%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : LAT006-1 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n002.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 07:05:36 AM UTC 2025
% Result : Unsatisfiable 3.44s 3.63s
% Output : CNFRefutation 3.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 3
% Syntax : Number of clauses : 62 ( 62 unt; 0 nHn; 3 RR)
% Number of literals : 62 ( 61 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 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 : 157 ( 14 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,join(X,Y)) = X,
file('theBenchmark.p',absorption) ).
cnf(c2,axiom,
meet(X,join(Y,Z)) = join(meet(Z,X),meet(Y,X)),
file('theBenchmark.p',distribution) ).
cnf(c3,plain,
join(X,meet(Y,join(X,Z))) = meet(join(X,Z),join(Y,X)),
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c4,plain,
meet(join(X,Y),join(X,X)) = join(X,X),
inference(equational,[status(thm)],[c1,c3]) ).
cnf(c5,plain,
join(meet(X,join(Y,Z)),Y) = meet(join(Y,Z),join(Y,X)),
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c6,plain,
meet(meet(X,Y),meet(Y,join(Z,X))) = meet(X,Y),
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c7,plain,
meet(meet(X,Y),Y) = meet(X,Y),
inference(equational,[status(thm)],[c1,c6]) ).
cnf(c9,plain,
join(meet(X,Y),meet(Z,Y)) = meet(Y,join(meet(Z,Y),X)),
inference(equational,[status(thm)],[c2,c7]) ).
cnf(c10,plain,
join(meet(X,Y),meet(Z,Y)) = meet(Y,join(Z,meet(X,Y))),
inference(equational,[status(thm)],[c2,c7]) ).
cnf(c11,plain,
meet(X,join(Y,meet(Z,X))) = meet(X,join(Y,Z)),
inference(equational,[status(thm)],[c2,c10]) ).
cnf(c12,plain,
meet(X,join(meet(Y,X),Z)) = meet(X,join(Y,Z)),
inference(equational,[status(thm)],[c2,c9]) ).
cnf(c13,plain,
join(X,meet(join(X,Y),join(X,Y))) = join(X,Y),
inference(equational,[status(thm)],[c1,c3]) ).
cnf(c14,plain,
join(X,join(X,X)) = join(X,X),
inference(equational,[status(thm)],[c4,c13]) ).
cnf(c15,plain,
join(meet(X,Y),meet(Z,Y)) = meet(Y,meet(Y,join(X,Z))),
inference(equational,[status(thm)],[c2,c7,c9]) ).
cnf(c16,plain,
meet(X,join(Y,Z)) = meet(X,meet(X,join(Z,Y))),
inference(equational,[status(thm)],[c7,c9,c12,c15]) ).
cnf(c17,plain,
meet(X,join(Y,X)) = meet(X,X),
inference(equational,[status(thm)],[c1,c16]) ).
cnf(c18,plain,
meet(X,X) = X,
inference(equational,[status(thm)],[c1,c17]) ).
cnf(c19,plain,
join(X,meet(Y,X)) = X,
inference(equational,[status(thm)],[c1,c15,c18]) ).
cnf(c20,plain,
join(X,X) = X,
inference(equational,[status(thm)],[c13,c18,c19]) ).
cnf(c21,plain,
meet(X,Y) = meet(Y,X),
inference(equational,[status(thm)],[c10,c11,c20]) ).
cnf(c22,plain,
join(meet(X,Y),Y) = Y,
inference(equational,[status(thm)],[c15,c17,c18]) ).
cnf(c25,plain,
meet(X,meet(X,Y)) = meet(X,Y),
inference(equational,[status(thm)],[c16,c19,c22]) ).
cnf(c26,plain,
join(X,join(Y,X)) = join(Y,X),
inference(equational,[status(thm)],[c17,c18,c22]) ).
cnf(c28,plain,
meet(X,join(Y,Z)) = meet(X,join(Z,Y)),
inference(equational,[status(thm)],[c7,c9,c12,c15,c25]) ).
cnf(c30,plain,
join(meet(X,Y),X) = X,
inference(equational,[status(thm)],[c21,c22]) ).
cnf(c31,plain,
join(meet(X,join(Y,Z)),Z) = meet(join(Z,Y),join(Z,X)),
inference(equational,[status(thm)],[c5,c28]) ).
cnf(c32,plain,
join(X,Y) = join(Y,X),
inference(equational,[status(thm)],[c1,c18,c31]) ).
cnf(c33,plain,
join(X,meet(Y,join(Z,X))) = meet(join(X,Z),join(Y,X)),
inference(equational,[status(thm)],[c3,c28]) ).
cnf(c35,plain,
join(X,meet(Y,join(X,Z))) = meet(join(X,Z),join(X,Y)),
inference(equational,[status(thm)],[c3,c28]) ).
cnf(c36,plain,
meet(X,meet(Y,X)) = meet(X,Y),
inference(equational,[status(thm)],[c21,c25]) ).
cnf(c38,plain,
join(X,meet(Y,join(Z,X))) = meet(join(X,Z),join(X,Y)),
inference(equational,[status(thm)],[c2,c15,c25,c35]) ).
cnf(c41,plain,
meet(meet(X,Y),meet(Y,join(X,Z))) = meet(X,Y),
inference(equational,[status(thm)],[c6,c28]) ).
cnf(c42,plain,
meet(X,join(join(X,Y),Z)) = X,
inference(equational,[status(thm)],[c1,c4,c20,c21,c25,c41]) ).
cnf(c47,plain,
meet(meet(X,Y),join(Y,Z)) = meet(X,Y),
inference(equational,[status(thm)],[c22,c42]) ).
cnf(c52,plain,
join(meet(X,Y),meet(Y,X)) = meet(Y,X),
inference(equational,[status(thm)],[c2,c14,c15,c20,c25]) ).
cnf(c66,plain,
meet(meet(X,Y),join(Z,meet(Y,X))) = meet(Y,X),
inference(equational,[status(thm)],[c19,c33,c52]) ).
cnf(c68,plain,
meet(join(X,Y),join(X,meet(Z,Y))) = meet(join(X,Z),join(X,Y)),
inference(equational,[status(thm)],[c5,c10,c15,c21,c25,c31]) ).
cnf(c69,plain,
meet(join(X,Y),join(X,join(Y,Z))) = join(X,Y),
inference(equational,[status(thm)],[c4,c18,c20,c21,c68]) ).
cnf(c70,plain,
join(join(X,Y),join(Y,Z)) = join(join(Y,Z),X),
inference(equational,[status(thm)],[c31,c69]) ).
cnf(c72,plain,
join(join(X,Y),join(X,Z)) = join(join(X,Z),Y),
inference(equational,[status(thm)],[c32,c70]) ).
cnf(c74,plain,
join(join(X,Y),join(Z,X)) = join(join(X,Y),Z),
inference(equational,[status(thm)],[c38,c69]) ).
cnf(c78,plain,
join(join(X,Y),join(X,Z)) = join(Y,join(X,Z)),
inference(equational,[status(thm)],[c32,c72]) ).
cnf(c79,plain,
join(join(X,Y),Z) = join(Y,join(X,Z)),
inference(equational,[status(thm)],[c32,c74,c78]) ).
cnf(c93,plain,
meet(join(X,Y),join(X,Z)) = meet(join(X,Z),join(meet(Y,Z),X)),
inference(equational,[status(thm)],[c28,c68]) ).
cnf(c94,plain,
join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)),
inference(equational,[status(thm)],[c33,c47,c93]) ).
cnf(c95,plain,
meet(join(X,Y),join(X,Z)) = join(meet(Y,Z),X),
inference(equational,[status(thm)],[c32,c94]) ).
cnf(c97,plain,
join(meet(X,Y),Z) = meet(join(Z,Y),join(X,Z)),
inference(equational,[status(thm)],[c3,c20,c26,c79,c95]) ).
cnf(c98,plain,
meet(X,join(Y,Z)) = meet(X,join(meet(X,Z),Y)),
inference(equational,[status(thm)],[c12,c21,c22,c30,c94,c95]) ).
cnf(c103,plain,
meet(X,meet(Y,join(X,Z))) = meet(X,Y),
inference(equational,[status(thm)],[c15,c22,c25,c98]) ).
cnf(c107,plain,
join(meet(X,Y),Z) = meet(join(Y,Z),join(X,Z)),
inference(equational,[status(thm)],[c32,c97]) ).
cnf(c127,plain,
meet(meet(X,Y),meet(join(X,Z),join(Y,Z))) = meet(X,Y),
inference(equational,[status(thm)],[c15,c20,c21,c25,c31,c52,c66,c107]) ).
cnf(c128,plain,
meet(X,meet(meet(Y,X),Z)) = meet(meet(Y,X),Z),
inference(equational,[status(thm)],[c17,c18,c21,c22,c127]) ).
cnf(c155,plain,
meet(X,meet(meet(X,Y),Z)) = meet(meet(Y,X),Z),
inference(equational,[status(thm)],[c21,c128]) ).
cnf(c157,plain,
meet(meet(X,Y),meet(Z,Y)) = meet(meet(X,Y),Z),
inference(equational,[status(thm)],[c22,c103]) ).
cnf(c158,plain,
meet(meet(X,Y),Z) = meet(meet(Z,Y),X),
inference(equational,[status(thm)],[c21,c157]) ).
cnf(c159,plain,
meet(meet(X,Y),Z) = meet(meet(Z,X),Y),
inference(equational,[status(thm)],[c21,c158]) ).
cnf(c160,plain,
meet(X,meet(Y,Z)) = meet(meet(Z,X),Y),
inference(equational,[status(thm)],[c36,c155,c158]) ).
cnf(c162,plain,
meet(meet(X,Y),Z) = meet(Y,meet(X,Z)),
inference(equational,[status(thm)],[c158,c160]) ).
cnf(c164,plain,
meet(X,meet(Y,Z)) = meet(Y,meet(X,Z)),
inference(equational,[status(thm)],[c159,c160,c162]) ).
cnf(g1,plain,
meet(meet(a,b),c) = meet(a,meet(b,c)),
inference(equational,[status(thm)],[c162,c164]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : LAT006-1 : TPTP v9.0.0. Released v2.2.0.
% 0.11/0.11 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n002.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 11:32:34 EDT 2025
% 0.11/0.32 % CPUTime :
% 3.44/3.63 % SZS status Unsatisfiable
% 3.44/3.63 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------