%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : REL028-2 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n014.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 07:41:23 AM UTC 2025
% Result : Unsatisfiable 72.51s 72.66s
% Output : CNFRefutation 72.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 16
% Syntax : Number of clauses : 111 ( 111 unt; 0 nHn; 14 RR)
% Number of literals : 111 ( 110 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 : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 182 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
composition(sk1,sk2) != meet(sk1,sk2),
file('theBenchmark.p',goals_19) ).
cnf(c1,axiom,
composition(X,one) = X,
file('REL001-0.ax',composition_identity_6) ).
cnf(c2,axiom,
converse(converse(X)) = X,
file('REL001-0.ax',converse_idempotence_8) ).
cnf(c3,axiom,
join(sk1,one) = one,
file('theBenchmark.p',goals_17) ).
cnf(c4,axiom,
join(sk2,one) = one,
file('theBenchmark.p',goals_18) ).
cnf(c5,axiom,
join(X,Y) = join(Y,X),
file('REL001-0.ax',maddux1_join_commutativity_1) ).
cnf(c6,axiom,
zero = meet(X,complement(X)),
file('REL001-0.ax',def_zero_13) ).
cnf(c7,plain,
meet(X,complement(X)) = zero,
inference(equational,[status(thm)],[c6]) ).
cnf(c8,axiom,
top = join(X,complement(X)),
file('REL001-0.ax',def_top_12) ).
cnf(c9,plain,
join(X,complement(X)) = top,
inference(equational,[status(thm)],[c8]) ).
cnf(c10,axiom,
converse(join(X,Y)) = join(converse(X),converse(Y)),
file('REL001-0.ax',converse_additivity_9) ).
cnf(c11,plain,
join(converse(X),converse(Y)) = converse(join(X,Y)),
inference(equational,[status(thm)],[c10]) ).
cnf(c12,axiom,
converse(composition(X,Y)) = composition(converse(Y),converse(X)),
file('REL001-0.ax',converse_multiplicativity_10) ).
cnf(c13,plain,
composition(converse(X),converse(Y)) = converse(composition(Y,X)),
inference(equational,[status(thm)],[c12]) ).
cnf(c14,axiom,
join(X,join(Y,Z)) = join(join(X,Y),Z),
file('REL001-0.ax',maddux2_join_associativity_2) ).
cnf(c15,plain,
join(join(X,Y),Z) = join(X,join(Y,Z)),
inference(equational,[status(thm)],[c14]) ).
cnf(c16,axiom,
composition(X,composition(Y,Z)) = composition(composition(X,Y),Z),
file('REL001-0.ax',composition_associativity_5) ).
cnf(c17,plain,
composition(composition(X,Y),Z) = composition(X,composition(Y,Z)),
inference(equational,[status(thm)],[c16]) ).
cnf(c18,plain,
composition(X,composition(one,Y)) = composition(X,Y),
inference(equational,[status(thm)],[c1,c17]) ).
cnf(c21,plain,
join(sk2,join(one,X)) = join(one,X),
inference(equational,[status(thm)],[c4,c15]) ).
cnf(c23,plain,
converse(join(X,converse(Y))) = join(converse(X),Y),
inference(equational,[status(thm)],[c2,c11]) ).
cnf(c24,plain,
converse(join(converse(X),Y)) = join(X,converse(Y)),
inference(equational,[status(thm)],[c2,c11]) ).
cnf(c25,plain,
converse(composition(converse(X),Y)) = composition(converse(Y),X),
inference(equational,[status(thm)],[c2,c13]) ).
cnf(c26,plain,
composition(converse(one),X) = X,
inference(equational,[status(thm)],[c1,c2,c25]) ).
cnf(c27,plain,
converse(one) = one,
inference(equational,[status(thm)],[c1,c26]) ).
cnf(c28,plain,
composition(one,X) = X,
inference(equational,[status(thm)],[c18,c26]) ).
cnf(c29,plain,
converse(composition(X,converse(Y))) = composition(Y,converse(X)),
inference(equational,[status(thm)],[c2,c13]) ).
cnf(c30,plain,
join(X,join(Y,Z)) = join(Y,join(X,Z)),
inference(equational,[status(thm)],[c5,c15]) ).
cnf(c31,axiom,
meet(X,Y) = complement(join(complement(X),complement(Y))),
file('REL001-0.ax',maddux4_definiton_of_meet_4) ).
cnf(c32,plain,
complement(join(complement(X),complement(Y))) = meet(X,Y),
inference(equational,[status(thm)],[c31]) ).
cnf(c33,plain,
complement(top) = zero,
inference(equational,[status(thm)],[c7,c9,c32]) ).
cnf(c34,plain,
meet(X,Y) = meet(Y,X),
inference(equational,[status(thm)],[c5,c32]) ).
cnf(c37,plain,
complement(join(zero,complement(X))) = meet(top,X),
inference(equational,[status(thm)],[c32,c33]) ).
cnf(c39,plain,
join(sk2,join(X,one)) = join(one,X),
inference(equational,[status(thm)],[c5,c21]) ).
cnf(c40,plain,
join(sk1,join(X,one)) = join(X,one),
inference(equational,[status(thm)],[c3,c30]) ).
cnf(c41,plain,
join(X,join(complement(X),Y)) = join(top,Y),
inference(equational,[status(thm)],[c9,c15]) ).
cnf(c43,plain,
join(one,complement(sk2)) = join(top,one),
inference(equational,[status(thm)],[c39,c41]) ).
cnf(c44,plain,
join(top,complement(complement(X))) = join(X,top),
inference(equational,[status(thm)],[c9,c41]) ).
cnf(c57,axiom,
composition(join(X,Y),Z) = join(composition(X,Z),composition(Y,Z)),
file('REL001-0.ax',composition_distributivity_7) ).
cnf(c58,plain,
join(composition(X,Y),composition(Z,Y)) = composition(join(X,Z),Y),
inference(equational,[status(thm)],[c57]) ).
cnf(c59,plain,
join(X,composition(Y,X)) = composition(join(one,Y),X),
inference(equational,[status(thm)],[c26,c27,c58]) ).
cnf(c60,plain,
join(X,composition(Y,X)) = composition(join(Y,one),X),
inference(equational,[status(thm)],[c5,c26,c27,c58]) ).
cnf(c61,plain,
join(X,composition(sk1,X)) = X,
inference(equational,[status(thm)],[c3,c28,c60]) ).
cnf(c75,plain,
join(X,join(Y,complement(join(X,Y)))) = top,
inference(equational,[status(thm)],[c9,c15]) ).
cnf(c79,plain,
join(converse(X),join(converse(Y),Z)) = join(converse(join(X,Y)),Z),
inference(equational,[status(thm)],[c11,c15]) ).
cnf(c81,plain,
join(X,composition(complement(one),X)) = composition(top,X),
inference(equational,[status(thm)],[c9,c59]) ).
cnf(c137,plain,
composition(join(X,converse(Y)),converse(Z)) = converse(composition(Z,join(converse(X),Y))),
inference(equational,[status(thm)],[c13,c24]) ).
cnf(c141,plain,
join(composition(X,converse(Y)),converse(Z)) = converse(join(composition(Y,converse(X)),Z)),
inference(equational,[status(thm)],[c11,c29]) ).
cnf(c148,plain,
composition(X,converse(join(one,Y))) = join(X,composition(X,converse(Y))),
inference(equational,[status(thm)],[c24,c29,c59]) ).
cnf(c149,plain,
composition(X,join(one,Y)) = join(X,composition(X,Y)),
inference(equational,[status(thm)],[c2,c23,c27,c148]) ).
cnf(c196,plain,
join(complement(converse(X)),converse(join(Y,X))) = join(top,converse(Y)),
inference(equational,[status(thm)],[c5,c9,c79]) ).
cnf(c197,plain,
join(complement(X),join(Y,X)) = join(top,Y),
inference(equational,[status(thm)],[c2,c11,c196]) ).
cnf(c203,plain,
join(X,complement(composition(sk1,X))) = join(top,X),
inference(equational,[status(thm)],[c5,c61,c197]) ).
cnf(c215,plain,
join(X,converse(join(complement(converse(X)),Y))) = converse(join(top,Y)),
inference(equational,[status(thm)],[c24,c41]) ).
cnf(c239,axiom,
join(composition(converse(X),complement(composition(X,Y))),complement(Y)) = complement(Y),
file('REL001-0.ax',converse_cancellativity_11) ).
cnf(c240,plain,
join(complement(X),composition(converse(Y),complement(composition(Y,X)))) = complement(X),
inference(equational,[status(thm)],[c5,c239]) ).
cnf(c241,plain,
join(complement(X),complement(X)) = complement(X),
inference(equational,[status(thm)],[c26,c28,c240]) ).
cnf(c242,plain,
join(zero,zero) = zero,
inference(equational,[status(thm)],[c33,c241]) ).
cnf(c244,plain,
join(top,complement(X)) = top,
inference(equational,[status(thm)],[c9,c41,c241]) ).
cnf(c245,plain,
join(X,top) = top,
inference(equational,[status(thm)],[c44,c244]) ).
cnf(c246,plain,
join(top,X) = top,
inference(equational,[status(thm)],[c5,c245]) ).
cnf(c247,plain,
converse(top) = top,
inference(equational,[status(thm)],[c215,c246]) ).
cnf(c248,plain,
composition(top,top) = top,
inference(equational,[status(thm)],[c81,c246]) ).
cnf(c249,plain,
join(zero,join(zero,X)) = join(zero,X),
inference(equational,[status(thm)],[c15,c242]) ).
cnf(c253,plain,
join(X,composition(top,X)) = composition(top,X),
inference(equational,[status(thm)],[c59,c245]) ).
cnf(c265,plain,
composition(top,zero) = zero,
inference(equational,[status(thm)],[c33,c240,c247,c248,c253]) ).
cnf(c294,plain,
join(X,join(Y,composition(sk1,X))) = join(Y,X),
inference(equational,[status(thm)],[c30,c61]) ).
cnf(c296,plain,
join(X,join(composition(sk1,X),Y)) = join(X,Y),
inference(equational,[status(thm)],[c15,c61]) ).
cnf(c321,plain,
join(X,composition(X,complement(sk2))) = composition(X,top),
inference(equational,[status(thm)],[c43,c149,c246]) ).
cnf(c323,plain,
meet(X,composition(sk1,complement(X))) = zero,
inference(equational,[status(thm)],[c32,c33,c203,c244]) ).
cnf(c332,plain,
join(composition(X,Y),join(composition(Z,Y),W)) = join(composition(join(X,Z),Y),W),
inference(equational,[status(thm)],[c15,c58]) ).
cnf(c333,plain,
join(X,join(composition(Y,X),Z)) = join(composition(join(one,Y),X),Z),
inference(equational,[status(thm)],[c26,c27,c332]) ).
cnf(c340,plain,
join(X,join(Y,composition(Z,X))) = join(composition(join(one,Z),X),Y),
inference(equational,[status(thm)],[c5,c333]) ).
cnf(c372,plain,
converse(join(composition(X,converse(Y)),composition(X,Z))) = converse(composition(X,join(converse(Y),Z))),
inference(equational,[status(thm)],[c13,c58,c137,c141]) ).
cnf(c383,plain,
converse(join(composition(X,Y),composition(X,Z))) = converse(composition(X,join(Y,Z))),
inference(equational,[status(thm)],[c2,c372]) ).
cnf(c384,plain,
join(composition(X,Y),composition(X,Z)) = composition(X,join(Y,Z)),
inference(equational,[status(thm)],[c2,c383]) ).
cnf(c510,plain,
join(complement(sk2),composition(sk1,top)) = join(sk1,complement(sk2)),
inference(equational,[status(thm)],[c294,c321]) ).
cnf(c599,plain,
join(X,join(Y,join(complement(join(X,Y)),Z))) = top,
inference(equational,[status(thm)],[c15,c41,c246]) ).
cnf(c600,plain,
join(X,join(one,complement(join(X,sk1)))) = top,
inference(equational,[status(thm)],[c5,c40,c599]) ).
cnf(c608,plain,
join(X,join(one,complement(join(sk1,X)))) = top,
inference(equational,[status(thm)],[c5,c600]) ).
cnf(c609,plain,
join(X,join(Y,composition(top,X))) = join(composition(top,X),Y),
inference(equational,[status(thm)],[c3,c9,c340,c608]) ).
cnf(c639,plain,
join(X,composition(sk1,join(X,Y))) = join(X,composition(sk1,Y)),
inference(equational,[status(thm)],[c296,c384]) ).
cnf(c640,plain,
join(X,composition(sk1,complement(X))) = join(X,composition(sk1,top)),
inference(equational,[status(thm)],[c9,c639]) ).
cnf(c889,axiom,
X = join(complement(join(complement(X),complement(Y))),complement(join(complement(X),Y))),
file('REL001-0.ax',maddux3_a_kind_of_de_Morgan_3) ).
cnf(c890,plain,
join(meet(X,Y),complement(join(complement(X),Y))) = X,
inference(equational,[status(thm)],[c32,c889]) ).
cnf(c891,plain,
join(zero,complement(complement(X))) = X,
inference(equational,[status(thm)],[c7,c241,c890]) ).
cnf(c893,plain,
join(zero,X) = X,
inference(equational,[status(thm)],[c249,c891]) ).
cnf(c895,plain,
join(X,zero) = X,
inference(equational,[status(thm)],[c265,c609,c893]) ).
cnf(c896,plain,
complement(complement(X)) = X,
inference(equational,[status(thm)],[c891,c893]) ).
cnf(c901,plain,
meet(top,X) = X,
inference(equational,[status(thm)],[c37,c893,c896]) ).
cnf(c909,plain,
join(complement(X),complement(Y)) = complement(meet(X,Y)),
inference(equational,[status(thm)],[c32,c891,c893]) ).
cnf(c910,plain,
complement(meet(complement(X),Y)) = join(X,complement(Y)),
inference(equational,[status(thm)],[c37,c893,c901,c909]) ).
cnf(c912,plain,
join(X,complement(meet(X,Y))) = top,
inference(equational,[status(thm)],[c41,c244,c909]) ).
cnf(c922,plain,
meet(X,join(X,complement(Y))) = X,
inference(equational,[status(thm)],[c33,c890,c895,c910,c912]) ).
cnf(c923,plain,
meet(X,join(X,Y)) = X,
inference(equational,[status(thm)],[c37,c901,c922]) ).
cnf(c930,plain,
join(meet(X,Y),meet(X,complement(Y))) = X,
inference(equational,[status(thm)],[c5,c32,c890]) ).
cnf(c946,plain,
join(meet(X,Y),meet(complement(Y),X)) = X,
inference(equational,[status(thm)],[c34,c930]) ).
cnf(c964,plain,
join(meet(X,Y),meet(complement(X),Y)) = Y,
inference(equational,[status(thm)],[c34,c946]) ).
cnf(c969,plain,
meet(X,composition(sk1,X)) = composition(sk1,X),
inference(equational,[status(thm)],[c323,c895,c896,c964]) ).
cnf(c985,plain,
join(complement(X),join(Y,complement(Z))) = join(Y,complement(meet(X,Z))),
inference(equational,[status(thm)],[c30,c909]) ).
cnf(c986,plain,
complement(meet(X,meet(Y,Z))) = complement(meet(Y,meet(X,Z))),
inference(equational,[status(thm)],[c909,c985]) ).
cnf(c987,plain,
meet(X,meet(Y,Z)) = meet(Y,meet(X,Z)),
inference(equational,[status(thm)],[c37,c893,c896,c901,c986]) ).
cnf(c989,plain,
meet(meet(X,Y),Z) = meet(X,meet(Z,Y)),
inference(equational,[status(thm)],[c34,c987]) ).
cnf(c1053,plain,
join(X,complement(meet(Y,join(X,complement(Y))))) = top,
inference(equational,[status(thm)],[c75,c909]) ).
cnf(c1055,plain,
meet(X,meet(Y,complement(meet(X,Y)))) = zero,
inference(equational,[status(thm)],[c32,c33,c909,c1053]) ).
cnf(c1056,plain,
meet(X,join(Y,complement(X))) = meet(X,Y),
inference(equational,[status(thm)],[c895,c910,c923,c946,c989,c1055]) ).
cnf(c1059,plain,
meet(X,join(complement(X),Y)) = meet(X,Y),
inference(equational,[status(thm)],[c5,c1056]) ).
cnf(c1069,plain,
meet(X,composition(sk1,top)) = composition(sk1,X),
inference(equational,[status(thm)],[c640,c896,c969,c1059]) ).
cnf(c1072,plain,
composition(sk1,sk2) = meet(sk1,sk2),
inference(equational,[status(thm)],[c34,c510,c1056,c1059,c1069]) ).
cnf(g1,plain,
composition(sk1,sk2) = meet(sk1,sk2),
inference(equational,[status(thm)],[c1072]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.13 % Problem : REL028-2 : TPTP v9.0.0. Released v4.0.0.
% 0.05/0.13 % Command : run_Leo-III %s %d THM
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Jul 14 16:13:04 EDT 2025
% 0.13/0.34 % CPUTime :
% 72.51/72.66 % SZS status Unsatisfiable
% 72.51/72.66 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------