%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LAT009-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:47:41 AM UTC 2026
% Result : Unsatisfiable 250.11s 45.54s
% Output : CNFRefutation 250.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 61
% Number of leaves : 10
% Syntax : Number of clauses : 266 ( 266 unt; 0 nHn; 7 RR)
% Number of literals : 266 ( 265 equ; 6 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 755 ( 53 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(distributivity_dual,axiom,
join(meet(join(meet(X0,X1),X2),X1),meet(X2,X0)) = meet(join(meet(join(X0,X1),X2),X1),join(X2,X0)) ).
cnf(prove_distributivity,negated_conjecture,
join(a,meet(b,c)) != meet(join(a,b),join(a,c)) ).
cnf(idempotence_of_meet,axiom,
meet(X0,X0) = X0 ).
cnf(idempotence_of_join,axiom,
join(X0,X0) = X0 ).
cnf(absorption1,axiom,
meet(X0,join(X0,X1)) = X0 ).
cnf(absorption2,axiom,
join(X0,meet(X0,X1)) = X0 ).
cnf(commutativity_of_meet,axiom,
meet(X0,X1) = meet(X1,X0) ).
cnf(commutativity_of_join,axiom,
join(X0,X1) = join(X1,X0) ).
cnf(associativity_of_meet,axiom,
meet(meet(X0,X1),X2) = meet(X0,meet(X1,X2)) ).
cnf(associativity_of_join,axiom,
join(join(X0,X1),X2) = join(X0,join(X1,X2)) ).
cnf(c0,plain,
join(meet(join(meet(X0,X1),X2),X1),meet(X2,X0)) = meet(join(meet(join(X0,X1),X2),X1),join(X2,X0)),
inference(clausification,[status(esa)],[distributivity_dual]) ).
cnf(c1,plain,
join(a,meet(b,c)) != meet(join(a,b),join(a,c)),
inference(clausification,[status(esa)],[prove_distributivity]) ).
cnf(c2,plain,
meet(X0,X0) = X0,
inference(clausification,[status(esa)],[idempotence_of_meet]) ).
cnf(c3,plain,
join(X0,X0) = X0,
inference(clausification,[status(esa)],[idempotence_of_join]) ).
cnf(c4,plain,
meet(X0,join(X0,X1)) = X0,
inference(clausification,[status(esa)],[absorption1]) ).
cnf(c5,plain,
join(X0,meet(X0,X1)) = X0,
inference(clausification,[status(esa)],[absorption2]) ).
cnf(c6,plain,
meet(X0,X1) = meet(X1,X0),
inference(clausification,[status(esa)],[commutativity_of_meet]) ).
cnf(c7,plain,
join(X0,X1) = join(X1,X0),
inference(clausification,[status(esa)],[commutativity_of_join]) ).
cnf(c8,plain,
meet(meet(X0,X1),X2) = meet(X0,meet(X1,X2)),
inference(clausification,[status(esa)],[associativity_of_meet]) ).
cnf(c9,plain,
join(join(X0,X1),X2) = join(X0,join(X1,X2)),
inference(clausification,[status(esa)],[associativity_of_join]) ).
cnf(d0,plain,
join(X0,meet(X1,X0)) = X0,
inference(superposition,[status(thm)],[c6,c5]) ).
cnf(d1,plain,
join(X2,meet(X0,meet(X1,X2))) = X2,
inference(superposition,[status(thm)],[c8,d0]) ).
cnf(d2,plain,
join(X0,X1) = join(X0,join(X1,meet(X2,meet(X3,join(X0,X1))))),
inference(superposition,[status(thm)],[d1,c9]) ).
cnf(d3,plain,
join(meet(X0,X1),meet(X0,meet(X1,X2))) = meet(X0,X1),
inference(superposition,[status(thm)],[c8,c5]) ).
cnf(d4,plain,
join(meet(X1,X0),meet(X0,meet(X1,X2))) = meet(X0,X1),
inference(superposition,[status(thm)],[c6,d3]) ).
cnf(d5,plain,
join(X2,meet(X0,X1)) = join(X2,meet(X1,X0)),
inference(superposition,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
join(X0,X2) = join(X0,join(meet(X0,X1),X2)),
inference(superposition,[status(thm)],[c5,c9]) ).
cnf(d7,plain,
meet(X0,meet(X1,X2)) = meet(X2,meet(X0,X1)),
inference(superposition,[status(thm)],[c8,c6]) ).
cnf(d8,plain,
join(meet(X1,X2),meet(X2,meet(X0,X1))) = meet(X1,X2),
inference(superposition,[status(thm)],[d7,d0]) ).
cnf(d9,plain,
join(join(X1,X0),X2) = join(X0,join(X1,X2)),
inference(superposition,[status(thm)],[c7,c9]) ).
cnf(d10,plain,
join(X2,join(X0,X1)) = join(X0,join(X1,X2)),
inference(superposition,[status(thm)],[c9,c7]) ).
cnf(d11,plain,
join(X2,join(X0,X1)) = join(join(X1,X2),X0),
inference(superposition,[status(thm)],[d10,c7]) ).
cnf(d12,plain,
join(X1,join(X2,X0)) = join(X1,join(X0,X2)),
inference(superposition,[status(thm)],[d11,d9]) ).
cnf(d13,plain,
meet(X0,join(X1,X0)) = X0,
inference(superposition,[status(thm)],[c7,c4]) ).
cnf(d14,plain,
meet(X2,join(X0,join(X1,X2))) = X2,
inference(superposition,[status(thm)],[c9,d13]) ).
cnf(d15,plain,
meet(meet(X0,X1),join(X2,X0)) = meet(X0,X1),
inference(superposition,[status(thm)],[c5,d14]) ).
cnf(d16,plain,
meet(X0,meet(X1,join(X2,X0))) = meet(X0,X1),
inference(demodulation,[status(thm)],[d15,c8]) ).
cnf(d17,plain,
meet(X2,meet(X1,X0)) = meet(X1,meet(X2,X0)),
inference(superposition,[status(thm)],[c6,d7]) ).
cnf(d18,plain,
meet(X2,X0) = meet(X0,meet(X2,join(X0,X1))),
inference(superposition,[status(thm)],[c4,d17]) ).
cnf(d19,plain,
join(join(X1,X0),X0) = join(X1,X0),
inference(superposition,[status(thm)],[d13,d0]) ).
cnf(d20,plain,
join(X1,join(X0,X1)) = join(X0,X1),
inference(demodulation,[status(thm)],[d19,c7]) ).
cnf(d21,plain,
join(X2,join(X0,join(X1,X2))) = join(join(X0,X1),X2),
inference(superposition,[status(thm)],[c9,d20]) ).
cnf(d22,plain,
join(X2,join(X0,join(X1,X2))) = join(X0,join(X1,X2)),
inference(demodulation,[status(thm)],[d21,c9]) ).
cnf(d23,plain,
join(X0,join(X1,join(X2,join(X0,X1)))) = join(X2,join(X0,X1)),
inference(superposition,[status(thm)],[c9,d20]) ).
cnf(d24,plain,
join(X2,join(X1,join(X2,X0))) = join(X1,join(X2,X0)),
inference(demodulation,[status(thm)],[d23,d22]) ).
cnf(d25,plain,
join(join(X0,X1),X0) = join(X0,X1),
inference(superposition,[status(thm)],[c4,d0]) ).
cnf(d26,plain,
join(X0,join(X0,X1)) = join(X0,X1),
inference(demodulation,[status(thm)],[d25,c7]) ).
cnf(d27,plain,
join(meet(join(meet(meet(join(X0,X1),X2),X1),join(X2,X0)),X1),meet(join(X2,X0),meet(join(X0,X1),X2))) = meet(join(join(meet(join(meet(X0,X1),X2),X1),meet(X2,X0)),X1),join(join(X2,X0),meet(join(X0,X1),X2))),
inference(superposition,[status(thm)],[c0,c0]) ).
cnf(d28,plain,
join(meet(join(X2,X0),meet(join(X0,X1),X2)),meet(join(meet(meet(join(X0,X1),X2),X1),join(X2,X0)),X1)) = meet(join(join(meet(join(meet(X0,X1),X2),X1),meet(X2,X0)),X1),join(join(X2,X0),meet(join(X0,X1),X2))),
inference(demodulation,[status(thm)],[d27,c7]) ).
cnf(d29,plain,
join(meet(join(X2,X0),meet(join(X0,X1),X2)),meet(X1,join(meet(meet(join(X0,X1),X2),X1),join(X2,X0)))) = meet(join(join(meet(join(meet(X0,X1),X2),X1),meet(X2,X0)),X1),join(join(X2,X0),meet(join(X0,X1),X2))),
inference(demodulation,[status(thm)],[d28,c6]) ).
cnf(d30,plain,
join(meet(join(X2,X0),meet(join(X0,X1),X2)),meet(X1,join(join(X2,X0),meet(meet(join(X0,X1),X2),X1)))) = meet(join(join(meet(join(meet(X0,X1),X2),X1),meet(X2,X0)),X1),join(join(X2,X0),meet(join(X0,X1),X2))),
inference(demodulation,[status(thm)],[d29,c7]) ).
cnf(d31,plain,
join(meet(join(X0,X1),meet(join(X1,X2),X0)),meet(X2,join(X0,join(X1,meet(meet(join(X1,X2),X0),X2))))) = meet(join(join(meet(join(meet(X1,X2),X0),X2),meet(X0,X1)),X2),join(join(X0,X1),meet(join(X1,X2),X0))),
inference(demodulation,[status(thm)],[d30,c9]) ).
cnf(d32,plain,
join(meet(join(X2,X0),meet(join(X0,X1),X2)),meet(X1,join(X2,join(X0,meet(join(X0,X1),meet(X2,X1)))))) = meet(join(join(meet(join(meet(X0,X1),X2),X1),meet(X2,X0)),X1),join(join(X2,X0),meet(join(X0,X1),X2))),
inference(demodulation,[status(thm)],[d31,c8]) ).
cnf(d33,plain,
join(meet(join(X2,X0),meet(join(X0,X1),X2)),meet(X1,join(X2,join(X0,meet(join(X0,X1),meet(X2,X1)))))) = meet(join(join(X2,X0),meet(join(X0,X1),X2)),join(join(meet(join(meet(X0,X1),X2),X1),meet(X2,X0)),X1)),
inference(demodulation,[status(thm)],[d32,c6]) ).
cnf(d34,plain,
join(meet(join(X0,X1),meet(join(X1,X2),X0)),meet(X2,join(X0,join(X1,meet(join(X1,X2),meet(X0,X2)))))) = meet(join(X0,join(X1,meet(join(X1,X2),X0))),join(join(meet(join(meet(X1,X2),X0),X2),meet(X0,X1)),X2)),
inference(demodulation,[status(thm)],[d33,c9]) ).
cnf(d35,plain,
join(meet(join(X2,X0),meet(join(X0,X1),X2)),meet(X1,join(X2,join(X0,meet(join(X0,X1),meet(X2,X1)))))) = meet(join(X2,join(X0,meet(join(X0,X1),X2))),join(meet(join(meet(X0,X1),X2),X1),join(meet(X2,X0),X1))),
inference(demodulation,[status(thm)],[d34,c9]) ).
cnf(d36,plain,
join(meet(join(X2,X0),meet(join(X0,X1),X2)),meet(X1,join(X2,join(X0,meet(join(X0,X1),meet(X2,X1)))))) = meet(join(X2,join(X0,meet(join(X0,X1),X2))),join(join(meet(X2,X0),X1),meet(join(meet(X0,X1),X2),X1))),
inference(demodulation,[status(thm)],[d35,c7]) ).
cnf(d37,plain,
join(meet(join(X0,X1),meet(join(X1,X2),X0)),meet(X2,join(X0,join(X1,meet(join(X1,X2),meet(X0,X2)))))) = meet(join(X0,join(X1,meet(join(X1,X2),X0))),join(meet(X0,X1),join(X2,meet(join(meet(X1,X2),X0),X2)))),
inference(demodulation,[status(thm)],[d36,c9]) ).
cnf(d38,plain,
join(meet(join(X2,X1),meet(join(X1,X0),X2)),meet(X0,join(X2,join(X1,meet(join(X1,X0),meet(X2,X0)))))) = meet(join(X2,join(X1,meet(join(X1,X0),X2))),join(meet(X2,X1),X0)),
inference(demodulation,[status(thm)],[d37,d0]) ).
cnf(d39,plain,
join(meet(join(X0,X1),meet(join(X1,X2),X0)),meet(X2,join(X0,join(X1,meet(join(X1,X2),meet(X0,X2)))))) = meet(join(meet(X0,X1),X2),join(X0,join(X1,meet(join(X1,X2),X0)))),
inference(demodulation,[status(thm)],[d38,c6]) ).
cnf(d40,plain,
join(meet(join(join(join(X0,X1),X2),X0),join(X0,X1)),meet(X1,join(join(join(X0,X1),X2),join(X0,meet(join(X0,X1),meet(join(join(X0,X1),X2),X1)))))) = meet(join(meet(join(join(X0,X1),X2),X0),X1),join(join(join(X0,X1),X2),join(X0,meet(join(X0,X1),join(join(X0,X1),X2))))),
inference(superposition,[status(thm)],[c4,d39]) ).
cnf(d41,plain,
join(meet(join(X0,X1),join(join(join(X0,X1),X2),X0)),meet(X1,join(join(join(X0,X1),X2),join(X0,meet(join(X0,X1),meet(join(join(X0,X1),X2),X1)))))) = meet(join(meet(join(join(X0,X1),X2),X0),X1),join(join(join(X0,X1),X2),join(X0,meet(join(X0,X1),join(join(X0,X1),X2))))),
inference(demodulation,[status(thm)],[d40,c6]) ).
cnf(d42,plain,
join(meet(join(X0,X1),join(join(X0,X1),join(X2,X0))),meet(X1,join(join(join(X0,X1),X2),join(X0,meet(join(X0,X1),meet(join(join(X0,X1),X2),X1)))))) = meet(join(meet(join(join(X0,X1),X2),X0),X1),join(join(join(X0,X1),X2),join(X0,meet(join(X0,X1),join(join(X0,X1),X2))))),
inference(demodulation,[status(thm)],[d41,c9]) ).
cnf(d43,plain,
join(join(X0,X1),meet(X1,join(join(join(X0,X1),X2),join(X0,meet(join(X0,X1),meet(join(join(X0,X1),X2),X1)))))) = meet(join(meet(join(join(X0,X1),X2),X0),X1),join(join(join(X0,X1),X2),join(X0,meet(join(X0,X1),join(join(X0,X1),X2))))),
inference(demodulation,[status(thm)],[d42,c4]) ).
cnf(d44,plain,
join(X0,join(X1,meet(X1,join(join(join(X0,X1),X2),join(X0,meet(join(X0,X1),meet(join(join(X0,X1),X2),X1))))))) = meet(join(meet(join(join(X0,X1),X2),X0),X1),join(join(join(X0,X1),X2),join(X0,meet(join(X0,X1),join(join(X0,X1),X2))))),
inference(demodulation,[status(thm)],[d43,c9]) ).
cnf(d45,plain,
join(X1,X0) = meet(join(meet(join(join(X1,X0),X2),X1),X0),join(join(join(X1,X0),X2),join(X1,meet(join(X1,X0),join(join(X1,X0),X2))))),
inference(demodulation,[status(thm)],[d44,c5]) ).
cnf(d46,plain,
join(X0,X1) = meet(join(X1,meet(join(join(X0,X1),X2),X0)),join(join(join(X0,X1),X2),join(X0,meet(join(X0,X1),join(join(X0,X1),X2))))),
inference(demodulation,[status(thm)],[d45,c7]) ).
cnf(d47,plain,
join(X0,X1) = meet(join(X1,meet(X0,join(join(X0,X1),X2))),join(join(join(X0,X1),X2),join(X0,meet(join(X0,X1),join(join(X0,X1),X2))))),
inference(demodulation,[status(thm)],[d46,c6]) ).
cnf(d48,plain,
join(X0,X1) = meet(join(X1,meet(X0,join(X0,join(X1,X2)))),join(join(join(X0,X1),X2),join(X0,meet(join(X0,X1),join(join(X0,X1),X2))))),
inference(demodulation,[status(thm)],[d47,c9]) ).
cnf(d49,plain,
join(X0,X1) = meet(join(X1,X0),join(join(join(X0,X1),X2),join(X0,meet(join(X0,X1),join(join(X0,X1),X2))))),
inference(demodulation,[status(thm)],[d48,c4]) ).
cnf(d50,plain,
join(X0,X1) = meet(join(X1,X0),join(join(X0,X1),join(X2,join(X0,meet(join(X0,X1),join(join(X0,X1),X2)))))),
inference(demodulation,[status(thm)],[d49,c9]) ).
cnf(d51,plain,
join(X0,X1) = meet(join(X1,X0),join(X0,join(X1,join(X2,join(X0,meet(join(X0,X1),join(join(X0,X1),X2))))))),
inference(demodulation,[status(thm)],[d50,c9]) ).
cnf(d52,plain,
join(X0,X1) = meet(join(X1,X0),join(X0,join(X1,join(X2,join(X0,join(X0,X1)))))),
inference(demodulation,[status(thm)],[d51,c4]) ).
cnf(d53,plain,
join(X0,X1) = meet(join(X1,X0),join(X0,join(X1,join(X2,join(X0,X1))))),
inference(demodulation,[status(thm)],[d52,d26]) ).
cnf(d54,plain,
join(X2,X0) = meet(join(X0,X2),join(X2,join(X1,join(X2,X0)))),
inference(demodulation,[status(thm)],[d53,d22]) ).
cnf(d55,plain,
join(X0,X2) = meet(join(X2,X0),join(X1,join(X0,X2))),
inference(demodulation,[status(thm)],[d54,d24]) ).
cnf(d56,plain,
meet(join(X0,X1),X2) = meet(X2,join(X1,X0)),
inference(superposition,[status(thm)],[d55,d18]) ).
cnf(d57,plain,
join(X0,X3) = join(X0,join(meet(X1,meet(X2,X0)),X3)),
inference(superposition,[status(thm)],[d1,c9]) ).
cnf(d58,plain,
X0 = meet(X0,X0),
inference(superposition,[status(thm)],[c2,c6]) ).
cnf(d59,plain,
meet(X0,X1) = meet(X0,meet(X0,X1)),
inference(superposition,[status(thm)],[d58,c8]) ).
cnf(d60,plain,
meet(X2,meet(X0,X1)) = meet(meet(X0,X1),meet(X2,X0)),
inference(superposition,[status(thm)],[d59,d7]) ).
cnf(d61,plain,
meet(X2,meet(X0,X1)) = meet(X0,meet(X1,meet(X2,X0))),
inference(demodulation,[status(thm)],[d60,c8]) ).
cnf(d62,plain,
join(meet(X1,X2),X0) = join(X0,meet(X2,X1)),
inference(superposition,[status(thm)],[d5,c7]) ).
cnf(d63,plain,
join(X0,join(X1,meet(X2,join(X0,X1)))) = join(X0,X1),
inference(superposition,[status(thm)],[c9,d0]) ).
cnf(d64,plain,
meet(meet(X1,X0),X0) = meet(X1,X0),
inference(superposition,[status(thm)],[d0,d13]) ).
cnf(d65,plain,
meet(X0,meet(X1,X1)) = meet(X0,X1),
inference(demodulation,[status(thm)],[d64,c8]) ).
cnf(d66,plain,
meet(X1,X0) = meet(X1,X0),
inference(demodulation,[status(thm)],[d65,c2]) ).
cnf(d67,plain,
join(meet(join(meet(meet(X0,X1),X2),X0),X2),meet(X0,meet(X0,X1))) = meet(join(meet(join(meet(X0,X1),X2),X0),X2),X0),
inference(superposition,[status(thm)],[c5,c0]) ).
cnf(d68,plain,
join(meet(X0,meet(X0,X1)),meet(join(meet(meet(X0,X1),X2),X0),X2)) = meet(join(meet(join(meet(X0,X1),X2),X0),X2),X0),
inference(demodulation,[status(thm)],[d67,c7]) ).
cnf(d69,plain,
join(meet(X0,X1),meet(join(meet(meet(X0,X1),X2),X0),X2)) = meet(join(meet(join(meet(X0,X1),X2),X0),X2),X0),
inference(demodulation,[status(thm)],[d68,d59]) ).
cnf(d70,plain,
join(meet(X0,X1),meet(X2,join(meet(meet(X0,X1),X2),X0))) = meet(join(meet(join(meet(X0,X1),X2),X0),X2),X0),
inference(demodulation,[status(thm)],[d69,c6]) ).
cnf(d71,plain,
join(meet(X0,X1),meet(X2,join(X0,meet(meet(X0,X1),X2)))) = meet(join(meet(join(meet(X0,X1),X2),X0),X2),X0),
inference(demodulation,[status(thm)],[d70,c7]) ).
cnf(d72,plain,
join(meet(X0,X1),meet(X2,join(X0,meet(X0,meet(X1,X2))))) = meet(join(meet(join(meet(X0,X1),X2),X0),X2),X0),
inference(demodulation,[status(thm)],[d71,c8]) ).
cnf(d73,plain,
join(meet(X0,X1),meet(X2,X0)) = meet(join(meet(join(meet(X0,X1),X2),X0),X2),X0),
inference(demodulation,[status(thm)],[d72,c5]) ).
cnf(d74,plain,
join(meet(X0,X1),meet(X2,X0)) = meet(X0,join(meet(join(meet(X0,X1),X2),X0),X2)),
inference(demodulation,[status(thm)],[d73,c6]) ).
cnf(d75,plain,
join(meet(X0,X1),meet(X2,X0)) = meet(X0,join(X2,meet(join(meet(X0,X1),X2),X0))),
inference(demodulation,[status(thm)],[d74,c7]) ).
cnf(d76,plain,
join(meet(X0,X1),meet(X2,X0)) = meet(X0,join(X2,meet(X0,join(meet(X0,X1),X2)))),
inference(demodulation,[status(thm)],[d75,c6]) ).
cnf(d77,plain,
meet(X0,join(X1,meet(X0,join(meet(X0,X2),X1)))) = join(meet(X0,X2),meet(X1,X0)),
inference(superposition,[status(thm)],[d76,d66]) ).
cnf(d78,plain,
join(meet(join(meet(X0,X1),join(X0,X1)),X1),meet(join(X0,X1),X0)) = meet(join(join(X0,X1),X1),join(join(X0,X1),X0)),
inference(superposition,[status(thm)],[c2,c0]) ).
cnf(d79,plain,
join(meet(join(X0,X1),X0),meet(join(meet(X0,X1),join(X0,X1)),X1)) = meet(join(join(X0,X1),X1),join(join(X0,X1),X0)),
inference(demodulation,[status(thm)],[d78,c7]) ).
cnf(d80,plain,
join(meet(X0,join(X0,X1)),meet(join(meet(X0,X1),join(X0,X1)),X1)) = meet(join(join(X0,X1),X1),join(join(X0,X1),X0)),
inference(demodulation,[status(thm)],[d79,c6]) ).
cnf(d81,plain,
join(X0,meet(join(meet(X0,X1),join(X0,X1)),X1)) = meet(join(join(X0,X1),X1),join(join(X0,X1),X0)),
inference(demodulation,[status(thm)],[d80,c4]) ).
cnf(d82,plain,
join(X0,meet(X1,join(meet(X0,X1),join(X0,X1)))) = meet(join(join(X0,X1),X1),join(join(X0,X1),X0)),
inference(demodulation,[status(thm)],[d81,c6]) ).
cnf(d83,plain,
join(X0,meet(X1,join(join(X0,X1),meet(X0,X1)))) = meet(join(join(X0,X1),X1),join(join(X0,X1),X0)),
inference(demodulation,[status(thm)],[d82,c7]) ).
cnf(d84,plain,
join(X0,meet(X1,join(X0,join(X1,meet(X0,X1))))) = meet(join(join(X0,X1),X1),join(join(X0,X1),X0)),
inference(demodulation,[status(thm)],[d83,c9]) ).
cnf(d85,plain,
join(X1,meet(X0,join(X1,X0))) = meet(join(join(X1,X0),X0),join(join(X1,X0),X1)),
inference(demodulation,[status(thm)],[d84,d0]) ).
cnf(d86,plain,
join(X1,X0) = meet(join(join(X1,X0),X0),join(join(X1,X0),X1)),
inference(demodulation,[status(thm)],[d85,d13]) ).
cnf(d87,plain,
join(X0,X1) = meet(join(X0,join(X1,X1)),join(join(X0,X1),X0)),
inference(demodulation,[status(thm)],[d86,c9]) ).
cnf(d88,plain,
join(X1,X0) = meet(join(X1,X0),join(join(X1,X0),X1)),
inference(demodulation,[status(thm)],[d87,c3]) ).
cnf(d89,plain,
join(X0,X1) = join(X0,X1),
inference(demodulation,[status(thm)],[d88,c4]) ).
cnf(d90,plain,
join(X2,meet(meet(X1,X2),X0)) = X2,
inference(superposition,[status(thm)],[c6,d1]) ).
cnf(d91,plain,
join(X1,meet(X0,meet(X1,X2))) = X1,
inference(demodulation,[status(thm)],[d90,c8]) ).
cnf(d92,plain,
X0 = join(X0,meet(X1,meet(X0,X2))),
inference(superposition,[status(thm)],[d91,d89]) ).
cnf(d93,plain,
meet(meet(X0,X1),X0) = meet(X0,X1),
inference(superposition,[status(thm)],[c5,d13]) ).
cnf(d94,plain,
meet(X0,meet(X1,X0)) = meet(X0,X1),
inference(demodulation,[status(thm)],[d93,c8]) ).
cnf(d95,plain,
join(meet(X0,meet(join(meet(X0,X1),X2),X0)),meet(X2,join(X0,join(meet(X0,X1),meet(join(meet(X0,X1),X2),meet(X0,X2)))))) = meet(join(meet(X0,meet(X0,X1)),X2),join(X0,join(meet(X0,X1),meet(join(meet(X0,X1),X2),X0)))),
inference(superposition,[status(thm)],[c5,d39]) ).
cnf(d96,plain,
join(meet(X0,join(meet(X0,X1),X2)),meet(X2,join(X0,join(meet(X0,X1),meet(join(meet(X0,X1),X2),meet(X0,X2)))))) = meet(join(meet(X0,meet(X0,X1)),X2),join(X0,join(meet(X0,X1),meet(join(meet(X0,X1),X2),X0)))),
inference(demodulation,[status(thm)],[d95,d94]) ).
cnf(d97,plain,
join(meet(X0,join(meet(X0,X1),X2)),meet(X2,join(X0,meet(join(meet(X0,X1),X2),meet(X0,X2))))) = meet(join(meet(X0,meet(X0,X1)),X2),join(X0,join(meet(X0,X1),meet(join(meet(X0,X1),X2),X0)))),
inference(demodulation,[status(thm)],[d96,d6]) ).
cnf(d98,plain,
join(meet(X0,join(meet(X0,X1),X2)),meet(X2,X0)) = meet(join(meet(X0,meet(X0,X1)),X2),join(X0,join(meet(X0,X1),meet(join(meet(X0,X1),X2),X0)))),
inference(demodulation,[status(thm)],[d97,d92]) ).
cnf(d99,plain,
join(meet(X2,X0),meet(X0,join(meet(X0,X1),X2))) = meet(join(meet(X0,meet(X0,X1)),X2),join(X0,join(meet(X0,X1),meet(join(meet(X0,X1),X2),X0)))),
inference(demodulation,[status(thm)],[d98,c7]) ).
cnf(d100,plain,
join(meet(X2,X0),meet(X0,join(meet(X0,X1),X2))) = meet(join(meet(X0,X1),X2),join(X0,join(meet(X0,X1),meet(join(meet(X0,X1),X2),X0)))),
inference(demodulation,[status(thm)],[d99,d59]) ).
cnf(d101,plain,
join(meet(X2,X0),meet(X0,join(meet(X0,X1),X2))) = meet(join(meet(X0,X1),X2),join(X0,meet(join(meet(X0,X1),X2),X0))),
inference(demodulation,[status(thm)],[d100,d6]) ).
cnf(d102,plain,
join(meet(X2,X0),meet(X0,join(meet(X0,X1),X2))) = meet(join(meet(X0,X1),X2),X0),
inference(demodulation,[status(thm)],[d101,d0]) ).
cnf(d103,plain,
join(meet(X2,X0),meet(X0,join(meet(X0,X1),X2))) = meet(X0,join(meet(X0,X1),X2)),
inference(demodulation,[status(thm)],[d102,c6]) ).
cnf(d104,plain,
join(join(X1,meet(X0,join(meet(X0,X2),X1))),join(meet(X0,X2),meet(X1,X0))) = join(X1,meet(X0,join(meet(X0,X2),X1))),
inference(superposition,[status(thm)],[d76,d0]) ).
cnf(d105,plain,
join(X0,join(meet(X1,join(meet(X1,X2),X0)),join(meet(X1,X2),meet(X0,X1)))) = join(X0,meet(X1,join(meet(X1,X2),X0))),
inference(demodulation,[status(thm)],[d104,c9]) ).
cnf(d106,plain,
join(X0,join(join(meet(X1,X2),meet(X0,X1)),meet(X1,join(meet(X1,X2),X0)))) = join(X0,meet(X1,join(meet(X1,X2),X0))),
inference(demodulation,[status(thm)],[d105,d12]) ).
cnf(d107,plain,
join(X2,join(meet(X0,X1),join(meet(X2,X0),meet(X0,join(meet(X0,X1),X2))))) = join(X2,meet(X0,join(meet(X0,X1),X2))),
inference(demodulation,[status(thm)],[d106,c9]) ).
cnf(d108,plain,
join(X0,join(meet(X1,X2),meet(X1,join(meet(X1,X2),X0)))) = join(X0,meet(X1,join(meet(X1,X2),X0))),
inference(demodulation,[status(thm)],[d107,d103]) ).
cnf(d109,plain,
join(X0,join(X1,X0)) = join(X0,X1),
inference(superposition,[status(thm)],[c7,d26]) ).
cnf(d110,plain,
join(meet(X0,X1),meet(join(X2,meet(X0,X1)),X0)) = meet(X0,join(join(X2,meet(X0,X1)),meet(X0,join(meet(X0,X1),X2)))),
inference(superposition,[status(thm)],[d109,d76]) ).
cnf(d111,plain,
join(meet(X1,X2),meet(X1,join(meet(X1,X2),X0))) = meet(X1,join(join(X0,meet(X1,X2)),meet(X1,join(meet(X1,X2),X0)))),
inference(demodulation,[status(thm)],[d110,d56]) ).
cnf(d112,plain,
join(meet(X1,X2),meet(X1,join(meet(X1,X2),X0))) = meet(X1,join(X0,join(meet(X1,X2),meet(X1,join(meet(X1,X2),X0))))),
inference(demodulation,[status(thm)],[d111,c9]) ).
cnf(d113,plain,
join(meet(X1,X2),meet(X1,join(meet(X1,X2),X0))) = meet(X1,join(X0,meet(X1,join(meet(X1,X2),X0)))),
inference(demodulation,[status(thm)],[d112,d108]) ).
cnf(d114,plain,
join(meet(X0,X2),meet(X0,join(meet(X0,X2),X1))) = join(meet(X0,X2),meet(X1,X0)),
inference(demodulation,[status(thm)],[d113,d77]) ).
cnf(d115,plain,
join(meet(X0,X1),meet(join(X2,meet(X0,X1)),X0)) = meet(X0,join(join(X2,meet(X0,X1)),meet(X0,join(X2,meet(X0,X1))))),
inference(superposition,[status(thm)],[d20,d76]) ).
cnf(d116,plain,
join(meet(X1,X2),meet(X1,join(meet(X1,X2),X0))) = meet(X1,join(join(X0,meet(X1,X2)),meet(X1,join(X0,meet(X1,X2))))),
inference(demodulation,[status(thm)],[d115,d56]) ).
cnf(d117,plain,
join(meet(X0,X1),meet(X2,X0)) = meet(X0,join(join(X2,meet(X0,X1)),meet(X0,join(X2,meet(X0,X1))))),
inference(demodulation,[status(thm)],[d116,d114]) ).
cnf(d118,plain,
join(meet(X1,X2),meet(X0,X1)) = meet(X1,join(X0,join(meet(X1,X2),meet(X1,join(X0,meet(X1,X2)))))),
inference(demodulation,[status(thm)],[d117,c9]) ).
cnf(d119,plain,
join(meet(X1,X2),meet(X0,X1)) = meet(X1,join(X0,meet(X1,X2))),
inference(demodulation,[status(thm)],[d118,d63]) ).
cnf(d120,plain,
join(X2,meet(X0,meet(X1,meet(X2,X3)))) = X2,
inference(superposition,[status(thm)],[c8,d91]) ).
cnf(d121,plain,
meet(X0,meet(X1,join(meet(X0,X1),X2))) = meet(X0,X1),
inference(superposition,[status(thm)],[c8,c4]) ).
cnf(d122,plain,
meet(X2,join(X1,X0)) = meet(X2,join(X0,X1)),
inference(superposition,[status(thm)],[d55,d121]) ).
cnf(d123,plain,
join(meet(X1,join(meet(X0,X1),X2)),meet(X2,X0)) = meet(join(meet(join(X0,X1),X2),X1),join(X2,X0)),
inference(demodulation,[status(thm)],[c0,c6]) ).
cnf(d124,plain,
join(meet(X1,join(meet(X0,X1),X2)),meet(X2,X0)) = meet(join(X2,X0),join(meet(join(X0,X1),X2),X1)),
inference(demodulation,[status(thm)],[d123,c6]) ).
cnf(d125,plain,
join(meet(X2,X1),meet(X0,join(meet(X1,X0),X2))) = meet(join(X2,X1),join(meet(join(X1,X0),X2),X0)),
inference(demodulation,[status(thm)],[d124,c7]) ).
cnf(d126,plain,
join(meet(X2,X0),meet(X1,join(meet(X0,X1),X2))) = meet(join(X2,X0),join(X1,meet(join(X0,X1),X2))),
inference(demodulation,[status(thm)],[d125,c7]) ).
cnf(d127,plain,
join(meet(X0,meet(X1,meet(X2,X0))),meet(X3,join(meet(meet(X1,meet(X2,X0)),X3),X0))) = meet(X0,join(X3,meet(join(meet(X1,meet(X2,X0)),X3),X0))),
inference(superposition,[status(thm)],[d1,d126]) ).
cnf(d128,plain,
join(meet(X2,meet(X0,X1)),meet(X3,join(meet(meet(X1,meet(X2,X0)),X3),X0))) = meet(X0,join(X3,meet(join(meet(X1,meet(X2,X0)),X3),X0))),
inference(demodulation,[status(thm)],[d127,d61]) ).
cnf(d129,plain,
join(meet(X2,meet(X3,X1)),meet(X0,join(X3,meet(meet(X1,meet(X2,X3)),X0)))) = meet(X3,join(X0,meet(join(meet(X1,meet(X2,X3)),X0),X3))),
inference(demodulation,[status(thm)],[d128,d122]) ).
cnf(d130,plain,
join(meet(X1,meet(X2,X0)),meet(X3,join(X2,meet(X0,meet(meet(X1,X2),X3))))) = meet(X2,join(X3,meet(join(meet(X0,meet(X1,X2)),X3),X2))),
inference(demodulation,[status(thm)],[d129,c8]) ).
cnf(d131,plain,
join(meet(X0,meet(X1,X3)),meet(X2,join(X1,meet(X3,meet(X0,meet(X1,X2)))))) = meet(X1,join(X2,meet(join(meet(X3,meet(X0,X1)),X2),X1))),
inference(demodulation,[status(thm)],[d130,c8]) ).
cnf(d132,plain,
join(meet(X2,meet(X0,X1)),meet(X3,X0)) = meet(X0,join(X3,meet(join(meet(X1,meet(X2,X0)),X3),X0))),
inference(demodulation,[status(thm)],[d131,d120]) ).
cnf(d133,plain,
join(meet(X2,meet(X3,X1)),meet(X0,X3)) = meet(X3,join(X0,meet(X3,join(meet(X1,meet(X2,X3)),X0)))),
inference(demodulation,[status(thm)],[d132,d5]) ).
cnf(d134,plain,
join(meet(X3,meet(X0,X2)),meet(X1,X0)) = join(meet(X0,join(meet(X2,meet(X3,X0)),X1)),meet(X1,X0)),
inference(demodulation,[status(thm)],[d133,d119]) ).
cnf(d135,plain,
join(meet(X2,meet(X0,X1)),meet(X3,X0)) = join(meet(X3,X0),meet(join(meet(X1,meet(X2,X0)),X3),X0)),
inference(demodulation,[status(thm)],[d134,d62]) ).
cnf(d136,plain,
join(meet(X3,meet(X1,X2)),meet(X0,X1)) = join(meet(X0,X1),meet(X1,join(meet(X2,meet(X3,X1)),X0))),
inference(demodulation,[status(thm)],[d135,d5]) ).
cnf(d137,plain,
X0 = join(X0,meet(X1,meet(X2,X0))),
inference(superposition,[status(thm)],[d1,d89]) ).
cnf(d138,plain,
join(meet(X0,meet(join(meet(X1,meet(X2,X0)),X3),X0)),meet(X3,join(X0,join(meet(X1,meet(X2,X0)),meet(join(meet(X1,meet(X2,X0)),X3),meet(X0,X3)))))) = meet(join(meet(X0,meet(X1,meet(X2,X0))),X3),join(X0,join(meet(X1,meet(X2,X0)),meet(join(meet(X1,meet(X2,X0)),X3),X0)))),
inference(superposition,[status(thm)],[d137,d39]) ).
cnf(d139,plain,
join(meet(X0,join(meet(X1,meet(X2,X0)),X3)),meet(X3,join(X0,join(meet(X1,meet(X2,X0)),meet(join(meet(X1,meet(X2,X0)),X3),meet(X0,X3)))))) = meet(join(meet(X0,meet(X1,meet(X2,X0))),X3),join(X0,join(meet(X1,meet(X2,X0)),meet(join(meet(X1,meet(X2,X0)),X3),X0)))),
inference(demodulation,[status(thm)],[d138,d94]) ).
cnf(d140,plain,
join(meet(X0,join(meet(X1,meet(X2,X0)),X3)),meet(X3,join(X0,meet(join(meet(X1,meet(X2,X0)),X3),meet(X0,X3))))) = meet(join(meet(X0,meet(X1,meet(X2,X0))),X3),join(X0,join(meet(X1,meet(X2,X0)),meet(join(meet(X1,meet(X2,X0)),X3),X0)))),
inference(demodulation,[status(thm)],[d139,d57]) ).
cnf(d141,plain,
join(meet(X0,join(meet(X1,meet(X2,X0)),X3)),meet(X3,X0)) = meet(join(meet(X0,meet(X1,meet(X2,X0))),X3),join(X0,join(meet(X1,meet(X2,X0)),meet(join(meet(X1,meet(X2,X0)),X3),X0)))),
inference(demodulation,[status(thm)],[d140,d92]) ).
cnf(d142,plain,
join(meet(X3,X0),meet(join(meet(X1,meet(X2,X0)),X3),X0)) = meet(join(meet(X0,meet(X1,meet(X2,X0))),X3),join(X0,join(meet(X1,meet(X2,X0)),meet(join(meet(X1,meet(X2,X0)),X3),X0)))),
inference(demodulation,[status(thm)],[d141,d62]) ).
cnf(d143,plain,
join(meet(X0,X1),meet(X1,join(meet(X2,meet(X3,X1)),X0))) = meet(join(meet(X1,meet(X2,meet(X3,X1))),X0),join(X1,join(meet(X2,meet(X3,X1)),meet(join(meet(X2,meet(X3,X1)),X0),X1)))),
inference(demodulation,[status(thm)],[d142,d5]) ).
cnf(d144,plain,
join(meet(X3,meet(X1,X2)),meet(X0,X1)) = meet(join(meet(X1,meet(X2,meet(X3,X1))),X0),join(X1,join(meet(X2,meet(X3,X1)),meet(join(meet(X2,meet(X3,X1)),X0),X1)))),
inference(demodulation,[status(thm)],[d143,d136]) ).
cnf(d145,plain,
join(meet(X2,meet(X0,X1)),meet(X3,X0)) = meet(join(meet(X2,meet(X0,X1)),X3),join(X0,join(meet(X1,meet(X2,X0)),meet(join(meet(X1,meet(X2,X0)),X3),X0)))),
inference(demodulation,[status(thm)],[d144,d61]) ).
cnf(d146,plain,
join(meet(X2,meet(X0,X1)),meet(X3,X0)) = meet(join(meet(X2,meet(X0,X1)),X3),join(X0,meet(join(meet(X1,meet(X2,X0)),X3),X0))),
inference(demodulation,[status(thm)],[d145,d57]) ).
cnf(d147,plain,
join(meet(X2,meet(X0,X1)),meet(X3,X0)) = meet(join(meet(X2,meet(X0,X1)),X3),X0),
inference(demodulation,[status(thm)],[d146,d0]) ).
cnf(d148,plain,
join(meet(X0,meet(X1,X2)),meet(X3,X1)) = meet(X1,join(X3,meet(X0,meet(X1,X2)))),
inference(demodulation,[status(thm)],[d147,d56]) ).
cnf(d149,plain,
join(join(X0,X1),meet(X2,X0)) = join(X0,X1),
inference(superposition,[status(thm)],[c4,d1]) ).
cnf(d150,plain,
join(X0,join(X1,meet(X2,X0))) = join(X0,X1),
inference(demodulation,[status(thm)],[d149,c9]) ).
cnf(d151,plain,
join(meet(X2,X0),meet(X2,meet(X1,X0))) = meet(X2,X0),
inference(superposition,[status(thm)],[c6,d3]) ).
cnf(d152,plain,
join(X1,join(X2,X0)) = join(X2,join(X1,X0)),
inference(superposition,[status(thm)],[c7,d10]) ).
cnf(d153,plain,
join(meet(meet(X0,X2),X1),meet(X0,join(meet(X1,X0),meet(X0,X2)))) = meet(join(meet(X0,X2),X1),X0),
inference(superposition,[status(thm)],[d91,d126]) ).
cnf(d154,plain,
join(meet(X0,meet(X1,X2)),meet(X0,join(meet(X2,X0),meet(X0,X1)))) = meet(join(meet(X0,X1),X2),X0),
inference(demodulation,[status(thm)],[d153,c8]) ).
cnf(d155,plain,
join(meet(X0,meet(X2,X1)),join(meet(X0,X2),meet(meet(X1,X0),X0))) = meet(join(meet(X0,X2),X1),X0),
inference(demodulation,[status(thm)],[d154,d119]) ).
cnf(d156,plain,
join(meet(X0,X1),join(meet(X0,meet(X1,X2)),meet(meet(X2,X0),X0))) = meet(join(meet(X0,X1),X2),X0),
inference(demodulation,[status(thm)],[d155,d152]) ).
cnf(d157,plain,
join(meet(X0,X1),join(meet(X0,meet(X1,X2)),meet(X0,meet(X2,X0)))) = meet(join(meet(X0,X1),X2),X0),
inference(demodulation,[status(thm)],[d156,d5]) ).
cnf(d158,plain,
join(meet(X0,X2),join(meet(X0,meet(X2,X1)),meet(X0,X1))) = meet(join(meet(X0,X2),X1),X0),
inference(demodulation,[status(thm)],[d157,d94]) ).
cnf(d159,plain,
join(meet(X0,X1),join(meet(X0,X2),meet(X0,meet(X1,X2)))) = meet(join(meet(X0,X1),X2),X0),
inference(demodulation,[status(thm)],[d158,d12]) ).
cnf(d160,plain,
join(meet(X0,X2),meet(X0,X1)) = meet(join(meet(X0,X2),X1),X0),
inference(demodulation,[status(thm)],[d159,d151]) ).
cnf(d161,plain,
join(meet(X0,X1),meet(X0,X2)) = meet(X0,join(X2,meet(X0,X1))),
inference(demodulation,[status(thm)],[d160,d56]) ).
cnf(d162,plain,
meet(X0,X2) = meet(X0,meet(join(X0,X1),X2)),
inference(superposition,[status(thm)],[c4,c8]) ).
cnf(d163,plain,
join(meet(join(X1,X0),meet(join(join(X1,X0),X2),X0)),meet(X2,join(X0,join(join(X1,X0),meet(join(join(X1,X0),X2),meet(X0,X2)))))) = meet(join(meet(X0,join(X1,X0)),X2),join(X0,join(join(X1,X0),meet(join(join(X1,X0),X2),X0)))),
inference(superposition,[status(thm)],[d20,d39]) ).
cnf(d164,plain,
join(meet(join(X0,X1),X1),meet(X2,join(X1,join(join(X0,X1),meet(join(join(X0,X1),X2),meet(X1,X2)))))) = meet(join(meet(X1,join(X0,X1)),X2),join(X1,join(join(X0,X1),meet(join(join(X0,X1),X2),X1)))),
inference(demodulation,[status(thm)],[d163,d162]) ).
cnf(d165,plain,
join(meet(X1,join(X0,X1)),meet(X2,join(X1,join(join(X0,X1),meet(join(join(X0,X1),X2),meet(X1,X2)))))) = meet(join(meet(X1,join(X0,X1)),X2),join(X1,join(join(X0,X1),meet(join(join(X0,X1),X2),X1)))),
inference(demodulation,[status(thm)],[d164,c6]) ).
cnf(d166,plain,
join(X0,meet(X2,join(X0,join(join(X1,X0),meet(join(join(X1,X0),X2),meet(X0,X2)))))) = meet(join(meet(X0,join(X1,X0)),X2),join(X0,join(join(X1,X0),meet(join(join(X1,X0),X2),X0)))),
inference(demodulation,[status(thm)],[d165,d13]) ).
cnf(d167,plain,
join(X1,meet(X2,join(X1,join(X0,join(X1,meet(join(join(X0,X1),X2),meet(X1,X2))))))) = meet(join(meet(X1,join(X0,X1)),X2),join(X1,join(join(X0,X1),meet(join(join(X0,X1),X2),X1)))),
inference(demodulation,[status(thm)],[d166,c9]) ).
cnf(d168,plain,
join(X0,meet(X2,join(X1,join(X0,meet(join(join(X1,X0),X2),meet(X0,X2)))))) = meet(join(meet(X0,join(X1,X0)),X2),join(X0,join(join(X1,X0),meet(join(join(X1,X0),X2),X0)))),
inference(demodulation,[status(thm)],[d167,d24]) ).
cnf(d169,plain,
join(X0,meet(X2,join(X1,X0))) = meet(join(meet(X0,join(X1,X0)),X2),join(X0,join(join(X1,X0),meet(join(join(X1,X0),X2),X0)))),
inference(demodulation,[status(thm)],[d168,d92]) ).
cnf(d170,plain,
join(X0,meet(X2,join(X1,X0))) = meet(join(X0,X2),join(X0,join(join(X1,X0),meet(join(join(X1,X0),X2),X0)))),
inference(demodulation,[status(thm)],[d169,d13]) ).
cnf(d171,plain,
join(X0,meet(X2,join(X1,X0))) = meet(join(X0,X2),join(X0,join(X1,X0))),
inference(demodulation,[status(thm)],[d170,d150]) ).
cnf(d172,plain,
join(X0,meet(X2,join(X1,X0))) = meet(join(X0,X2),join(X0,X1)),
inference(demodulation,[status(thm)],[d171,d109]) ).
cnf(d173,plain,
meet(X0,X2) = meet(X0,meet(join(X1,X0),X2)),
inference(superposition,[status(thm)],[d13,c8]) ).
cnf(d174,plain,
join(meet(join(X0,X1),meet(join(join(X0,X1),X2),X0)),meet(X2,join(X0,join(join(X0,X1),meet(join(join(X0,X1),X2),meet(X0,X2)))))) = meet(join(meet(X0,join(X0,X1)),X2),join(X0,join(join(X0,X1),meet(join(join(X0,X1),X2),X0)))),
inference(superposition,[status(thm)],[d26,d39]) ).
cnf(d175,plain,
join(meet(join(X0,X1),X0),meet(X2,join(X0,join(join(X0,X1),meet(join(join(X0,X1),X2),meet(X0,X2)))))) = meet(join(meet(X0,join(X0,X1)),X2),join(X0,join(join(X0,X1),meet(join(join(X0,X1),X2),X0)))),
inference(demodulation,[status(thm)],[d174,d162]) ).
cnf(d176,plain,
join(meet(X0,join(X0,X1)),meet(X2,join(X0,join(join(X0,X1),meet(join(join(X0,X1),X2),meet(X0,X2)))))) = meet(join(meet(X0,join(X0,X1)),X2),join(X0,join(join(X0,X1),meet(join(join(X0,X1),X2),X0)))),
inference(demodulation,[status(thm)],[d175,c6]) ).
cnf(d177,plain,
join(X0,meet(X2,join(X0,join(join(X0,X1),meet(join(join(X0,X1),X2),meet(X0,X2)))))) = meet(join(meet(X0,join(X0,X1)),X2),join(X0,join(join(X0,X1),meet(join(join(X0,X1),X2),X0)))),
inference(demodulation,[status(thm)],[d176,c4]) ).
cnf(d178,plain,
join(X0,meet(X2,join(X0,join(X0,join(X1,meet(join(join(X0,X1),X2),meet(X0,X2))))))) = meet(join(meet(X0,join(X0,X1)),X2),join(X0,join(join(X0,X1),meet(join(join(X0,X1),X2),X0)))),
inference(demodulation,[status(thm)],[d177,c9]) ).
cnf(d179,plain,
join(X0,meet(X2,join(X0,join(X1,meet(join(join(X0,X1),X2),meet(X0,X2)))))) = meet(join(meet(X0,join(X0,X1)),X2),join(X0,join(join(X0,X1),meet(join(join(X0,X1),X2),X0)))),
inference(demodulation,[status(thm)],[d178,d26]) ).
cnf(d180,plain,
join(X0,meet(X2,join(X0,join(X1,meet(X2,meet(join(join(X0,X1),X2),X0)))))) = meet(join(meet(X0,join(X0,X1)),X2),join(X0,join(join(X0,X1),meet(join(join(X0,X1),X2),X0)))),
inference(demodulation,[status(thm)],[d179,d7]) ).
cnf(d181,plain,
join(X1,meet(X0,join(X1,join(X2,meet(X0,X1))))) = meet(join(meet(X1,join(X1,X2)),X0),join(X1,join(join(X1,X2),meet(join(join(X1,X2),X0),X1)))),
inference(demodulation,[status(thm)],[d180,d173]) ).
cnf(d182,plain,
join(X0,meet(X2,join(X0,X1))) = meet(join(meet(X0,join(X0,X1)),X2),join(X0,join(join(X0,X1),meet(join(join(X0,X1),X2),X0)))),
inference(demodulation,[status(thm)],[d181,d150]) ).
cnf(d183,plain,
join(X0,meet(X2,join(X0,X1))) = meet(join(X0,X2),join(X0,join(join(X0,X1),meet(join(join(X0,X1),X2),X0)))),
inference(demodulation,[status(thm)],[d182,c4]) ).
cnf(d184,plain,
join(X0,meet(X1,join(X0,X2))) = join(X0,meet(X1,join(join(join(X0,X2),meet(join(join(X0,X2),X1),X0)),X0))),
inference(demodulation,[status(thm)],[d183,d172]) ).
cnf(d185,plain,
join(X0,meet(X2,join(X0,X1))) = join(X0,meet(X2,join(join(X0,X1),join(meet(join(join(X0,X1),X2),X0),X0)))),
inference(demodulation,[status(thm)],[d184,c9]) ).
cnf(d186,plain,
join(X0,meet(X2,join(X0,X1))) = join(X0,meet(X2,join(X0,join(X1,join(meet(join(join(X0,X1),X2),X0),X0))))),
inference(demodulation,[status(thm)],[d185,c9]) ).
cnf(d187,plain,
join(X0,meet(X2,join(X0,X1))) = join(X0,meet(X2,join(X1,join(meet(join(join(X0,X1),X2),X0),X0)))),
inference(demodulation,[status(thm)],[d186,d22]) ).
cnf(d188,plain,
join(X0,meet(X2,join(X0,X1))) = join(X0,meet(X2,join(X1,join(X0,meet(join(join(X0,X1),X2),X0))))),
inference(demodulation,[status(thm)],[d187,c7]) ).
cnf(d189,plain,
join(X0,meet(X2,join(X0,X1))) = join(X0,meet(X2,join(X1,X0))),
inference(demodulation,[status(thm)],[d188,d0]) ).
cnf(d190,plain,
join(X0,join(X1,meet(join(X0,X1),X2))) = join(X0,X1),
inference(superposition,[status(thm)],[c9,c5]) ).
cnf(d191,plain,
join(X0,X2) = join(X0,join(meet(X1,X0),X2)),
inference(superposition,[status(thm)],[d0,c9]) ).
cnf(d192,plain,
join(meet(X2,X0),meet(join(X0,X1),join(meet(X0,join(X0,X1)),X2))) = meet(join(X2,X0),join(join(X0,X1),meet(join(X0,X1),X2))),
inference(superposition,[status(thm)],[d26,d126]) ).
cnf(d193,plain,
join(meet(X2,X0),meet(join(X0,X1),join(X0,X2))) = meet(join(X2,X0),join(join(X0,X1),meet(join(X0,X1),X2))),
inference(demodulation,[status(thm)],[d192,c4]) ).
cnf(d194,plain,
join(meet(X2,X0),join(X0,meet(X1,join(X2,X0)))) = meet(join(X2,X0),join(join(X0,X1),meet(join(X0,X1),X2))),
inference(demodulation,[status(thm)],[d193,d172]) ).
cnf(d195,plain,
join(X1,join(meet(X0,X1),meet(X2,join(X0,X1)))) = meet(join(X0,X1),join(join(X1,X2),meet(join(X1,X2),X0))),
inference(demodulation,[status(thm)],[d194,d152]) ).
cnf(d196,plain,
join(X0,meet(X2,join(X1,X0))) = meet(join(X1,X0),join(join(X0,X2),meet(join(X0,X2),X1))),
inference(demodulation,[status(thm)],[d195,d191]) ).
cnf(d197,plain,
join(X0,meet(X1,join(X2,X0))) = meet(join(X2,X0),join(X0,join(X1,meet(join(X0,X1),X2)))),
inference(demodulation,[status(thm)],[d196,c9]) ).
cnf(d198,plain,
join(X0,meet(X1,join(X2,X0))) = meet(join(X2,X0),join(X0,X1)),
inference(demodulation,[status(thm)],[d197,d190]) ).
cnf(d199,plain,
join(meet(X2,X0),meet(join(X1,X0),join(meet(X0,join(X1,X0)),X2))) = meet(join(X2,X0),join(join(X1,X0),meet(join(X1,X0),X2))),
inference(superposition,[status(thm)],[d20,d126]) ).
cnf(d200,plain,
join(meet(X2,X0),meet(join(X1,X0),join(X0,X2))) = meet(join(X2,X0),join(join(X1,X0),meet(join(X1,X0),X2))),
inference(demodulation,[status(thm)],[d199,d13]) ).
cnf(d201,plain,
join(meet(X2,X1),join(X1,meet(X2,join(X0,X1)))) = meet(join(X2,X1),join(join(X0,X1),meet(join(X0,X1),X2))),
inference(demodulation,[status(thm)],[d200,d198]) ).
cnf(d202,plain,
join(X1,join(meet(X0,X1),meet(X0,join(X2,X1)))) = meet(join(X0,X1),join(join(X2,X1),meet(join(X2,X1),X0))),
inference(demodulation,[status(thm)],[d201,d152]) ).
cnf(d203,plain,
join(X0,meet(X1,join(X2,X0))) = meet(join(X1,X0),join(join(X2,X0),meet(join(X2,X0),X1))),
inference(demodulation,[status(thm)],[d202,d191]) ).
cnf(d204,plain,
join(X1,meet(X2,join(X0,X1))) = meet(join(X2,X1),join(X0,join(X1,meet(join(X0,X1),X2)))),
inference(demodulation,[status(thm)],[d203,c9]) ).
cnf(d205,plain,
join(X1,meet(X2,join(X0,X1))) = meet(join(X2,X1),join(X0,X1)),
inference(demodulation,[status(thm)],[d204,d190]) ).
cnf(d206,plain,
meet(X2,join(join(X1,X2),X0)) = X2,
inference(superposition,[status(thm)],[c7,d14]) ).
cnf(d207,plain,
meet(X1,join(X0,join(X1,X2))) = X1,
inference(demodulation,[status(thm)],[d206,c9]) ).
cnf(d208,plain,
join(meet(X0,join(X1,X0)),meet(X2,join(meet(join(X1,X0),X2),X0))) = meet(join(X0,X1),join(X2,meet(join(join(X1,X0),X2),X0))),
inference(superposition,[status(thm)],[d109,d126]) ).
cnf(d209,plain,
join(X0,meet(X2,join(meet(join(X1,X0),X2),X0))) = meet(join(X0,X1),join(X2,meet(join(join(X1,X0),X2),X0))),
inference(demodulation,[status(thm)],[d208,d13]) ).
cnf(d210,plain,
join(X0,meet(X1,join(X0,meet(join(X2,X0),X1)))) = meet(join(X0,X2),join(X1,meet(join(join(X2,X0),X1),X0))),
inference(demodulation,[status(thm)],[d209,d189]) ).
cnf(d211,plain,
join(X2,meet(X0,join(X2,meet(join(X1,X2),X0)))) = meet(join(X2,X1),join(X0,meet(X2,join(join(X1,X2),X0)))),
inference(demodulation,[status(thm)],[d210,d5]) ).
cnf(d212,plain,
join(X1,meet(X2,join(X1,meet(join(X0,X1),X2)))) = meet(join(X1,X0),join(X2,meet(X1,join(X0,join(X1,X2))))),
inference(demodulation,[status(thm)],[d211,c9]) ).
cnf(d213,plain,
join(X0,meet(X2,join(X0,meet(join(X1,X0),X2)))) = meet(join(X0,X1),join(X2,X0)),
inference(demodulation,[status(thm)],[d212,d207]) ).
cnf(d214,plain,
join(X1,X0) = join(X0,join(X1,X0)),
inference(superposition,[status(thm)],[d20,d89]) ).
cnf(d215,plain,
join(meet(X0,join(X1,X0)),meet(X2,join(meet(join(X1,X0),X2),X0))) = meet(join(X1,X0),join(X2,meet(join(join(X1,X0),X2),X0))),
inference(superposition,[status(thm)],[d214,d126]) ).
cnf(d216,plain,
join(X0,meet(X2,join(meet(join(X1,X0),X2),X0))) = meet(join(X1,X0),join(X2,meet(join(join(X1,X0),X2),X0))),
inference(demodulation,[status(thm)],[d215,d13]) ).
cnf(d217,plain,
join(X0,meet(X1,join(X0,meet(join(X2,X0),X1)))) = meet(join(X2,X0),join(X1,meet(join(join(X2,X0),X1),X0))),
inference(demodulation,[status(thm)],[d216,d189]) ).
cnf(d218,plain,
meet(join(X0,X2),join(X1,X0)) = meet(join(X2,X0),join(X1,meet(join(join(X2,X0),X1),X0))),
inference(demodulation,[status(thm)],[d217,d213]) ).
cnf(d219,plain,
meet(join(X2,X1),join(X0,X2)) = meet(join(X1,X2),join(X0,meet(X2,join(join(X1,X2),X0)))),
inference(demodulation,[status(thm)],[d218,d5]) ).
cnf(d220,plain,
meet(join(X1,X0),join(X2,X1)) = meet(join(X0,X1),join(X2,meet(X1,join(X0,join(X1,X2))))),
inference(demodulation,[status(thm)],[d219,c9]) ).
cnf(d221,plain,
meet(join(X0,X1),join(X2,X0)) = meet(join(X1,X0),join(X2,X0)),
inference(demodulation,[status(thm)],[d220,d207]) ).
cnf(d222,plain,
meet(join(X1,X0),join(X2,X1)) = join(X1,meet(X0,join(X2,X1))),
inference(demodulation,[status(thm)],[d221,d205]) ).
cnf(d223,plain,
meet(X2,join(meet(X0,X1),meet(meet(X2,join(X0,X1)),join(meet(X1,meet(X2,join(X0,X1))),X0)))) = meet(X2,join(X0,X1)),
inference(superposition,[status(thm)],[d126,d121]) ).
cnf(d224,plain,
meet(X0,join(meet(X1,X2),meet(X0,meet(join(X1,X2),join(meet(X2,meet(X0,join(X1,X2))),X1))))) = meet(X0,join(X1,X2)),
inference(demodulation,[status(thm)],[d223,c8]) ).
cnf(d225,plain,
join(meet(X0,meet(join(X1,X2),join(meet(X2,meet(X0,join(X1,X2))),X1))),meet(X0,meet(X1,X2))) = meet(X0,join(X1,X2)),
inference(demodulation,[status(thm)],[d224,d161]) ).
cnf(d226,plain,
join(meet(X0,meet(X1,X2)),meet(meet(join(X1,X2),join(meet(X2,meet(X0,join(X1,X2))),X1)),X0)) = meet(X0,join(X1,X2)),
inference(demodulation,[status(thm)],[d225,d62]) ).
cnf(d227,plain,
join(meet(X0,meet(X1,X2)),meet(X0,meet(join(X1,X2),join(meet(X2,meet(X0,join(X1,X2))),X1)))) = meet(X0,join(X1,X2)),
inference(demodulation,[status(thm)],[d226,d5]) ).
cnf(d228,plain,
join(meet(X2,meet(X0,X1)),meet(X2,join(X0,meet(X1,join(meet(X1,meet(X2,join(X0,X1))),X0))))) = meet(X2,join(X0,X1)),
inference(demodulation,[status(thm)],[d227,d222]) ).
cnf(d229,plain,
join(meet(X2,meet(X0,X1)),meet(X2,join(X0,meet(X1,join(X0,meet(X1,meet(X2,join(X0,X1)))))))) = meet(X2,join(X0,X1)),
inference(demodulation,[status(thm)],[d228,d189]) ).
cnf(d230,plain,
join(meet(X2,meet(X1,X0)),meet(X2,join(X1,join(meet(X0,meet(X2,join(X1,X0))),meet(X0,X1))))) = meet(X2,join(X1,X0)),
inference(demodulation,[status(thm)],[d229,d161]) ).
cnf(d231,plain,
join(meet(X2,meet(X0,X1)),meet(X2,join(X0,meet(X1,meet(X2,join(X0,X1)))))) = meet(X2,join(X0,X1)),
inference(demodulation,[status(thm)],[d230,d150]) ).
cnf(d232,plain,
join(meet(X0,meet(X1,X2)),join(meet(X2,meet(X0,join(X1,X2))),meet(X1,X0))) = meet(X0,join(X1,X2)),
inference(demodulation,[status(thm)],[d231,d148]) ).
cnf(d233,plain,
join(meet(X1,X0),join(meet(X0,meet(X1,X2)),meet(X2,meet(X0,join(X1,X2))))) = meet(X0,join(X1,X2)),
inference(demodulation,[status(thm)],[d232,d10]) ).
cnf(d234,plain,
join(meet(X2,X1),join(meet(X1,meet(X2,X0)),meet(X0,X1))) = meet(X1,join(X2,X0)),
inference(demodulation,[status(thm)],[d233,d16]) ).
cnf(d235,plain,
join(meet(X0,X1),join(meet(X2,X1),meet(X1,meet(X0,X2)))) = meet(X1,join(X0,X2)),
inference(demodulation,[status(thm)],[d234,d12]) ).
cnf(d236,plain,
join(meet(X2,X1),meet(X0,X1)) = meet(X1,join(X2,X0)),
inference(demodulation,[status(thm)],[d235,d8]) ).
cnf(d237,plain,
join(X0,meet(X2,X1)) = join(X0,meet(X1,join(X0,X2))),
inference(superposition,[status(thm)],[d236,d6]) ).
cnf(d238,plain,
join(a,meet(b,c)) != join(a,meet(b,join(c,a))),
inference(demodulation,[status(thm)],[c1,d172]) ).
cnf(d239,plain,
join(a,meet(b,c)) != join(a,meet(b,join(a,c))),
inference(demodulation,[status(thm)],[d238,d189]) ).
cnf(d240,plain,
join(a,meet(b,c)) != join(a,meet(c,b)),
inference(demodulation,[status(thm)],[d239,d237]) ).
cnf(d241,plain,
join(a,meet(b,c)) != join(a,meet(b,c)),
inference(demodulation,[status(thm)],[d240,d5]) ).
cnf(d242,plain,
join(X1,meet(meet(X1,X2),X0)) = X1,
inference(superposition,[status(thm)],[c6,d91]) ).
cnf(d243,plain,
join(X0,meet(X0,meet(X1,X2))) = X0,
inference(demodulation,[status(thm)],[d242,c8]) ).
cnf(d244,plain,
X0 = X0,
inference(demodulation,[status(thm)],[d243,c5]) ).
cnf(d245,plain,
$false,
inference(resolution,[status(thm)],[d244,d241]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT009-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n014.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Fri Sep 25 19:56:17 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 250.11/45.54 % SZS status Unsatisfiable for theBenchmark.p
% 250.11/45.54 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
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