%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : LAT010-1 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n005.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 259.23s 258.92s
% Output : CNFRefutation 259.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of clauses : 59 ( 59 unt; 0 nHn; 3 RR)
% Number of literals : 59 ( 58 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 157 ( 23 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
meet(a,meet(join(b,c),join(b,d))) != meet(meet(a,meet(join(b,c),join(b,d))),join(meet(a,join(b,meet(c,d))),join(meet(a,c),meet(a,d)))),
file('theBenchmark.p',prove_this) ).
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(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(c26,plain,
meet(X,meet(Y,join(X,Z))) = meet(Y,X),
inference(equational,[status(thm)],[c5,c14]) ).
cnf(c27,plain,
meet(X,meet(Y,join(Z,X))) = meet(Y,X),
inference(equational,[status(thm)],[c8,c14]) ).
cnf(c32,plain,
join(X,join(Y,join(Z,X))) = join(Y,join(X,Z)),
inference(equational,[status(thm)],[c13,c16]) ).
cnf(c37,plain,
join(meet(X,Y),join(Z,X)) = join(X,Z),
inference(equational,[status(thm)],[c17,c23,c32]) ).
cnf(c38,plain,
join(meet(X,Y),meet(X,meet(Y,Z))) = meet(X,Y),
inference(equational,[status(thm)],[c6,c9]) ).
cnf(c39,plain,
join(meet(X,Y),meet(Y,X)) = meet(X,Y),
inference(equational,[status(thm)],[c27,c38]) ).
cnf(c40,plain,
meet(join(X,Y),join(X,join(Y,Z))) = join(X,Y),
inference(equational,[status(thm)],[c5,c10]) ).
cnf(c42,plain,
meet(X,meet(Y,join(meet(X,Y),Z))) = meet(X,Y),
inference(equational,[status(thm)],[c5,c9]) ).
cnf(c43,plain,
meet(X,meet(Y,join(Z,meet(X,Y)))) = meet(X,Y),
inference(equational,[status(thm)],[c4,c42]) ).
cnf(c45,plain,
meet(join(X,Y),join(Y,join(X,Z))) = join(Y,X),
inference(equational,[status(thm)],[c4,c40]) ).
cnf(c46,plain,
join(meet(X,Y),meet(Y,meet(X,Z))) = meet(Y,X),
inference(equational,[status(thm)],[c3,c38]) ).
cnf(c47,plain,
join(meet(X,Y),meet(Y,meet(Z,X))) = meet(X,Y),
inference(equational,[status(thm)],[c3,c9,c38]) ).
cnf(c48,plain,
join(meet(X,Y),meet(X,meet(Z,Y))) = meet(X,Y),
inference(equational,[status(thm)],[c3,c38]) ).
cnf(c59,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(join(X,Y),join(meet(X,Z),Y)) = join(meet(X,Z),Y),
inference(equational,[status(thm)],[c3,c8,c17]) ).
cnf(c72,plain,
join(meet(X,Y),meet(Z,meet(Y,X))) = meet(X,Y),
inference(equational,[status(thm)],[c3,c9,c48]) ).
cnf(c75,plain,
meet(join(X,Y),join(meet(Z,X),Y)) = join(meet(X,Z),Y),
inference(equational,[status(thm)],[c3,c62]) ).
cnf(c80,plain,
join(X,join(Y,join(Z,meet(W,X)))) = join(Y,join(Z,X)),
inference(equational,[status(thm)],[c13,c24]) ).
cnf(c101,plain,
join(X,meet(join(X,Y),join(Z,X))) = meet(join(X,Y),join(Z,X)),
inference(equational,[status(thm)],[c8,c59]) ).
cnf(c103,plain,
join(X,meet(join(Y,Z),join(X,Y))) = join(Y,X),
inference(equational,[status(thm)],[c10,c16,c24,c101]) ).
cnf(c116,plain,
join(meet(X,Y),join(Z,meet(Y,X))) = join(Z,meet(Y,X)),
inference(equational,[status(thm)],[c39,c72,c80]) ).
cnf(c213,plain,
join(meet(X,Y),meet(Y,join(meet(X,Y),Z))) = meet(Y,join(meet(X,Y),Z)),
inference(equational,[status(thm)],[c4,c7,c42]) ).
cnf(c258,plain,
meet(join(meet(X,Y),Z),join(Z,meet(Y,X))) = join(Z,meet(X,Y)),
inference(equational,[status(thm)],[c45,c46]) ).
cnf(c314,plain,
join(meet(X,Y),meet(X,join(meet(X,Y),Z))) = meet(X,join(meet(X,Y),Z)),
inference(equational,[status(thm)],[c3,c4,c42,c47]) ).
cnf(c330,plain,
meet(join(X,meet(Y,Z)),meet(W,join(X,Z))) = meet(W,join(X,meet(Y,Z))),
inference(equational,[status(thm)],[c24,c27]) ).
cnf(c331,plain,
join(meet(X,Y),meet(X,join(Z,meet(X,Y)))) = meet(X,join(Z,meet(X,Y))),
inference(equational,[status(thm)],[c4,c43,c48]) ).
cnf(c348,plain,
join(meet(X,Y),meet(Y,join(meet(Y,X),Z))) = meet(Y,join(meet(X,Y),Z)),
inference(equational,[status(thm)],[c3,c213]) ).
cnf(c543,plain,
meet(join(X,meet(Y,Z)),meet(W,join(Z,X))) = meet(W,join(X,meet(Y,Z))),
inference(equational,[status(thm)],[c4,c330]) ).
cnf(c676,plain,
join(X,meet(join(Y,Z),join(X,meet(Y,W)))) = join(meet(Y,W),X),
inference(equational,[status(thm)],[c37,c103]) ).
cnf(c780,axiom,
meet(join(X,meet(Y,Z)),join(Z,meet(X,Y))) = join(meet(Z,join(X,meet(Y,Z))),meet(X,join(Y,Z))),
file('theBenchmark.p',nr_3) ).
cnf(c781,plain,
join(meet(X,join(Y,Z)),meet(Z,join(X,meet(Y,Z)))) = meet(join(X,meet(Y,Z)),join(Z,meet(X,Y))),
inference(equational,[status(thm)],[c4,c780]) ).
cnf(c782,plain,
join(X,meet(Y,join(Z,X))) = join(meet(Y,Z),X),
inference(equational,[status(thm)],[c4,c23,c676,c781]) ).
cnf(c783,plain,
meet(X,join(meet(Y,X),Z)) = meet(X,join(Y,Z)),
inference(equational,[status(thm)],[c8,c9,c75,c782]) ).
cnf(c787,plain,
meet(X,join(Y,meet(X,Z))) = join(meet(X,Y),meet(X,Z)),
inference(equational,[status(thm)],[c331,c782]) ).
cnf(c788,plain,
join(meet(X,Y),meet(X,Z)) = meet(X,join(Z,Y)),
inference(equational,[status(thm)],[c9,c10,c15,c17,c26,c116,c258,c314,c348,c781,c783,c787]) ).
cnf(c790,plain,
join(meet(X,Y),meet(Y,Z)) = meet(Y,join(Z,X)),
inference(equational,[status(thm)],[c75,c543,c787,c788]) ).
cnf(g1,plain,
meet(a,meet(join(b,c),join(b,d))) = meet(meet(a,meet(join(b,c),join(b,d))),join(meet(a,join(b,meet(c,d))),join(meet(a,c),meet(a,d)))),
inference(equational,[status(thm)],[c3,c4,c7,c9,c10,c12,c13,c14,c27,c790]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : LAT010-1 : TPTP v9.0.0. Released v2.2.0.
% 0.04/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.32 % Computer : n005.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Mon Jul 14 11:32:34 EDT 2025
% 0.12/0.32 % CPUTime :
% 259.23/258.92 % SZS status Unsatisfiable
% 259.23/258.92 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------