%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : LAT009-1 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Jul 15 07:05:37 AM UTC 2025
% Result : Unsatisfiable 9.69s 9.82s
% Output : CNFRefutation 9.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of clauses : 75 ( 75 unt; 0 nHn; 3 RR)
% Number of literals : 75 ( 74 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 : 204 ( 34 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
join(a,meet(b,c)) != meet(join(a,b),join(a,c)),
file('theBenchmark.p',prove_distributivity) ).
cnf(c1,axiom,
meet(X,X) = X,
file('LAT001-0.ax',idempotence_of_meet) ).
cnf(c2,axiom,
join(X,X) = X,
file('LAT001-0.ax',idempotence_of_join) ).
cnf(c3,axiom,
meet(X,Y) = meet(Y,X),
file('LAT001-0.ax',commutativity_of_meet) ).
cnf(c4,axiom,
join(X,Y) = join(Y,X),
file('LAT001-0.ax',commutativity_of_join) ).
cnf(c5,axiom,
meet(X,join(X,Y)) = X,
file('LAT001-0.ax',absorption1) ).
cnf(c6,axiom,
join(X,meet(X,Y)) = X,
file('LAT001-0.ax',absorption2) ).
cnf(c7,plain,
join(X,meet(Y,X)) = X,
inference(equational,[status(thm)],[c3,c6]) ).
cnf(c8,plain,
meet(X,join(Y,X)) = X,
inference(equational,[status(thm)],[c4,c5]) ).
cnf(c9,axiom,
meet(meet(X,Y),Z) = meet(X,meet(Y,Z)),
file('LAT001-0.ax',associativity_of_meet) ).
cnf(c10,axiom,
join(join(X,Y),Z) = join(X,join(Y,Z)),
file('LAT001-0.ax',associativity_of_join) ).
cnf(c11,plain,
join(X,join(X,Y)) = join(X,Y),
inference(equational,[status(thm)],[c2,c10]) ).
cnf(c12,plain,
meet(X,meet(X,Y)) = meet(X,Y),
inference(equational,[status(thm)],[c1,c9]) ).
cnf(c13,plain,
join(X,join(Y,Z)) = join(Y,join(X,Z)),
inference(equational,[status(thm)],[c4,c10]) ).
cnf(c14,plain,
meet(X,meet(Y,Z)) = meet(Y,meet(X,Z)),
inference(equational,[status(thm)],[c3,c9]) ).
cnf(c15,plain,
meet(X,meet(Y,X)) = meet(Y,X),
inference(equational,[status(thm)],[c1,c14]) ).
cnf(c16,plain,
join(X,join(Y,X)) = join(X,Y),
inference(equational,[status(thm)],[c4,c11]) ).
cnf(c17,plain,
join(X,join(meet(X,Y),Z)) = join(X,Z),
inference(equational,[status(thm)],[c6,c10]) ).
cnf(c18,plain,
meet(X,meet(join(X,Y),Z)) = meet(X,Z),
inference(equational,[status(thm)],[c5,c9]) ).
cnf(c19,plain,
join(X,meet(Y,meet(X,Z))) = X,
inference(equational,[status(thm)],[c6,c7,c17]) ).
cnf(c20,plain,
join(X,meet(Y,meet(Z,X))) = X,
inference(equational,[status(thm)],[c7,c9]) ).
cnf(c23,plain,
join(X,join(Y,meet(X,Z))) = join(Y,X),
inference(equational,[status(thm)],[c6,c13]) ).
cnf(c24,plain,
join(X,join(Y,meet(Z,X))) = join(Y,X),
inference(equational,[status(thm)],[c7,c13]) ).
cnf(c25,plain,
meet(X,meet(Y,join(X,Z))) = meet(Y,X),
inference(equational,[status(thm)],[c5,c14]) ).
cnf(c26,plain,
meet(X,meet(Y,join(Z,X))) = meet(Y,X),
inference(equational,[status(thm)],[c8,c14]) ).
cnf(c28,plain,
join(X,join(meet(Y,X),Z)) = join(X,Z),
inference(equational,[status(thm)],[c3,c17]) ).
cnf(c30,plain,
meet(X,meet(Y,meet(X,Z))) = meet(Y,meet(X,Z)),
inference(equational,[status(thm)],[c12,c14]) ).
cnf(c32,plain,
meet(X,meet(Y,meet(Z,X))) = meet(Y,meet(Z,X)),
inference(equational,[status(thm)],[c25,c30]) ).
cnf(c33,plain,
join(X,join(Y,Z)) = join(Y,join(X,join(Z,Y))),
inference(equational,[status(thm)],[c13,c16]) ).
cnf(c35,plain,
meet(join(X,Y),meet(Z,X)) = meet(Z,X),
inference(equational,[status(thm)],[c25,c32]) ).
cnf(c38,plain,
join(meet(X,Y),join(Z,Y)) = join(Y,Z),
inference(equational,[status(thm)],[c24,c28,c33]) ).
cnf(c39,plain,
meet(X,meet(Y,join(meet(X,Y),Z))) = meet(X,Y),
inference(equational,[status(thm)],[c5,c9]) ).
cnf(c40,plain,
join(X,join(Y,meet(join(X,Y),Z))) = join(X,Y),
inference(equational,[status(thm)],[c6,c10]) ).
cnf(c41,plain,
meet(join(X,Y),join(X,join(Y,Z))) = join(X,Y),
inference(equational,[status(thm)],[c5,c10]) ).
cnf(c42,plain,
join(meet(X,Y),meet(X,meet(Y,Z))) = meet(X,Y),
inference(equational,[status(thm)],[c6,c9]) ).
cnf(c46,plain,
join(X,join(Y,meet(join(Y,X),Z))) = join(X,Y),
inference(equational,[status(thm)],[c4,c40]) ).
cnf(c47,plain,
meet(X,meet(Y,join(meet(Y,X),Z))) = meet(X,Y),
inference(equational,[status(thm)],[c3,c39]) ).
cnf(c48,plain,
join(meet(X,Y),meet(Y,meet(X,Z))) = meet(Y,X),
inference(equational,[status(thm)],[c3,c42]) ).
cnf(c50,plain,
join(meet(X,Y),meet(Y,meet(Z,X))) = meet(X,Y),
inference(equational,[status(thm)],[c3,c9,c42]) ).
cnf(c51,plain,
meet(join(X,Y),join(Y,join(X,Z))) = join(Y,X),
inference(equational,[status(thm)],[c4,c41]) ).
cnf(c52,plain,
meet(join(X,Y),join(Y,join(Z,X))) = join(X,Y),
inference(equational,[status(thm)],[c4,c10,c41]) ).
cnf(c53,plain,
meet(join(X,Y),join(X,join(Z,Y))) = join(X,Y),
inference(equational,[status(thm)],[c4,c41]) ).
cnf(c61,plain,
join(meet(X,Y),meet(join(X,Z),Y)) = meet(join(X,Z),Y),
inference(equational,[status(thm)],[c4,c7,c18]) ).
cnf(c62,plain,
meet(X,meet(Y,meet(join(X,Z),W))) = meet(Y,meet(X,W)),
inference(equational,[status(thm)],[c14,c18]) ).
cnf(c63,plain,
meet(join(X,Y),join(meet(X,Z),Y)) = join(meet(X,Z),Y),
inference(equational,[status(thm)],[c3,c8,c17]) ).
cnf(c71,plain,
join(X,join(Y,meet(Z,join(Y,X)))) = join(X,Y),
inference(equational,[status(thm)],[c10,c19,c51]) ).
cnf(c72,plain,
meet(join(X,Y),join(Z,join(Y,X))) = join(X,Y),
inference(equational,[status(thm)],[c4,c10,c53]) ).
cnf(c74,plain,
join(meet(X,Y),meet(Z,meet(Y,X))) = meet(X,Y),
inference(equational,[status(thm)],[c9,c35,c50,c62]) ).
cnf(c83,plain,
join(meet(X,Y),meet(Y,join(X,Z))) = meet(join(X,Z),Y),
inference(equational,[status(thm)],[c3,c61]) ).
cnf(c84,plain,
join(meet(X,Y),meet(join(Z,X),Y)) = meet(join(Z,X),Y),
inference(equational,[status(thm)],[c24,c61]) ).
cnf(c95,plain,
join(X,join(Y,join(Z,meet(X,W)))) = join(Y,join(Z,X)),
inference(equational,[status(thm)],[c10,c23]) ).
cnf(c99,plain,
meet(join(meet(X,Y),Z),join(Z,Y)) = join(meet(X,Y),Z),
inference(equational,[status(thm)],[c7,c52]) ).
cnf(c100,plain,
join(meet(X,Y),meet(Y,join(meet(X,Y),Z))) = meet(Y,join(meet(X,Y),Z)),
inference(equational,[status(thm)],[c1,c9,c26,c83,c99]) ).
cnf(c104,plain,
join(meet(X,Y),join(meet(Y,X),Z)) = join(meet(Y,X),Z),
inference(equational,[status(thm)],[c9,c10,c25,c40,c48,c63,c83]) ).
cnf(c123,plain,
meet(X,join(meet(X,Y),meet(Z,X))) = join(meet(X,Y),meet(Z,X)),
inference(equational,[status(thm)],[c7,c63]) ).
cnf(c130,plain,
join(X,meet(join(X,Y),join(Z,X))) = meet(join(X,Y),join(Z,X)),
inference(equational,[status(thm)],[c8,c61]) ).
cnf(c131,plain,
join(X,meet(join(Y,X),join(Z,Y))) = join(X,Y),
inference(equational,[status(thm)],[c46,c130]) ).
cnf(c136,plain,
join(meet(X,Y),meet(join(Z,Y),X)) = meet(join(Z,Y),X),
inference(equational,[status(thm)],[c84,c104]) ).
cnf(c151,plain,
meet(join(X,meet(Y,Z)),join(Z,X)) = join(X,meet(Y,Z)),
inference(equational,[status(thm)],[c28,c72]) ).
cnf(c152,plain,
meet(join(X,Y),Z) = join(meet(Z,join(X,Y)),meet(X,Z)),
inference(equational,[status(thm)],[c9,c47,c51,c83]) ).
cnf(c153,plain,
join(meet(X,join(Y,Z)),meet(Y,X)) = meet(X,join(Y,Z)),
inference(equational,[status(thm)],[c18,c74]) ).
cnf(c174,plain,
meet(X,join(meet(Y,X),meet(Z,X))) = join(meet(X,Y),meet(Z,X)),
inference(equational,[status(thm)],[c3,c123]) ).
cnf(c248,axiom,
join(meet(join(meet(X,Y),Z),Y),meet(Z,X)) = meet(join(meet(join(X,Y),Z),Y),join(Z,X)),
file('theBenchmark.p',distributivity_dual) ).
cnf(c249,plain,
meet(join(X,Y),join(Z,meet(join(Y,Z),X))) = join(meet(Z,join(meet(Y,Z),X)),meet(X,Y)),
inference(equational,[status(thm)],[c1,c4,c9,c100,c152,c153,c248]) ).
cnf(c251,plain,
meet(X,join(meet(Y,X),Z)) = join(meet(X,Z),meet(Y,X)),
inference(equational,[status(thm)],[c3,c9,c10,c20,c42,c174,c249]) ).
cnf(c252,plain,
meet(X,join(Y,meet(Z,X))) = join(meet(X,Y),meet(Z,X)),
inference(equational,[status(thm)],[c4,c251]) ).
cnf(c255,plain,
meet(join(X,Y),join(X,Z)) = join(X,meet(join(X,Y),Z)),
inference(equational,[status(thm)],[c4,c5,c251]) ).
cnf(c260,plain,
meet(join(X,Y),join(Z,X)) = join(X,meet(join(X,Y),Z)),
inference(equational,[status(thm)],[c16,c130,c255]) ).
cnf(c261,plain,
meet(join(X,Y),join(Z,Y)) = join(Y,meet(join(Y,Z),X)),
inference(equational,[status(thm)],[c131,c136,c252,c260]) ).
cnf(c262,plain,
meet(join(X,Y),join(Z,Y)) = join(Y,meet(join(X,Y),Z)),
inference(equational,[status(thm)],[c4,c8,c252]) ).
cnf(c265,plain,
join(X,meet(join(Y,X),Z)) = join(X,meet(Y,join(X,Z))),
inference(equational,[status(thm)],[c3,c261,c262]) ).
cnf(c266,plain,
join(X,meet(join(X,Y),Z)) = join(X,meet(Y,join(X,Z))),
inference(equational,[status(thm)],[c9,c15,c151,c261,c262,c265]) ).
cnf(c269,plain,
join(X,meet(Y,join(X,Z))) = join(X,meet(Y,Z)),
inference(equational,[status(thm)],[c10,c38,c71,c95,c249,c251,c265,c266]) ).
cnf(g1,plain,
join(a,meet(b,c)) = meet(join(a,b),join(a,c)),
inference(equational,[status(thm)],[c255,c266,c269]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT009-1 : TPTP v9.0.0. Released v2.2.0.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n016.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Jul 14 11:32:34 EDT 2025
% 0.12/0.33 % CPUTime :
% 9.69/9.82 % SZS status Unsatisfiable
% 9.69/9.82 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------