TSTP Solution File: REL001-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : REL001-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 19:42:55 EDT 2022
% Result : Unsatisfiable 0.41s 0.58s
% Output : CNFRefutation 0.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 58
% Syntax : Number of clauses : 221 ( 117 unt; 0 nHn; 121 RR)
% Number of literals : 370 ( 369 equ; 152 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 : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 270 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(maddux1_join_commutativity_1,axiom,
join(A,B) = join(B,A) ).
cnf(maddux2_join_associativity_2,axiom,
join(A,join(B,C)) = join(join(A,B),C) ).
cnf(maddux3_a_kind_of_de_Morgan_3,axiom,
A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) ).
cnf(maddux4_definiton_of_meet_4,axiom,
meet(A,B) = complement(join(complement(A),complement(B))) ).
cnf(composition_identity_6,axiom,
composition(A,one) = A ).
cnf(composition_distributivity_7,axiom,
composition(join(A,B),C) = join(composition(A,C),composition(B,C)) ).
cnf(converse_idempotence_8,axiom,
converse(converse(A)) = A ).
cnf(converse_multiplicativity_10,axiom,
converse(composition(A,B)) = composition(converse(B),converse(A)) ).
cnf(converse_cancellativity_11,axiom,
join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B) ).
cnf(def_top_12,axiom,
top = join(A,complement(A)) ).
cnf(def_zero_13,axiom,
zero = meet(A,complement(A)) ).
cnf(goals_14,negated_conjecture,
join(zero,sk1) != sk1 ).
cnf(refute_0_0,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_1,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_2,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( join(A,B) != join(B,A)
| join(B,A) = join(A,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(A,B))),bind(Y,$fot(join(B,A)))]]) ).
cnf(refute_0_4,plain,
join(B,A) = join(A,B),
inference(resolve,[$cnf( $equal(join(A,B),join(B,A)) )],[maddux1_join_commutativity_1,refute_0_3]) ).
cnf(refute_0_5,plain,
join(zero,sk1) = join(sk1,zero),
inference(subst,[],[refute_0_4:[bind(A,$fot(sk1)),bind(B,$fot(zero))]]) ).
cnf(refute_0_6,plain,
( join(sk1,zero) != sk1
| join(zero,sk1) != join(sk1,zero)
| join(zero,sk1) = sk1 ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,sk1),join(sk1,zero)) ),[1],$fot(sk1)]]) ).
cnf(refute_0_7,plain,
( join(sk1,zero) != sk1
| join(zero,sk1) = sk1 ),
inference(resolve,[$cnf( $equal(join(zero,sk1),join(sk1,zero)) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
join(sk1,zero) != sk1,
inference(resolve,[$cnf( $equal(join(zero,sk1),sk1) )],[refute_0_7,goals_14]) ).
cnf(refute_0_9,plain,
join(zero,join(zero,C)) = join(join(zero,zero),C),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(zero)),bind(B,$fot(zero))]]) ).
cnf(refute_0_10,plain,
composition(join(X_32,one),X_34) = join(composition(X_32,X_34),composition(one,X_34)),
inference(subst,[],[composition_distributivity_7:[bind(A,$fot(X_32)),bind(B,$fot(one)),bind(C,$fot(X_34))]]) ).
cnf(refute_0_11,plain,
converse(composition(converse(A),X_7)) = composition(converse(X_7),converse(converse(A))),
inference(subst,[],[converse_multiplicativity_10:[bind(A,$fot(converse(A))),bind(B,$fot(X_7))]]) ).
cnf(refute_0_12,plain,
( converse(composition(converse(A),X_7)) != composition(converse(X_7),converse(converse(A)))
| converse(converse(A)) != A
| converse(composition(converse(A),X_7)) = composition(converse(X_7),A) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(A),X_7)),composition(converse(X_7),converse(converse(A)))) ),[1,1],$fot(A)]]) ).
cnf(refute_0_13,plain,
( converse(composition(converse(A),X_7)) != composition(converse(X_7),converse(converse(A)))
| converse(composition(converse(A),X_7)) = composition(converse(X_7),A) ),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_12]) ).
cnf(refute_0_14,plain,
converse(composition(converse(A),X_7)) = composition(converse(X_7),A),
inference(resolve,[$cnf( $equal(converse(composition(converse(A),X_7)),composition(converse(X_7),converse(converse(A)))) )],[refute_0_11,refute_0_13]) ).
cnf(refute_0_15,plain,
converse(composition(converse(X_13),one)) = composition(converse(one),X_13),
inference(subst,[],[refute_0_14:[bind(A,$fot(X_13)),bind(X_7,$fot(one))]]) ).
cnf(refute_0_16,plain,
composition(converse(X_13),one) = converse(X_13),
inference(subst,[],[composition_identity_6:[bind(A,$fot(converse(X_13)))]]) ).
cnf(refute_0_17,plain,
( composition(converse(X_13),one) != converse(X_13)
| converse(composition(converse(X_13),one)) != composition(converse(one),X_13)
| converse(converse(X_13)) = composition(converse(one),X_13) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(X_13),one)),composition(converse(one),X_13)) ),[0,0],$fot(converse(X_13))]]) ).
cnf(refute_0_18,plain,
( converse(composition(converse(X_13),one)) != composition(converse(one),X_13)
| converse(converse(X_13)) = composition(converse(one),X_13) ),
inference(resolve,[$cnf( $equal(composition(converse(X_13),one),converse(X_13)) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
converse(converse(X_13)) = composition(converse(one),X_13),
inference(resolve,[$cnf( $equal(converse(composition(converse(X_13),one)),composition(converse(one),X_13)) )],[refute_0_15,refute_0_18]) ).
cnf(refute_0_20,plain,
converse(converse(X_13)) = X_13,
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(X_13))]]) ).
cnf(refute_0_21,plain,
( converse(converse(X_13)) != X_13
| converse(converse(X_13)) != composition(converse(one),X_13)
| X_13 = composition(converse(one),X_13) ),
introduced(tautology,[equality,[$cnf( $equal(converse(converse(X_13)),composition(converse(one),X_13)) ),[0],$fot(X_13)]]) ).
cnf(refute_0_22,plain,
( converse(converse(X_13)) != composition(converse(one),X_13)
| X_13 = composition(converse(one),X_13) ),
inference(resolve,[$cnf( $equal(converse(converse(X_13)),X_13) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
X_13 = composition(converse(one),X_13),
inference(resolve,[$cnf( $equal(converse(converse(X_13)),composition(converse(one),X_13)) )],[refute_0_19,refute_0_22]) ).
cnf(refute_0_24,plain,
composition(converse(one),one) = converse(one),
inference(subst,[],[composition_identity_6:[bind(A,$fot(converse(one)))]]) ).
cnf(refute_0_25,plain,
one = composition(converse(one),one),
inference(subst,[],[refute_0_23:[bind(X_13,$fot(one))]]) ).
cnf(refute_0_26,plain,
( one != composition(converse(one),one)
| composition(converse(one),one) = one ),
inference(subst,[],[refute_0_2:[bind(X,$fot(one)),bind(Y,$fot(composition(converse(one),one)))]]) ).
cnf(refute_0_27,plain,
composition(converse(one),one) = one,
inference(resolve,[$cnf( $equal(one,composition(converse(one),one)) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
( composition(converse(one),one) != converse(one)
| composition(converse(one),one) != one
| one = converse(one) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(one),one),converse(one)) ),[0],$fot(one)]]) ).
cnf(refute_0_29,plain,
( composition(converse(one),one) != converse(one)
| one = converse(one) ),
inference(resolve,[$cnf( $equal(composition(converse(one),one),one) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
one = converse(one),
inference(resolve,[$cnf( $equal(composition(converse(one),one),converse(one)) )],[refute_0_24,refute_0_29]) ).
cnf(refute_0_31,plain,
( one != converse(one)
| converse(one) = one ),
inference(subst,[],[refute_0_2:[bind(X,$fot(one)),bind(Y,$fot(converse(one)))]]) ).
cnf(refute_0_32,plain,
converse(one) = one,
inference(resolve,[$cnf( $equal(one,converse(one)) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
composition(converse(one),X_13) = composition(converse(one),X_13),
introduced(tautology,[refl,[$fot(composition(converse(one),X_13))]]) ).
cnf(refute_0_34,plain,
( composition(converse(one),X_13) != composition(converse(one),X_13)
| converse(one) != one
| composition(converse(one),X_13) = composition(one,X_13) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(one),X_13),composition(converse(one),X_13)) ),[1,0],$fot(one)]]) ).
cnf(refute_0_35,plain,
( converse(one) != one
| composition(converse(one),X_13) = composition(one,X_13) ),
inference(resolve,[$cnf( $equal(composition(converse(one),X_13),composition(converse(one),X_13)) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
composition(converse(one),X_13) = composition(one,X_13),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_32,refute_0_35]) ).
cnf(refute_0_37,plain,
( X_13 != composition(converse(one),X_13)
| composition(converse(one),X_13) != composition(one,X_13)
| X_13 = composition(one,X_13) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_13,composition(one,X_13)) ),[0],$fot(composition(converse(one),X_13))]]) ).
cnf(refute_0_38,plain,
( X_13 != composition(converse(one),X_13)
| X_13 = composition(one,X_13) ),
inference(resolve,[$cnf( $equal(composition(converse(one),X_13),composition(one,X_13)) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
X_13 = composition(one,X_13),
inference(resolve,[$cnf( $equal(X_13,composition(converse(one),X_13)) )],[refute_0_23,refute_0_38]) ).
cnf(refute_0_40,plain,
X_34 = composition(one,X_34),
inference(subst,[],[refute_0_39:[bind(X_13,$fot(X_34))]]) ).
cnf(refute_0_41,plain,
( X_34 != composition(one,X_34)
| composition(one,X_34) = X_34 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_34)),bind(Y,$fot(composition(one,X_34)))]]) ).
cnf(refute_0_42,plain,
composition(one,X_34) = X_34,
inference(resolve,[$cnf( $equal(X_34,composition(one,X_34)) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
( composition(join(X_32,one),X_34) != join(composition(X_32,X_34),composition(one,X_34))
| composition(one,X_34) != X_34
| composition(join(X_32,one),X_34) = join(composition(X_32,X_34),X_34) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(X_32,one),X_34),join(composition(X_32,X_34),composition(one,X_34))) ),[1,1],$fot(X_34)]]) ).
cnf(refute_0_44,plain,
( composition(join(X_32,one),X_34) != join(composition(X_32,X_34),composition(one,X_34))
| composition(join(X_32,one),X_34) = join(composition(X_32,X_34),X_34) ),
inference(resolve,[$cnf( $equal(composition(one,X_34),X_34) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
composition(join(X_32,one),X_34) = join(composition(X_32,X_34),X_34),
inference(resolve,[$cnf( $equal(composition(join(X_32,one),X_34),join(composition(X_32,X_34),composition(one,X_34))) )],[refute_0_10,refute_0_44]) ).
cnf(refute_0_46,plain,
join(composition(X_32,X_34),X_34) = join(X_34,composition(X_32,X_34)),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_34)),bind(B,$fot(composition(X_32,X_34)))]]) ).
cnf(refute_0_47,plain,
( composition(join(X_32,one),X_34) != join(composition(X_32,X_34),X_34)
| join(composition(X_32,X_34),X_34) != join(X_34,composition(X_32,X_34))
| composition(join(X_32,one),X_34) = join(X_34,composition(X_32,X_34)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(join(X_32,one),X_34),join(X_34,composition(X_32,X_34))) ),[0],$fot(join(composition(X_32,X_34),X_34))]]) ).
cnf(refute_0_48,plain,
( composition(join(X_32,one),X_34) != join(composition(X_32,X_34),X_34)
| composition(join(X_32,one),X_34) = join(X_34,composition(X_32,X_34)) ),
inference(resolve,[$cnf( $equal(join(composition(X_32,X_34),X_34),join(X_34,composition(X_32,X_34))) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
composition(join(X_32,one),X_34) = join(X_34,composition(X_32,X_34)),
inference(resolve,[$cnf( $equal(composition(join(X_32,one),X_34),join(composition(X_32,X_34),X_34)) )],[refute_0_45,refute_0_48]) ).
cnf(refute_0_50,plain,
composition(join(one,one),X_36) = join(X_36,composition(one,X_36)),
inference(subst,[],[refute_0_49:[bind(X_32,$fot(one)),bind(X_34,$fot(X_36))]]) ).
cnf(refute_0_51,plain,
X_36 = composition(one,X_36),
inference(subst,[],[refute_0_39:[bind(X_13,$fot(X_36))]]) ).
cnf(refute_0_52,plain,
( X_36 != composition(one,X_36)
| composition(one,X_36) = X_36 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_36)),bind(Y,$fot(composition(one,X_36)))]]) ).
cnf(refute_0_53,plain,
composition(one,X_36) = X_36,
inference(resolve,[$cnf( $equal(X_36,composition(one,X_36)) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
( composition(join(one,one),X_36) != join(X_36,composition(one,X_36))
| composition(one,X_36) != X_36
| composition(join(one,one),X_36) = join(X_36,X_36) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,one),X_36),join(X_36,composition(one,X_36))) ),[1,1],$fot(X_36)]]) ).
cnf(refute_0_55,plain,
( composition(join(one,one),X_36) != join(X_36,composition(one,X_36))
| composition(join(one,one),X_36) = join(X_36,X_36) ),
inference(resolve,[$cnf( $equal(composition(one,X_36),X_36) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
composition(join(one,one),X_36) = join(X_36,X_36),
inference(resolve,[$cnf( $equal(composition(join(one,one),X_36),join(X_36,composition(one,X_36))) )],[refute_0_50,refute_0_55]) ).
cnf(refute_0_57,plain,
composition(join(one,one),complement(X_48)) = join(complement(X_48),complement(X_48)),
inference(subst,[],[refute_0_56:[bind(X_36,$fot(complement(X_48)))]]) ).
cnf(refute_0_58,plain,
join(composition(converse(A),complement(composition(A,B))),complement(B)) = join(complement(B),composition(converse(A),complement(composition(A,B)))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(B))),bind(B,$fot(composition(converse(A),complement(composition(A,B)))))]]) ).
cnf(refute_0_59,plain,
( join(composition(converse(A),complement(composition(A,B))),complement(B)) != complement(B)
| join(composition(converse(A),complement(composition(A,B))),complement(B)) != join(complement(B),composition(converse(A),complement(composition(A,B))))
| join(complement(B),composition(converse(A),complement(composition(A,B)))) = complement(B) ),
introduced(tautology,[equality,[$cnf( $equal(join(composition(converse(A),complement(composition(A,B))),complement(B)),complement(B)) ),[0],$fot(join(complement(B),composition(converse(A),complement(composition(A,B)))))]]) ).
cnf(refute_0_60,plain,
( join(composition(converse(A),complement(composition(A,B))),complement(B)) != complement(B)
| join(complement(B),composition(converse(A),complement(composition(A,B)))) = complement(B) ),
inference(resolve,[$cnf( $equal(join(composition(converse(A),complement(composition(A,B))),complement(B)),join(complement(B),composition(converse(A),complement(composition(A,B))))) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
join(complement(B),composition(converse(A),complement(composition(A,B)))) = complement(B),
inference(resolve,[$cnf( $equal(join(composition(converse(A),complement(composition(A,B))),complement(B)),complement(B)) )],[converse_cancellativity_11,refute_0_60]) ).
cnf(refute_0_62,plain,
join(complement(X_47),composition(converse(one),complement(composition(one,X_47)))) = complement(X_47),
inference(subst,[],[refute_0_61:[bind(A,$fot(one)),bind(B,$fot(X_47))]]) ).
cnf(refute_0_63,plain,
( converse(one) != one
| join(complement(X_47),composition(converse(one),complement(composition(one,X_47)))) != complement(X_47)
| join(complement(X_47),composition(one,complement(composition(one,X_47)))) = complement(X_47) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_47),composition(converse(one),complement(composition(one,X_47)))),complement(X_47)) ),[0,1,0],$fot(one)]]) ).
cnf(refute_0_64,plain,
( join(complement(X_47),composition(converse(one),complement(composition(one,X_47)))) != complement(X_47)
| join(complement(X_47),composition(one,complement(composition(one,X_47)))) = complement(X_47) ),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_32,refute_0_63]) ).
cnf(refute_0_65,plain,
join(complement(X_47),composition(one,complement(composition(one,X_47)))) = complement(X_47),
inference(resolve,[$cnf( $equal(join(complement(X_47),composition(converse(one),complement(composition(one,X_47)))),complement(X_47)) )],[refute_0_62,refute_0_64]) ).
cnf(refute_0_66,plain,
( X_13 != composition(one,X_13)
| composition(one,X_13) = X_13 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_13)),bind(Y,$fot(composition(one,X_13)))]]) ).
cnf(refute_0_67,plain,
composition(one,X_13) = X_13,
inference(resolve,[$cnf( $equal(X_13,composition(one,X_13)) )],[refute_0_39,refute_0_66]) ).
cnf(refute_0_68,plain,
composition(one,X_47) = X_47,
inference(subst,[],[refute_0_67:[bind(X_13,$fot(X_47))]]) ).
cnf(refute_0_69,plain,
complement(composition(one,X_47)) = complement(composition(one,X_47)),
introduced(tautology,[refl,[$fot(complement(composition(one,X_47)))]]) ).
cnf(refute_0_70,plain,
( complement(composition(one,X_47)) != complement(composition(one,X_47))
| composition(one,X_47) != X_47
| complement(composition(one,X_47)) = complement(X_47) ),
introduced(tautology,[equality,[$cnf( $equal(complement(composition(one,X_47)),complement(composition(one,X_47))) ),[1,0],$fot(X_47)]]) ).
cnf(refute_0_71,plain,
( composition(one,X_47) != X_47
| complement(composition(one,X_47)) = complement(X_47) ),
inference(resolve,[$cnf( $equal(complement(composition(one,X_47)),complement(composition(one,X_47))) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
complement(composition(one,X_47)) = complement(X_47),
inference(resolve,[$cnf( $equal(composition(one,X_47),X_47) )],[refute_0_68,refute_0_71]) ).
cnf(refute_0_73,plain,
composition(one,complement(composition(one,X_47))) = complement(composition(one,X_47)),
inference(subst,[],[refute_0_67:[bind(X_13,$fot(complement(composition(one,X_47))))]]) ).
cnf(refute_0_74,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_75,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_2,refute_0_74]) ).
cnf(refute_0_76,plain,
( complement(composition(one,X_47)) != complement(X_47)
| composition(one,complement(composition(one,X_47))) != complement(composition(one,X_47))
| composition(one,complement(composition(one,X_47))) = complement(X_47) ),
inference(subst,[],[refute_0_75:[bind(X,$fot(composition(one,complement(composition(one,X_47))))),bind(Y,$fot(complement(composition(one,X_47)))),bind(Z,$fot(complement(X_47)))]]) ).
cnf(refute_0_77,plain,
( complement(composition(one,X_47)) != complement(X_47)
| composition(one,complement(composition(one,X_47))) = complement(X_47) ),
inference(resolve,[$cnf( $equal(composition(one,complement(composition(one,X_47))),complement(composition(one,X_47))) )],[refute_0_73,refute_0_76]) ).
cnf(refute_0_78,plain,
composition(one,complement(composition(one,X_47))) = complement(X_47),
inference(resolve,[$cnf( $equal(complement(composition(one,X_47)),complement(X_47)) )],[refute_0_72,refute_0_77]) ).
cnf(refute_0_79,plain,
join(complement(X_47),composition(one,complement(composition(one,X_47)))) = join(complement(X_47),composition(one,complement(composition(one,X_47)))),
introduced(tautology,[refl,[$fot(join(complement(X_47),composition(one,complement(composition(one,X_47)))))]]) ).
cnf(refute_0_80,plain,
( composition(one,complement(composition(one,X_47))) != complement(X_47)
| join(complement(X_47),composition(one,complement(composition(one,X_47)))) != join(complement(X_47),composition(one,complement(composition(one,X_47))))
| join(complement(X_47),composition(one,complement(composition(one,X_47)))) = join(complement(X_47),complement(X_47)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_47),composition(one,complement(composition(one,X_47)))),join(complement(X_47),composition(one,complement(composition(one,X_47))))) ),[1,1],$fot(complement(X_47))]]) ).
cnf(refute_0_81,plain,
( composition(one,complement(composition(one,X_47))) != complement(X_47)
| join(complement(X_47),composition(one,complement(composition(one,X_47)))) = join(complement(X_47),complement(X_47)) ),
inference(resolve,[$cnf( $equal(join(complement(X_47),composition(one,complement(composition(one,X_47)))),join(complement(X_47),composition(one,complement(composition(one,X_47))))) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
join(complement(X_47),composition(one,complement(composition(one,X_47)))) = join(complement(X_47),complement(X_47)),
inference(resolve,[$cnf( $equal(composition(one,complement(composition(one,X_47))),complement(X_47)) )],[refute_0_78,refute_0_81]) ).
cnf(refute_0_83,plain,
( join(complement(X_47),composition(one,complement(composition(one,X_47)))) != complement(X_47)
| join(complement(X_47),composition(one,complement(composition(one,X_47)))) != join(complement(X_47),complement(X_47))
| join(complement(X_47),complement(X_47)) = complement(X_47) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_47),composition(one,complement(composition(one,X_47)))),complement(X_47)) ),[0],$fot(join(complement(X_47),complement(X_47)))]]) ).
cnf(refute_0_84,plain,
( join(complement(X_47),composition(one,complement(composition(one,X_47)))) != complement(X_47)
| join(complement(X_47),complement(X_47)) = complement(X_47) ),
inference(resolve,[$cnf( $equal(join(complement(X_47),composition(one,complement(composition(one,X_47)))),join(complement(X_47),complement(X_47))) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
join(complement(X_47),complement(X_47)) = complement(X_47),
inference(resolve,[$cnf( $equal(join(complement(X_47),composition(one,complement(composition(one,X_47)))),complement(X_47)) )],[refute_0_65,refute_0_84]) ).
cnf(refute_0_86,plain,
join(complement(X_48),complement(X_48)) = complement(X_48),
inference(subst,[],[refute_0_85:[bind(X_47,$fot(X_48))]]) ).
cnf(refute_0_87,plain,
( composition(join(one,one),complement(X_48)) != join(complement(X_48),complement(X_48))
| join(complement(X_48),complement(X_48)) != complement(X_48)
| composition(join(one,one),complement(X_48)) = complement(X_48) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(join(one,one),complement(X_48)),complement(X_48)) ),[0],$fot(join(complement(X_48),complement(X_48)))]]) ).
cnf(refute_0_88,plain,
( composition(join(one,one),complement(X_48)) != join(complement(X_48),complement(X_48))
| composition(join(one,one),complement(X_48)) = complement(X_48) ),
inference(resolve,[$cnf( $equal(join(complement(X_48),complement(X_48)),complement(X_48)) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
composition(join(one,one),complement(X_48)) = complement(X_48),
inference(resolve,[$cnf( $equal(composition(join(one,one),complement(X_48)),join(complement(X_48),complement(X_48))) )],[refute_0_57,refute_0_88]) ).
cnf(refute_0_90,plain,
composition(join(one,one),complement(top)) = complement(top),
inference(subst,[],[refute_0_89:[bind(X_48,$fot(top))]]) ).
cnf(refute_0_91,plain,
zero = meet(join(complement(X_54),complement(X_55)),complement(join(complement(X_54),complement(X_55)))),
inference(subst,[],[def_zero_13:[bind(A,$fot(join(complement(X_54),complement(X_55))))]]) ).
cnf(refute_0_92,plain,
meet(X_54,X_55) = complement(join(complement(X_54),complement(X_55))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(X_54)),bind(B,$fot(X_55))]]) ).
cnf(refute_0_93,plain,
( meet(X_54,X_55) != complement(join(complement(X_54),complement(X_55)))
| complement(join(complement(X_54),complement(X_55))) = meet(X_54,X_55) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(X_54,X_55))),bind(Y,$fot(complement(join(complement(X_54),complement(X_55)))))]]) ).
cnf(refute_0_94,plain,
complement(join(complement(X_54),complement(X_55))) = meet(X_54,X_55),
inference(resolve,[$cnf( $equal(meet(X_54,X_55),complement(join(complement(X_54),complement(X_55)))) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
( complement(join(complement(X_54),complement(X_55))) != meet(X_54,X_55)
| zero != meet(join(complement(X_54),complement(X_55)),complement(join(complement(X_54),complement(X_55))))
| zero = meet(join(complement(X_54),complement(X_55)),meet(X_54,X_55)) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(join(complement(X_54),complement(X_55)),complement(join(complement(X_54),complement(X_55))))) ),[1,1],$fot(meet(X_54,X_55))]]) ).
cnf(refute_0_96,plain,
( zero != meet(join(complement(X_54),complement(X_55)),complement(join(complement(X_54),complement(X_55))))
| zero = meet(join(complement(X_54),complement(X_55)),meet(X_54,X_55)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_54),complement(X_55))),meet(X_54,X_55)) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
zero = meet(join(complement(X_54),complement(X_55)),meet(X_54,X_55)),
inference(resolve,[$cnf( $equal(zero,meet(join(complement(X_54),complement(X_55)),complement(join(complement(X_54),complement(X_55))))) )],[refute_0_91,refute_0_96]) ).
cnf(refute_0_98,plain,
( top != join(A,complement(A))
| join(A,complement(A)) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(A,complement(A))))]]) ).
cnf(refute_0_99,plain,
join(A,complement(A)) = top,
inference(resolve,[$cnf( $equal(top,join(A,complement(A))) )],[def_top_12,refute_0_98]) ).
cnf(refute_0_100,plain,
join(meet(X_54,X_55),complement(meet(X_54,X_55))) = top,
inference(subst,[],[refute_0_99:[bind(A,$fot(meet(X_54,X_55)))]]) ).
cnf(refute_0_101,plain,
complement(join(meet(X_54,X_55),complement(meet(X_54,X_55)))) = complement(join(meet(X_54,X_55),complement(meet(X_54,X_55)))),
introduced(tautology,[refl,[$fot(complement(join(meet(X_54,X_55),complement(meet(X_54,X_55)))))]]) ).
cnf(refute_0_102,plain,
( complement(join(meet(X_54,X_55),complement(meet(X_54,X_55)))) != complement(join(meet(X_54,X_55),complement(meet(X_54,X_55))))
| join(meet(X_54,X_55),complement(meet(X_54,X_55))) != top
| complement(join(meet(X_54,X_55),complement(meet(X_54,X_55)))) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(meet(X_54,X_55),complement(meet(X_54,X_55)))),complement(join(meet(X_54,X_55),complement(meet(X_54,X_55))))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_103,plain,
( join(meet(X_54,X_55),complement(meet(X_54,X_55))) != top
| complement(join(meet(X_54,X_55),complement(meet(X_54,X_55)))) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(join(meet(X_54,X_55),complement(meet(X_54,X_55)))),complement(join(meet(X_54,X_55),complement(meet(X_54,X_55))))) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
complement(join(meet(X_54,X_55),complement(meet(X_54,X_55)))) = complement(top),
inference(resolve,[$cnf( $equal(join(meet(X_54,X_55),complement(meet(X_54,X_55))),top) )],[refute_0_100,refute_0_103]) ).
cnf(refute_0_105,plain,
meet(join(complement(X_54),complement(X_55)),B) = complement(join(complement(join(complement(X_54),complement(X_55))),complement(B))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(join(complement(X_54),complement(X_55))))]]) ).
cnf(refute_0_106,plain,
( complement(join(complement(X_54),complement(X_55))) != meet(X_54,X_55)
| meet(join(complement(X_54),complement(X_55)),B) != complement(join(complement(join(complement(X_54),complement(X_55))),complement(B)))
| meet(join(complement(X_54),complement(X_55)),B) = complement(join(meet(X_54,X_55),complement(B))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(complement(X_54),complement(X_55)),B),complement(join(complement(join(complement(X_54),complement(X_55))),complement(B)))) ),[1,0,0],$fot(meet(X_54,X_55))]]) ).
cnf(refute_0_107,plain,
( meet(join(complement(X_54),complement(X_55)),B) != complement(join(complement(join(complement(X_54),complement(X_55))),complement(B)))
| meet(join(complement(X_54),complement(X_55)),B) = complement(join(meet(X_54,X_55),complement(B))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_54),complement(X_55))),meet(X_54,X_55)) )],[refute_0_94,refute_0_106]) ).
cnf(refute_0_108,plain,
meet(join(complement(X_54),complement(X_55)),B) = complement(join(meet(X_54,X_55),complement(B))),
inference(resolve,[$cnf( $equal(meet(join(complement(X_54),complement(X_55)),B),complement(join(complement(join(complement(X_54),complement(X_55))),complement(B)))) )],[refute_0_105,refute_0_107]) ).
cnf(refute_0_109,plain,
meet(join(complement(X_54),complement(X_55)),meet(X_54,X_55)) = complement(join(meet(X_54,X_55),complement(meet(X_54,X_55)))),
inference(subst,[],[refute_0_108:[bind(B,$fot(meet(X_54,X_55)))]]) ).
cnf(refute_0_110,plain,
( complement(join(meet(X_54,X_55),complement(meet(X_54,X_55)))) != complement(top)
| meet(join(complement(X_54),complement(X_55)),meet(X_54,X_55)) != complement(join(meet(X_54,X_55),complement(meet(X_54,X_55))))
| meet(join(complement(X_54),complement(X_55)),meet(X_54,X_55)) = complement(top) ),
inference(subst,[],[refute_0_75:[bind(X,$fot(meet(join(complement(X_54),complement(X_55)),meet(X_54,X_55)))),bind(Y,$fot(complement(join(meet(X_54,X_55),complement(meet(X_54,X_55)))))),bind(Z,$fot(complement(top)))]]) ).
cnf(refute_0_111,plain,
( complement(join(meet(X_54,X_55),complement(meet(X_54,X_55)))) != complement(top)
| meet(join(complement(X_54),complement(X_55)),meet(X_54,X_55)) = complement(top) ),
inference(resolve,[$cnf( $equal(meet(join(complement(X_54),complement(X_55)),meet(X_54,X_55)),complement(join(meet(X_54,X_55),complement(meet(X_54,X_55))))) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
meet(join(complement(X_54),complement(X_55)),meet(X_54,X_55)) = complement(top),
inference(resolve,[$cnf( $equal(complement(join(meet(X_54,X_55),complement(meet(X_54,X_55)))),complement(top)) )],[refute_0_104,refute_0_111]) ).
cnf(refute_0_113,plain,
( meet(join(complement(X_54),complement(X_55)),meet(X_54,X_55)) != complement(top)
| zero != meet(join(complement(X_54),complement(X_55)),meet(X_54,X_55))
| zero = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(join(complement(X_54),complement(X_55)),meet(X_54,X_55))) ),[1],$fot(complement(top))]]) ).
cnf(refute_0_114,plain,
( zero != meet(join(complement(X_54),complement(X_55)),meet(X_54,X_55))
| zero = complement(top) ),
inference(resolve,[$cnf( $equal(meet(join(complement(X_54),complement(X_55)),meet(X_54,X_55)),complement(top)) )],[refute_0_112,refute_0_113]) ).
cnf(refute_0_115,plain,
zero = complement(top),
inference(resolve,[$cnf( $equal(zero,meet(join(complement(X_54),complement(X_55)),meet(X_54,X_55))) )],[refute_0_97,refute_0_114]) ).
cnf(refute_0_116,plain,
( zero != complement(top)
| complement(top) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(complement(top)))]]) ).
cnf(refute_0_117,plain,
complement(top) = zero,
inference(resolve,[$cnf( $equal(zero,complement(top)) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
( complement(top) != zero
| composition(join(one,one),complement(top)) != complement(top)
| composition(join(one,one),zero) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,one),complement(top)),complement(top)) ),[0,1],$fot(zero)]]) ).
cnf(refute_0_119,plain,
( composition(join(one,one),complement(top)) != complement(top)
| composition(join(one,one),zero) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_117,refute_0_118]) ).
cnf(refute_0_120,plain,
composition(join(one,one),zero) = complement(top),
inference(resolve,[$cnf( $equal(composition(join(one,one),complement(top)),complement(top)) )],[refute_0_90,refute_0_119]) ).
cnf(refute_0_121,plain,
composition(join(one,one),zero) = join(zero,zero),
inference(subst,[],[refute_0_56:[bind(X_36,$fot(zero))]]) ).
cnf(refute_0_122,plain,
( composition(join(one,one),zero) != complement(top)
| composition(join(one,one),zero) != join(zero,zero)
| join(zero,zero) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,one),zero),complement(top)) ),[0],$fot(join(zero,zero))]]) ).
cnf(refute_0_123,plain,
( composition(join(one,one),zero) != complement(top)
| join(zero,zero) = complement(top) ),
inference(resolve,[$cnf( $equal(composition(join(one,one),zero),join(zero,zero)) )],[refute_0_121,refute_0_122]) ).
cnf(refute_0_124,plain,
( complement(top) != zero
| join(zero,zero) != complement(top)
| join(zero,zero) = zero ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,zero),complement(top)) ),[1],$fot(zero)]]) ).
cnf(refute_0_125,plain,
( join(zero,zero) != complement(top)
| join(zero,zero) = zero ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_117,refute_0_124]) ).
cnf(refute_0_126,plain,
( composition(join(one,one),zero) != complement(top)
| join(zero,zero) = zero ),
inference(resolve,[$cnf( $equal(join(zero,zero),complement(top)) )],[refute_0_123,refute_0_125]) ).
cnf(refute_0_127,plain,
join(zero,zero) = zero,
inference(resolve,[$cnf( $equal(composition(join(one,one),zero),complement(top)) )],[refute_0_120,refute_0_126]) ).
cnf(refute_0_128,plain,
( join(zero,join(zero,C)) != join(join(zero,zero),C)
| join(zero,zero) != zero
| join(zero,join(zero,C)) = join(zero,C) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(zero,C)),join(join(zero,zero),C)) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_129,plain,
( join(zero,join(zero,C)) != join(join(zero,zero),C)
| join(zero,join(zero,C)) = join(zero,C) ),
inference(resolve,[$cnf( $equal(join(zero,zero),zero) )],[refute_0_127,refute_0_128]) ).
cnf(refute_0_130,plain,
join(zero,join(zero,C)) = join(zero,C),
inference(resolve,[$cnf( $equal(join(zero,join(zero,C)),join(join(zero,zero),C)) )],[refute_0_9,refute_0_129]) ).
cnf(refute_0_131,plain,
join(zero,join(zero,X_65)) = join(zero,X_65),
inference(subst,[],[refute_0_130:[bind(C,$fot(X_65))]]) ).
cnf(refute_0_132,plain,
join(X_65,zero) = join(zero,X_65),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(X_65)),bind(B,$fot(zero))]]) ).
cnf(refute_0_133,plain,
( join(X_65,zero) != join(zero,X_65)
| join(zero,X_65) = join(X_65,zero) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_65,zero))),bind(Y,$fot(join(zero,X_65)))]]) ).
cnf(refute_0_134,plain,
join(zero,X_65) = join(X_65,zero),
inference(resolve,[$cnf( $equal(join(X_65,zero),join(zero,X_65)) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
( join(zero,X_65) != join(X_65,zero)
| join(zero,join(zero,X_65)) != join(zero,X_65)
| join(zero,join(zero,X_65)) = join(X_65,zero) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(zero,X_65)),join(zero,X_65)) ),[1],$fot(join(X_65,zero))]]) ).
cnf(refute_0_136,plain,
( join(zero,join(zero,X_65)) != join(zero,X_65)
| join(zero,join(zero,X_65)) = join(X_65,zero) ),
inference(resolve,[$cnf( $equal(join(zero,X_65),join(X_65,zero)) )],[refute_0_134,refute_0_135]) ).
cnf(refute_0_137,plain,
join(zero,join(zero,X_65)) = join(X_65,zero),
inference(resolve,[$cnf( $equal(join(zero,join(zero,X_65)),join(zero,X_65)) )],[refute_0_131,refute_0_136]) ).
cnf(refute_0_138,plain,
join(zero,join(zero,complement(complement(X_21)))) = join(zero,complement(complement(X_21))),
inference(subst,[],[refute_0_130:[bind(C,$fot(complement(complement(X_21))))]]) ).
cnf(refute_0_139,plain,
join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(join(complement(A),B)))),bind(B,$fot(complement(join(complement(A),complement(B)))))]]) ).
cnf(refute_0_140,plain,
( A != join(complement(join(complement(A),complement(B))),complement(join(complement(A),B)))
| join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) != join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))
| A = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(A,join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))) ),[0],$fot(join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))))]]) ).
cnf(refute_0_141,plain,
( A != join(complement(join(complement(A),complement(B))),complement(join(complement(A),B)))
| A = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) ),
inference(resolve,[$cnf( $equal(join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))),join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))) )],[refute_0_139,refute_0_140]) ).
cnf(refute_0_142,plain,
A = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),
inference(resolve,[$cnf( $equal(A,join(complement(join(complement(A),complement(B))),complement(join(complement(A),B)))) )],[maddux3_a_kind_of_de_Morgan_3,refute_0_141]) ).
cnf(refute_0_143,plain,
join(complement(join(complement(A),B)),meet(A,B)) = join(meet(A,B),complement(join(complement(A),B))),
inference(subst,[],[refute_0_4:[bind(A,$fot(meet(A,B))),bind(B,$fot(complement(join(complement(A),B))))]]) ).
cnf(refute_0_144,plain,
( meet(A,B) != complement(join(complement(A),complement(B)))
| complement(join(complement(A),complement(B))) = meet(A,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(A,B))),bind(Y,$fot(complement(join(complement(A),complement(B)))))]]) ).
cnf(refute_0_145,plain,
complement(join(complement(A),complement(B))) = meet(A,B),
inference(resolve,[$cnf( $equal(meet(A,B),complement(join(complement(A),complement(B)))) )],[maddux4_definiton_of_meet_4,refute_0_144]) ).
cnf(refute_0_146,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),
introduced(tautology,[refl,[$fot(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))))]]) ).
cnf(refute_0_147,plain,
( complement(join(complement(A),complement(B))) != meet(A,B)
| join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) != join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))
| join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(complement(join(complement(A),B)),meet(A,B)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))) ),[1,1],$fot(meet(A,B))]]) ).
cnf(refute_0_148,plain,
( complement(join(complement(A),complement(B))) != meet(A,B)
| join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(complement(join(complement(A),B)),meet(A,B)) ),
inference(resolve,[$cnf( $equal(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))) )],[refute_0_146,refute_0_147]) ).
cnf(refute_0_149,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(complement(join(complement(A),B)),meet(A,B)),
inference(resolve,[$cnf( $equal(complement(join(complement(A),complement(B))),meet(A,B)) )],[refute_0_145,refute_0_148]) ).
cnf(refute_0_150,plain,
( join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) != join(complement(join(complement(A),B)),meet(A,B))
| join(complement(join(complement(A),B)),meet(A,B)) != join(meet(A,B),complement(join(complement(A),B)))
| join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(meet(A,B),complement(join(complement(A),B))) ),
inference(subst,[],[refute_0_75:[bind(X,$fot(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))))),bind(Y,$fot(join(complement(join(complement(A),B)),meet(A,B)))),bind(Z,$fot(join(meet(A,B),complement(join(complement(A),B)))))]]) ).
cnf(refute_0_151,plain,
( join(complement(join(complement(A),B)),meet(A,B)) != join(meet(A,B),complement(join(complement(A),B)))
| join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(meet(A,B),complement(join(complement(A),B))) ),
inference(resolve,[$cnf( $equal(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),join(complement(join(complement(A),B)),meet(A,B))) )],[refute_0_149,refute_0_150]) ).
cnf(refute_0_152,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(meet(A,B),complement(join(complement(A),B))),
inference(resolve,[$cnf( $equal(join(complement(join(complement(A),B)),meet(A,B)),join(meet(A,B),complement(join(complement(A),B)))) )],[refute_0_143,refute_0_151]) ).
cnf(refute_0_153,plain,
( A != join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))
| join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) != join(meet(A,B),complement(join(complement(A),B)))
| A = join(meet(A,B),complement(join(complement(A),B))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(A,join(meet(A,B),complement(join(complement(A),B)))) ),[0],$fot(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))))]]) ).
cnf(refute_0_154,plain,
( A != join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))
| A = join(meet(A,B),complement(join(complement(A),B))) ),
inference(resolve,[$cnf( $equal(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),join(meet(A,B),complement(join(complement(A),B)))) )],[refute_0_152,refute_0_153]) ).
cnf(refute_0_155,plain,
A = join(meet(A,B),complement(join(complement(A),B))),
inference(resolve,[$cnf( $equal(A,join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))) )],[refute_0_142,refute_0_154]) ).
cnf(refute_0_156,plain,
X_21 = join(meet(X_21,X_22),complement(join(complement(X_21),X_22))),
inference(subst,[],[refute_0_155:[bind(A,$fot(X_21)),bind(B,$fot(X_22))]]) ).
cnf(refute_0_157,plain,
join(X_22,complement(X_21)) = join(complement(X_21),X_22),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(X_22)),bind(B,$fot(complement(X_21)))]]) ).
cnf(refute_0_158,plain,
( join(X_22,complement(X_21)) != join(complement(X_21),X_22)
| join(complement(X_21),X_22) = join(X_22,complement(X_21)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_22,complement(X_21)))),bind(Y,$fot(join(complement(X_21),X_22)))]]) ).
cnf(refute_0_159,plain,
join(complement(X_21),X_22) = join(X_22,complement(X_21)),
inference(resolve,[$cnf( $equal(join(X_22,complement(X_21)),join(complement(X_21),X_22)) )],[refute_0_157,refute_0_158]) ).
cnf(refute_0_160,plain,
( X_21 != join(meet(X_21,X_22),complement(join(complement(X_21),X_22)))
| join(complement(X_21),X_22) != join(X_22,complement(X_21))
| X_21 = join(meet(X_21,X_22),complement(join(X_22,complement(X_21)))) ),
introduced(tautology,[equality,[$cnf( $equal(X_21,join(meet(X_21,X_22),complement(join(complement(X_21),X_22)))) ),[1,1,0],$fot(join(X_22,complement(X_21)))]]) ).
cnf(refute_0_161,plain,
( X_21 != join(meet(X_21,X_22),complement(join(complement(X_21),X_22)))
| X_21 = join(meet(X_21,X_22),complement(join(X_22,complement(X_21)))) ),
inference(resolve,[$cnf( $equal(join(complement(X_21),X_22),join(X_22,complement(X_21))) )],[refute_0_159,refute_0_160]) ).
cnf(refute_0_162,plain,
X_21 = join(meet(X_21,X_22),complement(join(X_22,complement(X_21)))),
inference(resolve,[$cnf( $equal(X_21,join(meet(X_21,X_22),complement(join(complement(X_21),X_22)))) )],[refute_0_156,refute_0_161]) ).
cnf(refute_0_163,plain,
X_21 = join(meet(X_21,complement(X_21)),complement(join(complement(X_21),complement(X_21)))),
inference(subst,[],[refute_0_162:[bind(X_22,$fot(complement(X_21)))]]) ).
cnf(refute_0_164,plain,
join(complement(X_21),complement(X_21)) = complement(X_21),
inference(subst,[],[refute_0_85:[bind(X_47,$fot(X_21))]]) ).
cnf(refute_0_165,plain,
( X_21 != join(meet(X_21,complement(X_21)),complement(join(complement(X_21),complement(X_21))))
| join(complement(X_21),complement(X_21)) != complement(X_21)
| X_21 = join(meet(X_21,complement(X_21)),complement(complement(X_21))) ),
introduced(tautology,[equality,[$cnf( $equal(X_21,join(meet(X_21,complement(X_21)),complement(join(complement(X_21),complement(X_21))))) ),[1,1,0],$fot(complement(X_21))]]) ).
cnf(refute_0_166,plain,
( X_21 != join(meet(X_21,complement(X_21)),complement(join(complement(X_21),complement(X_21))))
| X_21 = join(meet(X_21,complement(X_21)),complement(complement(X_21))) ),
inference(resolve,[$cnf( $equal(join(complement(X_21),complement(X_21)),complement(X_21)) )],[refute_0_164,refute_0_165]) ).
cnf(refute_0_167,plain,
X_21 = join(meet(X_21,complement(X_21)),complement(complement(X_21))),
inference(resolve,[$cnf( $equal(X_21,join(meet(X_21,complement(X_21)),complement(join(complement(X_21),complement(X_21))))) )],[refute_0_163,refute_0_166]) ).
cnf(refute_0_168,plain,
join(complement(complement(X_21)),zero) = join(zero,complement(complement(X_21))),
inference(subst,[],[refute_0_4:[bind(A,$fot(zero)),bind(B,$fot(complement(complement(X_21))))]]) ).
cnf(refute_0_169,plain,
( zero != meet(A,complement(A))
| meet(A,complement(A)) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(meet(A,complement(A))))]]) ).
cnf(refute_0_170,plain,
meet(A,complement(A)) = zero,
inference(resolve,[$cnf( $equal(zero,meet(A,complement(A))) )],[def_zero_13,refute_0_169]) ).
cnf(refute_0_171,plain,
meet(X_21,complement(X_21)) = zero,
inference(subst,[],[refute_0_170:[bind(A,$fot(X_21))]]) ).
cnf(refute_0_172,plain,
join(complement(complement(X_21)),meet(X_21,complement(X_21))) = join(complement(complement(X_21)),meet(X_21,complement(X_21))),
introduced(tautology,[refl,[$fot(join(complement(complement(X_21)),meet(X_21,complement(X_21))))]]) ).
cnf(refute_0_173,plain,
( join(complement(complement(X_21)),meet(X_21,complement(X_21))) != join(complement(complement(X_21)),meet(X_21,complement(X_21)))
| meet(X_21,complement(X_21)) != zero
| join(complement(complement(X_21)),meet(X_21,complement(X_21))) = join(complement(complement(X_21)),zero) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(complement(X_21)),meet(X_21,complement(X_21))),join(complement(complement(X_21)),meet(X_21,complement(X_21)))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_174,plain,
( meet(X_21,complement(X_21)) != zero
| join(complement(complement(X_21)),meet(X_21,complement(X_21))) = join(complement(complement(X_21)),zero) ),
inference(resolve,[$cnf( $equal(join(complement(complement(X_21)),meet(X_21,complement(X_21))),join(complement(complement(X_21)),meet(X_21,complement(X_21)))) )],[refute_0_172,refute_0_173]) ).
cnf(refute_0_175,plain,
join(complement(complement(X_21)),meet(X_21,complement(X_21))) = join(complement(complement(X_21)),zero),
inference(resolve,[$cnf( $equal(meet(X_21,complement(X_21)),zero) )],[refute_0_171,refute_0_174]) ).
cnf(refute_0_176,plain,
( join(complement(complement(X_21)),meet(X_21,complement(X_21))) != join(complement(complement(X_21)),zero)
| join(complement(complement(X_21)),zero) != join(zero,complement(complement(X_21)))
| join(complement(complement(X_21)),meet(X_21,complement(X_21))) = join(zero,complement(complement(X_21))) ),
inference(subst,[],[refute_0_75:[bind(X,$fot(join(complement(complement(X_21)),meet(X_21,complement(X_21))))),bind(Y,$fot(join(complement(complement(X_21)),zero))),bind(Z,$fot(join(zero,complement(complement(X_21)))))]]) ).
cnf(refute_0_177,plain,
( join(complement(complement(X_21)),zero) != join(zero,complement(complement(X_21)))
| join(complement(complement(X_21)),meet(X_21,complement(X_21))) = join(zero,complement(complement(X_21))) ),
inference(resolve,[$cnf( $equal(join(complement(complement(X_21)),meet(X_21,complement(X_21))),join(complement(complement(X_21)),zero)) )],[refute_0_175,refute_0_176]) ).
cnf(refute_0_178,plain,
join(complement(complement(X_21)),meet(X_21,complement(X_21))) = join(zero,complement(complement(X_21))),
inference(resolve,[$cnf( $equal(join(complement(complement(X_21)),zero),join(zero,complement(complement(X_21)))) )],[refute_0_168,refute_0_177]) ).
cnf(refute_0_179,plain,
join(meet(X_21,complement(X_21)),complement(complement(X_21))) = join(complement(complement(X_21)),meet(X_21,complement(X_21))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(complement(X_21)))),bind(B,$fot(meet(X_21,complement(X_21))))]]) ).
cnf(refute_0_180,plain,
( join(complement(complement(X_21)),meet(X_21,complement(X_21))) != join(zero,complement(complement(X_21)))
| join(meet(X_21,complement(X_21)),complement(complement(X_21))) != join(complement(complement(X_21)),meet(X_21,complement(X_21)))
| join(meet(X_21,complement(X_21)),complement(complement(X_21))) = join(zero,complement(complement(X_21))) ),
inference(subst,[],[refute_0_75:[bind(X,$fot(join(meet(X_21,complement(X_21)),complement(complement(X_21))))),bind(Y,$fot(join(complement(complement(X_21)),meet(X_21,complement(X_21))))),bind(Z,$fot(join(zero,complement(complement(X_21)))))]]) ).
cnf(refute_0_181,plain,
( join(complement(complement(X_21)),meet(X_21,complement(X_21))) != join(zero,complement(complement(X_21)))
| join(meet(X_21,complement(X_21)),complement(complement(X_21))) = join(zero,complement(complement(X_21))) ),
inference(resolve,[$cnf( $equal(join(meet(X_21,complement(X_21)),complement(complement(X_21))),join(complement(complement(X_21)),meet(X_21,complement(X_21)))) )],[refute_0_179,refute_0_180]) ).
cnf(refute_0_182,plain,
join(meet(X_21,complement(X_21)),complement(complement(X_21))) = join(zero,complement(complement(X_21))),
inference(resolve,[$cnf( $equal(join(complement(complement(X_21)),meet(X_21,complement(X_21))),join(zero,complement(complement(X_21)))) )],[refute_0_178,refute_0_181]) ).
cnf(refute_0_183,plain,
( X_21 != join(meet(X_21,complement(X_21)),complement(complement(X_21)))
| join(meet(X_21,complement(X_21)),complement(complement(X_21))) != join(zero,complement(complement(X_21)))
| X_21 = join(zero,complement(complement(X_21))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_21,join(zero,complement(complement(X_21)))) ),[0],$fot(join(meet(X_21,complement(X_21)),complement(complement(X_21))))]]) ).
cnf(refute_0_184,plain,
( X_21 != join(meet(X_21,complement(X_21)),complement(complement(X_21)))
| X_21 = join(zero,complement(complement(X_21))) ),
inference(resolve,[$cnf( $equal(join(meet(X_21,complement(X_21)),complement(complement(X_21))),join(zero,complement(complement(X_21)))) )],[refute_0_182,refute_0_183]) ).
cnf(refute_0_185,plain,
X_21 = join(zero,complement(complement(X_21))),
inference(resolve,[$cnf( $equal(X_21,join(meet(X_21,complement(X_21)),complement(complement(X_21)))) )],[refute_0_167,refute_0_184]) ).
cnf(refute_0_186,plain,
( X_21 != join(zero,complement(complement(X_21)))
| join(zero,complement(complement(X_21))) = X_21 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_21)),bind(Y,$fot(join(zero,complement(complement(X_21)))))]]) ).
cnf(refute_0_187,plain,
join(zero,complement(complement(X_21))) = X_21,
inference(resolve,[$cnf( $equal(X_21,join(zero,complement(complement(X_21)))) )],[refute_0_185,refute_0_186]) ).
cnf(refute_0_188,plain,
( join(zero,complement(complement(X_21))) != X_21
| join(zero,join(zero,complement(complement(X_21)))) != join(zero,complement(complement(X_21)))
| join(zero,X_21) = join(zero,complement(complement(X_21))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(zero,complement(complement(X_21)))),join(zero,complement(complement(X_21)))) ),[0,1],$fot(X_21)]]) ).
cnf(refute_0_189,plain,
( join(zero,join(zero,complement(complement(X_21)))) != join(zero,complement(complement(X_21)))
| join(zero,X_21) = join(zero,complement(complement(X_21))) ),
inference(resolve,[$cnf( $equal(join(zero,complement(complement(X_21))),X_21) )],[refute_0_187,refute_0_188]) ).
cnf(refute_0_190,plain,
join(zero,X_21) = join(zero,complement(complement(X_21))),
inference(resolve,[$cnf( $equal(join(zero,join(zero,complement(complement(X_21)))),join(zero,complement(complement(X_21)))) )],[refute_0_138,refute_0_189]) ).
cnf(refute_0_191,plain,
( join(zero,X_21) != join(zero,complement(complement(X_21)))
| join(zero,complement(complement(X_21))) != X_21
| join(zero,X_21) = X_21 ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(zero,X_21),X_21) ),[0],$fot(join(zero,complement(complement(X_21))))]]) ).
cnf(refute_0_192,plain,
( join(zero,X_21) != join(zero,complement(complement(X_21)))
| join(zero,X_21) = X_21 ),
inference(resolve,[$cnf( $equal(join(zero,complement(complement(X_21))),X_21) )],[refute_0_187,refute_0_191]) ).
cnf(refute_0_193,plain,
join(zero,X_21) = X_21,
inference(resolve,[$cnf( $equal(join(zero,X_21),join(zero,complement(complement(X_21)))) )],[refute_0_190,refute_0_192]) ).
cnf(refute_0_194,plain,
join(zero,X_65) = X_65,
inference(subst,[],[refute_0_193:[bind(X_21,$fot(X_65))]]) ).
cnf(refute_0_195,plain,
( join(zero,X_65) != X_65
| join(zero,join(zero,X_65)) != join(zero,X_65)
| join(zero,join(zero,X_65)) = X_65 ),
inference(subst,[],[refute_0_75:[bind(X,$fot(join(zero,join(zero,X_65)))),bind(Y,$fot(join(zero,X_65))),bind(Z,$fot(X_65))]]) ).
cnf(refute_0_196,plain,
( join(zero,X_65) != X_65
| join(zero,join(zero,X_65)) = X_65 ),
inference(resolve,[$cnf( $equal(join(zero,join(zero,X_65)),join(zero,X_65)) )],[refute_0_131,refute_0_195]) ).
cnf(refute_0_197,plain,
join(zero,join(zero,X_65)) = X_65,
inference(resolve,[$cnf( $equal(join(zero,X_65),X_65) )],[refute_0_194,refute_0_196]) ).
cnf(refute_0_198,plain,
( join(zero,join(zero,X_65)) != X_65
| join(zero,join(zero,X_65)) != join(X_65,zero)
| X_65 = join(X_65,zero) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(zero,X_65)),join(X_65,zero)) ),[0],$fot(X_65)]]) ).
cnf(refute_0_199,plain,
( join(zero,join(zero,X_65)) != join(X_65,zero)
| X_65 = join(X_65,zero) ),
inference(resolve,[$cnf( $equal(join(zero,join(zero,X_65)),X_65) )],[refute_0_197,refute_0_198]) ).
cnf(refute_0_200,plain,
X_65 = join(X_65,zero),
inference(resolve,[$cnf( $equal(join(zero,join(zero,X_65)),join(X_65,zero)) )],[refute_0_137,refute_0_199]) ).
cnf(refute_0_201,plain,
( X_65 != join(X_65,zero)
| join(X_65,zero) = X_65 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_65)),bind(Y,$fot(join(X_65,zero)))]]) ).
cnf(refute_0_202,plain,
join(X_65,zero) = X_65,
inference(resolve,[$cnf( $equal(X_65,join(X_65,zero)) )],[refute_0_200,refute_0_201]) ).
cnf(refute_0_203,plain,
join(sk1,zero) = sk1,
inference(subst,[],[refute_0_202:[bind(X_65,$fot(sk1))]]) ).
cnf(refute_0_204,plain,
( join(sk1,zero) != sk1
| sk1 != sk1
| join(sk1,zero) = sk1 ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(sk1,zero),sk1) ),[0],$fot(sk1)]]) ).
cnf(refute_0_205,plain,
( sk1 != sk1
| join(sk1,zero) = sk1 ),
inference(resolve,[$cnf( $equal(join(sk1,zero),sk1) )],[refute_0_203,refute_0_204]) ).
cnf(refute_0_206,plain,
sk1 != sk1,
inference(resolve,[$cnf( $equal(join(sk1,zero),sk1) )],[refute_0_205,refute_0_8]) ).
cnf(refute_0_207,plain,
sk1 = sk1,
introduced(tautology,[refl,[$fot(sk1)]]) ).
cnf(refute_0_208,plain,
$false,
inference(resolve,[$cnf( $equal(sk1,sk1) )],[refute_0_207,refute_0_206]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : REL001-1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n010.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Fri Jul 8 08:50:31 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.41/0.58 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.41/0.58
% 0.41/0.58 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.43/0.60
%------------------------------------------------------------------------------