%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : REL028-1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n003.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 67.28s 67.44s
% Output : CNFRefutation 67.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 16
% Syntax : Number of clauses : 107 ( 107 unt; 0 nHn; 16 RR)
% Number of literals : 107 ( 106 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 : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 171 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
composition(sk1,sk2) != meet(sk1,sk2),
file('theBenchmark.p',goals_16) ).
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_14) ).
cnf(c4,axiom,
join(sk2,one) = one,
file('theBenchmark.p',goals_15) ).
cnf(c5,axiom,
join(X,Y) = join(Y,X),
file('REL001-0.ax',maddux1_join_commutativity_1) ).
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,
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(c19,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,c13]) ).
cnf(c25,plain,
converse(composition(X,converse(Y))) = composition(Y,converse(X)),
inference(equational,[status(thm)],[c2,c11]) ).
cnf(c26,plain,
converse(composition(converse(X),Y)) = composition(converse(Y),X),
inference(equational,[status(thm)],[c2,c11]) ).
cnf(c27,plain,
composition(converse(one),X) = X,
inference(equational,[status(thm)],[c1,c2,c26]) ).
cnf(c28,plain,
converse(one) = one,
inference(equational,[status(thm)],[c1,c27]) ).
cnf(c29,plain,
composition(one,X) = X,
inference(equational,[status(thm)],[c18,c27]) ).
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(c38,plain,
complement(join(zero,complement(X))) = meet(top,X),
inference(equational,[status(thm)],[c32,c33]) ).
cnf(c39,plain,
complement(join(zero,zero)) = meet(top,top),
inference(equational,[status(thm)],[c33,c38]) ).
cnf(c40,plain,
join(sk2,join(X,one)) = join(one,X),
inference(equational,[status(thm)],[c5,c19]) ).
cnf(c41,plain,
join(X,join(complement(X),Y)) = join(top,Y),
inference(equational,[status(thm)],[c7,c15]) ).
cnf(c43,plain,
join(one,complement(sk2)) = join(top,one),
inference(equational,[status(thm)],[c40,c41]) ).
cnf(c44,plain,
join(top,complement(complement(X))) = join(X,top),
inference(equational,[status(thm)],[c7,c41]) ).
cnf(c61,axiom,
composition(join(X,Y),Z) = join(composition(X,Z),composition(Y,Z)),
file('REL001-0.ax',composition_distributivity_7) ).
cnf(c62,plain,
join(composition(X,Y),composition(Z,Y)) = composition(join(X,Z),Y),
inference(equational,[status(thm)],[c61]) ).
cnf(c66,plain,
join(X,join(Y,complement(join(X,Y)))) = top,
inference(equational,[status(thm)],[c7,c15]) ).
cnf(c68,plain,
join(converse(X),join(converse(Y),Z)) = join(converse(join(X,Y)),Z),
inference(equational,[status(thm)],[c13,c15]) ).
cnf(c72,plain,
complement(join(meet(X,Y),complement(Z))) = meet(join(complement(X),complement(Y)),Z),
inference(equational,[status(thm)],[c32]) ).
cnf(c73,plain,
complement(join(complement(X),meet(Y,Z))) = meet(X,join(complement(Y),complement(Z))),
inference(equational,[status(thm)],[c32]) ).
cnf(c100,plain,
join(complement(X),join(complement(Y),meet(X,Y))) = top,
inference(equational,[status(thm)],[c7,c15,c32]) ).
cnf(c101,plain,
join(zero,join(complement(X),meet(top,X))) = top,
inference(equational,[status(thm)],[c33,c100]) ).
cnf(c102,plain,
join(zero,join(zero,meet(top,top))) = top,
inference(equational,[status(thm)],[c33,c101]) ).
cnf(c125,plain,
composition(join(converse(X),Y),converse(Z)) = converse(composition(Z,join(X,converse(Y)))),
inference(equational,[status(thm)],[c11,c23]) ).
cnf(c128,plain,
join(converse(X),composition(Y,converse(Z))) = converse(join(X,composition(Z,converse(Y)))),
inference(equational,[status(thm)],[c23,c25]) ).
cnf(c177,plain,
join(complement(converse(X)),converse(join(Y,X))) = join(top,converse(Y)),
inference(equational,[status(thm)],[c5,c7,c68]) ).
cnf(c178,plain,
join(complement(X),join(Y,X)) = join(top,Y),
inference(equational,[status(thm)],[c2,c13,c177]) ).
cnf(c179,plain,
join(zero,join(X,top)) = join(top,X),
inference(equational,[status(thm)],[c33,c178]) ).
cnf(c190,axiom,
join(composition(converse(X),complement(composition(X,Y))),complement(Y)) = complement(Y),
file('REL001-0.ax',converse_cancellativity_11) ).
cnf(c191,plain,
join(complement(X),composition(converse(Y),complement(composition(Y,X)))) = complement(X),
inference(equational,[status(thm)],[c5,c190]) ).
cnf(c192,plain,
join(complement(X),complement(X)) = complement(X),
inference(equational,[status(thm)],[c27,c29,c191]) ).
cnf(c193,plain,
join(zero,zero) = zero,
inference(equational,[status(thm)],[c33,c192]) ).
cnf(c194,plain,
complement(complement(X)) = meet(X,X),
inference(equational,[status(thm)],[c32,c192]) ).
cnf(c195,plain,
meet(top,top) = complement(zero),
inference(equational,[status(thm)],[c33,c194]) ).
cnf(c196,plain,
join(top,complement(X)) = top,
inference(equational,[status(thm)],[c5,c7,c66,c192]) ).
cnf(c197,plain,
join(X,top) = top,
inference(equational,[status(thm)],[c44,c196]) ).
cnf(c198,plain,
join(top,X) = top,
inference(equational,[status(thm)],[c179,c197]) ).
cnf(c201,plain,
join(zero,join(zero,X)) = join(zero,X),
inference(equational,[status(thm)],[c15,c193]) ).
cnf(c252,plain,
join(composition(X,Y),join(composition(Z,Y),W)) = join(composition(join(X,Z),Y),W),
inference(equational,[status(thm)],[c15,c62]) ).
cnf(c254,plain,
join(X,join(composition(Y,X),Z)) = join(composition(join(Y,one),X),Z),
inference(equational,[status(thm)],[c27,c28,c30,c252]) ).
cnf(c255,plain,
join(X,join(composition(sk1,X),Y)) = join(X,Y),
inference(equational,[status(thm)],[c3,c29,c254]) ).
cnf(c258,plain,
join(X,complement(composition(sk1,X))) = top,
inference(equational,[status(thm)],[c7,c197,c255]) ).
cnf(c261,plain,
meet(X,composition(sk1,complement(X))) = zero,
inference(equational,[status(thm)],[c32,c33,c258]) ).
cnf(c280,plain,
join(X,join(X,Y)) = join(composition(join(one,one),X),Y),
inference(equational,[status(thm)],[c27,c28,c254]) ).
cnf(c310,plain,
converse(join(composition(X,Y),composition(X,converse(Z)))) = converse(composition(X,join(Y,converse(Z)))),
inference(equational,[status(thm)],[c11,c62,c125,c128]) ).
cnf(c311,plain,
composition(X,converse(join(Y,Y))) = composition(join(X,X),converse(Y)),
inference(equational,[status(thm)],[c13,c25,c62,c310]) ).
cnf(c312,plain,
composition(join(X,X),Y) = composition(X,join(Y,Y)),
inference(equational,[status(thm)],[c2,c13,c311]) ).
cnf(c315,plain,
composition(join(X,X),complement(Y)) = composition(X,complement(Y)),
inference(equational,[status(thm)],[c192,c312]) ).
cnf(c323,plain,
converse(join(composition(X,Y),composition(X,Z))) = converse(composition(X,join(Y,Z))),
inference(equational,[status(thm)],[c2,c310]) ).
cnf(c324,plain,
join(composition(X,Y),composition(X,Z)) = composition(X,join(Y,Z)),
inference(equational,[status(thm)],[c2,c323]) ).
cnf(c335,plain,
composition(join(X,X),meet(Y,Z)) = composition(X,meet(Y,Z)),
inference(equational,[status(thm)],[c32,c315]) ).
cnf(c351,plain,
join(X,composition(sk1,join(X,Y))) = join(X,composition(sk1,Y)),
inference(equational,[status(thm)],[c255,c324]) ).
cnf(c352,plain,
join(X,composition(sk1,complement(X))) = join(X,composition(sk1,top)),
inference(equational,[status(thm)],[c7,c351]) ).
cnf(c759,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(c760,plain,
join(meet(X,Y),complement(join(complement(X),Y))) = X,
inference(equational,[status(thm)],[c32,c759]) ).
cnf(c761,plain,
join(zero,complement(complement(X))) = X,
inference(equational,[status(thm)],[c9,c192,c760]) ).
cnf(c764,plain,
join(zero,X) = X,
inference(equational,[status(thm)],[c201,c761]) ).
cnf(c765,plain,
complement(zero) = top,
inference(equational,[status(thm)],[c102,c195,c764]) ).
cnf(c766,plain,
complement(complement(X)) = X,
inference(equational,[status(thm)],[c761,c764]) ).
cnf(c767,plain,
join(X,zero) = X,
inference(equational,[status(thm)],[c5,c764]) ).
cnf(c770,plain,
meet(X,X) = X,
inference(equational,[status(thm)],[c7,c33,c760,c766,c767]) ).
cnf(c772,plain,
complement(join(complement(X),Y)) = meet(X,complement(Y)),
inference(equational,[status(thm)],[c73,c192,c770]) ).
cnf(c773,plain,
meet(zero,complement(X)) = zero,
inference(equational,[status(thm)],[c33,c39,c193,c195,c198,c765,c772]) ).
cnf(c775,plain,
meet(top,X) = X,
inference(equational,[status(thm)],[c72,c198,c764,c765,c766,c773]) ).
cnf(c778,plain,
complement(join(X,complement(Y))) = meet(complement(X),Y),
inference(equational,[status(thm)],[c72,c192,c770]) ).
cnf(c779,plain,
meet(sk2,complement(one)) = zero,
inference(equational,[status(thm)],[c33,c34,c43,c198,c778]) ).
cnf(c780,plain,
meet(sk2,one) = sk2,
inference(equational,[status(thm)],[c32,c760,c764,c779]) ).
cnf(c783,plain,
complement(meet(X,complement(Y))) = join(complement(X),Y),
inference(equational,[status(thm)],[c761,c764,c772]) ).
cnf(c787,plain,
join(X,meet(X,Y)) = X,
inference(equational,[status(thm)],[c5,c29,c280,c335,c760]) ).
cnf(c799,plain,
join(X,meet(Y,X)) = X,
inference(equational,[status(thm)],[c34,c787]) ).
cnf(c800,plain,
join(meet(X,Y),meet(X,complement(Y))) = X,
inference(equational,[status(thm)],[c5,c32,c760]) ).
cnf(c812,plain,
join(meet(X,Y),meet(Y,complement(X))) = Y,
inference(equational,[status(thm)],[c34,c800]) ).
cnf(c837,plain,
meet(meet(X,complement(Y)),Z) = meet(X,meet(complement(Y),Z)),
inference(equational,[status(thm)],[c15,c32,c772,c778,c783]) ).
cnf(c838,plain,
meet(meet(X,Y),Z) = meet(X,meet(Y,Z)),
inference(equational,[status(thm)],[c38,c764,c766,c775,c837]) ).
cnf(c840,plain,
meet(sk2,meet(one,X)) = meet(sk2,X),
inference(equational,[status(thm)],[c780,c838]) ).
cnf(c844,plain,
join(meet(X,Y),meet(complement(X),Y)) = Y,
inference(equational,[status(thm)],[c34,c812]) ).
cnf(c850,plain,
meet(X,composition(sk1,X)) = composition(sk1,X),
inference(equational,[status(thm)],[c261,c766,c767,c844]) ).
cnf(c897,plain,
complement(join(X,meet(complement(Y),Z))) = meet(complement(X),join(Y,complement(Z))),
inference(equational,[status(thm)],[c778]) ).
cnf(c898,plain,
meet(join(X,Y),join(complement(Y),X)) = X,
inference(equational,[status(thm)],[c34,c766,c783,c812,c897]) ).
cnf(c906,plain,
meet(X,join(complement(X),Y)) = meet(X,Y),
inference(equational,[status(thm)],[c15,c783,c799,c800,c898]) ).
cnf(c911,plain,
meet(X,composition(sk1,top)) = composition(sk1,X),
inference(equational,[status(thm)],[c352,c766,c850,c906]) ).
cnf(c913,plain,
composition(sk1,sk2) = meet(sk1,sk2),
inference(equational,[status(thm)],[c1,c34,c840,c911]) ).
cnf(g1,plain,
composition(sk1,sk2) = meet(sk1,sk2),
inference(equational,[status(thm)],[c913]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : REL028-1 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.11 % Command : run_Leo-III %s %d THM
% 0.12/0.32 % Computer : n003.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 16:12:49 EDT 2025
% 0.12/0.32 % CPUTime :
% 67.28/67.44 % SZS status Unsatisfiable
% 67.28/67.44 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------