%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : LAT043-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n004.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 07:05:40 AM UTC 2025
% Result : Unsatisfiable 27.00s 27.15s
% Output : CNFRefutation 27.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 12
% Syntax : Number of clauses : 47 ( 47 unt; 0 nHn; 5 RR)
% Number of literals : 47 ( 46 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 78 ( 11 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
complement(join(c,d)) != meet(complement(c),complement(d)),
file('theBenchmark.p',prove_compatability_law) ).
cnf(c2,axiom,
join(X,X) = X,
file('LAT001-0.ax',idempotence_of_join) ).
cnf(c3,axiom,
complement(complement(X)) = X,
file('theBenchmark.p',invertability3) ).
cnf(c4,axiom,
join(X,Y) = join(Y,X),
file('LAT001-0.ax',commutativity_of_join) ).
cnf(c5,axiom,
meet(X,Y) = meet(Y,X),
file('LAT001-0.ax',commutativity_of_meet) ).
cnf(c6,axiom,
join(complement(X),X) = n1,
file('theBenchmark.p',invertability1) ).
cnf(c7,plain,
join(X,complement(X)) = n1,
inference(equational,[status(thm)],[c4,c6]) ).
cnf(c8,axiom,
meet(complement(X),X) = n0,
file('theBenchmark.p',invertability2) ).
cnf(c9,plain,
meet(X,complement(X)) = n0,
inference(equational,[status(thm)],[c5,c8]) ).
cnf(c10,axiom,
meet(X,join(X,Y)) = X,
file('LAT001-0.ax',absorption1) ).
cnf(c11,plain,
meet(X,n1) = X,
inference(equational,[status(thm)],[c7,c10]) ).
cnf(c13,axiom,
join(X,meet(X,Y)) = X,
file('LAT001-0.ax',absorption2) ).
cnf(c14,plain,
join(X,n0) = X,
inference(equational,[status(thm)],[c9,c13]) ).
cnf(c15,plain,
join(n0,X) = X,
inference(equational,[status(thm)],[c4,c14]) ).
cnf(c16,plain,
complement(n0) = n1,
inference(equational,[status(thm)],[c7,c15]) ).
cnf(c17,plain,
n0 = complement(n1),
inference(equational,[status(thm)],[c3,c16]) ).
cnf(c18,plain,
meet(complement(n1),X) = complement(n1),
inference(equational,[status(thm)],[c13,c15,c17]) ).
cnf(c20,plain,
join(X,meet(Y,X)) = X,
inference(equational,[status(thm)],[c5,c13]) ).
cnf(c23,axiom,
meet(meet(X,Y),Z) = meet(X,meet(Y,Z)),
file('LAT001-0.ax',associativity_of_meet) ).
cnf(c24,axiom,
join(join(X,Y),Z) = join(X,join(Y,Z)),
file('LAT001-0.ax',associativity_of_join) ).
cnf(c25,plain,
join(X,join(X,Y)) = join(X,Y),
inference(equational,[status(thm)],[c2,c24]) ).
cnf(c26,plain,
join(X,complement(n1)) = X,
inference(equational,[status(thm)],[c2,c14,c17,c25]) ).
cnf(c27,plain,
join(complement(n1),X) = X,
inference(equational,[status(thm)],[c4,c26]) ).
cnf(c31,plain,
meet(X,complement(n1)) = complement(n1),
inference(equational,[status(thm)],[c15,c17,c20]) ).
cnf(c32,plain,
join(X,join(Y,Z)) = join(Y,join(X,Z)),
inference(equational,[status(thm)],[c4,c24]) ).
cnf(c37,plain,
complement(n1) = meet(X,meet(complement(X),Y)),
inference(equational,[status(thm)],[c9,c17,c18,c23]) ).
cnf(c44,plain,
join(meet(X,complement(X)),Y) = Y,
inference(equational,[status(thm)],[c9,c15]) ).
cnf(c50,axiom,
meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)),
file('theBenchmark.p',distributivity) ).
cnf(c55,plain,
meet(X,meet(join(X,Y),Z)) = meet(X,Z),
inference(equational,[status(thm)],[c10,c23]) ).
cnf(c56,plain,
complement(n1) = meet(X,complement(join(X,Y))),
inference(equational,[status(thm)],[c9,c17,c31,c55]) ).
cnf(c66,plain,
join(meet(X,Y),meet(X,complement(Y))) = X,
inference(equational,[status(thm)],[c7,c11,c50]) ).
cnf(c67,plain,
meet(X,complement(meet(complement(X),Y))) = X,
inference(equational,[status(thm)],[c27,c37,c66]) ).
cnf(c71,plain,
join(X,join(Y,meet(Z,X))) = join(Y,X),
inference(equational,[status(thm)],[c20,c32]) ).
cnf(c75,plain,
join(X,join(meet(Y,X),Z)) = join(X,Z),
inference(equational,[status(thm)],[c20,c24]) ).
cnf(c76,plain,
join(X,meet(Y,complement(X))) = join(X,Y),
inference(equational,[status(thm)],[c66,c75]) ).
cnf(c87,plain,
join(X,meet(complement(X),Y)) = join(X,Y),
inference(equational,[status(thm)],[c5,c76]) ).
cnf(c106,plain,
join(meet(X,Y),meet(complement(Y),X)) = X,
inference(equational,[status(thm)],[c5,c66]) ).
cnf(c189,plain,
meet(X,complement(join(complement(X),Y))) = complement(join(complement(X),Y)),
inference(equational,[status(thm)],[c5,c26,c56,c106]) ).
cnf(c191,plain,
join(X,complement(meet(complement(X),Y))) = complement(meet(complement(X),Y)),
inference(equational,[status(thm)],[c4,c20,c67]) ).
cnf(c506,plain,
join(complement(join(complement(X),Y)),meet(X,Y)) = X,
inference(equational,[status(thm)],[c4,c44,c50,c66,c189]) ).
cnf(c507,plain,
join(X,complement(join(complement(Y),X))) = join(X,Y),
inference(equational,[status(thm)],[c4,c71,c506]) ).
cnf(c508,plain,
join(X,complement(join(Y,X))) = join(X,complement(Y)),
inference(equational,[status(thm)],[c3,c507]) ).
cnf(c509,plain,
join(X,complement(join(X,Y))) = join(X,complement(Y)),
inference(equational,[status(thm)],[c4,c508]) ).
cnf(c510,plain,
complement(meet(complement(X),Y)) = join(X,complement(Y)),
inference(equational,[status(thm)],[c87,c191,c509]) ).
cnf(c513,plain,
meet(complement(X),Y) = complement(join(X,complement(Y))),
inference(equational,[status(thm)],[c3,c510]) ).
cnf(g1,plain,
complement(join(c,d)) = meet(complement(c),complement(d)),
inference(equational,[status(thm)],[c3,c513]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LAT043-1 : TPTP v9.0.0. Released v2.5.0.
% 0.11/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n004.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
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Mon Jul 14 11:35:04 EDT 2025
% 0.11/0.33 % CPUTime :
% 27.00/27.15 % SZS status Unsatisfiable
% 27.00/27.15 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------