%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LAT021-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 11:42:51 AM UTC 2026
% Result : Unsatisfiable 1.81s 0.66s
% Output : CNFRefutation 2.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 8
% Syntax : Number of clauses : 108 ( 108 unt; 0 nHn; 16 RR)
% Number of literals : 108 ( 107 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 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 : 251 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
meet(a,join(b,c)) != join(meet(a,b),meet(a,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_distributivity) ).
cnf(c2,axiom,
join(X,Y) = join(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_join) ).
cnf(c3,plain,
join(c,b) = join(b,c),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
join(b,c) = join(c,b),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
meet(a,join(b,c)) = meet(a,join(c,b)),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,axiom,
meet(X2,Y2) = meet(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_meet) ).
cnf(c7,plain,
meet(X3,X2) = meet(X2,X3),
inference(substitution,[status(thm)],[c6]) ).
cnf(c8,plain,
meet(X2,X3) = meet(X3,X2),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c9,plain,
join(meet(X4,X3),meet(X2,X3)) = join(meet(X4,X3),meet(X3,X2)),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,plain,
meet(X2,X3) = meet(X3,X2),
inference(substitution,[status(thm)],[c6]) ).
cnf(c11,plain,
meet(X3,X2) = meet(X2,X3),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c12,plain,
join(meet(X4,X3),meet(X3,X2)) = join(meet(X3,X4),meet(X3,X2)),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,plain,
meet(X2,X3) = meet(X3,X2),
inference(substitution,[status(thm)],[c6]) ).
cnf(c14,plain,
meet(X3,X2) = meet(X2,X3),
inference(symmetry,[status(thm)],[c13]) ).
cnf(c15,plain,
join(meet(X4,X3),meet(X4,X2)) = join(meet(X4,X3),meet(X2,X4)),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,plain,
join(X2,X3) = join(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c17,plain,
join(X3,X2) = join(X2,X3),
inference(symmetry,[status(thm)],[c16]) ).
cnf(c18,plain,
meet(X3,join(X4,X2)) = meet(X3,join(X2,X4)),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,plain,
join(X4,meet(X3,join(X4,X2))) = join(X4,meet(X3,join(X2,X4))),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
join(X3,X2) = join(X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c21,plain,
join(X2,X3) = join(X3,X2),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c22,plain,
meet(join(X2,X4),X3) = meet(join(X4,X2),X3),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,plain,
join(meet(X4,X3),meet(join(X2,X4),X3)) = join(meet(X4,X3),meet(join(X4,X2),X3)),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,plain,
meet(X3,join(X4,X2)) = meet(join(X4,X2),X3),
inference(substitution,[status(thm)],[c6]) ).
cnf(c25,plain,
meet(join(X4,X2),X3) = meet(X3,join(X4,X2)),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c26,plain,
join(meet(X4,X3),meet(join(X4,X2),X3)) = join(meet(X4,X3),meet(X3,join(X4,X2))),
inference(congruence,[status(thm)],[c25]) ).
cnf(c27,plain,
meet(X2,X3) = meet(X3,X2),
inference(substitution,[status(thm)],[c6]) ).
cnf(c28,plain,
meet(X3,X2) = meet(X2,X3),
inference(symmetry,[status(thm)],[c27]) ).
cnf(c29,plain,
join(meet(X4,X3),meet(X3,join(X4,X2))) = join(meet(X3,X4),meet(X3,join(X4,X2))),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
join(meet(X4,join(X3,X2)),meet(X4,X3)) = join(meet(X4,X3),meet(X4,join(X3,X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c31,plain,
join(meet(X4,X3),meet(X4,join(X3,X2))) = join(meet(X4,join(X3,X2)),meet(X4,X3)),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c32,axiom,
join(meet(X2,join(Y2,Z)),meet(X2,Y2)) = meet(X2,join(Y2,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quasi_lattice1) ).
cnf(c33,plain,
join(meet(X4,join(X3,X2)),meet(X4,X3)) = meet(X4,join(X3,X2)),
inference(substitution,[status(thm)],[c32]) ).
cnf(c34,plain,
join(meet(X4,X3),meet(X4,join(X3,X2))) = meet(X4,join(X3,X2)),
inference(transitivity,[status(thm)],[c31,c33]) ).
cnf(c35,plain,
join(meet(X3,X4),meet(X3,join(X4,X2))) = meet(X3,join(X4,X2)),
inference(substitution,[status(thm)],[c34]) ).
cnf(c36,plain,
join(meet(X4,X3),meet(X3,join(X4,X2))) = meet(X3,join(X4,X2)),
inference(transitivity,[status(thm)],[c29,c35]) ).
cnf(c37,plain,
join(meet(X4,X3),meet(join(X4,X2),X3)) = meet(X3,join(X4,X2)),
inference(transitivity,[status(thm)],[c26,c36]) ).
cnf(c38,plain,
join(meet(X4,X3),meet(join(X2,X4),X3)) = meet(X3,join(X4,X2)),
inference(transitivity,[status(thm)],[c23,c37]) ).
cnf(c39,plain,
join(meet(X2,X3),meet(join(X4,X2),X3)) = meet(X3,join(X2,X4)),
inference(substitution,[status(thm)],[c38]) ).
cnf(c40,plain,
meet(X3,join(X2,X4)) = join(meet(X2,X3),meet(join(X4,X2),X3)),
inference(symmetry,[status(thm)],[c39]) ).
cnf(c41,plain,
join(X4,meet(X3,join(X2,X4))) = join(X4,join(meet(X2,X3),meet(join(X4,X2),X3))),
inference(congruence,[status(thm)],[c40]) ).
cnf(c42,axiom,
join(join(X2,Y2),Z2) = join(X2,join(Y2,Z2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_join) ).
cnf(c43,plain,
join(join(X4,meet(X3,X2)),meet(join(X4,X3),X2)) = join(X4,join(meet(X3,X2),meet(join(X4,X3),X2))),
inference(substitution,[status(thm)],[c42]) ).
cnf(c44,plain,
join(X4,join(meet(X3,X2),meet(join(X4,X3),X2))) = join(join(X4,meet(X3,X2)),meet(join(X4,X3),X2)),
inference(symmetry,[status(thm)],[c43]) ).
cnf(c45,hypothesis,
join(join(X2,meet(Y2,Z2)),meet(join(X2,Y2),Z2)) = join(X2,meet(Y2,Z2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bowden) ).
cnf(c46,plain,
join(join(X4,meet(X3,X2)),meet(join(X4,X3),X2)) = join(X4,meet(X3,X2)),
inference(substitution,[status(thm)],[c45]) ).
cnf(c47,plain,
join(X4,join(meet(X3,X2),meet(join(X4,X3),X2))) = join(X4,meet(X3,X2)),
inference(transitivity,[status(thm)],[c44,c46]) ).
cnf(c48,plain,
join(X4,join(meet(X2,X3),meet(join(X4,X2),X3))) = join(X4,meet(X2,X3)),
inference(substitution,[status(thm)],[c47]) ).
cnf(c49,plain,
join(X4,meet(X3,join(X2,X4))) = join(X4,meet(X2,X3)),
inference(transitivity,[status(thm)],[c41,c48]) ).
cnf(c50,plain,
join(X4,meet(X3,join(X4,X2))) = join(X4,meet(X2,X3)),
inference(transitivity,[status(thm)],[c19,c49]) ).
cnf(c51,plain,
join(meet(X4,X3),meet(X4,join(meet(X4,X3),X2))) = join(meet(X4,X3),meet(X2,X4)),
inference(substitution,[status(thm)],[c50]) ).
cnf(c52,plain,
join(meet(X4,X3),meet(X2,X4)) = join(meet(X4,X3),meet(X4,join(meet(X4,X3),X2))),
inference(symmetry,[status(thm)],[c51]) ).
cnf(c53,axiom,
meet(meet(X2,Y2),Z2) = meet(X2,meet(Y2,Z2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_meet) ).
cnf(c54,plain,
meet(meet(X3,X3),X2) = meet(X3,meet(X3,X2)),
inference(substitution,[status(thm)],[c53]) ).
cnf(c55,plain,
meet(X3,meet(X3,X2)) = meet(meet(X3,X3),X2),
inference(symmetry,[status(thm)],[c54]) ).
cnf(c56,axiom,
meet(X2,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c57,plain,
meet(meet(X3,X3),X2) = meet(X3,X2),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
meet(X3,meet(X3,X2)) = meet(X3,X2),
inference(transitivity,[status(thm)],[c55,c57]) ).
cnf(c59,plain,
meet(X3,X2) = meet(X3,meet(X3,X2)),
inference(symmetry,[status(thm)],[c58]) ).
cnf(c60,plain,
join(meet(X4,X3),meet(X4,join(meet(X4,X3),X2))) = join(meet(X4,meet(X4,X3)),meet(X4,join(meet(X4,X3),X2))),
inference(congruence,[status(thm)],[c59]) ).
cnf(c61,plain,
join(meet(X4,meet(X4,X3)),meet(X4,join(meet(X4,X3),X2))) = meet(X4,join(meet(X4,X3),X2)),
inference(substitution,[status(thm)],[c34]) ).
cnf(c62,plain,
join(meet(X4,X3),X2) = join(X2,meet(X4,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c63,plain,
meet(X4,join(meet(X4,X3),X2)) = meet(X4,join(X2,meet(X4,X3))),
inference(congruence,[status(thm)],[c62]) ).
cnf(c64,plain,
join(meet(X4,meet(X4,X3)),meet(X4,join(meet(X4,X3),X2))) = meet(X4,join(X2,meet(X4,X3))),
inference(transitivity,[status(thm)],[c61,c63]) ).
cnf(c65,plain,
join(meet(X4,X3),meet(X4,join(meet(X4,X3),X2))) = meet(X4,join(X2,meet(X4,X3))),
inference(transitivity,[status(thm)],[c60,c64]) ).
cnf(c66,plain,
join(meet(X4,X3),meet(X2,X4)) = meet(X4,join(X2,meet(X4,X3))),
inference(transitivity,[status(thm)],[c52,c65]) ).
cnf(c67,plain,
join(meet(X4,X3),meet(X4,X2)) = meet(X4,join(X2,meet(X4,X3))),
inference(transitivity,[status(thm)],[c15,c66]) ).
cnf(c68,plain,
join(meet(X3,X4),meet(X3,X2)) = meet(X3,join(X2,meet(X3,X4))),
inference(substitution,[status(thm)],[c67]) ).
cnf(c69,plain,
meet(X2,X3) = meet(X3,X2),
inference(substitution,[status(thm)],[c6]) ).
cnf(c70,plain,
join(X2,meet(X3,X4)) = join(X2,meet(X4,X3)),
inference(congruence,[status(thm)],[c69]) ).
cnf(c71,plain,
meet(X3,join(X2,meet(X3,X4))) = meet(X3,join(X2,meet(X4,X3))),
inference(congruence,[status(thm)],[c70]) ).
cnf(c72,plain,
join(meet(X3,X4),meet(X3,X2)) = meet(X3,join(X2,meet(X4,X3))),
inference(transitivity,[status(thm)],[c68,c71]) ).
cnf(c73,plain,
join(meet(X4,X3),meet(X3,X2)) = meet(X3,join(X2,meet(X4,X3))),
inference(transitivity,[status(thm)],[c12,c72]) ).
cnf(c74,plain,
meet(X3,X2) = meet(X2,X3),
inference(substitution,[status(thm)],[c6]) ).
cnf(c75,plain,
join(X2,meet(X4,X3)) = join(X2,meet(X3,X4)),
inference(congruence,[status(thm)],[c74]) ).
cnf(c76,plain,
meet(X3,join(X2,meet(X4,X3))) = meet(X3,join(X2,meet(X3,X4))),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,plain,
meet(X2,X3) = meet(X3,X2),
inference(substitution,[status(thm)],[c6]) ).
cnf(c78,plain,
meet(X3,X2) = meet(X2,X3),
inference(symmetry,[status(thm)],[c77]) ).
cnf(c79,plain,
join(X3,meet(X4,X2)) = join(X3,meet(X2,X4)),
inference(congruence,[status(thm)],[c78]) ).
cnf(c80,plain,
meet(X4,join(X3,meet(X4,X2))) = meet(X4,join(X3,meet(X2,X4))),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,plain,
join(X3,meet(X4,join(X3,X2))) = join(X3,meet(X2,X4)),
inference(substitution,[status(thm)],[c50]) ).
cnf(c82,plain,
join(X3,meet(X2,X4)) = join(X3,meet(X4,join(X3,X2))),
inference(symmetry,[status(thm)],[c81]) ).
cnf(c83,plain,
meet(X4,join(X3,meet(X2,X4))) = meet(X4,join(X3,meet(X4,join(X3,X2)))),
inference(congruence,[status(thm)],[c82]) ).
cnf(c84,plain,
join(meet(X4,X2),meet(X4,X3)) = join(meet(X4,X3),meet(X4,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c85,plain,
join(meet(X4,X3),meet(X4,X2)) = join(meet(X4,X2),meet(X4,X3)),
inference(symmetry,[status(thm)],[c84]) ).
cnf(c86,plain,
join(meet(X4,X2),meet(X4,X3)) = meet(X4,join(X3,meet(X4,X2))),
inference(substitution,[status(thm)],[c67]) ).
cnf(c87,plain,
join(meet(X4,X3),meet(X4,X2)) = meet(X4,join(X3,meet(X4,X2))),
inference(transitivity,[status(thm)],[c85,c86]) ).
cnf(c88,plain,
join(meet(X4,X3),meet(X4,join(X3,X2))) = meet(X4,join(X3,meet(X4,join(X3,X2)))),
inference(substitution,[status(thm)],[c87]) ).
cnf(c89,plain,
meet(X4,join(X3,meet(X4,join(X3,X2)))) = join(meet(X4,X3),meet(X4,join(X3,X2))),
inference(symmetry,[status(thm)],[c88]) ).
cnf(c90,plain,
meet(X4,join(X3,meet(X4,join(X3,X2)))) = meet(X4,join(X3,X2)),
inference(transitivity,[status(thm)],[c89,c34]) ).
cnf(c91,plain,
meet(X4,join(X3,meet(X2,X4))) = meet(X4,join(X3,X2)),
inference(transitivity,[status(thm)],[c83,c90]) ).
cnf(c92,plain,
meet(X4,join(X3,meet(X4,X2))) = meet(X4,join(X3,X2)),
inference(transitivity,[status(thm)],[c80,c91]) ).
cnf(c93,plain,
meet(X3,join(X2,meet(X3,X4))) = meet(X3,join(X2,X4)),
inference(substitution,[status(thm)],[c92]) ).
cnf(c94,plain,
meet(X3,join(X2,meet(X4,X3))) = meet(X3,join(X2,X4)),
inference(transitivity,[status(thm)],[c76,c93]) ).
cnf(c95,plain,
join(meet(X4,X3),meet(X3,X2)) = meet(X3,join(X2,X4)),
inference(transitivity,[status(thm)],[c73,c94]) ).
cnf(c96,plain,
join(meet(X4,X3),meet(X2,X3)) = meet(X3,join(X2,X4)),
inference(transitivity,[status(thm)],[c9,c95]) ).
cnf(c97,plain,
join(meet(b,a),meet(c,a)) = meet(a,join(c,b)),
inference(substitution,[status(thm)],[c96]) ).
cnf(c98,plain,
meet(a,join(c,b)) = join(meet(b,a),meet(c,a)),
inference(symmetry,[status(thm)],[c97]) ).
cnf(c99,plain,
meet(a,c) = meet(c,a),
inference(substitution,[status(thm)],[c6]) ).
cnf(c100,plain,
meet(c,a) = meet(a,c),
inference(symmetry,[status(thm)],[c99]) ).
cnf(c101,plain,
join(meet(b,a),meet(c,a)) = join(meet(b,a),meet(a,c)),
inference(congruence,[status(thm)],[c100]) ).
cnf(c102,plain,
meet(a,b) = meet(b,a),
inference(substitution,[status(thm)],[c6]) ).
cnf(c103,plain,
meet(b,a) = meet(a,b),
inference(symmetry,[status(thm)],[c102]) ).
cnf(c104,plain,
join(meet(b,a),meet(a,c)) = join(meet(a,b),meet(a,c)),
inference(congruence,[status(thm)],[c103]) ).
cnf(c105,plain,
join(meet(b,a),meet(c,a)) = join(meet(a,b),meet(a,c)),
inference(transitivity,[status(thm)],[c101,c104]) ).
cnf(c106,plain,
meet(a,join(c,b)) = join(meet(a,b),meet(a,c)),
inference(transitivity,[status(thm)],[c98,c105]) ).
cnf(c107,plain,
meet(a,join(b,c)) = join(meet(a,b),meet(a,c)),
inference(transitivity,[status(thm)],[c5,c106]) ).
cnf(c108,plain,
$false,
inference(resolution,[status(thm)],[c1,c107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT021-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n009.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 13:56:45 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.81/0.66 Command-line arguments: --no-flatten-goal
% 1.81/0.66
% 1.81/0.66 % SZS status Unsatisfiable
% 1.81/0.66
% 1.81/0.66 % SZS output start CNFRefutation
% See solution above
% 2.11/0.71
% 2.11/0.71 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------