TSTP Solution File: REL046-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : REL046-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n019.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 19:46:09 EDT 2022
% Result : Unsatisfiable 1.29s 1.44s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 23
% Syntax : Number of clauses : 78 ( 40 unt; 0 nHn; 52 RR)
% Number of literals : 132 ( 131 equ; 57 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 98 ( 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(goals_14,negated_conjecture,
join(sk1,meet(sk2,sk3)) = meet(sk2,sk3) ).
cnf(goals_15,negated_conjecture,
( join(sk1,sk2) != sk2
| join(sk1,sk3) != sk3 ) ).
cnf(refute_0_0,plain,
join(sk1,join(meet(sk2,sk3),X_74)) = join(join(sk1,meet(sk2,sk3)),X_74),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(sk1)),bind(B,$fot(meet(sk2,sk3))),bind(C,$fot(X_74))]]) ).
cnf(refute_0_1,plain,
( join(sk1,join(meet(sk2,sk3),X_74)) != join(join(sk1,meet(sk2,sk3)),X_74)
| join(sk1,meet(sk2,sk3)) != meet(sk2,sk3)
| join(sk1,join(meet(sk2,sk3),X_74)) = join(meet(sk2,sk3),X_74) ),
introduced(tautology,[equality,[$cnf( $equal(join(sk1,join(meet(sk2,sk3),X_74)),join(join(sk1,meet(sk2,sk3)),X_74)) ),[1,0],$fot(meet(sk2,sk3))]]) ).
cnf(refute_0_2,plain,
( join(sk1,join(meet(sk2,sk3),X_74)) != join(join(sk1,meet(sk2,sk3)),X_74)
| join(sk1,join(meet(sk2,sk3),X_74)) = join(meet(sk2,sk3),X_74) ),
inference(resolve,[$cnf( $equal(join(sk1,meet(sk2,sk3)),meet(sk2,sk3)) )],[goals_14,refute_0_1]) ).
cnf(refute_0_3,plain,
join(sk1,join(meet(sk2,sk3),X_74)) = join(meet(sk2,sk3),X_74),
inference(resolve,[$cnf( $equal(join(sk1,join(meet(sk2,sk3),X_74)),join(join(sk1,meet(sk2,sk3)),X_74)) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
join(sk1,join(meet(sk2,sk3),meet(sk3,complement(sk2)))) = join(meet(sk2,sk3),meet(sk3,complement(sk2))),
inference(subst,[],[refute_0_3:[bind(X_74,$fot(meet(sk3,complement(sk2))))]]) ).
cnf(refute_0_5,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_6,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_7,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( join(A,B) != join(B,A)
| join(B,A) = join(A,B) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(A,B))),bind(Y,$fot(join(B,A)))]]) ).
cnf(refute_0_9,plain,
join(B,A) = join(A,B),
inference(resolve,[$cnf( $equal(join(A,B),join(B,A)) )],[maddux1_join_commutativity_1,refute_0_8]) ).
cnf(refute_0_10,plain,
join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),
inference(subst,[],[refute_0_9:[bind(A,$fot(complement(join(complement(A),B)))),bind(B,$fot(complement(join(complement(A),complement(B)))))]]) ).
cnf(refute_0_11,plain,
( A != join(complement(join(complement(A),complement(B))),complement(join(complement(A),B)))
| join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) != join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))
| A = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) ),
introduced(tautology,[equality,[$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_12,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( $equal(join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))),join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
A = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),
inference(resolve,[$cnf( $equal(A,join(complement(join(complement(A),complement(B))),complement(join(complement(A),B)))) )],[maddux3_a_kind_of_de_Morgan_3,refute_0_12]) ).
cnf(refute_0_14,plain,
join(complement(join(complement(A),B)),meet(A,B)) = join(meet(A,B),complement(join(complement(A),B))),
inference(subst,[],[refute_0_9:[bind(A,$fot(meet(A,B))),bind(B,$fot(complement(join(complement(A),B))))]]) ).
cnf(refute_0_15,plain,
( meet(A,B) != complement(join(complement(A),complement(B)))
| complement(join(complement(A),complement(B))) = meet(A,B) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(meet(A,B))),bind(Y,$fot(complement(join(complement(A),complement(B)))))]]) ).
cnf(refute_0_16,plain,
complement(join(complement(A),complement(B))) = meet(A,B),
inference(resolve,[$cnf( $equal(meet(A,B),complement(join(complement(A),complement(B)))) )],[maddux4_definiton_of_meet_4,refute_0_15]) ).
cnf(refute_0_17,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),
introduced(tautology,[refl,[$fot(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))))]]) ).
cnf(refute_0_18,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_19,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( $equal(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(complement(join(complement(A),B)),meet(A,B)),
inference(resolve,[$cnf( $equal(complement(join(complement(A),complement(B))),meet(A,B)) )],[refute_0_16,refute_0_19]) ).
cnf(refute_0_21,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_22,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_7,refute_0_21]) ).
cnf(refute_0_23,plain,
( join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) != join(complement(join(complement(A),B)),meet(A,B))
| join(complement(join(complement(A),B)),meet(A,B)) != join(meet(A,B),complement(join(complement(A),B)))
| join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(meet(A,B),complement(join(complement(A),B))) ),
inference(subst,[],[refute_0_22:[bind(X,$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_24,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( $equal(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),join(complement(join(complement(A),B)),meet(A,B))) )],[refute_0_20,refute_0_23]) ).
cnf(refute_0_25,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(meet(A,B),complement(join(complement(A),B))),
inference(resolve,[$cnf( $equal(join(complement(join(complement(A),B)),meet(A,B)),join(meet(A,B),complement(join(complement(A),B)))) )],[refute_0_14,refute_0_24]) ).
cnf(refute_0_26,plain,
( A != join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))
| join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) != join(meet(A,B),complement(join(complement(A),B)))
| A = join(meet(A,B),complement(join(complement(A),B))) ),
introduced(tautology,[equality,[$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_27,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( $equal(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),join(meet(A,B),complement(join(complement(A),B)))) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
A = join(meet(A,B),complement(join(complement(A),B))),
inference(resolve,[$cnf( $equal(A,join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))) )],[refute_0_13,refute_0_27]) ).
cnf(refute_0_29,plain,
X_40 = join(meet(X_40,X_41),complement(join(complement(X_40),X_41))),
inference(subst,[],[refute_0_28:[bind(A,$fot(X_40)),bind(B,$fot(X_41))]]) ).
cnf(refute_0_30,plain,
join(X_41,complement(X_40)) = join(complement(X_40),X_41),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(X_41)),bind(B,$fot(complement(X_40)))]]) ).
cnf(refute_0_31,plain,
( join(X_41,complement(X_40)) != join(complement(X_40),X_41)
| join(complement(X_40),X_41) = join(X_41,complement(X_40)) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(X_41,complement(X_40)))),bind(Y,$fot(join(complement(X_40),X_41)))]]) ).
cnf(refute_0_32,plain,
join(complement(X_40),X_41) = join(X_41,complement(X_40)),
inference(resolve,[$cnf( $equal(join(X_41,complement(X_40)),join(complement(X_40),X_41)) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
( X_40 != join(meet(X_40,X_41),complement(join(complement(X_40),X_41)))
| join(complement(X_40),X_41) != join(X_41,complement(X_40))
| X_40 = join(meet(X_40,X_41),complement(join(X_41,complement(X_40)))) ),
introduced(tautology,[equality,[$cnf( $equal(X_40,join(meet(X_40,X_41),complement(join(complement(X_40),X_41)))) ),[1,1,0],$fot(join(X_41,complement(X_40)))]]) ).
cnf(refute_0_34,plain,
( X_40 != join(meet(X_40,X_41),complement(join(complement(X_40),X_41)))
| X_40 = join(meet(X_40,X_41),complement(join(X_41,complement(X_40)))) ),
inference(resolve,[$cnf( $equal(join(complement(X_40),X_41),join(X_41,complement(X_40))) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
X_40 = join(meet(X_40,X_41),complement(join(X_41,complement(X_40)))),
inference(resolve,[$cnf( $equal(X_40,join(meet(X_40,X_41),complement(join(complement(X_40),X_41)))) )],[refute_0_29,refute_0_34]) ).
cnf(refute_0_36,plain,
X_59 = join(meet(X_59,complement(A)),complement(join(complement(A),complement(X_59)))),
inference(subst,[],[refute_0_35:[bind(X_40,$fot(X_59)),bind(X_41,$fot(complement(A)))]]) ).
cnf(refute_0_37,plain,
meet(A,X_59) = complement(join(complement(A),complement(X_59))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(B,$fot(X_59))]]) ).
cnf(refute_0_38,plain,
( meet(A,X_59) != complement(join(complement(A),complement(X_59)))
| complement(join(complement(A),complement(X_59))) = meet(A,X_59) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(meet(A,X_59))),bind(Y,$fot(complement(join(complement(A),complement(X_59)))))]]) ).
cnf(refute_0_39,plain,
complement(join(complement(A),complement(X_59))) = meet(A,X_59),
inference(resolve,[$cnf( $equal(meet(A,X_59),complement(join(complement(A),complement(X_59)))) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
( X_59 != join(meet(X_59,complement(A)),complement(join(complement(A),complement(X_59))))
| complement(join(complement(A),complement(X_59))) != meet(A,X_59)
| X_59 = join(meet(X_59,complement(A)),meet(A,X_59)) ),
introduced(tautology,[equality,[$cnf( $equal(X_59,join(meet(X_59,complement(A)),complement(join(complement(A),complement(X_59))))) ),[1,1],$fot(meet(A,X_59))]]) ).
cnf(refute_0_41,plain,
( X_59 != join(meet(X_59,complement(A)),complement(join(complement(A),complement(X_59))))
| X_59 = join(meet(X_59,complement(A)),meet(A,X_59)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),complement(X_59))),meet(A,X_59)) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
X_59 = join(meet(X_59,complement(A)),meet(A,X_59)),
inference(resolve,[$cnf( $equal(X_59,join(meet(X_59,complement(A)),complement(join(complement(A),complement(X_59))))) )],[refute_0_36,refute_0_41]) ).
cnf(refute_0_43,plain,
join(meet(X_59,complement(A)),meet(A,X_59)) = join(meet(A,X_59),meet(X_59,complement(A))),
inference(subst,[],[refute_0_9:[bind(A,$fot(meet(A,X_59))),bind(B,$fot(meet(X_59,complement(A))))]]) ).
cnf(refute_0_44,plain,
( X_59 != join(meet(X_59,complement(A)),meet(A,X_59))
| join(meet(X_59,complement(A)),meet(A,X_59)) != join(meet(A,X_59),meet(X_59,complement(A)))
| X_59 = join(meet(A,X_59),meet(X_59,complement(A))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_59,join(meet(A,X_59),meet(X_59,complement(A)))) ),[0],$fot(join(meet(X_59,complement(A)),meet(A,X_59)))]]) ).
cnf(refute_0_45,plain,
( X_59 != join(meet(X_59,complement(A)),meet(A,X_59))
| X_59 = join(meet(A,X_59),meet(X_59,complement(A))) ),
inference(resolve,[$cnf( $equal(join(meet(X_59,complement(A)),meet(A,X_59)),join(meet(A,X_59),meet(X_59,complement(A)))) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
X_59 = join(meet(A,X_59),meet(X_59,complement(A))),
inference(resolve,[$cnf( $equal(X_59,join(meet(X_59,complement(A)),meet(A,X_59))) )],[refute_0_42,refute_0_45]) ).
cnf(refute_0_47,plain,
sk3 = join(meet(sk2,sk3),meet(sk3,complement(sk2))),
inference(subst,[],[refute_0_46:[bind(A,$fot(sk2)),bind(X_59,$fot(sk3))]]) ).
cnf(refute_0_48,plain,
( sk3 != join(meet(sk2,sk3),meet(sk3,complement(sk2)))
| join(meet(sk2,sk3),meet(sk3,complement(sk2))) = sk3 ),
inference(subst,[],[refute_0_7:[bind(X,$fot(sk3)),bind(Y,$fot(join(meet(sk2,sk3),meet(sk3,complement(sk2)))))]]) ).
cnf(refute_0_49,plain,
join(meet(sk2,sk3),meet(sk3,complement(sk2))) = sk3,
inference(resolve,[$cnf( $equal(sk3,join(meet(sk2,sk3),meet(sk3,complement(sk2)))) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
( join(meet(sk2,sk3),meet(sk3,complement(sk2))) != sk3
| join(sk1,join(meet(sk2,sk3),meet(sk3,complement(sk2)))) != join(meet(sk2,sk3),meet(sk3,complement(sk2)))
| join(sk1,sk3) = join(meet(sk2,sk3),meet(sk3,complement(sk2))) ),
introduced(tautology,[equality,[$cnf( $equal(join(sk1,join(meet(sk2,sk3),meet(sk3,complement(sk2)))),join(meet(sk2,sk3),meet(sk3,complement(sk2)))) ),[0,1],$fot(sk3)]]) ).
cnf(refute_0_51,plain,
( join(sk1,join(meet(sk2,sk3),meet(sk3,complement(sk2)))) != join(meet(sk2,sk3),meet(sk3,complement(sk2)))
| join(sk1,sk3) = join(meet(sk2,sk3),meet(sk3,complement(sk2))) ),
inference(resolve,[$cnf( $equal(join(meet(sk2,sk3),meet(sk3,complement(sk2))),sk3) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
join(sk1,sk3) = join(meet(sk2,sk3),meet(sk3,complement(sk2))),
inference(resolve,[$cnf( $equal(join(sk1,join(meet(sk2,sk3),meet(sk3,complement(sk2)))),join(meet(sk2,sk3),meet(sk3,complement(sk2)))) )],[refute_0_4,refute_0_51]) ).
cnf(refute_0_53,plain,
( join(meet(sk2,sk3),meet(sk3,complement(sk2))) != sk3
| join(sk1,sk3) != join(meet(sk2,sk3),meet(sk3,complement(sk2)))
| join(sk1,sk3) = sk3 ),
introduced(tautology,[equality,[$cnf( $equal(join(sk1,sk3),join(meet(sk2,sk3),meet(sk3,complement(sk2)))) ),[1],$fot(sk3)]]) ).
cnf(refute_0_54,plain,
( join(sk1,sk3) != join(meet(sk2,sk3),meet(sk3,complement(sk2)))
| join(sk1,sk3) = sk3 ),
inference(resolve,[$cnf( $equal(join(meet(sk2,sk3),meet(sk3,complement(sk2))),sk3) )],[refute_0_49,refute_0_53]) ).
cnf(refute_0_55,plain,
join(sk1,sk3) = sk3,
inference(resolve,[$cnf( $equal(join(sk1,sk3),join(meet(sk2,sk3),meet(sk3,complement(sk2)))) )],[refute_0_52,refute_0_54]) ).
cnf(refute_0_56,plain,
join(sk1,join(meet(sk2,sk3),complement(join(complement(sk2),sk3)))) = join(meet(sk2,sk3),complement(join(complement(sk2),sk3))),
inference(subst,[],[refute_0_3:[bind(X_74,$fot(complement(join(complement(sk2),sk3))))]]) ).
cnf(refute_0_57,plain,
sk2 = join(meet(sk2,sk3),complement(join(complement(sk2),sk3))),
inference(subst,[],[refute_0_28:[bind(A,$fot(sk2)),bind(B,$fot(sk3))]]) ).
cnf(refute_0_58,plain,
( sk2 != join(meet(sk2,sk3),complement(join(complement(sk2),sk3)))
| join(meet(sk2,sk3),complement(join(complement(sk2),sk3))) = sk2 ),
inference(subst,[],[refute_0_7:[bind(X,$fot(sk2)),bind(Y,$fot(join(meet(sk2,sk3),complement(join(complement(sk2),sk3)))))]]) ).
cnf(refute_0_59,plain,
join(meet(sk2,sk3),complement(join(complement(sk2),sk3))) = sk2,
inference(resolve,[$cnf( $equal(sk2,join(meet(sk2,sk3),complement(join(complement(sk2),sk3)))) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
( join(meet(sk2,sk3),complement(join(complement(sk2),sk3))) != sk2
| join(sk1,join(meet(sk2,sk3),complement(join(complement(sk2),sk3)))) != join(meet(sk2,sk3),complement(join(complement(sk2),sk3)))
| join(sk1,sk2) = join(meet(sk2,sk3),complement(join(complement(sk2),sk3))) ),
introduced(tautology,[equality,[$cnf( $equal(join(sk1,join(meet(sk2,sk3),complement(join(complement(sk2),sk3)))),join(meet(sk2,sk3),complement(join(complement(sk2),sk3)))) ),[0,1],$fot(sk2)]]) ).
cnf(refute_0_61,plain,
( join(sk1,join(meet(sk2,sk3),complement(join(complement(sk2),sk3)))) != join(meet(sk2,sk3),complement(join(complement(sk2),sk3)))
| join(sk1,sk2) = join(meet(sk2,sk3),complement(join(complement(sk2),sk3))) ),
inference(resolve,[$cnf( $equal(join(meet(sk2,sk3),complement(join(complement(sk2),sk3))),sk2) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
join(sk1,sk2) = join(meet(sk2,sk3),complement(join(complement(sk2),sk3))),
inference(resolve,[$cnf( $equal(join(sk1,join(meet(sk2,sk3),complement(join(complement(sk2),sk3)))),join(meet(sk2,sk3),complement(join(complement(sk2),sk3)))) )],[refute_0_56,refute_0_61]) ).
cnf(refute_0_63,plain,
( join(meet(sk2,sk3),complement(join(complement(sk2),sk3))) != sk2
| join(sk1,sk2) != join(meet(sk2,sk3),complement(join(complement(sk2),sk3)))
| join(sk1,sk2) = sk2 ),
introduced(tautology,[equality,[$cnf( $equal(join(sk1,sk2),join(meet(sk2,sk3),complement(join(complement(sk2),sk3)))) ),[1],$fot(sk2)]]) ).
cnf(refute_0_64,plain,
( join(sk1,sk2) != join(meet(sk2,sk3),complement(join(complement(sk2),sk3)))
| join(sk1,sk2) = sk2 ),
inference(resolve,[$cnf( $equal(join(meet(sk2,sk3),complement(join(complement(sk2),sk3))),sk2) )],[refute_0_59,refute_0_63]) ).
cnf(refute_0_65,plain,
join(sk1,sk2) = sk2,
inference(resolve,[$cnf( $equal(join(sk1,sk2),join(meet(sk2,sk3),complement(join(complement(sk2),sk3)))) )],[refute_0_62,refute_0_64]) ).
cnf(refute_0_66,plain,
( join(sk1,sk2) != sk2
| sk2 != sk2
| join(sk1,sk2) = sk2 ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(sk1,sk2),sk2) ),[0],$fot(sk2)]]) ).
cnf(refute_0_67,plain,
( sk2 != sk2
| join(sk1,sk2) = sk2 ),
inference(resolve,[$cnf( $equal(join(sk1,sk2),sk2) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
( join(sk1,sk3) != sk3
| sk2 != sk2 ),
inference(resolve,[$cnf( $equal(join(sk1,sk2),sk2) )],[refute_0_67,goals_15]) ).
cnf(refute_0_69,plain,
sk2 = sk2,
introduced(tautology,[refl,[$fot(sk2)]]) ).
cnf(refute_0_70,plain,
join(sk1,sk3) != sk3,
inference(resolve,[$cnf( $equal(sk2,sk2) )],[refute_0_69,refute_0_68]) ).
cnf(refute_0_71,plain,
$false,
inference(resolve,[$cnf( $equal(join(sk1,sk3),sk3) )],[refute_0_55,refute_0_70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : REL046-1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n019.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Fri Jul 8 12:29:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.29/1.44 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.29/1.44
% 1.29/1.44 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.29/1.45
%------------------------------------------------------------------------------