,c))
| meet(join(a,b),join(a,c)) != join(a,meet(c,b))
| meet(join(a,b),join(a,c)) = join(a,meet(b,c)) ),
inference(subst,[],[refute_0_110:[bind(X0,$fot(meet(join(a,b),join(a,c)))),bind(Y0,$fot(join(a,meet(c,b)))),bind(Z0,$fot(join(a,meet(b,c))))]]) ).
cnf(refute_0_234,plain,
( join(a,meet(c,b)) != join(a,meet(b,c))
| meet(join(a,b),join(a,c)) = join(a,meet(b,c)) ),
inference(resolve,[$cnf( $equal(meet(join(a,b),join(a,c)),join(a,meet(c,b))) )],[refute_0_232,refute_0_233]) ).
cnf(refute_0_235,plain,
meet(join(a,b),join(a,c)) = join(a,meet(b,c)),
inference(resolve,[$cnf( $equal(join(a,meet(c,b)),join(a,meet(b,c))) )],[refute_0_222,refute_0_234]) ).
cnf(refute_0_236,plain,
( join(a,meet(b,c)) != join(a,meet(b,c))
| meet(join(a,b),join(a,c)) != join(a,meet(b,c))
| join(a,meet(b,c)) = meet(join(a,b),join(a,c)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(a,meet(b,c)),meet(join(a,b),join(a,c))) ),[1],$fot(join(a,meet(b,c)))]]) ).
cnf(refute_0_237,plain,
( join(a,meet(b,c)) != join(a,meet(b,c))
| join(a,meet(b,c)) = meet(join(a,b),join(a,c)) ),
inference(resolve,[$cnf( $equal(meet(join(a,b),join(a,c)),join(a,meet(b,c))) )],[refute_0_235,refute_0_236]) ).
cnf(refute_0_238,plain,
join(a,meet(b,c)) != join(a,meet(b,c)),
inference(resolve,[$cnf( $equal(join(a,meet(b,c)),meet(join(a,b),join(a,c))) )],[refute_0_237,refute_0_23]) ).
cnf(refute_0_239,plain,
join(a,meet(b,c)) = join(a,meet(b,c)),
introduced(tautology,[refl,[$fot(join(a,meet(b,c)))]]) ).
cnf(refute_0_240,plain,
$false,
inference(resolve,[$cnf( $equal(join(a,meet(b,c)),join(a,meet(b,c))) )],[refute_0_239,refute_0_238]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT042-1 : TPTP v8.1.0. Released v2.5.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 28 19:29:37 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 20.65/20.83 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.65/20.83
% 20.65/20.83 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 20.65/20.86
%------------------------------------------------------------------------------