%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LAT009-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /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 : Tue Sep 29 11:42:49 AM UTC 2026
% Result : Unsatisfiable 15.04s 2.31s
% Output : CNFRefutation 16.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 63
% Number of leaves : 10
% Syntax : Number of clauses : 372 ( 372 unt; 0 nHn; 12 RR)
% Number of literals : 372 ( 371 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 : 1000 ( 52 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
join(a,meet(b,c)) != meet(join(a,b),join(a,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_distributivity) ).
cnf(c2,axiom,
join(X,Y) = join(Y,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_join) ).
cnf(c3,plain,
join(X3,X2) = join(X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
join(X2,X3) = join(X3,X2),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
meet(join(X4,X3),join(X2,X3)) = meet(join(X4,X3),join(X3,X2)),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,plain,
join(X2,X3) = join(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c7,plain,
join(X3,X2) = join(X2,X3),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,plain,
meet(join(X4,X3),join(X3,X2)) = meet(join(X4,X3),join(X2,X3)),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,axiom,
meet(X2,Y2) = meet(Y2,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_meet) ).
cnf(c10,plain,
meet(join(X2,X3),join(X4,X3)) = meet(join(X4,X3),join(X2,X3)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c11,plain,
meet(join(X4,X3),join(X2,X3)) = meet(join(X2,X3),join(X4,X3)),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c12,plain,
meet(X3,X2) = meet(X2,X3),
inference(substitution,[status(thm)],[c9]) ).
cnf(c13,plain,
meet(X2,X3) = meet(X3,X2),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,plain,
join(meet(X4,X3),meet(X2,X3)) = join(meet(X4,X3),meet(X3,X2)),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,plain,
meet(X2,X3) = meet(X3,X2),
inference(substitution,[status(thm)],[c9]) ).
cnf(c16,plain,
meet(X3,X2) = meet(X2,X3),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c17,plain,
join(meet(X4,X3),meet(X3,X2)) = join(meet(X3,X4),meet(X3,X2)),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,plain,
meet(X2,X3) = meet(X3,X2),
inference(substitution,[status(thm)],[c9]) ).
cnf(c19,plain,
meet(X3,X2) = meet(X2,X3),
inference(symmetry,[status(thm)],[c18]) ).
cnf(c20,plain,
join(meet(X4,X3),meet(X4,X2)) = join(meet(X4,X3),meet(X2,X4)),
inference(congruence,[status(thm)],[c19]) ).
cnf(c21,plain,
join(X4,meet(X2,X3)) = join(meet(X2,X3),X4),
inference(substitution,[status(thm)],[c2]) ).
cnf(c22,plain,
join(meet(X2,X3),X4) = join(X4,meet(X2,X3)),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c23,plain,
meet(X3,join(meet(X2,X3),X4)) = meet(X3,join(X4,meet(X2,X3))),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,plain,
join(X4,meet(X3,join(meet(X2,X3),X4))) = join(X4,meet(X3,join(X4,meet(X2,X3)))),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,plain,
meet(X3,X2) = meet(X2,X3),
inference(substitution,[status(thm)],[c9]) ).
cnf(c26,plain,
meet(X2,X3) = meet(X3,X2),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c27,plain,
join(X4,meet(X2,X3)) = join(X4,meet(X3,X2)),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,plain,
meet(X3,join(X4,meet(X2,X3))) = meet(X3,join(X4,meet(X3,X2))),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,plain,
join(X4,meet(X3,join(X4,meet(X2,X3)))) = join(X4,meet(X3,join(X4,meet(X3,X2)))),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
meet(X2,X3) = meet(X3,X2),
inference(substitution,[status(thm)],[c9]) ).
cnf(c31,plain,
meet(X3,X2) = meet(X2,X3),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c32,plain,
join(meet(X4,X3),meet(X4,join(X2,meet(X4,X3)))) = join(meet(X3,X4),meet(X4,join(X2,meet(X4,X3)))),
inference(congruence,[status(thm)],[c31]) ).
cnf(c33,plain,
meet(X2,X3) = meet(X3,X2),
inference(substitution,[status(thm)],[c9]) ).
cnf(c34,plain,
meet(X3,X2) = meet(X2,X3),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c35,plain,
join(X2,meet(X4,X3)) = join(X2,meet(X3,X4)),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,plain,
meet(X4,join(X2,meet(X4,X3))) = meet(X4,join(X2,meet(X3,X4))),
inference(congruence,[status(thm)],[c35]) ).
cnf(c37,plain,
join(meet(X3,X4),meet(X4,join(X2,meet(X4,X3)))) = join(meet(X3,X4),meet(X4,join(X2,meet(X3,X4)))),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,plain,
join(meet(X4,join(X2,meet(X3,X4))),meet(X3,X4)) = join(meet(X3,X4),meet(X4,join(X2,meet(X3,X4)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c39,plain,
join(meet(X3,X4),meet(X4,join(X2,meet(X3,X4)))) = join(meet(X4,join(X2,meet(X3,X4))),meet(X3,X4)),
inference(symmetry,[status(thm)],[c38]) ).
cnf(c40,plain,
meet(X2,X3) = meet(X3,X2),
inference(substitution,[status(thm)],[c9]) ).
cnf(c41,plain,
meet(X3,X2) = meet(X2,X3),
inference(symmetry,[status(thm)],[c40]) ).
cnf(c42,plain,
join(X2,meet(X4,X3)) = join(X2,meet(X3,X4)),
inference(congruence,[status(thm)],[c41]) ).
cnf(c43,plain,
meet(X3,join(X2,meet(X4,X3))) = meet(X3,join(X2,meet(X3,X4))),
inference(congruence,[status(thm)],[c42]) ).
cnf(c44,plain,
meet(X4,meet(X3,join(X2,meet(X4,X3)))) = meet(X4,meet(X3,join(X2,meet(X3,X4)))),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,plain,
join(meet(X3,X4),X2) = join(X2,meet(X3,X4)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c46,plain,
join(X2,meet(X3,X4)) = join(meet(X3,X4),X2),
inference(symmetry,[status(thm)],[c45]) ).
cnf(c47,plain,
meet(X3,join(X2,meet(X3,X4))) = meet(X3,join(meet(X3,X4),X2)),
inference(congruence,[status(thm)],[c46]) ).
cnf(c48,plain,
meet(X4,meet(X3,join(X2,meet(X3,X4)))) = meet(X4,meet(X3,join(meet(X3,X4),X2))),
inference(congruence,[status(thm)],[c47]) ).
cnf(c49,plain,
meet(meet(X3,X2),X4) = meet(X4,meet(X3,X2)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c50,plain,
meet(X4,meet(X3,X2)) = meet(meet(X3,X2),X4),
inference(symmetry,[status(thm)],[c49]) ).
cnf(c51,axiom,
meet(meet(X2,Y2),Z) = meet(X2,meet(Y2,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_meet) ).
cnf(c52,plain,
meet(meet(X3,X2),X4) = meet(X3,meet(X2,X4)),
inference(substitution,[status(thm)],[c51]) ).
cnf(c53,plain,
meet(X2,X3) = meet(X3,X2),
inference(substitution,[status(thm)],[c9]) ).
cnf(c54,plain,
meet(X3,meet(X2,X4)) = meet(X3,meet(X4,X2)),
inference(congruence,[status(thm)],[c53]) ).
cnf(c55,plain,
meet(meet(X3,X2),X4) = meet(X3,meet(X4,X2)),
inference(transitivity,[status(thm)],[c52,c54]) ).
cnf(c56,plain,
meet(X4,meet(X3,X2)) = meet(X3,meet(X4,X2)),
inference(transitivity,[status(thm)],[c50,c55]) ).
cnf(c57,plain,
meet(X3,meet(X4,join(meet(X3,X4),X2))) = meet(X4,meet(X3,join(meet(X3,X4),X2))),
inference(substitution,[status(thm)],[c56]) ).
cnf(c58,plain,
meet(X4,meet(X3,join(meet(X3,X4),X2))) = meet(X3,meet(X4,join(meet(X3,X4),X2))),
inference(symmetry,[status(thm)],[c57]) ).
cnf(c59,plain,
meet(meet(X3,X4),join(meet(X3,X4),X2)) = meet(X3,meet(X4,join(meet(X3,X4),X2))),
inference(substitution,[status(thm)],[c51]) ).
cnf(c60,plain,
meet(X3,meet(X4,join(meet(X3,X4),X2))) = meet(meet(X3,X4),join(meet(X3,X4),X2)),
inference(symmetry,[status(thm)],[c59]) ).
cnf(c61,axiom,
meet(X2,join(X2,Y2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorption1) ).
cnf(c62,plain,
meet(meet(X3,X4),join(meet(X3,X4),X2)) = meet(X3,X4),
inference(substitution,[status(thm)],[c61]) ).
cnf(c63,plain,
meet(X2,X3) = meet(X3,X2),
inference(substitution,[status(thm)],[c9]) ).
cnf(c64,plain,
meet(meet(X3,X4),join(meet(X3,X4),X2)) = meet(X4,X3),
inference(transitivity,[status(thm)],[c62,c63]) ).
cnf(c65,plain,
meet(X3,meet(X4,join(meet(X3,X4),X2))) = meet(X4,X3),
inference(transitivity,[status(thm)],[c60,c64]) ).
cnf(c66,plain,
meet(X4,meet(X3,join(meet(X3,X4),X2))) = meet(X4,X3),
inference(transitivity,[status(thm)],[c58,c65]) ).
cnf(c67,plain,
meet(X4,meet(X3,join(X2,meet(X3,X4)))) = meet(X4,X3),
inference(transitivity,[status(thm)],[c48,c66]) ).
cnf(c68,plain,
meet(X4,meet(X3,join(X2,meet(X4,X3)))) = meet(X4,X3),
inference(transitivity,[status(thm)],[c44,c67]) ).
cnf(c69,plain,
meet(X3,meet(X4,join(X2,meet(X3,X4)))) = meet(X3,X4),
inference(substitution,[status(thm)],[c68]) ).
cnf(c70,plain,
meet(X3,X4) = meet(X3,meet(X4,join(X2,meet(X3,X4)))),
inference(symmetry,[status(thm)],[c69]) ).
cnf(c71,plain,
join(meet(X4,join(X2,meet(X3,X4))),meet(X3,X4)) = join(meet(X4,join(X2,meet(X3,X4))),meet(X3,meet(X4,join(X2,meet(X3,X4))))),
inference(congruence,[status(thm)],[c70]) ).
cnf(c72,plain,
meet(X3,X2) = meet(X2,X3),
inference(substitution,[status(thm)],[c9]) ).
cnf(c73,plain,
meet(X2,X3) = meet(X3,X2),
inference(symmetry,[status(thm)],[c72]) ).
cnf(c74,plain,
join(X3,meet(X2,X3)) = join(X3,meet(X3,X2)),
inference(congruence,[status(thm)],[c73]) ).
cnf(c75,axiom,
join(X2,meet(X2,Y2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorption2) ).
cnf(c76,plain,
join(X3,meet(X3,X2)) = X3,
inference(substitution,[status(thm)],[c75]) ).
cnf(c77,plain,
join(X3,meet(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c74,c76]) ).
cnf(c78,plain,
join(meet(X4,join(X2,meet(X3,X4))),meet(X3,meet(X4,join(X2,meet(X3,X4))))) = meet(X4,join(X2,meet(X3,X4))),
inference(substitution,[status(thm)],[c77]) ).
cnf(c79,plain,
meet(X2,X3) = meet(X3,X2),
inference(substitution,[status(thm)],[c9]) ).
cnf(c80,plain,
join(X2,meet(X3,X4)) = join(X2,meet(X4,X3)),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,plain,
meet(X4,join(X2,meet(X3,X4))) = meet(X4,join(X2,meet(X4,X3))),
inference(congruence,[status(thm)],[c80]) ).
cnf(c82,plain,
join(meet(X4,join(X2,meet(X3,X4))),meet(X3,meet(X4,join(X2,meet(X3,X4))))) = meet(X4,join(X2,meet(X4,X3))),
inference(transitivity,[status(thm)],[c78,c81]) ).
cnf(c83,plain,
join(meet(X4,join(X2,meet(X3,X4))),meet(X3,X4)) = meet(X4,join(X2,meet(X4,X3))),
inference(transitivity,[status(thm)],[c71,c82]) ).
cnf(c84,plain,
join(meet(X3,X4),meet(X4,join(X2,meet(X3,X4)))) = meet(X4,join(X2,meet(X4,X3))),
inference(transitivity,[status(thm)],[c39,c83]) ).
cnf(c85,plain,
join(meet(X3,X4),meet(X4,join(X2,meet(X4,X3)))) = meet(X4,join(X2,meet(X4,X3))),
inference(transitivity,[status(thm)],[c37,c84]) ).
cnf(c86,plain,
join(meet(X4,X3),meet(X4,join(X2,meet(X4,X3)))) = meet(X4,join(X2,meet(X4,X3))),
inference(transitivity,[status(thm)],[c32,c85]) ).
cnf(c87,plain,
join(meet(X3,X2),meet(X3,join(X4,meet(X3,X2)))) = meet(X3,join(X4,meet(X3,X2))),
inference(substitution,[status(thm)],[c86]) ).
cnf(c88,plain,
meet(X3,join(X4,meet(X3,X2))) = join(meet(X3,X2),meet(X3,join(X4,meet(X3,X2)))),
inference(symmetry,[status(thm)],[c87]) ).
cnf(c89,plain,
join(X4,meet(X3,join(X4,meet(X3,X2)))) = join(X4,join(meet(X3,X2),meet(X3,join(X4,meet(X3,X2))))),
inference(congruence,[status(thm)],[c88]) ).
cnf(c90,plain,
join(X2,X3) = join(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c91,plain,
join(X3,X2) = join(X2,X3),
inference(symmetry,[status(thm)],[c90]) ).
cnf(c92,plain,
meet(X2,join(X4,X3)) = meet(X2,join(X3,X4)),
inference(congruence,[status(thm)],[c91]) ).
cnf(c93,plain,
join(X3,meet(X2,join(X4,X3))) = join(X3,meet(X2,join(X3,X4))),
inference(congruence,[status(thm)],[c92]) ).
cnf(c94,plain,
join(X4,join(X3,meet(X2,join(X4,X3)))) = join(X4,join(X3,meet(X2,join(X3,X4)))),
inference(congruence,[status(thm)],[c93]) ).
cnf(c95,plain,
meet(join(X3,X4),X2) = meet(X2,join(X3,X4)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c96,plain,
meet(X2,join(X3,X4)) = meet(join(X3,X4),X2),
inference(symmetry,[status(thm)],[c95]) ).
cnf(c97,plain,
join(X3,meet(X2,join(X3,X4))) = join(X3,meet(join(X3,X4),X2)),
inference(congruence,[status(thm)],[c96]) ).
cnf(c98,plain,
join(X4,join(X3,meet(X2,join(X3,X4)))) = join(X4,join(X3,meet(join(X3,X4),X2))),
inference(congruence,[status(thm)],[c97]) ).
cnf(c99,plain,
join(join(X4,X2),X3) = join(X3,join(X4,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c100,plain,
join(X3,join(X4,X2)) = join(join(X4,X2),X3),
inference(symmetry,[status(thm)],[c99]) ).
cnf(c101,axiom,
join(join(X2,Y2),Z2) = join(X2,join(Y2,Z2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_join) ).
cnf(c102,plain,
join(join(X4,X2),X3) = join(X4,join(X2,X3)),
inference(substitution,[status(thm)],[c101]) ).
cnf(c103,plain,
join(X2,X3) = join(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c104,plain,
join(X4,join(X2,X3)) = join(X4,join(X3,X2)),
inference(congruence,[status(thm)],[c103]) ).
cnf(c105,plain,
join(join(X4,X2),X3) = join(X4,join(X3,X2)),
inference(transitivity,[status(thm)],[c102,c104]) ).
cnf(c106,plain,
join(X3,join(X4,X2)) = join(X4,join(X3,X2)),
inference(transitivity,[status(thm)],[c100,c105]) ).
cnf(c107,plain,
join(X4,join(X3,meet(join(X3,X4),X2))) = join(X3,join(X4,meet(join(X3,X4),X2))),
inference(substitution,[status(thm)],[c106]) ).
cnf(c108,plain,
join(join(X3,X4),meet(join(X3,X4),X2)) = join(X3,join(X4,meet(join(X3,X4),X2))),
inference(substitution,[status(thm)],[c101]) ).
cnf(c109,plain,
join(X3,join(X4,meet(join(X3,X4),X2))) = join(join(X3,X4),meet(join(X3,X4),X2)),
inference(symmetry,[status(thm)],[c108]) ).
cnf(c110,plain,
join(join(X3,X4),meet(join(X3,X4),X2)) = join(X3,X4),
inference(substitution,[status(thm)],[c75]) ).
cnf(c111,plain,
join(X2,X3) = join(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c112,plain,
join(join(X3,X4),meet(join(X3,X4),X2)) = join(X4,X3),
inference(transitivity,[status(thm)],[c110,c111]) ).
cnf(c113,plain,
join(X3,join(X4,meet(join(X3,X4),X2))) = join(X4,X3),
inference(transitivity,[status(thm)],[c109,c112]) ).
cnf(c114,plain,
join(X4,join(X3,meet(join(X3,X4),X2))) = join(X4,X3),
inference(transitivity,[status(thm)],[c107,c113]) ).
cnf(c115,plain,
join(X4,join(X3,meet(X2,join(X3,X4)))) = join(X4,X3),
inference(transitivity,[status(thm)],[c98,c114]) ).
cnf(c116,plain,
join(X4,join(X3,meet(X2,join(X4,X3)))) = join(X4,X3),
inference(transitivity,[status(thm)],[c94,c115]) ).
cnf(c117,plain,
join(X4,join(meet(X3,X2),meet(X3,join(X4,meet(X3,X2))))) = join(X4,meet(X3,X2)),
inference(substitution,[status(thm)],[c116]) ).
cnf(c118,plain,
join(X4,meet(X3,join(X4,meet(X3,X2)))) = join(X4,meet(X3,X2)),
inference(transitivity,[status(thm)],[c89,c117]) ).
cnf(c119,plain,
join(X4,meet(X3,join(X4,meet(X2,X3)))) = join(X4,meet(X3,X2)),
inference(transitivity,[status(thm)],[c29,c118]) ).
cnf(c120,plain,
join(X4,meet(X3,join(meet(X2,X3),X4))) = join(X4,meet(X3,X2)),
inference(transitivity,[status(thm)],[c24,c119]) ).
cnf(c121,plain,
join(meet(X4,X3),meet(X2,join(meet(X4,X2),meet(X4,X3)))) = join(meet(X4,X3),meet(X2,X4)),
inference(substitution,[status(thm)],[c120]) ).
cnf(c122,plain,
join(meet(X4,X3),meet(X2,X4)) = join(meet(X4,X3),meet(X2,join(meet(X4,X2),meet(X4,X3)))),
inference(symmetry,[status(thm)],[c121]) ).
cnf(c123,plain,
meet(meet(X3,X3),X2) = meet(X3,meet(X3,X2)),
inference(substitution,[status(thm)],[c51]) ).
cnf(c124,plain,
meet(X3,meet(X3,X2)) = meet(meet(X3,X3),X2),
inference(symmetry,[status(thm)],[c123]) ).
cnf(c125,axiom,
meet(X2,X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c126,plain,
meet(meet(X3,X3),X2) = meet(X3,X2),
inference(congruence,[status(thm)],[c125]) ).
cnf(c127,plain,
meet(X3,meet(X3,X2)) = meet(X3,X2),
inference(transitivity,[status(thm)],[c124,c126]) ).
cnf(c128,plain,
meet(X3,X2) = meet(X3,meet(X3,X2)),
inference(symmetry,[status(thm)],[c127]) ).
cnf(c129,plain,
join(meet(X4,X3),meet(X2,join(meet(X4,X2),meet(X4,X3)))) = join(meet(X4,meet(X4,X3)),meet(X2,join(meet(X4,X2),meet(X4,X3)))),
inference(congruence,[status(thm)],[c128]) ).
cnf(c130,plain,
meet(X2,X3) = meet(X3,X2),
inference(substitution,[status(thm)],[c9]) ).
cnf(c131,plain,
meet(X3,X2) = meet(X2,X3),
inference(symmetry,[status(thm)],[c130]) ).
cnf(c132,plain,
join(meet(X4,X3),meet(X2,join(meet(X4,X2),X3))) = join(meet(X3,X4),meet(X2,join(meet(X4,X2),X3))),
inference(congruence,[status(thm)],[c131]) ).
cnf(c133,plain,
meet(join(meet(X3,X2),X4),X2) = meet(X2,join(meet(X3,X2),X4)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c134,plain,
meet(X2,join(meet(X3,X2),X4)) = meet(join(meet(X3,X2),X4),X2),
inference(symmetry,[status(thm)],[c133]) ).
cnf(c135,plain,
join(meet(X4,X3),meet(X2,join(meet(X3,X2),X4))) = join(meet(X4,X3),meet(join(meet(X3,X2),X4),X2)),
inference(congruence,[status(thm)],[c134]) ).
cnf(c136,plain,
join(meet(join(meet(X3,X2),X4),X2),meet(X4,X3)) = join(meet(X4,X3),meet(join(meet(X3,X2),X4),X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c137,plain,
join(meet(X4,X3),meet(join(meet(X3,X2),X4),X2)) = join(meet(join(meet(X3,X2),X4),X2),meet(X4,X3)),
inference(symmetry,[status(thm)],[c136]) ).
cnf(c138,axiom,
join(meet(join(meet(X2,Y2),Z2),Y2),meet(Z2,X2)) = meet(join(meet(join(X2,Y2),Z2),Y2),join(Z2,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity_dual) ).
cnf(c139,plain,
join(meet(join(meet(X3,X2),X4),X2),meet(X4,X3)) = meet(join(meet(join(X3,X2),X4),X2),join(X4,X3)),
inference(substitution,[status(thm)],[c138]) ).
cnf(c140,plain,
meet(join(meet(join(X3,X2),X4),X2),join(X4,X3)) = meet(join(X4,X3),join(meet(join(X3,X2),X4),X2)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c141,plain,
join(meet(join(X3,X2),X4),X2) = join(X2,meet(join(X3,X2),X4)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c142,plain,
meet(join(X4,X3),join(meet(join(X3,X2),X4),X2)) = meet(join(X4,X3),join(X2,meet(join(X3,X2),X4))),
inference(congruence,[status(thm)],[c141]) ).
cnf(c143,plain,
meet(join(meet(join(X3,X2),X4),X2),join(X4,X3)) = meet(join(X4,X3),join(X2,meet(join(X3,X2),X4))),
inference(transitivity,[status(thm)],[c140,c142]) ).
cnf(c144,plain,
join(meet(join(meet(X3,X2),X4),X2),meet(X4,X3)) = meet(join(X4,X3),join(X2,meet(join(X3,X2),X4))),
inference(transitivity,[status(thm)],[c139,c143]) ).
cnf(c145,plain,
join(meet(X4,X3),meet(join(meet(X3,X2),X4),X2)) = meet(join(X4,X3),join(X2,meet(join(X3,X2),X4))),
inference(transitivity,[status(thm)],[c137,c144]) ).
cnf(c146,plain,
join(meet(X4,X3),meet(X2,join(meet(X3,X2),X4))) = meet(join(X4,X3),join(X2,meet(join(X3,X2),X4))),
inference(transitivity,[status(thm)],[c135,c145]) ).
cnf(c147,plain,
join(meet(X3,X4),meet(X2,join(meet(X4,X2),X3))) = meet(join(X3,X4),join(X2,meet(join(X4,X2),X3))),
inference(substitution,[status(thm)],[c146]) ).
cnf(c148,plain,
join(X2,X3) = join(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c149,plain,
meet(join(X3,X4),join(X2,meet(join(X4,X2),X3))) = meet(join(X4,X3),join(X2,meet(join(X4,X2),X3))),
inference(congruence,[status(thm)],[c148]) ).
cnf(c150,plain,
meet(join(X4,X2),X3) = meet(X3,join(X4,X2)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c151,plain,
join(X2,meet(join(X4,X2),X3)) = join(X2,meet(X3,join(X4,X2))),
inference(congruence,[status(thm)],[c150]) ).
cnf(c152,plain,
meet(join(X4,X3),join(X2,meet(join(X4,X2),X3))) = meet(join(X4,X3),join(X2,meet(X3,join(X4,X2)))),
inference(congruence,[status(thm)],[c151]) ).
cnf(c153,plain,
join(X3,X2) = join(X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c154,plain,
meet(X3,join(X4,X2)) = meet(X3,join(X2,X4)),
inference(congruence,[status(thm)],[c153]) ).
cnf(c155,plain,
join(X2,meet(X3,join(X4,X2))) = join(X2,meet(X3,join(X2,X4))),
inference(congruence,[status(thm)],[c154]) ).
cnf(c156,plain,
meet(join(X4,X3),join(X2,meet(X3,join(X4,X2)))) = meet(join(X4,X3),join(X2,meet(X3,join(X2,X4)))),
inference(congruence,[status(thm)],[c155]) ).
cnf(c157,plain,
meet(join(X4,X3),join(X2,meet(join(X4,X2),X3))) = meet(join(X4,X3),join(X2,meet(X3,join(X2,X4)))),
inference(transitivity,[status(thm)],[c152,c156]) ).
cnf(c158,plain,
meet(join(X3,X4),join(X2,meet(join(X4,X2),X3))) = meet(join(X4,X3),join(X2,meet(X3,join(X2,X4)))),
inference(transitivity,[status(thm)],[c149,c157]) ).
cnf(c159,plain,
join(meet(X3,X4),meet(X2,join(meet(X4,X2),X3))) = meet(join(X4,X3),join(X2,meet(X3,join(X2,X4)))),
inference(transitivity,[status(thm)],[c147,c158]) ).
cnf(c160,plain,
join(meet(X4,X3),meet(X2,join(meet(X4,X2),X3))) = meet(join(X4,X3),join(X2,meet(X3,join(X2,X4)))),
inference(transitivity,[status(thm)],[c132,c159]) ).
cnf(c161,plain,
join(meet(X4,meet(X4,X3)),meet(X2,join(meet(X4,X2),meet(X4,X3)))) = meet(join(X4,meet(X4,X3)),join(X2,meet(meet(X4,X3),join(X2,X4)))),
inference(substitution,[status(thm)],[c160]) ).
cnf(c162,plain,
join(X3,meet(X3,X2)) = X3,
inference(substitution,[status(thm)],[c75]) ).
cnf(c163,plain,
meet(join(X4,meet(X4,X3)),join(X2,meet(meet(X4,X3),join(X2,X4)))) = meet(X4,join(X2,meet(meet(X4,X3),join(X2,X4)))),
inference(congruence,[status(thm)],[c162]) ).
cnf(c164,plain,
meet(meet(X4,X3),join(X2,X4)) = meet(X4,meet(X3,join(X2,X4))),
inference(substitution,[status(thm)],[c51]) ).
cnf(c165,plain,
join(X2,meet(meet(X4,X3),join(X2,X4))) = join(X2,meet(X4,meet(X3,join(X2,X4)))),
inference(congruence,[status(thm)],[c164]) ).
cnf(c166,plain,
meet(X4,join(X2,meet(meet(X4,X3),join(X2,X4)))) = meet(X4,join(X2,meet(X4,meet(X3,join(X2,X4))))),
inference(congruence,[status(thm)],[c165]) ).
cnf(c167,plain,
meet(X3,meet(X4,join(X2,X4))) = meet(X4,meet(X3,join(X2,X4))),
inference(substitution,[status(thm)],[c56]) ).
cnf(c168,plain,
meet(X4,meet(X3,join(X2,X4))) = meet(X3,meet(X4,join(X2,X4))),
inference(symmetry,[status(thm)],[c167]) ).
cnf(c169,plain,
join(X3,X2) = join(X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c170,plain,
join(X2,X3) = join(X3,X2),
inference(symmetry,[status(thm)],[c169]) ).
cnf(c171,plain,
meet(X3,join(X2,X3)) = meet(X3,join(X3,X2)),
inference(congruence,[status(thm)],[c170]) ).
cnf(c172,plain,
meet(X3,join(X3,X2)) = X3,
inference(substitution,[status(thm)],[c61]) ).
cnf(c173,plain,
meet(X3,join(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c171,c172]) ).
cnf(c174,plain,
meet(X3,meet(X4,join(X2,X4))) = meet(X3,X4),
inference(congruence,[status(thm)],[c173]) ).
cnf(c175,plain,
meet(X2,X3) = meet(X3,X2),
inference(substitution,[status(thm)],[c9]) ).
cnf(c176,plain,
meet(X3,meet(X4,join(X2,X4))) = meet(X4,X3),
inference(transitivity,[status(thm)],[c174,c175]) ).
cnf(c177,plain,
meet(X4,meet(X3,join(X2,X4))) = meet(X4,X3),
inference(transitivity,[status(thm)],[c168,c176]) ).
cnf(c178,plain,
join(X2,meet(X4,meet(X3,join(X2,X4)))) = join(X2,meet(X4,X3)),
inference(congruence,[status(thm)],[c177]) ).
cnf(c179,plain,
meet(X4,join(X2,meet(X4,meet(X3,join(X2,X4))))) = meet(X4,join(X2,meet(X4,X3))),
inference(congruence,[status(thm)],[c178]) ).
cnf(c180,plain,
meet(X4,join(X2,meet(meet(X4,X3),join(X2,X4)))) = meet(X4,join(X2,meet(X4,X3))),
inference(transitivity,[status(thm)],[c166,c179]) ).
cnf(c181,plain,
meet(join(X4,meet(X4,X3)),join(X2,meet(meet(X4,X3),join(X2,X4)))) = meet(X4,join(X2,meet(X4,X3))),
inference(transitivity,[status(thm)],[c163,c180]) ).
cnf(c182,plain,
join(meet(X4,meet(X4,X3)),meet(X2,join(meet(X4,X2),meet(X4,X3)))) = meet(X4,join(X2,meet(X4,X3))),
inference(transitivity,[status(thm)],[c161,c181]) ).
cnf(c183,plain,
join(meet(X4,X3),meet(X2,join(meet(X4,X2),meet(X4,X3)))) = meet(X4,join(X2,meet(X4,X3))),
inference(transitivity,[status(thm)],[c129,c182]) ).
cnf(c184,plain,
join(meet(X4,X3),meet(X2,X4)) = meet(X4,join(X2,meet(X4,X3))),
inference(transitivity,[status(thm)],[c122,c183]) ).
cnf(c185,plain,
join(meet(X4,X3),meet(X4,X2)) = meet(X4,join(X2,meet(X4,X3))),
inference(transitivity,[status(thm)],[c20,c184]) ).
cnf(c186,plain,
join(meet(X3,X4),meet(X3,X2)) = meet(X3,join(X2,meet(X3,X4))),
inference(substitution,[status(thm)],[c185]) ).
cnf(c187,plain,
meet(X2,X3) = meet(X3,X2),
inference(substitution,[status(thm)],[c9]) ).
cnf(c188,plain,
join(X2,meet(X3,X4)) = join(X2,meet(X4,X3)),
inference(congruence,[status(thm)],[c187]) ).
cnf(c189,plain,
meet(X3,join(X2,meet(X3,X4))) = meet(X3,join(X2,meet(X4,X3))),
inference(congruence,[status(thm)],[c188]) ).
cnf(c190,plain,
join(meet(X3,X4),meet(X3,X2)) = meet(X3,join(X2,meet(X4,X3))),
inference(transitivity,[status(thm)],[c186,c189]) ).
cnf(c191,plain,
join(meet(X4,X3),meet(X3,X2)) = meet(X3,join(X2,meet(X4,X3))),
inference(transitivity,[status(thm)],[c17,c190]) ).
cnf(c192,plain,
meet(X3,X2) = meet(X2,X3),
inference(substitution,[status(thm)],[c9]) ).
cnf(c193,plain,
join(X2,meet(X4,X3)) = join(X2,meet(X3,X4)),
inference(congruence,[status(thm)],[c192]) ).
cnf(c194,plain,
meet(X3,join(X2,meet(X4,X3))) = meet(X3,join(X2,meet(X3,X4))),
inference(congruence,[status(thm)],[c193]) ).
cnf(c195,plain,
join(meet(X4,X2),meet(X4,X3)) = join(meet(X4,X3),meet(X4,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c196,plain,
join(meet(X4,X3),meet(X4,X2)) = join(meet(X4,X2),meet(X4,X3)),
inference(symmetry,[status(thm)],[c195]) ).
cnf(c197,plain,
join(meet(X4,X2),meet(X4,X3)) = meet(X4,join(X3,meet(X4,X2))),
inference(substitution,[status(thm)],[c185]) ).
cnf(c198,plain,
join(meet(X4,X3),meet(X4,X2)) = meet(X4,join(X3,meet(X4,X2))),
inference(transitivity,[status(thm)],[c196,c197]) ).
cnf(c199,plain,
meet(X4,join(X3,meet(X4,X2))) = join(meet(X4,X3),meet(X4,X2)),
inference(symmetry,[status(thm)],[c198]) ).
cnf(c200,plain,
join(X3,meet(X3,X2)) = X3,
inference(substitution,[status(thm)],[c75]) ).
cnf(c201,plain,
X3 = join(X3,meet(X3,X2)),
inference(symmetry,[status(thm)],[c200]) ).
cnf(c202,plain,
meet(X4,join(meet(X4,X3),meet(X4,X2))) = meet(join(X4,meet(X4,X3)),join(meet(X4,X3),meet(X4,X2))),
inference(congruence,[status(thm)],[c201]) ).
cnf(c203,plain,
join(X2,X3) = join(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c204,plain,
join(X3,X2) = join(X2,X3),
inference(symmetry,[status(thm)],[c203]) ).
cnf(c205,plain,
meet(join(X4,X3),join(X3,meet(X4,X2))) = meet(join(X3,X4),join(X3,meet(X4,X2))),
inference(congruence,[status(thm)],[c204]) ).
cnf(c206,plain,
join(X2,X3) = join(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c207,plain,
join(X3,X2) = join(X2,X3),
inference(symmetry,[status(thm)],[c206]) ).
cnf(c208,plain,
meet(join(X4,X3),join(X4,meet(X3,X2))) = meet(join(X3,X4),join(X4,meet(X3,X2))),
inference(congruence,[status(thm)],[c207]) ).
cnf(c209,plain,
meet(join(X4,meet(X3,X2)),join(X3,X4)) = meet(join(X3,X4),join(X4,meet(X3,X2))),
inference(substitution,[status(thm)],[c9]) ).
cnf(c210,plain,
meet(join(X3,X4),join(X4,meet(X3,X2))) = meet(join(X4,meet(X3,X2)),join(X3,X4)),
inference(symmetry,[status(thm)],[c209]) ).
cnf(c211,plain,
join(meet(X4,X2),X3) = join(X3,meet(X4,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c212,plain,
join(X3,meet(X4,X2)) = join(meet(X4,X2),X3),
inference(symmetry,[status(thm)],[c211]) ).
cnf(c213,plain,
join(X4,join(X3,meet(X4,X2))) = join(X4,join(meet(X4,X2),X3)),
inference(congruence,[status(thm)],[c212]) ).
cnf(c214,plain,
join(join(X4,meet(X4,X2)),X3) = join(X4,join(meet(X4,X2),X3)),
inference(substitution,[status(thm)],[c101]) ).
cnf(c215,plain,
join(X4,join(meet(X4,X2),X3)) = join(join(X4,meet(X4,X2)),X3),
inference(symmetry,[status(thm)],[c214]) ).
cnf(c216,plain,
join(X3,meet(X3,X2)) = X3,
inference(substitution,[status(thm)],[c75]) ).
cnf(c217,plain,
join(join(X4,meet(X4,X2)),X3) = join(X4,X3),
inference(congruence,[status(thm)],[c216]) ).
cnf(c218,plain,
join(X4,join(meet(X4,X2),X3)) = join(X4,X3),
inference(transitivity,[status(thm)],[c215,c217]) ).
cnf(c219,plain,
join(X4,join(X3,meet(X4,X2))) = join(X4,X3),
inference(transitivity,[status(thm)],[c213,c218]) ).
cnf(c220,plain,
join(X3,join(X4,meet(X3,X2))) = join(X3,X4),
inference(substitution,[status(thm)],[c219]) ).
cnf(c221,plain,
join(X3,X4) = join(X3,join(X4,meet(X3,X2))),
inference(symmetry,[status(thm)],[c220]) ).
cnf(c222,plain,
meet(join(X4,meet(X3,X2)),join(X3,X4)) = meet(join(X4,meet(X3,X2)),join(X3,join(X4,meet(X3,X2)))),
inference(congruence,[status(thm)],[c221]) ).
cnf(c223,plain,
meet(join(X4,meet(X3,X2)),join(X3,join(X4,meet(X3,X2)))) = join(X4,meet(X3,X2)),
inference(substitution,[status(thm)],[c173]) ).
cnf(c224,plain,
meet(join(X4,meet(X3,X2)),join(X3,X4)) = join(X4,meet(X3,X2)),
inference(transitivity,[status(thm)],[c222,c223]) ).
cnf(c225,plain,
meet(join(X3,X4),join(X4,meet(X3,X2))) = join(X4,meet(X3,X2)),
inference(transitivity,[status(thm)],[c210,c224]) ).
cnf(c226,plain,
meet(join(X4,X3),join(X4,meet(X3,X2))) = join(X4,meet(X3,X2)),
inference(transitivity,[status(thm)],[c208,c225]) ).
cnf(c227,plain,
meet(join(X3,X4),join(X3,meet(X4,X2))) = join(X3,meet(X4,X2)),
inference(substitution,[status(thm)],[c226]) ).
cnf(c228,plain,
meet(join(X4,X3),join(X3,meet(X4,X2))) = join(X3,meet(X4,X2)),
inference(transitivity,[status(thm)],[c205,c227]) ).
cnf(c229,plain,
meet(join(X4,meet(X4,X3)),join(meet(X4,X3),meet(X4,X2))) = join(meet(X4,X3),meet(X4,X2)),
inference(substitution,[status(thm)],[c228]) ).
cnf(c230,plain,
meet(X4,join(meet(X4,X3),meet(X4,X2))) = join(meet(X4,X3),meet(X4,X2)),
inference(transitivity,[status(thm)],[c202,c229]) ).
cnf(c231,plain,
join(meet(X4,X3),meet(X4,X2)) = meet(X4,join(meet(X4,X3),meet(X4,X2))),
inference(symmetry,[status(thm)],[c230]) ).
cnf(c232,plain,
join(meet(X4,X2),meet(X4,meet(X4,X3))) = meet(X4,join(meet(X4,X3),meet(X4,X2))),
inference(substitution,[status(thm)],[c185]) ).
cnf(c233,plain,
meet(X4,join(meet(X4,X3),meet(X4,X2))) = join(meet(X4,X2),meet(X4,meet(X4,X3))),
inference(symmetry,[status(thm)],[c232]) ).
cnf(c234,plain,
join(meet(X4,X2),meet(X4,meet(X4,X3))) = join(meet(X4,X2),meet(X4,X3)),
inference(congruence,[status(thm)],[c127]) ).
cnf(c235,plain,
join(meet(X4,X2),meet(X4,X3)) = meet(X4,join(X2,meet(X4,X3))),
inference(substitution,[status(thm)],[c198]) ).
cnf(c236,plain,
join(meet(X4,X2),meet(X4,meet(X4,X3))) = meet(X4,join(X2,meet(X4,X3))),
inference(transitivity,[status(thm)],[c234,c235]) ).
cnf(c237,plain,
meet(X4,join(meet(X4,X3),meet(X4,X2))) = meet(X4,join(X2,meet(X4,X3))),
inference(transitivity,[status(thm)],[c233,c236]) ).
cnf(c238,plain,
join(meet(X4,X3),meet(X4,X2)) = meet(X4,join(X2,meet(X4,X3))),
inference(transitivity,[status(thm)],[c231,c237]) ).
cnf(c239,plain,
meet(X4,join(X3,meet(X4,X2))) = meet(X4,join(X2,meet(X4,X3))),
inference(transitivity,[status(thm)],[c199,c238]) ).
cnf(c240,plain,
meet(X4,join(X2,meet(X4,X3))) = meet(X4,join(X3,meet(X4,X2))),
inference(substitution,[status(thm)],[c239]) ).
cnf(c241,plain,
meet(X4,join(X3,meet(X4,X2))) = meet(X4,join(X2,meet(X4,X3))),
inference(symmetry,[status(thm)],[c240]) ).
cnf(c242,plain,
meet(X2,X3) = meet(X3,X2),
inference(substitution,[status(thm)],[c9]) ).
cnf(c243,plain,
meet(X3,X2) = meet(X2,X3),
inference(symmetry,[status(thm)],[c242]) ).
cnf(c244,plain,
join(X2,meet(X4,X3)) = join(X2,meet(X3,X4)),
inference(congruence,[status(thm)],[c243]) ).
cnf(c245,plain,
meet(X4,join(X2,meet(X4,X3))) = meet(X4,join(X2,meet(X3,X4))),
inference(congruence,[status(thm)],[c244]) ).
cnf(c246,plain,
join(meet(X3,X4),X2) = join(X2,meet(X3,X4)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c247,plain,
join(X2,meet(X3,X4)) = join(meet(X3,X4),X2),
inference(symmetry,[status(thm)],[c246]) ).
cnf(c248,plain,
meet(X4,join(X2,meet(X3,X4))) = meet(X4,join(meet(X3,X4),X2)),
inference(congruence,[status(thm)],[c247]) ).
cnf(c249,plain,
meet(X2,X3) = meet(X3,X2),
inference(substitution,[status(thm)],[c9]) ).
cnf(c250,plain,
meet(X3,X2) = meet(X2,X3),
inference(symmetry,[status(thm)],[c249]) ).
cnf(c251,plain,
meet(X3,meet(X4,X2)) = meet(X3,meet(X2,X4)),
inference(congruence,[status(thm)],[c250]) ).
cnf(c252,plain,
join(X4,meet(X3,meet(X4,X2))) = join(X4,meet(X3,meet(X2,X4))),
inference(congruence,[status(thm)],[c251]) ).
cnf(c253,plain,
meet(meet(X3,X2),X4) = meet(X3,meet(X2,X4)),
inference(substitution,[status(thm)],[c51]) ).
cnf(c254,plain,
meet(X3,meet(X2,X4)) = meet(meet(X3,X2),X4),
inference(symmetry,[status(thm)],[c253]) ).
cnf(c255,plain,
join(X4,meet(X3,meet(X2,X4))) = join(X4,meet(meet(X3,X2),X4)),
inference(congruence,[status(thm)],[c254]) ).
cnf(c256,plain,
join(X4,meet(meet(X3,X2),X4)) = X4,
inference(substitution,[status(thm)],[c77]) ).
cnf(c257,plain,
join(X4,meet(X3,meet(X2,X4))) = X4,
inference(transitivity,[status(thm)],[c255,c256]) ).
cnf(c258,plain,
join(X4,meet(X3,meet(X4,X2))) = X4,
inference(transitivity,[status(thm)],[c252,c257]) ).
cnf(c259,plain,
join(X2,meet(X4,meet(X2,X3))) = X2,
inference(substitution,[status(thm)],[c258]) ).
cnf(c260,plain,
X2 = join(X2,meet(X4,meet(X2,X3))),
inference(symmetry,[status(thm)],[c259]) ).
cnf(c261,plain,
join(meet(X3,X4),X2) = join(meet(X3,X4),join(X2,meet(X4,meet(X2,X3)))),
inference(congruence,[status(thm)],[c260]) ).
cnf(c262,plain,
meet(X4,join(meet(X3,X4),X2)) = meet(X4,join(meet(X3,X4),join(X2,meet(X4,meet(X2,X3))))),
inference(congruence,[status(thm)],[c261]) ).
cnf(c263,plain,
join(join(meet(X3,X4),X2),meet(X4,meet(X2,X3))) = join(meet(X3,X4),join(X2,meet(X4,meet(X2,X3)))),
inference(substitution,[status(thm)],[c101]) ).
cnf(c264,plain,
join(meet(X3,X4),join(X2,meet(X4,meet(X2,X3)))) = join(join(meet(X3,X4),X2),meet(X4,meet(X2,X3))),
inference(symmetry,[status(thm)],[c263]) ).
cnf(c265,plain,
meet(X4,join(meet(X3,X4),join(X2,meet(X4,meet(X2,X3))))) = meet(X4,join(join(meet(X3,X4),X2),meet(X4,meet(X2,X3)))),
inference(congruence,[status(thm)],[c264]) ).
cnf(c266,plain,
meet(X4,join(meet(X2,X3),meet(X4,join(meet(X3,X4),X2)))) = meet(X4,join(join(meet(X3,X4),X2),meet(X4,meet(X2,X3)))),
inference(substitution,[status(thm)],[c239]) ).
cnf(c267,plain,
meet(X4,join(join(meet(X3,X4),X2),meet(X4,meet(X2,X3)))) = meet(X4,join(meet(X2,X3),meet(X4,join(meet(X3,X4),X2)))),
inference(symmetry,[status(thm)],[c266]) ).
cnf(c268,plain,
join(meet(X2,X3),meet(X4,join(meet(X3,X4),X2))) = meet(join(X2,X3),join(X4,meet(join(X3,X4),X2))),
inference(substitution,[status(thm)],[c146]) ).
cnf(c269,plain,
meet(X4,join(meet(X2,X3),meet(X4,join(meet(X3,X4),X2)))) = meet(X4,meet(join(X2,X3),join(X4,meet(join(X3,X4),X2)))),
inference(congruence,[status(thm)],[c268]) ).
cnf(c270,plain,
meet(join(X4,X2),X3) = meet(X3,join(X4,X2)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c271,plain,
meet(X3,join(X4,X2)) = meet(join(X4,X2),X3),
inference(symmetry,[status(thm)],[c270]) ).
cnf(c272,plain,
meet(X4,meet(X3,join(X4,X2))) = meet(X4,meet(join(X4,X2),X3)),
inference(congruence,[status(thm)],[c271]) ).
cnf(c273,plain,
meet(meet(X4,join(X4,X2)),X3) = meet(X4,meet(join(X4,X2),X3)),
inference(substitution,[status(thm)],[c51]) ).
cnf(c274,plain,
meet(X4,meet(join(X4,X2),X3)) = meet(meet(X4,join(X4,X2)),X3),
inference(symmetry,[status(thm)],[c273]) ).
cnf(c275,plain,
meet(X3,join(X3,X2)) = X3,
inference(substitution,[status(thm)],[c61]) ).
cnf(c276,plain,
meet(meet(X4,join(X4,X2)),X3) = meet(X4,X3),
inference(congruence,[status(thm)],[c275]) ).
cnf(c277,plain,
meet(X4,meet(join(X4,X2),X3)) = meet(X4,X3),
inference(transitivity,[status(thm)],[c274,c276]) ).
cnf(c278,plain,
meet(X4,meet(X3,join(X4,X2))) = meet(X4,X3),
inference(transitivity,[status(thm)],[c272,c277]) ).
cnf(c279,plain,
meet(X4,meet(join(X2,X3),join(X4,meet(join(X3,X4),X2)))) = meet(X4,join(X2,X3)),
inference(substitution,[status(thm)],[c278]) ).
cnf(c280,plain,
join(X2,X3) = join(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c281,plain,
meet(X4,join(X2,X3)) = meet(X4,join(X3,X2)),
inference(congruence,[status(thm)],[c280]) ).
cnf(c282,plain,
meet(X4,meet(join(X2,X3),join(X4,meet(join(X3,X4),X2)))) = meet(X4,join(X3,X2)),
inference(transitivity,[status(thm)],[c279,c281]) ).
cnf(c283,plain,
meet(X4,join(meet(X2,X3),meet(X4,join(meet(X3,X4),X2)))) = meet(X4,join(X3,X2)),
inference(transitivity,[status(thm)],[c269,c282]) ).
cnf(c284,plain,
meet(X4,join(join(meet(X3,X4),X2),meet(X4,meet(X2,X3)))) = meet(X4,join(X3,X2)),
inference(transitivity,[status(thm)],[c267,c283]) ).
cnf(c285,plain,
meet(X4,join(meet(X3,X4),join(X2,meet(X4,meet(X2,X3))))) = meet(X4,join(X3,X2)),
inference(transitivity,[status(thm)],[c265,c284]) ).
cnf(c286,plain,
meet(X4,join(meet(X3,X4),X2)) = meet(X4,join(X3,X2)),
inference(transitivity,[status(thm)],[c262,c285]) ).
cnf(c287,plain,
meet(X4,join(X2,meet(X3,X4))) = meet(X4,join(X3,X2)),
inference(transitivity,[status(thm)],[c248,c286]) ).
cnf(c288,plain,
meet(X4,join(X2,meet(X4,X3))) = meet(X4,join(X3,X2)),
inference(transitivity,[status(thm)],[c245,c287]) ).
cnf(c289,plain,
meet(X4,join(X3,meet(X4,X2))) = meet(X4,join(X3,X2)),
inference(transitivity,[status(thm)],[c241,c288]) ).
cnf(c290,plain,
meet(X3,join(X2,meet(X3,X4))) = meet(X3,join(X2,X4)),
inference(substitution,[status(thm)],[c289]) ).
cnf(c291,plain,
meet(X3,join(X2,meet(X4,X3))) = meet(X3,join(X2,X4)),
inference(transitivity,[status(thm)],[c194,c290]) ).
cnf(c292,plain,
join(meet(X4,X3),meet(X3,X2)) = meet(X3,join(X2,X4)),
inference(transitivity,[status(thm)],[c191,c291]) ).
cnf(c293,plain,
join(meet(X4,X3),meet(X2,X3)) = meet(X3,join(X2,X4)),
inference(transitivity,[status(thm)],[c14,c292]) ).
cnf(c294,plain,
join(meet(X3,join(X2,X3)),meet(X4,join(X2,X3))) = meet(join(X2,X3),join(X4,X3)),
inference(substitution,[status(thm)],[c293]) ).
cnf(c295,plain,
meet(join(X2,X3),join(X4,X3)) = join(meet(X3,join(X2,X3)),meet(X4,join(X2,X3))),
inference(symmetry,[status(thm)],[c294]) ).
cnf(c296,plain,
join(meet(X3,join(X2,X3)),meet(X4,join(X2,X3))) = join(X3,meet(X4,join(X2,X3))),
inference(congruence,[status(thm)],[c173]) ).
cnf(c297,plain,
join(X2,X3) = join(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c298,plain,
meet(X4,join(X2,X3)) = meet(X4,join(X3,X2)),
inference(congruence,[status(thm)],[c297]) ).
cnf(c299,plain,
join(X3,meet(X4,join(X2,X3))) = join(X3,meet(X4,join(X3,X2))),
inference(congruence,[status(thm)],[c298]) ).
cnf(c300,plain,
meet(join(X4,X2),join(X4,X3)) = meet(join(X4,X3),join(X4,X2)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c301,plain,
meet(join(X4,X3),join(X4,X2)) = meet(join(X4,X2),join(X4,X3)),
inference(symmetry,[status(thm)],[c300]) ).
cnf(c302,plain,
meet(join(X4,X2),X3) = meet(X3,join(X4,X2)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c303,plain,
meet(X3,join(X4,X2)) = meet(join(X4,X2),X3),
inference(symmetry,[status(thm)],[c302]) ).
cnf(c304,plain,
join(X4,meet(X3,join(X4,X2))) = join(X4,meet(join(X4,X2),X3)),
inference(congruence,[status(thm)],[c303]) ).
cnf(c305,plain,
meet(X3,join(X3,X2)) = X3,
inference(substitution,[status(thm)],[c61]) ).
cnf(c306,plain,
X3 = meet(X3,join(X3,X2)),
inference(symmetry,[status(thm)],[c305]) ).
cnf(c307,plain,
join(X4,meet(join(X4,X2),X3)) = join(meet(X4,join(X4,X2)),meet(join(X4,X2),X3)),
inference(congruence,[status(thm)],[c306]) ).
cnf(c308,plain,
join(meet(X4,join(X4,X2)),meet(join(X4,X2),X3)) = meet(join(X4,X2),join(X3,meet(X4,join(X4,X2)))),
inference(substitution,[status(thm)],[c191]) ).
cnf(c309,plain,
meet(X3,join(X3,X2)) = X3,
inference(substitution,[status(thm)],[c61]) ).
cnf(c310,plain,
join(X3,meet(X4,join(X4,X2))) = join(X3,X4),
inference(congruence,[status(thm)],[c309]) ).
cnf(c311,plain,
meet(join(X4,X2),join(X3,meet(X4,join(X4,X2)))) = meet(join(X4,X2),join(X3,X4)),
inference(congruence,[status(thm)],[c310]) ).
cnf(c312,plain,
join(X2,X3) = join(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c313,plain,
meet(join(X4,X2),join(X3,X4)) = meet(join(X4,X2),join(X4,X3)),
inference(congruence,[status(thm)],[c312]) ).
cnf(c314,plain,
meet(join(X4,X2),join(X3,meet(X4,join(X4,X2)))) = meet(join(X4,X2),join(X4,X3)),
inference(transitivity,[status(thm)],[c311,c313]) ).
cnf(c315,plain,
join(meet(X4,join(X4,X2)),meet(join(X4,X2),X3)) = meet(join(X4,X2),join(X4,X3)),
inference(transitivity,[status(thm)],[c308,c314]) ).
cnf(c316,plain,
join(X4,meet(join(X4,X2),X3)) = meet(join(X4,X2),join(X4,X3)),
inference(transitivity,[status(thm)],[c307,c315]) ).
cnf(c317,plain,
join(X4,meet(X3,join(X4,X2))) = meet(join(X4,X2),join(X4,X3)),
inference(transitivity,[status(thm)],[c304,c316]) ).
cnf(c318,plain,
meet(join(X4,X2),join(X4,X3)) = join(X4,meet(X3,join(X4,X2))),
inference(symmetry,[status(thm)],[c317]) ).
cnf(c319,plain,
meet(X2,X3) = meet(X3,X2),
inference(substitution,[status(thm)],[c9]) ).
cnf(c320,plain,
meet(X3,X2) = meet(X2,X3),
inference(symmetry,[status(thm)],[c319]) ).
cnf(c321,plain,
join(meet(X4,X3),meet(X4,join(X2,X3))) = join(meet(X3,X4),meet(X4,join(X2,X3))),
inference(congruence,[status(thm)],[c320]) ).
cnf(c322,plain,
join(meet(X4,join(X2,X3)),meet(X3,X4)) = join(meet(X3,X4),meet(X4,join(X2,X3))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c323,plain,
join(meet(X3,X4),meet(X4,join(X2,X3))) = join(meet(X4,join(X2,X3)),meet(X3,X4)),
inference(symmetry,[status(thm)],[c322]) ).
cnf(c324,plain,
meet(X3,meet(X4,join(X2,X3))) = meet(X3,X4),
inference(substitution,[status(thm)],[c177]) ).
cnf(c325,plain,
meet(X3,X4) = meet(X3,meet(X4,join(X2,X3))),
inference(symmetry,[status(thm)],[c324]) ).
cnf(c326,plain,
join(meet(X4,join(X2,X3)),meet(X3,X4)) = join(meet(X4,join(X2,X3)),meet(X3,meet(X4,join(X2,X3)))),
inference(congruence,[status(thm)],[c325]) ).
cnf(c327,plain,
join(meet(X4,join(X2,X3)),meet(X3,meet(X4,join(X2,X3)))) = meet(X4,join(X2,X3)),
inference(substitution,[status(thm)],[c77]) ).
cnf(c328,plain,
join(meet(X4,join(X2,X3)),meet(X3,X4)) = meet(X4,join(X2,X3)),
inference(transitivity,[status(thm)],[c326,c327]) ).
cnf(c329,plain,
join(meet(X3,X4),meet(X4,join(X2,X3))) = meet(X4,join(X2,X3)),
inference(transitivity,[status(thm)],[c323,c328]) ).
cnf(c330,plain,
join(meet(X4,X3),meet(X4,join(X2,X3))) = meet(X4,join(X2,X3)),
inference(transitivity,[status(thm)],[c321,c329]) ).
cnf(c331,plain,
join(meet(X3,X2),meet(X3,join(X4,X2))) = meet(X3,join(X4,X2)),
inference(substitution,[status(thm)],[c330]) ).
cnf(c332,plain,
meet(X3,join(X4,X2)) = join(meet(X3,X2),meet(X3,join(X4,X2))),
inference(symmetry,[status(thm)],[c331]) ).
cnf(c333,plain,
join(X4,meet(X3,join(X4,X2))) = join(X4,join(meet(X3,X2),meet(X3,join(X4,X2)))),
inference(congruence,[status(thm)],[c332]) ).
cnf(c334,plain,
join(join(X4,meet(X3,X2)),meet(X3,join(X4,X2))) = join(X4,join(meet(X3,X2),meet(X3,join(X4,X2)))),
inference(substitution,[status(thm)],[c101]) ).
cnf(c335,plain,
join(X4,join(meet(X3,X2),meet(X3,join(X4,X2)))) = join(join(X4,meet(X3,X2)),meet(X3,join(X4,X2))),
inference(symmetry,[status(thm)],[c334]) ).
cnf(c336,plain,
meet(X3,join(X4,meet(X3,X2))) = meet(X3,join(X4,X2)),
inference(substitution,[status(thm)],[c289]) ).
cnf(c337,plain,
meet(X3,join(X4,X2)) = meet(X3,join(X4,meet(X3,X2))),
inference(symmetry,[status(thm)],[c336]) ).
cnf(c338,plain,
join(join(X4,meet(X3,X2)),meet(X3,join(X4,X2))) = join(join(X4,meet(X3,X2)),meet(X3,join(X4,meet(X3,X2)))),
inference(congruence,[status(thm)],[c337]) ).
cnf(c339,plain,
join(join(X4,meet(X3,X2)),meet(X3,join(X4,meet(X3,X2)))) = join(X4,meet(X3,X2)),
inference(substitution,[status(thm)],[c77]) ).
cnf(c340,plain,
join(join(X4,meet(X3,X2)),meet(X3,join(X4,X2))) = join(X4,meet(X3,X2)),
inference(transitivity,[status(thm)],[c338,c339]) ).
cnf(c341,plain,
join(X4,join(meet(X3,X2),meet(X3,join(X4,X2)))) = join(X4,meet(X3,X2)),
inference(transitivity,[status(thm)],[c335,c340]) ).
cnf(c342,plain,
join(X4,meet(X3,join(X4,X2))) = join(X4,meet(X3,X2)),
inference(transitivity,[status(thm)],[c333,c341]) ).
cnf(c343,plain,
meet(join(X4,X2),join(X4,X3)) = join(X4,meet(X3,X2)),
inference(transitivity,[status(thm)],[c318,c342]) ).
cnf(c344,plain,
meet(join(X4,X3),join(X4,X2)) = join(X4,meet(X3,X2)),
inference(transitivity,[status(thm)],[c301,c343]) ).
cnf(c345,plain,
meet(join(X4,X3),join(X4,join(X4,X2))) = join(X4,meet(X3,join(X4,X2))),
inference(substitution,[status(thm)],[c344]) ).
cnf(c346,plain,
join(X4,meet(X3,join(X4,X2))) = meet(join(X4,X3),join(X4,join(X4,X2))),
inference(symmetry,[status(thm)],[c345]) ).
cnf(c347,plain,
join(join(X3,X3),X2) = join(X3,join(X3,X2)),
inference(substitution,[status(thm)],[c101]) ).
cnf(c348,plain,
join(X3,join(X3,X2)) = join(join(X3,X3),X2),
inference(symmetry,[status(thm)],[c347]) ).
cnf(c349,axiom,
join(X2,X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c350,plain,
join(join(X3,X3),X2) = join(X3,X2),
inference(congruence,[status(thm)],[c349]) ).
cnf(c351,plain,
join(X3,join(X3,X2)) = join(X3,X2),
inference(transitivity,[status(thm)],[c348,c350]) ).
cnf(c352,plain,
meet(join(X4,X3),join(X4,join(X4,X2))) = meet(join(X4,X3),join(X4,X2)),
inference(congruence,[status(thm)],[c351]) ).
cnf(c353,plain,
meet(join(X4,X3),join(X4,join(X4,X2))) = join(X4,meet(X3,X2)),
inference(transitivity,[status(thm)],[c352,c344]) ).
cnf(c354,plain,
join(X4,meet(X3,join(X4,X2))) = join(X4,meet(X3,X2)),
inference(transitivity,[status(thm)],[c346,c353]) ).
cnf(c355,plain,
join(X3,meet(X4,join(X3,X2))) = join(X3,meet(X4,X2)),
inference(substitution,[status(thm)],[c354]) ).
cnf(c356,plain,
join(X3,meet(X4,join(X2,X3))) = join(X3,meet(X4,X2)),
inference(transitivity,[status(thm)],[c299,c355]) ).
cnf(c357,plain,
join(meet(X3,join(X2,X3)),meet(X4,join(X2,X3))) = join(X3,meet(X4,X2)),
inference(transitivity,[status(thm)],[c296,c356]) ).
cnf(c358,plain,
meet(join(X2,X3),join(X4,X3)) = join(X3,meet(X4,X2)),
inference(transitivity,[status(thm)],[c295,c357]) ).
cnf(c359,plain,
meet(join(X4,X3),join(X2,X3)) = join(X3,meet(X4,X2)),
inference(transitivity,[status(thm)],[c11,c358]) ).
cnf(c360,plain,
meet(join(X4,X3),join(X3,X2)) = join(X3,meet(X4,X2)),
inference(transitivity,[status(thm)],[c8,c359]) ).
cnf(c361,plain,
meet(join(X4,X3),join(X2,X3)) = join(X3,meet(X4,X2)),
inference(transitivity,[status(thm)],[c5,c360]) ).
cnf(c362,plain,
meet(join(b,a),join(c,a)) = join(a,meet(b,c)),
inference(substitution,[status(thm)],[c361]) ).
cnf(c363,plain,
join(a,meet(b,c)) = meet(join(b,a),join(c,a)),
inference(symmetry,[status(thm)],[c362]) ).
cnf(c364,plain,
join(a,c) = join(c,a),
inference(substitution,[status(thm)],[c2]) ).
cnf(c365,plain,
join(c,a) = join(a,c),
inference(symmetry,[status(thm)],[c364]) ).
cnf(c366,plain,
meet(join(b,a),join(c,a)) = meet(join(b,a),join(a,c)),
inference(congruence,[status(thm)],[c365]) ).
cnf(c367,plain,
join(a,b) = join(b,a),
inference(substitution,[status(thm)],[c2]) ).
cnf(c368,plain,
join(b,a) = join(a,b),
inference(symmetry,[status(thm)],[c367]) ).
cnf(c369,plain,
meet(join(b,a),join(a,c)) = meet(join(a,b),join(a,c)),
inference(congruence,[status(thm)],[c368]) ).
cnf(c370,plain,
meet(join(b,a),join(c,a)) = meet(join(a,b),join(a,c)),
inference(transitivity,[status(thm)],[c366,c369]) ).
cnf(c371,plain,
join(a,meet(b,c)) = meet(join(a,b),join(a,c)),
inference(transitivity,[status(thm)],[c363,c370]) ).
cnf(c372,plain,
$false,
inference(resolution,[status(thm)],[c1,c371]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT009-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n014.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Sun Sep 27 13:56:01 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.04/2.31 Command-line arguments: --no-flatten-goal
% 15.04/2.31
% 15.04/2.31 % SZS status Unsatisfiable
% 15.04/2.31
% 15.04/2.33 % SZS output start CNFRefutation
% See solution above
% 16.40/2.52
% 16.40/2.52 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------