%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : LAT026-1 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n006.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 11.38s 11.58s
% Output : CNFRefutation 11.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 8
% Syntax : Number of clauses : 72 ( 72 unt; 0 nHn; 3 RR)
% Number of literals : 72 ( 71 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 : 190 ( 48 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
meet(meet(a,b),c) != meet(a,meet(b,c)),
file('theBenchmark.p',prove_associativity_of_meet) ).
cnf(c1,axiom,
meet(X,X) = X,
file('LAT005-0.ax',idempotence_of_meet) ).
cnf(c2,axiom,
join(X,X) = X,
file('LAT005-0.ax',idempotence_of_join) ).
cnf(c3,axiom,
meet(X,Y) = meet(Y,X),
file('LAT005-0.ax',commutativity_of_meet) ).
cnf(c4,axiom,
join(X,Y) = join(Y,X),
file('LAT005-0.ax',commutativity_of_join) ).
cnf(c5,axiom,
meet(X,join(Y,join(X,Z))) = X,
file('theBenchmark.p',absorbtion) ).
cnf(c6,plain,
meet(X,join(X,Y)) = X,
inference(equational,[status(thm)],[c2,c5]) ).
cnf(c7,plain,
meet(X,join(Y,X)) = X,
inference(equational,[status(thm)],[c2,c5]) ).
cnf(c8,plain,
meet(X,join(join(X,Y),Z)) = X,
inference(equational,[status(thm)],[c4,c5]) ).
cnf(c9,plain,
meet(X,join(Y,join(Z,X))) = X,
inference(equational,[status(thm)],[c4,c5]) ).
cnf(c10,plain,
meet(X,join(join(Y,X),Z)) = X,
inference(equational,[status(thm)],[c4,c9]) ).
cnf(c11,axiom,
meet(meet(join(X,Y),join(Z,Y)),Y) = Y,
file('LAT005-0.ax',wal_1) ).
cnf(c12,plain,
meet(X,meet(join(Y,X),join(Z,X))) = X,
inference(equational,[status(thm)],[c3,c11]) ).
cnf(c13,axiom,
join(join(meet(X,Y),meet(Z,Y)),Y) = Y,
file('LAT005-0.ax',wal_2) ).
cnf(c14,plain,
join(X,join(meet(Y,X),meet(Z,X))) = X,
inference(equational,[status(thm)],[c4,c13]) ).
cnf(c15,plain,
join(X,meet(Y,X)) = X,
inference(equational,[status(thm)],[c2,c14]) ).
cnf(c16,plain,
meet(X,meet(Y,X)) = meet(Y,X),
inference(equational,[status(thm)],[c3,c5,c14]) ).
cnf(c17,plain,
join(X,meet(X,Y)) = X,
inference(equational,[status(thm)],[c3,c15]) ).
cnf(c18,plain,
meet(X,meet(X,Y)) = meet(Y,X),
inference(equational,[status(thm)],[c3,c16]) ).
cnf(c19,plain,
join(X,join(Y,X)) = join(Y,X),
inference(equational,[status(thm)],[c4,c7,c15]) ).
cnf(c20,plain,
join(X,join(X,Y)) = join(Y,X),
inference(equational,[status(thm)],[c4,c19]) ).
cnf(c22,plain,
meet(X,meet(X,Y)) = meet(X,Y),
inference(equational,[status(thm)],[c3,c18]) ).
cnf(c23,plain,
join(X,join(X,Y)) = join(X,Y),
inference(equational,[status(thm)],[c4,c20]) ).
cnf(c24,plain,
meet(meet(X,Y),join(Z,Y)) = meet(X,Y),
inference(equational,[status(thm)],[c9,c15]) ).
cnf(c25,plain,
join(X,join(Y,join(X,Z))) = join(Y,join(X,Z)),
inference(equational,[status(thm)],[c5,c15,c20,c23]) ).
cnf(c26,plain,
meet(meet(X,Y),join(Y,Z)) = meet(X,Y),
inference(equational,[status(thm)],[c10,c15]) ).
cnf(c27,plain,
meet(meet(X,Y),join(Z,X)) = meet(Y,X),
inference(equational,[status(thm)],[c18,c22,c24]) ).
cnf(c28,plain,
meet(join(X,Y),meet(Z,Y)) = meet(Z,Y),
inference(equational,[status(thm)],[c1,c18,c24]) ).
cnf(c29,plain,
join(join(X,Y),meet(Z,Y)) = join(X,Y),
inference(equational,[status(thm)],[c15,c24]) ).
cnf(c32,plain,
join(X,meet(Y,meet(Z,X))) = X,
inference(equational,[status(thm)],[c15,c29]) ).
cnf(c33,plain,
join(X,meet(Y,meet(X,Z))) = X,
inference(equational,[status(thm)],[c17,c29]) ).
cnf(c34,plain,
join(X,join(meet(X,Y),meet(Z,X))) = X,
inference(equational,[status(thm)],[c3,c14]) ).
cnf(c35,plain,
join(X,join(meet(Y,X),meet(X,Z))) = X,
inference(equational,[status(thm)],[c3,c14]) ).
cnf(c38,plain,
join(X,join(join(X,Y),Z)) = join(Z,join(X,Y)),
inference(equational,[status(thm)],[c4,c25]) ).
cnf(c39,plain,
join(X,join(Y,join(Z,X))) = join(Y,join(Z,X)),
inference(equational,[status(thm)],[c19,c25]) ).
cnf(c40,plain,
meet(X,meet(Y,meet(X,Z))) = meet(Y,meet(X,Z)),
inference(equational,[status(thm)],[c17,c18,c22,c24]) ).
cnf(c41,plain,
meet(X,meet(Y,meet(Z,X))) = meet(Y,meet(Z,X)),
inference(equational,[status(thm)],[c15,c18,c22,c24]) ).
cnf(c42,plain,
meet(meet(X,Y),meet(Y,X)) = meet(X,Y),
inference(equational,[status(thm)],[c16,c18,c22]) ).
cnf(c49,plain,
meet(X,Y) = meet(join(Z,Y),meet(Y,X)),
inference(equational,[status(thm)],[c3,c27]) ).
cnf(c56,plain,
join(X,join(Y,Z)) = join(Z,join(join(Y,Z),X)),
inference(equational,[status(thm)],[c19,c38]) ).
cnf(c58,plain,
meet(join(X,Y),meet(Y,meet(meet(Y,X),Z))) = meet(Z,meet(Y,X)),
inference(equational,[status(thm)],[c17,c27,c49]) ).
cnf(c60,plain,
join(join(X,Y),join(Y,X)) = join(X,Y),
inference(equational,[status(thm)],[c19,c20,c23]) ).
cnf(c61,plain,
join(X,join(join(Y,X),Z)) = join(Z,join(X,Y)),
inference(equational,[status(thm)],[c20,c23,c38]) ).
cnf(c62,plain,
meet(X,meet(meet(X,Y),Z)) = meet(Z,meet(X,Y)),
inference(equational,[status(thm)],[c3,c40]) ).
cnf(c72,plain,
join(X,join(join(Y,X),Z)) = join(join(Y,X),Z),
inference(equational,[status(thm)],[c19,c56,c60]) ).
cnf(c75,plain,
meet(X,meet(meet(X,Y),Z)) = meet(meet(X,Y),Z),
inference(equational,[status(thm)],[c16,c42,c62]) ).
cnf(c134,plain,
meet(join(X,Y),meet(Z,join(Y,X))) = meet(Z,join(Y,X)),
inference(equational,[status(thm)],[c20,c28]) ).
cnf(c135,plain,
meet(join(X,Y),meet(Z,meet(W,X))) = meet(Z,meet(W,X)),
inference(equational,[status(thm)],[c26,c41]) ).
cnf(c169,plain,
join(join(X,Y),join(Y,meet(Z,join(X,Y)))) = join(X,Y),
inference(equational,[status(thm)],[c7,c14]) ).
cnf(c170,plain,
join(join(X,Y),join(join(Z,X),Y)) = join(join(Z,X),Y),
inference(equational,[status(thm)],[c10,c61,c72,c169]) ).
cnf(c171,plain,
join(join(X,Y),join(join(X,Z),Y)) = join(join(X,Z),Y),
inference(equational,[status(thm)],[c8,c61,c72,c169]) ).
cnf(c172,plain,
meet(join(X,Y),join(join(X,Z),Y)) = join(X,Y),
inference(equational,[status(thm)],[c6,c171]) ).
cnf(c174,plain,
meet(join(X,Y),join(join(Z,X),Y)) = join(X,Y),
inference(equational,[status(thm)],[c6,c170]) ).
cnf(c187,plain,
meet(join(X,join(Y,Z)),join(Y,X)) = join(Y,X),
inference(equational,[status(thm)],[c134,c172]) ).
cnf(c189,plain,
join(join(X,Y),join(X,meet(Z,join(X,Y)))) = join(X,Y),
inference(equational,[status(thm)],[c6,c14]) ).
cnf(c190,plain,
join(X,join(Y,meet(Z,join(Y,X)))) = join(Y,X),
inference(equational,[status(thm)],[c174,c187,c189]) ).
cnf(c191,plain,
join(X,join(Y,meet(Z,X))) = join(Y,X),
inference(equational,[status(thm)],[c27,c190]) ).
cnf(c192,plain,
join(join(X,Y),join(Y,Z)) = join(join(X,Y),Z),
inference(equational,[status(thm)],[c39,c174,c190]) ).
cnf(c200,plain,
join(X,join(meet(X,Y),Z)) = join(X,Z),
inference(equational,[status(thm)],[c17,c192]) ).
cnf(c202,plain,
join(X,join(Y,meet(X,Z))) = join(Y,X),
inference(equational,[status(thm)],[c18,c22,c191]) ).
cnf(c203,plain,
meet(meet(X,Y),meet(Y,join(Z,meet(X,Y)))) = meet(X,Y),
inference(equational,[status(thm)],[c12,c15]) ).
cnf(c252,plain,
meet(join(X,Y),meet(meet(Y,X),Z)) = meet(Z,meet(Y,X)),
inference(equational,[status(thm)],[c58,c75]) ).
cnf(c311,plain,
meet(meet(X,Y),meet(Y,join(Z,meet(Y,X)))) = meet(X,Y),
inference(equational,[status(thm)],[c3,c203]) ).
cnf(c312,plain,
meet(meet(meet(X,Y),Z),meet(Z,Y)) = meet(meet(X,Y),Z),
inference(equational,[status(thm)],[c32,c311]) ).
cnf(c313,plain,
meet(meet(meet(X,Y),Z),meet(Z,X)) = meet(meet(X,Y),Z),
inference(equational,[status(thm)],[c33,c311]) ).
cnf(c314,plain,
join(meet(X,Y),meet(meet(Y,Z),X)) = meet(X,Y),
inference(equational,[status(thm)],[c34,c200,c313]) ).
cnf(c315,plain,
join(meet(meet(X,Y),Z),meet(Z,X)) = meet(Z,X),
inference(equational,[status(thm)],[c35,c202,c313]) ).
cnf(c318,plain,
meet(meet(X,Y),Z) = meet(meet(Z,Y),meet(X,Y)),
inference(equational,[status(thm)],[c312,c314,c315]) ).
cnf(c324,plain,
meet(meet(X,Y),meet(Z,Y)) = meet(X,meet(Z,Y)),
inference(equational,[status(thm)],[c3,c318]) ).
cnf(c325,plain,
meet(X,meet(Y,Z)) = meet(Y,meet(X,Z)),
inference(equational,[status(thm)],[c135,c252,c324]) ).
cnf(g1,plain,
meet(meet(a,b),c) = meet(a,meet(b,c)),
inference(equational,[status(thm)],[c3,c325]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LAT026-1 : TPTP v9.0.0. Released v2.2.0.
% 0.03/0.11 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n006.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Jul 14 11:33:34 EDT 2025
% 0.11/0.32 % CPUTime :
% 11.38/11.58 % SZS status Unsatisfiable
% 11.38/11.58 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------