%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LAT019-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 : Tue Sep 29 11:42:50 AM UTC 2026
% Result : Unsatisfiable 2.18s 0.78s
% Output : CNFRefutation 3.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 9
% Syntax : Number of clauses : 280 ( 280 unt; 0 nHn; 4 RR)
% Number of literals : 280 ( 279 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 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 : 802 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
join(a,meet(b,c)) != meet(join(a,b),join(a,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_distributivity_law_dual) ).
cnf(c2,axiom,
meet(X,Y) = meet(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_meet) ).
cnf(c3,plain,
meet(join(X4,meet(X3,X2)),meet(join(X4,X3),join(X4,X2))) = meet(meet(join(X4,X3),join(X4,X2)),join(X4,meet(X3,X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
meet(meet(join(X4,X3),join(X4,X2)),join(X4,meet(X3,X2))) = meet(join(X4,meet(X3,X2)),meet(join(X4,X3),join(X4,X2))),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
meet(meet(X4,X2),X3) = meet(X3,meet(X4,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c6,plain,
meet(X3,meet(X4,X2)) = meet(meet(X4,X2),X3),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,axiom,
meet(meet(X2,Y2),Z) = meet(X2,meet(Y2,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_meet) ).
cnf(c8,plain,
meet(meet(X4,X2),X3) = meet(X4,meet(X2,X3)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c9,plain,
meet(X2,X3) = meet(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c10,plain,
meet(X4,meet(X2,X3)) = meet(X4,meet(X3,X2)),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,plain,
meet(meet(X4,X2),X3) = meet(X4,meet(X3,X2)),
inference(transitivity,[status(thm)],[c8,c10]) ).
cnf(c12,plain,
meet(X3,meet(X4,X2)) = meet(X4,meet(X3,X2)),
inference(transitivity,[status(thm)],[c6,c11]) ).
cnf(c13,plain,
meet(join(X4,meet(X3,X2)),meet(join(X4,X3),join(X4,X2))) = meet(join(X4,X3),meet(join(X4,meet(X3,X2)),join(X4,X2))),
inference(substitution,[status(thm)],[c12]) ).
cnf(c14,plain,
meet(join(X4,X2),join(X4,meet(X3,X2))) = meet(join(X4,meet(X3,X2)),join(X4,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c15,plain,
meet(join(X4,meet(X3,X2)),join(X4,X2)) = meet(join(X4,X2),join(X4,meet(X3,X2))),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c16,plain,
meet(X3,X2) = meet(X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c17,plain,
meet(X2,X3) = meet(X3,X2),
inference(symmetry,[status(thm)],[c16]) ).
cnf(c18,plain,
join(X4,meet(X2,X3)) = join(X4,meet(X3,X2)),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,plain,
meet(join(X4,X3),join(X4,meet(X2,X3))) = meet(join(X4,X3),join(X4,meet(X3,X2))),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
meet(join(X4,meet(X3,X2)),join(X4,X3)) = meet(join(X4,X3),join(X4,meet(X3,X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c21,plain,
meet(join(X4,X3),join(X4,meet(X3,X2))) = meet(join(X4,meet(X3,X2)),join(X4,X3)),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c22,axiom,
meet(join(X2,meet(Y2,Z2)),join(X2,Y2)) = join(X2,meet(Y2,Z2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quasi_lattice2) ).
cnf(c23,plain,
meet(join(X4,meet(X3,X2)),join(X4,X3)) = join(X4,meet(X3,X2)),
inference(substitution,[status(thm)],[c22]) ).
cnf(c24,plain,
meet(join(X4,X3),join(X4,meet(X3,X2))) = join(X4,meet(X3,X2)),
inference(transitivity,[status(thm)],[c21,c23]) ).
cnf(c25,plain,
meet(X3,X2) = meet(X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c26,plain,
join(X4,meet(X3,X2)) = join(X4,meet(X2,X3)),
inference(congruence,[status(thm)],[c25]) ).
cnf(c27,plain,
meet(join(X4,X3),join(X4,meet(X3,X2))) = join(X4,meet(X2,X3)),
inference(transitivity,[status(thm)],[c24,c26]) ).
cnf(c28,plain,
meet(join(X4,X3),join(X4,meet(X2,X3))) = join(X4,meet(X2,X3)),
inference(transitivity,[status(thm)],[c19,c27]) ).
cnf(c29,plain,
meet(join(X4,X2),join(X4,meet(X3,X2))) = join(X4,meet(X3,X2)),
inference(substitution,[status(thm)],[c28]) ).
cnf(c30,plain,
meet(join(X4,meet(X3,X2)),join(X4,X2)) = join(X4,meet(X3,X2)),
inference(transitivity,[status(thm)],[c15,c29]) ).
cnf(c31,plain,
meet(join(X4,X3),meet(join(X4,meet(X3,X2)),join(X4,X2))) = meet(join(X4,X3),join(X4,meet(X3,X2))),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,plain,
meet(join(X4,X3),join(X4,meet(X3,X2))) = meet(join(X4,meet(X3,X2)),join(X4,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c33,plain,
meet(join(X4,X3),join(X4,meet(X3,X2))) = meet(join(X4,meet(X3,X2)),join(X4,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c34,plain,
meet(join(X4,meet(X3,X2)),join(X4,X3)) = meet(join(X4,X3),join(X4,meet(X3,X2))),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c35,plain,
meet(join(X4,meet(X3,X2)),join(X4,X3)) = join(X4,meet(X3,X2)),
inference(transitivity,[status(thm)],[c34,c24]) ).
cnf(c36,plain,
meet(join(X4,X3),join(X4,meet(X3,X2))) = join(X4,meet(X3,X2)),
inference(transitivity,[status(thm)],[c32,c35]) ).
cnf(c37,plain,
meet(join(X4,X3),meet(join(X4,meet(X3,X2)),join(X4,X2))) = join(X4,meet(X3,X2)),
inference(transitivity,[status(thm)],[c31,c36]) ).
cnf(c38,plain,
meet(join(X4,meet(X3,X2)),meet(join(X4,X3),join(X4,X2))) = join(X4,meet(X3,X2)),
inference(transitivity,[status(thm)],[c13,c37]) ).
cnf(c39,plain,
meet(meet(join(X4,X3),join(X4,X2)),join(X4,meet(X3,X2))) = join(X4,meet(X3,X2)),
inference(transitivity,[status(thm)],[c4,c38]) ).
cnf(c40,plain,
join(X4,meet(X3,X2)) = meet(meet(join(X4,X3),join(X4,X2)),join(X4,meet(X3,X2))),
inference(symmetry,[status(thm)],[c39]) ).
cnf(c41,plain,
join(meet(join(X4,X3),join(X4,X2)),join(X4,meet(X3,X2))) = join(meet(join(X4,X3),join(X4,X2)),meet(meet(join(X4,X3),join(X4,X2)),join(X4,meet(X3,X2)))),
inference(congruence,[status(thm)],[c40]) ).
cnf(c42,hypothesis,
meet(X2,join(Y2,Z2)) = join(meet(X2,Y2),meet(X2,Z2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity_law) ).
cnf(c43,plain,
meet(X3,join(X3,X2)) = join(meet(X3,X3),meet(X3,X2)),
inference(substitution,[status(thm)],[c42]) ).
cnf(c44,axiom,
meet(X2,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c45,plain,
join(meet(X3,X3),meet(X3,X2)) = join(X3,meet(X3,X2)),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,plain,
meet(X3,join(X3,X2)) = join(X3,meet(X3,X2)),
inference(transitivity,[status(thm)],[c43,c45]) ).
cnf(c47,plain,
meet(meet(join(X4,X3),join(X4,X2)),join(meet(join(X4,X3),join(X4,X2)),join(X4,meet(X3,X2)))) = join(meet(join(X4,X3),join(X4,X2)),meet(meet(join(X4,X3),join(X4,X2)),join(X4,meet(X3,X2)))),
inference(substitution,[status(thm)],[c46]) ).
cnf(c48,plain,
join(meet(join(X4,X3),join(X4,X2)),meet(meet(join(X4,X3),join(X4,X2)),join(X4,meet(X3,X2)))) = meet(meet(join(X4,X3),join(X4,X2)),join(meet(join(X4,X3),join(X4,X2)),join(X4,meet(X3,X2)))),
inference(symmetry,[status(thm)],[c47]) ).
cnf(c49,plain,
meet(join(meet(join(X4,X3),join(X4,X2)),join(X4,meet(X3,X2))),meet(join(X4,X3),join(X4,X2))) = meet(meet(join(X4,X3),join(X4,X2)),join(meet(join(X4,X3),join(X4,X2)),join(X4,meet(X3,X2)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c50,plain,
meet(meet(join(X4,X3),join(X4,X2)),join(meet(join(X4,X3),join(X4,X2)),join(X4,meet(X3,X2)))) = meet(join(meet(join(X4,X3),join(X4,X2)),join(X4,meet(X3,X2))),meet(join(X4,X3),join(X4,X2))),
inference(symmetry,[status(thm)],[c49]) ).
cnf(c51,plain,
meet(join(X3,meet(X4,X2)),join(X3,X2)) = join(X3,meet(X4,X2)),
inference(substitution,[status(thm)],[c30]) ).
cnf(c52,plain,
join(X3,meet(X4,X2)) = meet(join(X3,meet(X4,X2)),join(X3,X2)),
inference(symmetry,[status(thm)],[c51]) ).
cnf(c53,plain,
meet(X4,join(X3,meet(X4,X2))) = meet(X4,meet(join(X3,meet(X4,X2)),join(X3,X2))),
inference(congruence,[status(thm)],[c52]) ).
cnf(c54,plain,
meet(X4,meet(join(X3,meet(X4,X2)),join(X3,X2))) = meet(join(X3,meet(X4,X2)),meet(X4,join(X3,X2))),
inference(substitution,[status(thm)],[c12]) ).
cnf(c55,plain,
meet(X3,X2) = meet(X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c56,plain,
meet(X2,X3) = meet(X3,X2),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c57,plain,
join(meet(X4,X2),meet(X3,X4)) = join(meet(X4,X2),meet(X4,X3)),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
meet(X4,join(X2,X3)) = join(meet(X4,X2),meet(X4,X3)),
inference(substitution,[status(thm)],[c42]) ).
cnf(c59,plain,
join(meet(X4,X2),meet(X4,X3)) = meet(X4,join(X2,X3)),
inference(symmetry,[status(thm)],[c58]) ).
cnf(c60,axiom,
join(X2,Y2) = join(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_join) ).
cnf(c61,plain,
join(X2,X3) = join(X3,X2),
inference(substitution,[status(thm)],[c60]) ).
cnf(c62,plain,
meet(X4,join(X2,X3)) = meet(X4,join(X3,X2)),
inference(congruence,[status(thm)],[c61]) ).
cnf(c63,plain,
join(meet(X4,X2),meet(X4,X3)) = meet(X4,join(X3,X2)),
inference(transitivity,[status(thm)],[c59,c62]) ).
cnf(c64,plain,
join(meet(X4,X2),meet(X3,X4)) = meet(X4,join(X3,X2)),
inference(transitivity,[status(thm)],[c57,c63]) ).
cnf(c65,plain,
meet(X4,join(X3,X2)) = join(meet(X4,X2),meet(X3,X4)),
inference(symmetry,[status(thm)],[c64]) ).
cnf(c66,plain,
meet(join(X3,meet(X4,X2)),meet(X4,join(X3,X2))) = meet(join(X3,meet(X4,X2)),join(meet(X4,X2),meet(X3,X4))),
inference(congruence,[status(thm)],[c65]) ).
cnf(c67,plain,
join(X2,X3) = join(X3,X2),
inference(substitution,[status(thm)],[c60]) ).
cnf(c68,plain,
join(X3,X2) = join(X2,X3),
inference(symmetry,[status(thm)],[c67]) ).
cnf(c69,plain,
meet(join(X4,X3),join(X3,meet(X4,X2))) = meet(join(X3,X4),join(X3,meet(X4,X2))),
inference(congruence,[status(thm)],[c68]) ).
cnf(c70,plain,
meet(join(X3,X4),join(X3,meet(X4,X2))) = join(X3,meet(X4,X2)),
inference(substitution,[status(thm)],[c24]) ).
cnf(c71,plain,
meet(join(X4,X3),join(X3,meet(X4,X2))) = join(X3,meet(X4,X2)),
inference(transitivity,[status(thm)],[c69,c70]) ).
cnf(c72,plain,
meet(join(X3,meet(X4,X2)),join(meet(X4,X2),meet(X3,X4))) = join(meet(X4,X2),meet(X3,X4)),
inference(substitution,[status(thm)],[c71]) ).
cnf(c73,plain,
meet(join(X3,meet(X4,X2)),join(meet(X4,X2),meet(X3,X4))) = meet(X4,join(X3,X2)),
inference(transitivity,[status(thm)],[c72,c64]) ).
cnf(c74,plain,
meet(join(X3,meet(X4,X2)),meet(X4,join(X3,X2))) = meet(X4,join(X3,X2)),
inference(transitivity,[status(thm)],[c66,c73]) ).
cnf(c75,plain,
meet(X4,meet(join(X3,meet(X4,X2)),join(X3,X2))) = meet(X4,join(X3,X2)),
inference(transitivity,[status(thm)],[c54,c74]) ).
cnf(c76,plain,
meet(X3,join(X2,meet(X3,X4))) = meet(X3,join(X2,X4)),
inference(transitivity,[status(thm)],[c53,c75]) ).
cnf(c77,plain,
join(meet(join(X5,X4),join(X3,X2)),meet(X4,join(X3,meet(X4,X2)))) = join(meet(join(X5,X4),join(X3,X2)),meet(X4,join(X3,X2))),
inference(congruence,[status(thm)],[c76]) ).
cnf(c78,plain,
meet(X3,X2) = meet(X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c79,plain,
meet(X2,X3) = meet(X3,X2),
inference(symmetry,[status(thm)],[c78]) ).
cnf(c80,plain,
join(meet(X2,X4),meet(X3,X4)) = join(meet(X2,X4),meet(X4,X3)),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,plain,
join(meet(X4,X3),meet(X2,X4)) = join(meet(X2,X4),meet(X4,X3)),
inference(substitution,[status(thm)],[c60]) ).
cnf(c82,plain,
join(meet(X2,X4),meet(X4,X3)) = join(meet(X4,X3),meet(X2,X4)),
inference(symmetry,[status(thm)],[c81]) ).
cnf(c83,plain,
join(meet(X4,X3),meet(X2,X4)) = meet(X4,join(X2,X3)),
inference(substitution,[status(thm)],[c64]) ).
cnf(c84,plain,
join(X2,X3) = join(X3,X2),
inference(substitution,[status(thm)],[c60]) ).
cnf(c85,plain,
meet(X4,join(X2,X3)) = meet(X4,join(X3,X2)),
inference(congruence,[status(thm)],[c84]) ).
cnf(c86,plain,
join(meet(X4,X3),meet(X2,X4)) = meet(X4,join(X3,X2)),
inference(transitivity,[status(thm)],[c83,c85]) ).
cnf(c87,plain,
join(meet(X2,X4),meet(X4,X3)) = meet(X4,join(X3,X2)),
inference(transitivity,[status(thm)],[c82,c86]) ).
cnf(c88,plain,
join(meet(X2,X4),meet(X3,X4)) = meet(X4,join(X3,X2)),
inference(transitivity,[status(thm)],[c80,c87]) ).
cnf(c89,plain,
join(meet(join(X4,X3),X2),meet(X3,X2)) = meet(X2,join(X3,join(X4,X3))),
inference(substitution,[status(thm)],[c88]) ).
cnf(c90,plain,
join(join(X4,X2),X3) = join(X3,join(X4,X2)),
inference(substitution,[status(thm)],[c60]) ).
cnf(c91,plain,
join(X3,join(X4,X2)) = join(join(X4,X2),X3),
inference(symmetry,[status(thm)],[c90]) ).
cnf(c92,axiom,
join(join(X2,Y2),Z2) = join(X2,join(Y2,Z2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_join) ).
cnf(c93,plain,
join(join(X4,X2),X3) = join(X4,join(X2,X3)),
inference(substitution,[status(thm)],[c92]) ).
cnf(c94,plain,
join(X2,X3) = join(X3,X2),
inference(substitution,[status(thm)],[c60]) ).
cnf(c95,plain,
join(X4,join(X2,X3)) = join(X4,join(X3,X2)),
inference(congruence,[status(thm)],[c94]) ).
cnf(c96,plain,
join(join(X4,X2),X3) = join(X4,join(X3,X2)),
inference(transitivity,[status(thm)],[c93,c95]) ).
cnf(c97,plain,
join(X3,join(X4,X2)) = join(X4,join(X3,X2)),
inference(transitivity,[status(thm)],[c91,c96]) ).
cnf(c98,plain,
join(X3,join(X2,X3)) = join(X2,join(X3,X3)),
inference(substitution,[status(thm)],[c97]) ).
cnf(c99,axiom,
join(X2,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c100,plain,
join(X2,join(X3,X3)) = join(X2,X3),
inference(congruence,[status(thm)],[c99]) ).
cnf(c101,plain,
join(X3,join(X2,X3)) = join(X2,X3),
inference(transitivity,[status(thm)],[c98,c100]) ).
cnf(c102,plain,
join(X2,join(X3,X2)) = join(X3,X2),
inference(substitution,[status(thm)],[c101]) ).
cnf(c103,plain,
meet(X2,join(X3,join(X4,X3))) = meet(X2,join(X4,X3)),
inference(congruence,[status(thm)],[c102]) ).
cnf(c104,plain,
meet(X2,join(X4,X3)) = meet(join(X4,X3),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c105,plain,
meet(X2,join(X3,join(X4,X3))) = meet(join(X4,X3),X2),
inference(transitivity,[status(thm)],[c103,c104]) ).
cnf(c106,plain,
join(meet(join(X4,X3),X2),meet(X3,X2)) = meet(join(X4,X3),X2),
inference(transitivity,[status(thm)],[c89,c105]) ).
cnf(c107,plain,
join(meet(join(X5,X4),join(X3,X2)),meet(X4,join(X3,X2))) = meet(join(X5,X4),join(X3,X2)),
inference(substitution,[status(thm)],[c106]) ).
cnf(c108,plain,
join(meet(join(X5,X4),join(X3,X2)),meet(X4,join(X3,meet(X4,X2)))) = meet(join(X5,X4),join(X3,X2)),
inference(transitivity,[status(thm)],[c77,c107]) ).
cnf(c109,plain,
join(meet(join(X4,X3),join(X4,X2)),meet(X3,join(X4,meet(X3,X2)))) = meet(join(X4,X3),join(X4,X2)),
inference(substitution,[status(thm)],[c108]) ).
cnf(c110,plain,
meet(join(X4,X3),join(X4,X2)) = join(meet(join(X4,X3),join(X4,X2)),meet(X3,join(X4,meet(X3,X2)))),
inference(symmetry,[status(thm)],[c109]) ).
cnf(c111,plain,
meet(join(meet(join(X4,X3),join(X4,X2)),join(X4,meet(X3,X2))),meet(join(X4,X3),join(X4,X2))) = meet(join(meet(join(X4,X3),join(X4,X2)),join(X4,meet(X3,X2))),join(meet(join(X4,X3),join(X4,X2)),meet(X3,join(X4,meet(X3,X2))))),
inference(congruence,[status(thm)],[c110]) ).
cnf(c112,plain,
meet(join(meet(join(X4,X3),join(X4,X2)),join(X4,meet(X3,X2))),join(meet(join(X4,X3),join(X4,X2)),meet(X3,join(X4,meet(X3,X2))))) = join(meet(join(X4,X3),join(X4,X2)),meet(X3,join(X4,meet(X3,X2)))),
inference(substitution,[status(thm)],[c28]) ).
cnf(c113,plain,
join(meet(join(X4,X3),join(X4,X2)),meet(X3,join(X4,meet(X3,X2)))) = meet(join(X4,X3),join(X4,X2)),
inference(substitution,[status(thm)],[c108]) ).
cnf(c114,plain,
meet(join(meet(join(X4,X3),join(X4,X2)),join(X4,meet(X3,X2))),join(meet(join(X4,X3),join(X4,X2)),meet(X3,join(X4,meet(X3,X2))))) = meet(join(X4,X3),join(X4,X2)),
inference(transitivity,[status(thm)],[c112,c113]) ).
cnf(c115,plain,
meet(join(meet(join(X4,X3),join(X4,X2)),join(X4,meet(X3,X2))),meet(join(X4,X3),join(X4,X2))) = meet(join(X4,X3),join(X4,X2)),
inference(transitivity,[status(thm)],[c111,c114]) ).
cnf(c116,plain,
meet(meet(join(X4,X3),join(X4,X2)),join(meet(join(X4,X3),join(X4,X2)),join(X4,meet(X3,X2)))) = meet(join(X4,X3),join(X4,X2)),
inference(transitivity,[status(thm)],[c50,c115]) ).
cnf(c117,plain,
join(meet(join(X4,X3),join(X4,X2)),meet(meet(join(X4,X3),join(X4,X2)),join(X4,meet(X3,X2)))) = meet(join(X4,X3),join(X4,X2)),
inference(transitivity,[status(thm)],[c48,c116]) ).
cnf(c118,plain,
join(meet(join(X4,X3),join(X4,X2)),join(X4,meet(X3,X2))) = meet(join(X4,X3),join(X4,X2)),
inference(transitivity,[status(thm)],[c41,c117]) ).
cnf(c119,plain,
meet(join(X4,X3),join(X4,X2)) = join(meet(join(X4,X3),join(X4,X2)),join(X4,meet(X3,X2))),
inference(symmetry,[status(thm)],[c118]) ).
cnf(c120,plain,
join(X4,meet(X3,X2)) = meet(join(X4,meet(X3,X2)),join(X4,X3)),
inference(symmetry,[status(thm)],[c35]) ).
cnf(c121,plain,
meet(meet(X3,X2),join(X4,meet(X3,X2))) = meet(meet(X3,X2),meet(join(X4,meet(X3,X2)),join(X4,X3))),
inference(congruence,[status(thm)],[c120]) ).
cnf(c122,plain,
join(meet(join(X4,X3),join(X4,X2)),meet(meet(X3,X2),join(X4,meet(X3,X2)))) = join(meet(join(X4,X3),join(X4,X2)),meet(meet(X3,X2),meet(join(X4,meet(X3,X2)),join(X4,X3)))),
inference(congruence,[status(thm)],[c121]) ).
cnf(c123,plain,
meet(meet(meet(X3,X2),join(X4,meet(X3,X2))),join(X4,X3)) = meet(meet(X3,X2),meet(join(X4,meet(X3,X2)),join(X4,X3))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c124,plain,
meet(meet(X3,X2),meet(join(X4,meet(X3,X2)),join(X4,X3))) = meet(meet(meet(X3,X2),join(X4,meet(X3,X2))),join(X4,X3)),
inference(symmetry,[status(thm)],[c123]) ).
cnf(c125,plain,
join(meet(join(X4,X3),join(X4,X2)),meet(meet(X3,X2),meet(join(X4,meet(X3,X2)),join(X4,X3)))) = join(meet(join(X4,X3),join(X4,X2)),meet(meet(meet(X3,X2),join(X4,meet(X3,X2))),join(X4,X3))),
inference(congruence,[status(thm)],[c124]) ).
cnf(c126,plain,
join(meet(X4,X3),meet(X2,X4)) = meet(X4,join(X2,X3)),
inference(substitution,[status(thm)],[c64]) ).
cnf(c127,plain,
join(X2,X3) = join(X3,X2),
inference(substitution,[status(thm)],[c60]) ).
cnf(c128,plain,
meet(X4,join(X2,X3)) = meet(X4,join(X3,X2)),
inference(congruence,[status(thm)],[c127]) ).
cnf(c129,plain,
join(meet(X4,X3),meet(X2,X4)) = meet(X4,join(X3,X2)),
inference(transitivity,[status(thm)],[c126,c128]) ).
cnf(c130,plain,
join(meet(join(X4,X3),join(X4,X2)),meet(meet(meet(X3,X2),join(X4,meet(X3,X2))),join(X4,X3))) = meet(join(X4,X3),join(join(X4,X2),meet(meet(X3,X2),join(X4,meet(X3,X2))))),
inference(substitution,[status(thm)],[c129]) ).
cnf(c131,plain,
join(X3,X2) = join(X2,X3),
inference(substitution,[status(thm)],[c60]) ).
cnf(c132,plain,
join(X2,X3) = join(X3,X2),
inference(symmetry,[status(thm)],[c131]) ).
cnf(c133,plain,
meet(X3,join(X2,X3)) = meet(X3,join(X3,X2)),
inference(congruence,[status(thm)],[c132]) ).
cnf(c134,plain,
meet(X3,join(X2,X3)) = join(X3,meet(X3,X2)),
inference(transitivity,[status(thm)],[c133,c46]) ).
cnf(c135,plain,
meet(X3,X2) = meet(X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c136,plain,
join(X3,meet(X3,X2)) = join(X3,meet(X2,X3)),
inference(congruence,[status(thm)],[c135]) ).
cnf(c137,plain,
meet(X3,join(X2,X3)) = join(X3,meet(X2,X3)),
inference(transitivity,[status(thm)],[c134,c136]) ).
cnf(c138,plain,
meet(meet(X4,X3),join(X2,meet(X4,X3))) = join(meet(X4,X3),meet(X2,meet(X4,X3))),
inference(substitution,[status(thm)],[c137]) ).
cnf(c139,plain,
meet(meet(X4,X3),X2) = meet(X2,meet(X4,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c140,plain,
meet(X2,meet(X4,X3)) = meet(meet(X4,X3),X2),
inference(symmetry,[status(thm)],[c139]) ).
cnf(c141,plain,
join(meet(X4,X3),meet(X2,meet(X4,X3))) = join(meet(X4,X3),meet(meet(X4,X3),X2)),
inference(congruence,[status(thm)],[c140]) ).
cnf(c142,plain,
join(meet(meet(X4,X3),X2),meet(X4,X3)) = join(meet(X4,X3),meet(meet(X4,X3),X2)),
inference(substitution,[status(thm)],[c60]) ).
cnf(c143,plain,
join(meet(X4,X3),meet(meet(X4,X3),X2)) = join(meet(meet(X4,X3),X2),meet(X4,X3)),
inference(symmetry,[status(thm)],[c142]) ).
cnf(c144,plain,
meet(X3,meet(X2,X3)) = meet(X2,meet(X3,X3)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c145,plain,
meet(X2,meet(X3,X3)) = meet(X2,X3),
inference(congruence,[status(thm)],[c44]) ).
cnf(c146,plain,
meet(X3,meet(X2,X3)) = meet(X2,X3),
inference(transitivity,[status(thm)],[c144,c145]) ).
cnf(c147,plain,
meet(X2,meet(X3,X2)) = meet(X3,X2),
inference(substitution,[status(thm)],[c146]) ).
cnf(c148,plain,
meet(X3,X2) = meet(X2,meet(X3,X2)),
inference(symmetry,[status(thm)],[c147]) ).
cnf(c149,plain,
join(meet(meet(X4,X3),X2),meet(X4,X3)) = join(meet(meet(X4,X3),X2),meet(X3,meet(X4,X3))),
inference(congruence,[status(thm)],[c148]) ).
cnf(c150,plain,
join(meet(meet(X4,X3),X2),meet(X3,meet(X4,X3))) = meet(meet(X4,X3),join(X3,X2)),
inference(substitution,[status(thm)],[c64]) ).
cnf(c151,plain,
join(X3,X2) = join(X2,X3),
inference(substitution,[status(thm)],[c60]) ).
cnf(c152,plain,
meet(meet(X4,X3),join(X3,X2)) = meet(meet(X4,X3),join(X2,X3)),
inference(congruence,[status(thm)],[c151]) ).
cnf(c153,plain,
join(meet(meet(X4,X3),X2),meet(X3,meet(X4,X3))) = meet(meet(X4,X3),join(X2,X3)),
inference(transitivity,[status(thm)],[c150,c152]) ).
cnf(c154,plain,
join(meet(meet(X4,X3),X2),meet(X4,X3)) = meet(meet(X4,X3),join(X2,X3)),
inference(transitivity,[status(thm)],[c149,c153]) ).
cnf(c155,plain,
join(meet(X4,X3),meet(meet(X4,X3),X2)) = meet(meet(X4,X3),join(X2,X3)),
inference(transitivity,[status(thm)],[c143,c154]) ).
cnf(c156,plain,
join(meet(X4,X3),meet(X2,meet(X4,X3))) = meet(meet(X4,X3),join(X2,X3)),
inference(transitivity,[status(thm)],[c141,c155]) ).
cnf(c157,plain,
meet(meet(X4,X3),join(X2,meet(X4,X3))) = meet(meet(X4,X3),join(X2,X3)),
inference(transitivity,[status(thm)],[c138,c156]) ).
cnf(c158,plain,
meet(meet(X2,X3),join(X4,meet(X2,X3))) = meet(meet(X2,X3),join(X4,X3)),
inference(substitution,[status(thm)],[c157]) ).
cnf(c159,plain,
join(join(X4,X3),meet(meet(X2,X3),join(X4,meet(X2,X3)))) = join(join(X4,X3),meet(meet(X2,X3),join(X4,X3))),
inference(congruence,[status(thm)],[c158]) ).
cnf(c160,plain,
meet(join(X4,X3),meet(X2,X3)) = meet(meet(X2,X3),join(X4,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c161,plain,
meet(meet(X2,X3),join(X4,X3)) = meet(join(X4,X3),meet(X2,X3)),
inference(symmetry,[status(thm)],[c160]) ).
cnf(c162,plain,
join(join(X4,X3),meet(meet(X2,X3),join(X4,X3))) = join(join(X4,X3),meet(join(X4,X3),meet(X2,X3))),
inference(congruence,[status(thm)],[c161]) ).
cnf(c163,plain,
meet(join(X4,X3),join(join(X4,X3),meet(X2,X3))) = join(join(X4,X3),meet(join(X4,X3),meet(X2,X3))),
inference(substitution,[status(thm)],[c46]) ).
cnf(c164,plain,
join(join(X4,X3),meet(join(X4,X3),meet(X2,X3))) = meet(join(X4,X3),join(join(X4,X3),meet(X2,X3))),
inference(symmetry,[status(thm)],[c163]) ).
cnf(c165,plain,
join(X2,join(X3,X2)) = join(X3,X2),
inference(substitution,[status(thm)],[c101]) ).
cnf(c166,plain,
join(X3,X2) = join(X2,join(X3,X2)),
inference(symmetry,[status(thm)],[c165]) ).
cnf(c167,plain,
meet(join(X4,X3),join(join(X4,X3),meet(X2,X3))) = meet(join(X3,join(X4,X3)),join(join(X4,X3),meet(X2,X3))),
inference(congruence,[status(thm)],[c166]) ).
cnf(c168,plain,
join(X2,X3) = join(X3,X2),
inference(substitution,[status(thm)],[c60]) ).
cnf(c169,plain,
join(X3,X2) = join(X2,X3),
inference(symmetry,[status(thm)],[c168]) ).
cnf(c170,plain,
meet(join(X4,X3),join(X3,meet(X2,X4))) = meet(join(X3,X4),join(X3,meet(X2,X4))),
inference(congruence,[status(thm)],[c169]) ).
cnf(c171,plain,
meet(join(X3,X4),join(X3,meet(X2,X4))) = join(X3,meet(X2,X4)),
inference(substitution,[status(thm)],[c28]) ).
cnf(c172,plain,
meet(join(X4,X3),join(X3,meet(X2,X4))) = join(X3,meet(X2,X4)),
inference(transitivity,[status(thm)],[c170,c171]) ).
cnf(c173,plain,
meet(join(X3,join(X4,X3)),join(join(X4,X3),meet(X2,X3))) = join(join(X4,X3),meet(X2,X3)),
inference(substitution,[status(thm)],[c172]) ).
cnf(c174,plain,
join(join(X4,X3),meet(X2,X3)) = join(meet(X2,X3),join(X4,X3)),
inference(substitution,[status(thm)],[c60]) ).
cnf(c175,plain,
join(X2,join(X3,X4)) = join(X3,join(X2,X4)),
inference(substitution,[status(thm)],[c97]) ).
cnf(c176,plain,
join(X2,join(X4,X3)) = join(X4,join(X2,X3)),
inference(substitution,[status(thm)],[c97]) ).
cnf(c177,plain,
join(X2,X3) = join(X3,X2),
inference(substitution,[status(thm)],[c60]) ).
cnf(c178,plain,
join(X4,join(X2,X3)) = join(X4,join(X3,X2)),
inference(congruence,[status(thm)],[c177]) ).
cnf(c179,plain,
join(X2,join(X4,X3)) = join(X4,join(X3,X2)),
inference(transitivity,[status(thm)],[c176,c178]) ).
cnf(c180,plain,
join(X4,join(X3,X2)) = join(X3,join(X2,X4)),
inference(substitution,[status(thm)],[c179]) ).
cnf(c181,plain,
join(X3,join(X2,X4)) = join(X4,join(X3,X2)),
inference(symmetry,[status(thm)],[c180]) ).
cnf(c182,plain,
join(X2,join(X3,X4)) = join(X4,join(X3,X2)),
inference(transitivity,[status(thm)],[c175,c181]) ).
cnf(c183,plain,
join(X3,join(X4,meet(X2,X3))) = join(meet(X2,X3),join(X4,X3)),
inference(substitution,[status(thm)],[c182]) ).
cnf(c184,plain,
join(meet(X2,X3),join(X4,X3)) = join(X3,join(X4,meet(X2,X3))),
inference(symmetry,[status(thm)],[c183]) ).
cnf(c185,plain,
join(join(X4,X3),meet(X2,X3)) = join(X3,join(X4,meet(X2,X3))),
inference(transitivity,[status(thm)],[c174,c184]) ).
cnf(c186,plain,
meet(join(X3,join(X4,X3)),join(join(X4,X3),meet(X2,X3))) = join(X3,join(X4,meet(X2,X3))),
inference(transitivity,[status(thm)],[c173,c185]) ).
cnf(c187,plain,
meet(join(X4,X3),join(join(X4,X3),meet(X2,X3))) = join(X3,join(X4,meet(X2,X3))),
inference(transitivity,[status(thm)],[c167,c186]) ).
cnf(c188,plain,
join(join(X4,X3),meet(join(X4,X3),meet(X2,X3))) = join(X3,join(X4,meet(X2,X3))),
inference(transitivity,[status(thm)],[c164,c187]) ).
cnf(c189,plain,
join(join(X4,X3),meet(meet(X2,X3),join(X4,X3))) = join(X3,join(X4,meet(X2,X3))),
inference(transitivity,[status(thm)],[c162,c188]) ).
cnf(c190,plain,
join(join(X4,X3),meet(meet(X2,X3),join(X4,meet(X2,X3)))) = join(X3,join(X4,meet(X2,X3))),
inference(transitivity,[status(thm)],[c159,c189]) ).
cnf(c191,plain,
join(join(X4,X2),meet(meet(X3,X2),join(X4,meet(X3,X2)))) = join(X2,join(X4,meet(X3,X2))),
inference(substitution,[status(thm)],[c190]) ).
cnf(c192,plain,
meet(join(X4,X3),join(join(X4,X2),meet(meet(X3,X2),join(X4,meet(X3,X2))))) = meet(join(X4,X3),join(X2,join(X4,meet(X3,X2)))),
inference(congruence,[status(thm)],[c191]) ).
cnf(c193,plain,
join(join(X5,meet(X4,X2)),X3) = join(X3,join(X5,meet(X4,X2))),
inference(substitution,[status(thm)],[c60]) ).
cnf(c194,plain,
join(X3,join(X5,meet(X4,X2))) = join(join(X5,meet(X4,X2)),X3),
inference(symmetry,[status(thm)],[c193]) ).
cnf(c195,plain,
meet(join(X5,X4),join(X3,join(X5,meet(X4,X2)))) = meet(join(X5,X4),join(join(X5,meet(X4,X2)),X3)),
inference(congruence,[status(thm)],[c194]) ).
cnf(c196,plain,
join(meet(join(X5,X4),X3),meet(join(X5,meet(X4,X2)),join(X5,X4))) = meet(join(X5,X4),join(join(X5,meet(X4,X2)),X3)),
inference(substitution,[status(thm)],[c64]) ).
cnf(c197,plain,
meet(join(X5,X4),join(join(X5,meet(X4,X2)),X3)) = join(meet(join(X5,X4),X3),meet(join(X5,meet(X4,X2)),join(X5,X4))),
inference(symmetry,[status(thm)],[c196]) ).
cnf(c198,plain,
join(meet(join(X5,X4),X3),meet(join(X5,meet(X4,X2)),join(X5,X4))) = join(meet(join(X5,X4),X3),join(X5,meet(X4,X2))),
inference(congruence,[status(thm)],[c35]) ).
cnf(c199,plain,
join(meet(join(X5,X4),X3),join(X5,meet(X4,X2))) = join(join(X5,meet(X4,X2)),meet(join(X5,X4),X3)),
inference(substitution,[status(thm)],[c60]) ).
cnf(c200,plain,
meet(join(X4,X3),X2) = meet(X2,join(X4,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c201,plain,
join(join(X5,meet(X4,X2)),meet(join(X5,X4),X3)) = join(join(X5,meet(X4,X2)),meet(X3,join(X5,X4))),
inference(congruence,[status(thm)],[c200]) ).
cnf(c202,plain,
join(meet(join(X5,X4),X3),join(X5,meet(X4,X2))) = join(join(X5,meet(X4,X2)),meet(X3,join(X5,X4))),
inference(transitivity,[status(thm)],[c199,c201]) ).
cnf(c203,plain,
join(meet(join(X5,X4),X3),meet(join(X5,meet(X4,X2)),join(X5,X4))) = join(join(X5,meet(X4,X2)),meet(X3,join(X5,X4))),
inference(transitivity,[status(thm)],[c198,c202]) ).
cnf(c204,plain,
meet(join(X5,X4),join(join(X5,meet(X4,X2)),X3)) = join(join(X5,meet(X4,X2)),meet(X3,join(X5,X4))),
inference(transitivity,[status(thm)],[c197,c203]) ).
cnf(c205,plain,
meet(join(X5,X4),join(X3,join(X5,meet(X4,X2)))) = join(join(X5,meet(X4,X2)),meet(X3,join(X5,X4))),
inference(transitivity,[status(thm)],[c195,c204]) ).
cnf(c206,plain,
meet(join(X4,X3),join(X2,join(X4,meet(X3,X2)))) = join(join(X4,meet(X3,X2)),meet(X2,join(X4,X3))),
inference(substitution,[status(thm)],[c205]) ).
cnf(c207,plain,
meet(join(X4,X3),X2) = meet(X2,join(X4,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c208,plain,
meet(X2,join(X4,X3)) = meet(join(X4,X3),X2),
inference(symmetry,[status(thm)],[c207]) ).
cnf(c209,plain,
meet(join(X5,meet(X4,X3)),meet(X2,join(X5,X4))) = meet(join(X5,meet(X4,X3)),meet(join(X5,X4),X2)),
inference(congruence,[status(thm)],[c208]) ).
cnf(c210,plain,
meet(meet(join(X5,meet(X4,X3)),join(X5,X4)),X2) = meet(join(X5,meet(X4,X3)),meet(join(X5,X4),X2)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c211,plain,
meet(join(X5,meet(X4,X3)),meet(join(X5,X4),X2)) = meet(meet(join(X5,meet(X4,X3)),join(X5,X4)),X2),
inference(symmetry,[status(thm)],[c210]) ).
cnf(c212,plain,
meet(meet(join(X5,meet(X4,X3)),join(X5,X4)),X2) = meet(join(X5,meet(X4,X3)),X2),
inference(congruence,[status(thm)],[c35]) ).
cnf(c213,plain,
meet(join(X5,meet(X4,X3)),X2) = meet(X2,join(X5,meet(X4,X3))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c214,plain,
meet(meet(join(X5,meet(X4,X3)),join(X5,X4)),X2) = meet(X2,join(X5,meet(X4,X3))),
inference(transitivity,[status(thm)],[c212,c213]) ).
cnf(c215,plain,
meet(join(X5,meet(X4,X3)),meet(join(X5,X4),X2)) = meet(X2,join(X5,meet(X4,X3))),
inference(transitivity,[status(thm)],[c211,c214]) ).
cnf(c216,plain,
meet(join(X5,meet(X4,X3)),meet(X2,join(X5,X4))) = meet(X2,join(X5,meet(X4,X3))),
inference(transitivity,[status(thm)],[c209,c215]) ).
cnf(c217,plain,
meet(join(X3,meet(X2,X4)),meet(X4,join(X3,X2))) = meet(X4,join(X3,meet(X2,X4))),
inference(substitution,[status(thm)],[c216]) ).
cnf(c218,plain,
meet(X4,join(X3,meet(X2,X4))) = meet(join(X3,meet(X2,X4)),meet(X4,join(X3,X2))),
inference(symmetry,[status(thm)],[c217]) ).
cnf(c219,plain,
meet(X4,join(X3,X2)) = join(meet(X2,X4),meet(X3,X4)),
inference(symmetry,[status(thm)],[c88]) ).
cnf(c220,plain,
meet(join(X3,meet(X2,X4)),meet(X4,join(X3,X2))) = meet(join(X3,meet(X2,X4)),join(meet(X2,X4),meet(X3,X4))),
inference(congruence,[status(thm)],[c219]) ).
cnf(c221,plain,
meet(join(X3,meet(X2,X4)),join(meet(X2,X4),meet(X3,X4))) = join(meet(X2,X4),meet(X3,X4)),
inference(substitution,[status(thm)],[c71]) ).
cnf(c222,plain,
meet(join(X3,meet(X2,X4)),join(meet(X2,X4),meet(X3,X4))) = meet(X4,join(X3,X2)),
inference(transitivity,[status(thm)],[c221,c88]) ).
cnf(c223,plain,
meet(join(X3,meet(X2,X4)),meet(X4,join(X3,X2))) = meet(X4,join(X3,X2)),
inference(transitivity,[status(thm)],[c220,c222]) ).
cnf(c224,plain,
meet(X4,join(X3,meet(X2,X4))) = meet(X4,join(X3,X2)),
inference(transitivity,[status(thm)],[c218,c223]) ).
cnf(c225,plain,
meet(X2,join(X4,meet(X3,X2))) = meet(X2,join(X4,X3)),
inference(substitution,[status(thm)],[c224]) ).
cnf(c226,plain,
meet(X2,join(X4,X3)) = meet(X2,join(X4,meet(X3,X2))),
inference(symmetry,[status(thm)],[c225]) ).
cnf(c227,plain,
join(join(X4,meet(X3,X2)),meet(X2,join(X4,X3))) = join(join(X4,meet(X3,X2)),meet(X2,join(X4,meet(X3,X2)))),
inference(congruence,[status(thm)],[c226]) ).
cnf(c228,plain,
meet(join(X4,meet(X3,X2)),X2) = meet(X2,join(X4,meet(X3,X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c229,plain,
meet(X2,join(X4,meet(X3,X2))) = meet(join(X4,meet(X3,X2)),X2),
inference(symmetry,[status(thm)],[c228]) ).
cnf(c230,plain,
join(join(X4,meet(X3,X2)),meet(X2,join(X4,meet(X3,X2)))) = join(join(X4,meet(X3,X2)),meet(join(X4,meet(X3,X2)),X2)),
inference(congruence,[status(thm)],[c229]) ).
cnf(c231,plain,
meet(join(X4,meet(X3,X2)),join(X2,join(X4,meet(X3,X2)))) = join(join(X4,meet(X3,X2)),meet(join(X4,meet(X3,X2)),X2)),
inference(substitution,[status(thm)],[c134]) ).
cnf(c232,plain,
join(join(X4,meet(X3,X2)),meet(join(X4,meet(X3,X2)),X2)) = meet(join(X4,meet(X3,X2)),join(X2,join(X4,meet(X3,X2)))),
inference(symmetry,[status(thm)],[c231]) ).
cnf(c233,plain,
join(join(X4,X2),join(X4,X3)) = join(join(X4,X3),join(X4,X2)),
inference(substitution,[status(thm)],[c60]) ).
cnf(c234,plain,
join(join(X4,X3),join(X4,X2)) = join(join(X4,X2),join(X4,X3)),
inference(symmetry,[status(thm)],[c233]) ).
cnf(c235,plain,
join(join(X4,X2),join(X4,X3)) = join(X4,join(X3,join(X4,X2))),
inference(substitution,[status(thm)],[c179]) ).
cnf(c236,plain,
join(join(X4,X2),X3) = join(X3,join(X4,X2)),
inference(substitution,[status(thm)],[c60]) ).
cnf(c237,plain,
join(X3,join(X4,X2)) = join(join(X4,X2),X3),
inference(symmetry,[status(thm)],[c236]) ).
cnf(c238,plain,
join(X4,join(X3,join(X4,X2))) = join(X4,join(join(X4,X2),X3)),
inference(congruence,[status(thm)],[c237]) ).
cnf(c239,plain,
join(join(X4,join(X4,X2)),X3) = join(X4,join(join(X4,X2),X3)),
inference(substitution,[status(thm)],[c92]) ).
cnf(c240,plain,
join(X4,join(join(X4,X2),X3)) = join(join(X4,join(X4,X2)),X3),
inference(symmetry,[status(thm)],[c239]) ).
cnf(c241,plain,
join(join(X3,X3),X2) = join(X3,join(X3,X2)),
inference(substitution,[status(thm)],[c92]) ).
cnf(c242,plain,
join(X3,join(X3,X2)) = join(join(X3,X3),X2),
inference(symmetry,[status(thm)],[c241]) ).
cnf(c243,plain,
join(join(X3,X3),X2) = join(X3,X2),
inference(congruence,[status(thm)],[c99]) ).
cnf(c244,plain,
join(X3,join(X3,X2)) = join(X3,X2),
inference(transitivity,[status(thm)],[c242,c243]) ).
cnf(c245,plain,
join(join(X4,join(X4,X2)),X3) = join(join(X4,X2),X3),
inference(congruence,[status(thm)],[c244]) ).
cnf(c246,plain,
join(join(X4,X2),X3) = join(X3,join(X4,X2)),
inference(substitution,[status(thm)],[c60]) ).
cnf(c247,plain,
join(join(X4,join(X4,X2)),X3) = join(X3,join(X4,X2)),
inference(transitivity,[status(thm)],[c245,c246]) ).
cnf(c248,plain,
join(X4,join(join(X4,X2),X3)) = join(X3,join(X4,X2)),
inference(transitivity,[status(thm)],[c240,c247]) ).
cnf(c249,plain,
join(X4,join(X3,join(X4,X2))) = join(X3,join(X4,X2)),
inference(transitivity,[status(thm)],[c238,c248]) ).
cnf(c250,plain,
join(X2,join(X4,X3)) = join(X3,join(X4,X2)),
inference(substitution,[status(thm)],[c182]) ).
cnf(c251,plain,
join(X3,join(X4,X2)) = join(X2,join(X4,X3)),
inference(symmetry,[status(thm)],[c250]) ).
cnf(c252,plain,
join(X4,join(X3,join(X4,X2))) = join(X2,join(X4,X3)),
inference(transitivity,[status(thm)],[c249,c251]) ).
cnf(c253,plain,
join(join(X4,X2),join(X4,X3)) = join(X2,join(X4,X3)),
inference(transitivity,[status(thm)],[c235,c252]) ).
cnf(c254,plain,
join(join(X4,X3),join(X4,X2)) = join(X2,join(X4,X3)),
inference(transitivity,[status(thm)],[c234,c253]) ).
cnf(c255,plain,
join(join(X4,meet(X3,X2)),join(X4,X2)) = join(X2,join(X4,meet(X3,X2))),
inference(substitution,[status(thm)],[c254]) ).
cnf(c256,plain,
join(X2,join(X4,meet(X3,X2))) = join(join(X4,meet(X3,X2)),join(X4,X2)),
inference(symmetry,[status(thm)],[c255]) ).
cnf(c257,plain,
meet(join(X4,meet(X3,X2)),join(X2,join(X4,meet(X3,X2)))) = meet(join(X4,meet(X3,X2)),join(join(X4,meet(X3,X2)),join(X4,X2))),
inference(congruence,[status(thm)],[c256]) ).
cnf(c258,plain,
meet(join(X4,meet(X3,X2)),join(join(X4,meet(X3,X2)),join(X4,X2))) = join(join(X4,meet(X3,X2)),meet(join(X4,meet(X3,X2)),join(X4,X2))),
inference(substitution,[status(thm)],[c46]) ).
cnf(c259,plain,
join(join(X4,meet(X3,X2)),meet(join(X4,meet(X3,X2)),join(X4,X2))) = join(join(X4,meet(X3,X2)),join(X4,meet(X3,X2))),
inference(congruence,[status(thm)],[c30]) ).
cnf(c260,plain,
join(join(X4,meet(X3,X2)),join(X4,meet(X3,X2))) = join(X4,meet(X3,X2)),
inference(substitution,[status(thm)],[c99]) ).
cnf(c261,plain,
join(join(X4,meet(X3,X2)),meet(join(X4,meet(X3,X2)),join(X4,X2))) = join(X4,meet(X3,X2)),
inference(transitivity,[status(thm)],[c259,c260]) ).
cnf(c262,plain,
meet(join(X4,meet(X3,X2)),join(join(X4,meet(X3,X2)),join(X4,X2))) = join(X4,meet(X3,X2)),
inference(transitivity,[status(thm)],[c258,c261]) ).
cnf(c263,plain,
meet(join(X4,meet(X3,X2)),join(X2,join(X4,meet(X3,X2)))) = join(X4,meet(X3,X2)),
inference(transitivity,[status(thm)],[c257,c262]) ).
cnf(c264,plain,
join(join(X4,meet(X3,X2)),meet(join(X4,meet(X3,X2)),X2)) = join(X4,meet(X3,X2)),
inference(transitivity,[status(thm)],[c232,c263]) ).
cnf(c265,plain,
join(join(X4,meet(X3,X2)),meet(X2,join(X4,meet(X3,X2)))) = join(X4,meet(X3,X2)),
inference(transitivity,[status(thm)],[c230,c264]) ).
cnf(c266,plain,
join(join(X4,meet(X3,X2)),meet(X2,join(X4,X3))) = join(X4,meet(X3,X2)),
inference(transitivity,[status(thm)],[c227,c265]) ).
cnf(c267,plain,
meet(join(X4,X3),join(X2,join(X4,meet(X3,X2)))) = join(X4,meet(X3,X2)),
inference(transitivity,[status(thm)],[c206,c266]) ).
cnf(c268,plain,
meet(join(X4,X3),join(join(X4,X2),meet(meet(X3,X2),join(X4,meet(X3,X2))))) = join(X4,meet(X3,X2)),
inference(transitivity,[status(thm)],[c192,c267]) ).
cnf(c269,plain,
join(meet(join(X4,X3),join(X4,X2)),meet(meet(meet(X3,X2),join(X4,meet(X3,X2))),join(X4,X3))) = join(X4,meet(X3,X2)),
inference(transitivity,[status(thm)],[c130,c268]) ).
cnf(c270,plain,
join(meet(join(X4,X3),join(X4,X2)),meet(meet(X3,X2),meet(join(X4,meet(X3,X2)),join(X4,X3)))) = join(X4,meet(X3,X2)),
inference(transitivity,[status(thm)],[c125,c269]) ).
cnf(c271,plain,
join(meet(join(X4,X3),join(X4,X2)),meet(meet(X3,X2),join(X4,meet(X3,X2)))) = join(X4,meet(X3,X2)),
inference(transitivity,[status(thm)],[c122,c270]) ).
cnf(c272,plain,
join(X4,meet(X3,X2)) = join(meet(join(X4,X3),join(X4,X2)),meet(meet(X3,X2),join(X4,meet(X3,X2)))),
inference(symmetry,[status(thm)],[c271]) ).
cnf(c273,plain,
join(meet(join(X4,X3),join(X4,X2)),join(X4,meet(X3,X2))) = join(meet(join(X4,X3),join(X4,X2)),join(meet(join(X4,X3),join(X4,X2)),meet(meet(X3,X2),join(X4,meet(X3,X2))))),
inference(congruence,[status(thm)],[c272]) ).
cnf(c274,plain,
join(meet(join(X4,X3),join(X4,X2)),join(meet(join(X4,X3),join(X4,X2)),meet(meet(X3,X2),join(X4,meet(X3,X2))))) = join(meet(join(X4,X3),join(X4,X2)),meet(meet(X3,X2),join(X4,meet(X3,X2)))),
inference(substitution,[status(thm)],[c244]) ).
cnf(c275,plain,
join(meet(join(X4,X3),join(X4,X2)),join(meet(join(X4,X3),join(X4,X2)),meet(meet(X3,X2),join(X4,meet(X3,X2))))) = join(X4,meet(X3,X2)),
inference(transitivity,[status(thm)],[c274,c271]) ).
cnf(c276,plain,
join(meet(join(X4,X3),join(X4,X2)),join(X4,meet(X3,X2))) = join(X4,meet(X3,X2)),
inference(transitivity,[status(thm)],[c273,c275]) ).
cnf(c277,plain,
meet(join(X4,X3),join(X4,X2)) = join(X4,meet(X3,X2)),
inference(transitivity,[status(thm)],[c119,c276]) ).
cnf(c278,plain,
meet(join(a,b),join(a,c)) = join(a,meet(b,c)),
inference(substitution,[status(thm)],[c277]) ).
cnf(c279,plain,
join(a,meet(b,c)) = meet(join(a,b),join(a,c)),
inference(symmetry,[status(thm)],[c278]) ).
cnf(c280,plain,
$false,
inference(resolution,[status(thm)],[c1,c279]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT019-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n001.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 14:02:45 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.18/0.78 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-regeneralise
% 2.18/0.78
% 2.18/0.78 % SZS status Unsatisfiable
% 2.18/0.78
% 2.18/0.79 % SZS output start CNFRefutation
% See solution above
% 3.00/0.87
% 3.00/0.87 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------