%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : LAT023-1 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n009.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 07:05:38 AM UTC 2025
% Result : Unsatisfiable 12.19s 12.37s
% Output : CNFRefutation 12.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of clauses : 64 ( 64 unt; 0 nHn; 3 RR)
% Number of literals : 64 ( 63 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 : 171 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
meet(a,join(b,meet(a,c))) != join(meet(a,b),meet(a,c)),
file('theBenchmark.p',prove_modularity) ).
cnf(c1,axiom,
meet(X,X) = X,
file('LAT004-0.ax',idempotence_of_meet) ).
cnf(c2,axiom,
join(X,X) = X,
file('LAT004-0.ax',idempotence_of_join) ).
cnf(c3,axiom,
meet(X,Y) = meet(Y,X),
file('LAT004-0.ax',commutativity_of_meet) ).
cnf(c4,axiom,
join(X,Y) = join(Y,X),
file('LAT004-0.ax',commutativity_of_join) ).
cnf(c5,axiom,
meet(meet(X,Y),Z) = meet(X,meet(Y,Z)),
file('LAT004-0.ax',associativity_of_meet) ).
cnf(c6,axiom,
join(join(X,Y),Z) = join(X,join(Y,Z)),
file('LAT004-0.ax',associativity_of_join) ).
cnf(c7,plain,
join(X,join(X,Y)) = join(X,Y),
inference(equational,[status(thm)],[c2,c6]) ).
cnf(c8,plain,
meet(X,meet(X,Y)) = meet(X,Y),
inference(equational,[status(thm)],[c1,c5]) ).
cnf(c9,plain,
join(X,join(Y,Z)) = join(Y,join(X,Z)),
inference(equational,[status(thm)],[c4,c6]) ).
cnf(c10,plain,
meet(X,meet(Y,Z)) = meet(Y,meet(X,Z)),
inference(equational,[status(thm)],[c3,c5]) ).
cnf(c11,plain,
meet(X,meet(Y,X)) = meet(Y,X),
inference(equational,[status(thm)],[c1,c10]) ).
cnf(c12,plain,
join(X,join(Y,X)) = join(X,Y),
inference(equational,[status(thm)],[c4,c7]) ).
cnf(c13,axiom,
join(meet(join(X,Y),Z),Y) = join(meet(join(Z,Y),X),Y),
file('theBenchmark.p',modularity_axiom) ).
cnf(c14,plain,
join(X,meet(join(Y,X),Z)) = join(X,meet(join(Z,X),Y)),
inference(equational,[status(thm)],[c4,c13]) ).
cnf(c15,plain,
join(X,meet(X,join(Y,X))) = join(X,meet(X,Y)),
inference(equational,[status(thm)],[c2,c3,c14]) ).
cnf(c16,plain,
join(X,meet(join(Y,X),Z)) = join(X,meet(Y,join(Z,X))),
inference(equational,[status(thm)],[c3,c14]) ).
cnf(c18,plain,
join(X,join(Y,join(X,Z))) = join(X,join(Y,Z)),
inference(equational,[status(thm)],[c7,c9]) ).
cnf(c19,plain,
meet(X,meet(Y,meet(X,Z))) = meet(Y,meet(X,Z)),
inference(equational,[status(thm)],[c8,c10]) ).
cnf(c20,plain,
join(X,meet(X,join(X,Y))) = join(X,meet(X,Y)),
inference(equational,[status(thm)],[c4,c15]) ).
cnf(c22,plain,
join(X,meet(join(X,Y),Z)) = join(X,meet(Y,join(Z,X))),
inference(equational,[status(thm)],[c4,c16]) ).
cnf(c23,plain,
join(X,meet(Y,join(Z,X))) = join(X,meet(Z,join(Y,X))),
inference(equational,[status(thm)],[c7,c14,c16]) ).
cnf(c26,axiom,
join(meet(X,join(Y,Z)),meet(X,Y)) = meet(X,join(Y,Z)),
file('LAT004-0.ax',quasi_lattice1) ).
cnf(c27,plain,
join(meet(X,Y),meet(X,join(Y,Z))) = meet(X,join(Y,Z)),
inference(equational,[status(thm)],[c4,c26]) ).
cnf(c28,plain,
meet(X,join(X,Y)) = join(X,meet(X,Y)),
inference(equational,[status(thm)],[c1,c20,c27]) ).
cnf(c29,plain,
meet(X,join(Y,X)) = join(X,meet(X,Y)),
inference(equational,[status(thm)],[c4,c28]) ).
cnf(c30,plain,
join(X,join(Y,meet(X,Y))) = join(X,Y),
inference(equational,[status(thm)],[c1,c6,c7,c16,c18,c28,c29]) ).
cnf(c31,plain,
meet(X,join(Y,meet(Y,Z))) = meet(Y,meet(X,join(Y,Z))),
inference(equational,[status(thm)],[c10,c28]) ).
cnf(c32,plain,
meet(join(X,meet(X,Y)),Z) = meet(X,meet(join(X,Y),Z)),
inference(equational,[status(thm)],[c5,c28]) ).
cnf(c34,plain,
join(X,join(Y,meet(Y,X))) = join(X,Y),
inference(equational,[status(thm)],[c3,c30]) ).
cnf(c35,axiom,
meet(join(X,meet(Y,Z)),join(X,Y)) = join(X,meet(Y,Z)),
file('LAT004-0.ax',quasi_lattice2) ).
cnf(c36,plain,
meet(join(X,Y),join(X,meet(Y,Z))) = join(X,meet(Y,Z)),
inference(equational,[status(thm)],[c3,c35]) ).
cnf(c42,plain,
meet(join(X,meet(Y,X)),Z) = meet(X,meet(join(X,Y),Z)),
inference(equational,[status(thm)],[c2,c12,c23,c32]) ).
cnf(c47,plain,
join(meet(X,Y),meet(X,join(Z,Y))) = meet(X,join(Y,Z)),
inference(equational,[status(thm)],[c4,c27]) ).
cnf(c48,plain,
meet(join(X,Y),join(Y,meet(X,Z))) = join(Y,meet(X,Z)),
inference(equational,[status(thm)],[c4,c36]) ).
cnf(c50,plain,
join(meet(X,Y),meet(Y,join(X,Z))) = meet(Y,join(X,Z)),
inference(equational,[status(thm)],[c3,c27]) ).
cnf(c51,plain,
meet(join(X,Y),join(meet(Y,Z),X)) = join(X,meet(Y,Z)),
inference(equational,[status(thm)],[c4,c36]) ).
cnf(c52,plain,
meet(join(X,Y),join(X,meet(Z,Y))) = join(X,meet(Y,Z)),
inference(equational,[status(thm)],[c3,c36]) ).
cnf(c59,plain,
meet(join(meet(X,Y),Z),join(Z,X)) = join(Z,meet(X,Y)),
inference(equational,[status(thm)],[c3,c51]) ).
cnf(c62,plain,
join(X,join(meet(X,Y),meet(Y,Z))) = join(X,meet(Y,Z)),
inference(equational,[status(thm)],[c6,c18,c28,c50,c52]) ).
cnf(c63,plain,
meet(X,meet(join(X,Y),join(Y,Z))) = meet(X,join(Y,Z)),
inference(equational,[status(thm)],[c10,c19,c42,c48,c50]) ).
cnf(c68,plain,
join(meet(X,Y),meet(Y,join(Z,X))) = meet(Y,join(X,Z)),
inference(equational,[status(thm)],[c4,c50]) ).
cnf(c70,plain,
join(meet(X,Y),meet(X,join(Z,Y))) = meet(X,join(Z,Y)),
inference(equational,[status(thm)],[c4,c47]) ).
cnf(c73,plain,
join(X,meet(Y,join(X,meet(Y,Z)))) = join(X,meet(Y,Z)),
inference(equational,[status(thm)],[c6,c7,c12,c16,c48]) ).
cnf(c80,plain,
meet(X,join(Y,meet(Z,join(W,Y)))) = meet(X,join(Y,meet(W,join(Z,Y)))),
inference(equational,[status(thm)],[c14,c16,c27]) ).
cnf(c91,plain,
join(meet(X,Y),meet(Y,join(Z,X))) = meet(Y,join(Z,X)),
inference(equational,[status(thm)],[c3,c70]) ).
cnf(c102,plain,
join(X,join(meet(Y,Z),meet(X,Y))) = join(X,meet(Y,Z)),
inference(equational,[status(thm)],[c4,c62]) ).
cnf(c121,plain,
meet(X,meet(Y,join(meet(X,Y),Z))) = join(meet(X,Y),meet(X,meet(Y,Z))),
inference(equational,[status(thm)],[c5,c28]) ).
cnf(c124,plain,
meet(X,join(Y,meet(Z,join(Y,W)))) = meet(X,join(Y,meet(W,join(Z,Y)))),
inference(equational,[status(thm)],[c47,c70,c80]) ).
cnf(c131,plain,
meet(X,meet(Y,join(X,meet(X,Z)))) = meet(Y,join(X,meet(X,Z))),
inference(equational,[status(thm)],[c7,c31,c73]) ).
cnf(c134,plain,
meet(X,meet(Y,join(Z,meet(X,Y)))) = meet(X,meet(Y,join(Z,X))),
inference(equational,[status(thm)],[c5,c59,c63]) ).
cnf(c135,plain,
meet(X,meet(Y,join(Z,X))) = meet(X,join(Y,meet(Y,Z))),
inference(equational,[status(thm)],[c5,c11,c19,c29,c131,c134]) ).
cnf(c136,plain,
meet(X,meet(Y,join(X,Z))) = meet(X,join(Y,meet(Y,Z))),
inference(equational,[status(thm)],[c68,c91,c135]) ).
cnf(c146,plain,
meet(X,join(Y,meet(Y,Z))) = meet(Y,join(X,meet(X,meet(Y,Z)))),
inference(equational,[status(thm)],[c8,c31,c136]) ).
cnf(c177,plain,
join(X,join(meet(Y,Z),meet(Y,X))) = join(X,meet(Y,Z)),
inference(equational,[status(thm)],[c3,c102]) ).
cnf(c223,plain,
meet(X,join(Y,meet(Z,join(Y,W)))) = meet(X,join(Y,meet(W,join(Y,Z)))),
inference(equational,[status(thm)],[c6,c12,c22,c124]) ).
cnf(c224,plain,
meet(X,join(Y,meet(Z,join(Y,X)))) = meet(X,join(Y,Z)),
inference(equational,[status(thm)],[c6,c12,c16,c28,c34,c36,c134,c135,c223]) ).
cnf(c228,plain,
meet(X,join(Y,meet(Y,Z))) = join(meet(X,Y),meet(X,meet(Y,Z))),
inference(equational,[status(thm)],[c4,c121,c134,c135]) ).
cnf(c231,plain,
join(X,meet(Y,join(Z,join(W,X)))) = join(X,meet(join(Z,W),join(Y,X))),
inference(equational,[status(thm)],[c6,c23]) ).
cnf(c232,plain,
meet(join(X,Y),join(Y,Z)) = join(Y,meet(X,join(Z,Y))),
inference(equational,[status(thm)],[c2,c6,c22,c48,c224,c231]) ).
cnf(c234,plain,
meet(join(X,Y),join(Z,Y)) = join(Y,meet(X,join(Z,Y))),
inference(equational,[status(thm)],[c4,c232]) ).
cnf(c237,plain,
join(meet(X,Y),meet(Z,X)) = meet(X,join(Z,meet(X,Y))),
inference(equational,[status(thm)],[c2,c6,c16,c30,c146,c177,c228,c234]) ).
cnf(g1,plain,
meet(a,join(b,meet(a,c))) = join(meet(a,b),meet(a,c)),
inference(equational,[status(thm)],[c3,c4,c237]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : LAT023-1 : TPTP v9.0.0. Released v2.2.0.
% 0.12/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n009.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 11:33:04 EDT 2025
% 0.18/0.33 % CPUTime :
% 12.19/12.37 % SZS status Unsatisfiable
% 12.19/12.37 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------