%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : REL030-3 : TPTP v9.0.0. Released v4.0.0.
% 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 07:41:25 AM UTC 2025
% Result : Unsatisfiable 89.66s 89.61s
% Output : CNFRefutation 89.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 15
% Syntax : Number of clauses : 106 ( 106 unt; 0 nHn; 8 RR)
% Number of literals : 106 ( 105 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 : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 189 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
meet(composition(sk1,sk2),complement(sk3)) != meet(composition(sk1,sk2),complement(composition(sk1,sk3))),
file('theBenchmark.p',goals_18) ).
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(X,Y) = join(Y,X),
file('REL001-0.ax',maddux1_join_commutativity_1) ).
cnf(c5,plain,
join(one,sk1) = one,
inference(equational,[status(thm)],[c3,c4]) ).
cnf(c6,axiom,
top = join(X,complement(X)),
file('REL001-0.ax',def_top_12) ).
cnf(c7,plain,
join(X,complement(X)) = top,
inference(equational,[status(thm)],[c6]) ).
cnf(c8,axiom,
zero = meet(X,complement(X)),
file('REL001-0.ax',def_zero_13) ).
cnf(c9,plain,
meet(X,complement(X)) = zero,
inference(equational,[status(thm)],[c8]) ).
cnf(c10,axiom,
converse(composition(X,Y)) = composition(converse(Y),converse(X)),
file('REL001-0.ax',converse_multiplicativity_10) ).
cnf(c11,plain,
composition(converse(X),converse(Y)) = converse(composition(Y,X)),
inference(equational,[status(thm)],[c10]) ).
cnf(c12,axiom,
converse(join(X,Y)) = join(converse(X),converse(Y)),
file('REL001-0.ax',converse_additivity_9) ).
cnf(c13,plain,
join(converse(X),converse(Y)) = converse(join(X,Y)),
inference(equational,[status(thm)],[c12]) ).
cnf(c14,axiom,
composition(X,composition(Y,Z)) = composition(composition(X,Y),Z),
file('REL001-0.ax',composition_associativity_5) ).
cnf(c15,plain,
composition(composition(X,Y),Z) = composition(X,composition(Y,Z)),
inference(equational,[status(thm)],[c14]) ).
cnf(c16,axiom,
join(X,join(Y,Z)) = join(join(X,Y),Z),
file('REL001-0.ax',maddux2_join_associativity_2) ).
cnf(c17,plain,
join(join(X,Y),Z) = join(X,join(Y,Z)),
inference(equational,[status(thm)],[c16]) ).
cnf(c18,plain,
composition(X,composition(one,Y)) = composition(X,Y),
inference(equational,[status(thm)],[c1,c15]) ).
cnf(c19,plain,
join(sk1,join(one,X)) = join(one,X),
inference(equational,[status(thm)],[c3,c17]) ).
cnf(c21,plain,
converse(join(X,converse(Y))) = join(converse(X),Y),
inference(equational,[status(thm)],[c2,c13]) ).
cnf(c23,plain,
converse(composition(X,converse(Y))) = composition(Y,converse(X)),
inference(equational,[status(thm)],[c2,c11]) ).
cnf(c24,plain,
converse(composition(converse(X),Y)) = composition(converse(Y),X),
inference(equational,[status(thm)],[c2,c11]) ).
cnf(c25,plain,
composition(converse(one),X) = X,
inference(equational,[status(thm)],[c1,c2,c24]) ).
cnf(c26,plain,
converse(one) = one,
inference(equational,[status(thm)],[c1,c25]) ).
cnf(c27,plain,
composition(one,X) = X,
inference(equational,[status(thm)],[c18,c25]) ).
cnf(c28,plain,
join(X,join(Y,Z)) = join(Y,join(X,Z)),
inference(equational,[status(thm)],[c4,c17]) ).
cnf(c29,axiom,
meet(X,Y) = complement(join(complement(X),complement(Y))),
file('REL001-0.ax',maddux4_definiton_of_meet_4) ).
cnf(c30,plain,
complement(join(complement(X),complement(Y))) = meet(X,Y),
inference(equational,[status(thm)],[c29]) ).
cnf(c31,plain,
complement(top) = zero,
inference(equational,[status(thm)],[c7,c9,c30]) ).
cnf(c32,plain,
meet(X,Y) = meet(Y,X),
inference(equational,[status(thm)],[c4,c30]) ).
cnf(c35,plain,
complement(join(zero,complement(X))) = meet(top,X),
inference(equational,[status(thm)],[c30,c31]) ).
cnf(c37,plain,
join(one,join(sk1,X)) = join(one,X),
inference(equational,[status(thm)],[c19,c28]) ).
cnf(c41,plain,
join(X,join(complement(X),Y)) = join(top,Y),
inference(equational,[status(thm)],[c7,c17]) ).
cnf(c54,axiom,
composition(join(X,Y),Z) = join(composition(X,Z),composition(Y,Z)),
file('REL001-0.ax',composition_distributivity_7) ).
cnf(c55,plain,
join(composition(X,Y),composition(Z,Y)) = composition(join(X,Z),Y),
inference(equational,[status(thm)],[c54]) ).
cnf(c56,plain,
join(X,composition(Y,X)) = composition(join(one,Y),X),
inference(equational,[status(thm)],[c25,c26,c55]) ).
cnf(c57,plain,
join(X,composition(sk1,X)) = X,
inference(equational,[status(thm)],[c5,c27,c56]) ).
cnf(c75,plain,
meet(join(complement(X),complement(Y)),Z) = complement(join(meet(X,Y),complement(Z))),
inference(equational,[status(thm)],[c30]) ).
cnf(c106,plain,
complement(join(meet(top,X),complement(Y))) = meet(join(zero,complement(X)),Y),
inference(equational,[status(thm)],[c31,c75]) ).
cnf(c111,plain,
composition(join(converse(X),Y),converse(Z)) = converse(composition(Z,join(X,converse(Y)))),
inference(equational,[status(thm)],[c11,c21]) ).
cnf(c121,plain,
join(converse(X),composition(Y,converse(Z))) = converse(join(X,composition(Z,converse(Y)))),
inference(equational,[status(thm)],[c21,c23]) ).
cnf(c182,axiom,
join(composition(converse(X),complement(composition(X,Y))),complement(Y)) = complement(Y),
file('REL001-0.ax',converse_cancellativity_11) ).
cnf(c183,plain,
join(complement(X),composition(converse(Y),complement(composition(Y,X)))) = complement(X),
inference(equational,[status(thm)],[c4,c182]) ).
cnf(c184,plain,
join(complement(X),complement(X)) = complement(X),
inference(equational,[status(thm)],[c25,c27,c183]) ).
cnf(c185,plain,
join(zero,zero) = zero,
inference(equational,[status(thm)],[c31,c184]) ).
cnf(c187,plain,
join(top,complement(X)) = top,
inference(equational,[status(thm)],[c7,c41,c184]) ).
cnf(c192,plain,
join(zero,join(zero,X)) = join(zero,X),
inference(equational,[status(thm)],[c17,c185]) ).
cnf(c228,plain,
join(X,composition(join(sk1,Y),X)) = composition(join(one,Y),X),
inference(equational,[status(thm)],[c37,c56]) ).
cnf(c232,plain,
join(X,join(Y,composition(sk1,X))) = join(Y,X),
inference(equational,[status(thm)],[c28,c57]) ).
cnf(c266,plain,
join(X,composition(join(one,Y),Z)) = join(Z,join(X,composition(Y,Z))),
inference(equational,[status(thm)],[c28,c56]) ).
cnf(c300,plain,
converse(join(composition(X,Y),composition(X,converse(Z)))) = converse(composition(X,join(Y,converse(Z)))),
inference(equational,[status(thm)],[c11,c55,c111,c121]) ).
cnf(c301,plain,
composition(X,converse(join(Y,Y))) = composition(join(X,X),converse(Y)),
inference(equational,[status(thm)],[c13,c23,c55,c300]) ).
cnf(c302,plain,
composition(join(X,X),Y) = composition(X,join(Y,Y)),
inference(equational,[status(thm)],[c2,c13,c301]) ).
cnf(c311,plain,
join(X,composition(sk1,join(X,X))) = X,
inference(equational,[status(thm)],[c5,c27,c228,c302]) ).
cnf(c312,plain,
join(composition(X,Y),composition(X,converse(Z))) = composition(X,join(Y,converse(Z))),
inference(equational,[status(thm)],[c2,c300]) ).
cnf(c313,plain,
join(composition(X,Y),composition(X,Z)) = composition(X,join(Y,Z)),
inference(equational,[status(thm)],[c2,c312]) ).
cnf(c350,plain,
join(X,join(Y,X)) = join(Y,composition(join(one,one),X)),
inference(equational,[status(thm)],[c27,c266]) ).
cnf(c483,plain,
join(X,composition(sk1,join(Y,X))) = join(composition(sk1,Y),X),
inference(equational,[status(thm)],[c232,c313]) ).
cnf(c540,plain,
join(complement(X),composition(sk1,top)) = join(complement(X),composition(sk1,X)),
inference(equational,[status(thm)],[c4,c7,c483]) ).
cnf(c701,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(c702,plain,
join(meet(X,Y),complement(join(complement(X),Y))) = X,
inference(equational,[status(thm)],[c30,c701]) ).
cnf(c703,plain,
join(zero,complement(complement(X))) = X,
inference(equational,[status(thm)],[c9,c184,c702]) ).
cnf(c705,plain,
join(zero,X) = X,
inference(equational,[status(thm)],[c192,c703]) ).
cnf(c707,plain,
join(X,zero) = X,
inference(equational,[status(thm)],[c4,c705]) ).
cnf(c708,plain,
complement(complement(X)) = X,
inference(equational,[status(thm)],[c703,c705]) ).
cnf(c711,plain,
join(X,X) = X,
inference(equational,[status(thm)],[c184,c708]) ).
cnf(c712,plain,
meet(top,X) = X,
inference(equational,[status(thm)],[c35,c705,c708]) ).
cnf(c718,plain,
join(complement(X),complement(Y)) = complement(meet(X,Y)),
inference(equational,[status(thm)],[c30,c703,c705]) ).
cnf(c719,plain,
complement(meet(complement(X),Y)) = join(X,complement(Y)),
inference(equational,[status(thm)],[c35,c705,c712,c718]) ).
cnf(c720,plain,
complement(meet(X,complement(Y))) = join(complement(X),Y),
inference(equational,[status(thm)],[c35,c705,c712,c718]) ).
cnf(c722,plain,
join(X,complement(meet(X,Y))) = top,
inference(equational,[status(thm)],[c41,c187,c718]) ).
cnf(c723,plain,
complement(join(complement(X),Y)) = meet(X,complement(Y)),
inference(equational,[status(thm)],[c35,c705,c712,c720]) ).
cnf(c724,plain,
complement(join(X,complement(Y))) = meet(complement(X),Y),
inference(equational,[status(thm)],[c703,c705,c719]) ).
cnf(c729,plain,
meet(X,join(X,complement(Y))) = X,
inference(equational,[status(thm)],[c31,c702,c707,c719,c722]) ).
cnf(c730,plain,
join(X,meet(X,Y)) = X,
inference(equational,[status(thm)],[c708,c718,c719,c729]) ).
cnf(c731,plain,
meet(X,join(X,Y)) = X,
inference(equational,[status(thm)],[c35,c712,c729]) ).
cnf(c736,plain,
meet(X,join(Y,X)) = X,
inference(equational,[status(thm)],[c4,c731]) ).
cnf(c737,plain,
join(meet(X,Y),meet(X,complement(Y))) = X,
inference(equational,[status(thm)],[c4,c30,c702]) ).
cnf(c754,plain,
join(X,join(Y,X)) = join(Y,X),
inference(equational,[status(thm)],[c27,c350,c711]) ).
cnf(c758,plain,
join(meet(X,Y),meet(Y,complement(X))) = Y,
inference(equational,[status(thm)],[c32,c737]) ).
cnf(c760,plain,
join(meet(X,Y),meet(complement(Y),X)) = X,
inference(equational,[status(thm)],[c32,c737]) ).
cnf(c769,plain,
join(meet(X,Y),meet(complement(X),Y)) = Y,
inference(equational,[status(thm)],[c32,c760]) ).
cnf(c772,plain,
meet(X,composition(sk1,X)) = composition(sk1,X),
inference(equational,[status(thm)],[c32,c311,c711,c736]) ).
cnf(c780,plain,
join(complement(X),join(complement(Y),Z)) = join(complement(meet(X,Y)),Z),
inference(equational,[status(thm)],[c17,c718]) ).
cnf(c781,plain,
complement(meet(meet(X,Y),Z)) = complement(meet(X,meet(Y,Z))),
inference(equational,[status(thm)],[c718,c780]) ).
cnf(c782,plain,
meet(meet(X,Y),Z) = meet(X,meet(Y,Z)),
inference(equational,[status(thm)],[c703,c705,c708,c781]) ).
cnf(c783,plain,
meet(X,meet(Y,Z)) = meet(Y,meet(X,Z)),
inference(equational,[status(thm)],[c32,c782]) ).
cnf(c835,plain,
meet(complement(X),meet(complement(Y),Z)) = complement(join(X,join(Y,complement(Z)))),
inference(equational,[status(thm)],[c106,c705,c712,c719]) ).
cnf(c851,plain,
join(X,join(meet(X,Y),Z)) = join(X,Z),
inference(equational,[status(thm)],[c17,c730]) ).
cnf(c852,plain,
join(X,meet(Y,complement(X))) = join(X,Y),
inference(equational,[status(thm)],[c758,c851]) ).
cnf(c935,plain,
meet(X,meet(complement(Y),join(complement(X),Y))) = zero,
inference(equational,[status(thm)],[c9,c720,c782]) ).
cnf(c936,plain,
meet(complement(X),join(complement(Y),X)) = complement(join(X,Y)),
inference(equational,[status(thm)],[c705,c723,c754,c769,c835,c852,c935]) ).
cnf(c937,plain,
meet(complement(X),join(Y,X)) = meet(complement(X),Y),
inference(equational,[status(thm)],[c35,c705,c712,c724,c936]) ).
cnf(c938,plain,
join(X,complement(join(X,Y))) = join(complement(Y),X),
inference(equational,[status(thm)],[c4,c708,c736,c769,c936]) ).
cnf(c939,plain,
meet(X,complement(meet(Y,X))) = meet(X,complement(Y)),
inference(equational,[status(thm)],[c35,c705,c712,c718,c723,c936]) ).
cnf(c940,plain,
meet(X,join(complement(X),Y)) = meet(Y,X),
inference(equational,[status(thm)],[c30,c708,c718,c938]) ).
cnf(c943,plain,
meet(X,complement(meet(X,Y))) = meet(X,complement(Y)),
inference(equational,[status(thm)],[c32,c939]) ).
cnf(c944,plain,
meet(complement(X),join(X,Y)) = meet(complement(X),Y),
inference(equational,[status(thm)],[c4,c937]) ).
cnf(c946,plain,
meet(composition(sk1,top),X) = composition(sk1,X),
inference(equational,[status(thm)],[c540,c708,c772,c940,c944]) ).
cnf(c949,plain,
meet(X,composition(sk1,top)) = composition(sk1,X),
inference(equational,[status(thm)],[c32,c540,c708,c772,c940,c944]) ).
cnf(c958,plain,
meet(X,composition(sk1,Y)) = meet(Y,composition(sk1,X)),
inference(equational,[status(thm)],[c783,c949]) ).
cnf(c959,plain,
meet(composition(sk1,X),Y) = meet(X,composition(sk1,Y)),
inference(equational,[status(thm)],[c782,c946,c949]) ).
cnf(c1432,plain,
composition(sk1,complement(composition(sk1,X))) = composition(sk1,complement(X)),
inference(equational,[status(thm)],[c943,c946]) ).
cnf(g1,plain,
meet(composition(sk1,sk2),complement(sk3)) = meet(composition(sk1,sk2),complement(composition(sk1,sk3))),
inference(equational,[status(thm)],[c32,c958,c959,c1432]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : REL030-3 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.13 % Command : run_Leo-III %s %d THM
% 0.13/0.35 % Computer : n004.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Jul 14 16:13:49 EDT 2025
% 0.13/0.35 % CPUTime :
% 89.66/89.61 % SZS status Unsatisfiable
% 89.66/89.61 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------