%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : REL019-1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n001.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 07:41:20 AM UTC 2025
% Result : Unsatisfiable 71.00s 71.20s
% Output : CNFRefutation 71.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 16
% Syntax : Number of clauses : 121 ( 121 unt; 0 nHn; 26 RR)
% Number of literals : 121 ( 120 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 : 171 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
composition(meet(sk1,sk2),top) != 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,
composition(sk1,top) = sk1,
file('theBenchmark.p',goals_14) ).
cnf(c4,axiom,
composition(sk2,top) = sk2,
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(c21,plain,
converse(join(X,converse(Y))) = join(converse(X),Y),
inference(equational,[status(thm)],[c2,c13]) ).
cnf(c22,plain,
converse(join(converse(X),Y)) = join(X,converse(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)],[c5,c15]) ).
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)],[c5,c30]) ).
cnf(c33,plain,
join(zero,top) = top,
inference(equational,[status(thm)],[c5,c7,c31]) ).
cnf(c35,plain,
complement(join(zero,complement(X))) = meet(top,X),
inference(equational,[status(thm)],[c30,c31]) ).
cnf(c37,plain,
join(X,join(complement(X),Y)) = join(top,Y),
inference(equational,[status(thm)],[c7,c15]) ).
cnf(c38,plain,
join(top,complement(complement(X))) = join(X,top),
inference(equational,[status(thm)],[c7,c37]) ).
cnf(c40,plain,
join(zero,join(top,X)) = join(top,X),
inference(equational,[status(thm)],[c28,c31,c37]) ).
cnf(c41,plain,
join(one,converse(X)) = converse(join(one,X)),
inference(equational,[status(thm)],[c22,c26]) ).
cnf(c43,plain,
join(X,converse(complement(converse(X)))) = converse(top),
inference(equational,[status(thm)],[c7,c22]) ).
cnf(c44,plain,
join(zero,converse(top)) = converse(top),
inference(equational,[status(thm)],[c40,c43]) ).
cnf(c45,plain,
join(top,converse(zero)) = top,
inference(equational,[status(thm)],[c2,c5,c21,c44]) ).
cnf(c46,plain,
join(X,join(Y,complement(X))) = join(top,Y),
inference(equational,[status(thm)],[c5,c37]) ).
cnf(c48,axiom,
composition(join(X,Y),Z) = join(composition(X,Z),composition(Y,Z)),
file('REL001-0.ax',composition_distributivity_7) ).
cnf(c49,plain,
join(composition(X,Y),composition(Z,Y)) = composition(join(X,Z),Y),
inference(equational,[status(thm)],[c48]) ).
cnf(c57,plain,
join(X,composition(Y,X)) = composition(join(one,Y),X),
inference(equational,[status(thm)],[c25,c26,c49]) ).
cnf(c62,plain,
join(converse(X),join(converse(Y),Z)) = join(converse(join(X,Y)),Z),
inference(equational,[status(thm)],[c13,c15]) ).
cnf(c66,plain,
complement(join(meet(X,Y),complement(Z))) = meet(join(complement(X),complement(Y)),Z),
inference(equational,[status(thm)],[c30]) ).
cnf(c81,plain,
join(complement(X),join(complement(Y),meet(X,Y))) = top,
inference(equational,[status(thm)],[c7,c15,c30]) ).
cnf(c82,plain,
join(zero,join(complement(X),meet(X,top))) = top,
inference(equational,[status(thm)],[c28,c31,c81]) ).
cnf(c83,plain,
join(zero,join(zero,meet(top,top))) = top,
inference(equational,[status(thm)],[c31,c82]) ).
cnf(c85,plain,
meet(meet(X,Y),join(complement(X),complement(Y))) = zero,
inference(equational,[status(thm)],[c9,c30,c32]) ).
cnf(c92,plain,
join(converse(X),composition(Y,converse(Z))) = converse(join(X,composition(Z,converse(Y)))),
inference(equational,[status(thm)],[c21,c23]) ).
cnf(c102,plain,
converse(join(X,composition(X,Y))) = converse(composition(X,join(one,Y))),
inference(equational,[status(thm)],[c11,c13,c41,c57]) ).
cnf(c103,plain,
join(X,composition(X,Y)) = composition(X,join(one,Y)),
inference(equational,[status(thm)],[c2,c102]) ).
cnf(c132,plain,
join(X,converse(join(complement(converse(X)),Y))) = converse(join(top,Y)),
inference(equational,[status(thm)],[c22,c37]) ).
cnf(c138,plain,
join(complement(converse(X)),converse(join(Y,X))) = join(top,converse(Y)),
inference(equational,[status(thm)],[c5,c7,c62]) ).
cnf(c152,plain,
meet(meet(X,Y),join(complement(Y),complement(X))) = zero,
inference(equational,[status(thm)],[c32,c85]) ).
cnf(c155,axiom,
join(composition(converse(X),complement(composition(X,Y))),complement(Y)) = complement(Y),
file('REL001-0.ax',converse_cancellativity_11) ).
cnf(c156,plain,
join(complement(X),composition(converse(Y),complement(composition(Y,X)))) = complement(X),
inference(equational,[status(thm)],[c5,c155]) ).
cnf(c157,plain,
join(complement(X),complement(X)) = complement(X),
inference(equational,[status(thm)],[c25,c27,c156]) ).
cnf(c158,plain,
join(zero,zero) = zero,
inference(equational,[status(thm)],[c31,c157]) ).
cnf(c159,plain,
complement(complement(X)) = meet(X,X),
inference(equational,[status(thm)],[c30,c157]) ).
cnf(c160,plain,
meet(top,top) = complement(zero),
inference(equational,[status(thm)],[c31,c159]) ).
cnf(c161,plain,
join(top,complement(X)) = top,
inference(equational,[status(thm)],[c7,c46,c157]) ).
cnf(c162,plain,
join(X,top) = top,
inference(equational,[status(thm)],[c38,c161]) ).
cnf(c163,plain,
join(top,X) = top,
inference(equational,[status(thm)],[c5,c162]) ).
cnf(c164,plain,
converse(top) = top,
inference(equational,[status(thm)],[c132,c163]) ).
cnf(c167,plain,
join(zero,composition(converse(sk1),complement(sk1))) = zero,
inference(equational,[status(thm)],[c3,c31,c156]) ).
cnf(c168,plain,
join(zero,composition(converse(sk2),complement(sk2))) = zero,
inference(equational,[status(thm)],[c4,c31,c156]) ).
cnf(c170,plain,
join(zero,join(zero,X)) = join(zero,X),
inference(equational,[status(thm)],[c15,c158]) ).
cnf(c196,plain,
join(complement(X),join(Y,complement(X))) = join(Y,complement(X)),
inference(equational,[status(thm)],[c28,c157]) ).
cnf(c265,plain,
join(complement(X),composition(Y,complement(composition(converse(Y),X)))) = complement(X),
inference(equational,[status(thm)],[c2,c156]) ).
cnf(c467,plain,
join(converse(zero),complement(composition(converse(complement(sk2)),sk2))) = top,
inference(equational,[status(thm)],[c5,c24,c45,c138,c168]) ).
cnf(c468,plain,
join(converse(zero),complement(composition(converse(complement(sk1)),sk1))) = top,
inference(equational,[status(thm)],[c5,c24,c45,c138,c167]) ).
cnf(c779,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(c780,plain,
join(meet(X,Y),complement(join(complement(X),Y))) = X,
inference(equational,[status(thm)],[c30,c779]) ).
cnf(c781,plain,
join(zero,complement(complement(X))) = X,
inference(equational,[status(thm)],[c9,c157,c780]) ).
cnf(c784,plain,
join(zero,X) = X,
inference(equational,[status(thm)],[c170,c781]) ).
cnf(c785,plain,
complement(zero) = top,
inference(equational,[status(thm)],[c83,c160,c784]) ).
cnf(c786,plain,
complement(complement(X)) = X,
inference(equational,[status(thm)],[c781,c784]) ).
cnf(c787,plain,
join(X,zero) = X,
inference(equational,[status(thm)],[c5,c784]) ).
cnf(c792,plain,
meet(top,X) = X,
inference(equational,[status(thm)],[c35,c784,c786]) ).
cnf(c793,plain,
meet(X,top) = X,
inference(equational,[status(thm)],[c32,c792]) ).
cnf(c797,plain,
join(complement(X),complement(Y)) = complement(meet(X,Y)),
inference(equational,[status(thm)],[c30,c781,c784]) ).
cnf(c798,plain,
complement(meet(complement(X),Y)) = join(X,complement(Y)),
inference(equational,[status(thm)],[c35,c784,c792,c797]) ).
cnf(c799,plain,
complement(meet(X,complement(Y))) = join(complement(X),Y),
inference(equational,[status(thm)],[c35,c784,c792,c797]) ).
cnf(c801,plain,
join(X,complement(meet(Y,X))) = top,
inference(equational,[status(thm)],[c46,c161,c797]) ).
cnf(c804,plain,
meet(X,join(complement(Y),X)) = X,
inference(equational,[status(thm)],[c31,c780,c787,c799,c801]) ).
cnf(c805,plain,
meet(X,join(Y,X)) = X,
inference(equational,[status(thm)],[c35,c792,c804]) ).
cnf(c808,plain,
join(converse(zero),X) = X,
inference(equational,[status(thm)],[c2,c21,c784]) ).
cnf(c809,plain,
converse(zero) = zero,
inference(equational,[status(thm)],[c787,c808]) ).
cnf(c813,plain,
join(meet(X,Y),meet(X,complement(Y))) = X,
inference(equational,[status(thm)],[c5,c30,c780]) ).
cnf(c825,plain,
join(meet(X,Y),meet(complement(Y),X)) = X,
inference(equational,[status(thm)],[c32,c813]) ).
cnf(c826,plain,
join(X,join(X,complement(Y))) = join(X,complement(Y)),
inference(equational,[status(thm)],[c15,c157,c196,c798]) ).
cnf(c832,plain,
complement(composition(converse(complement(sk1)),sk1)) = top,
inference(equational,[status(thm)],[c33,c468,c784,c809,c826]) ).
cnf(c833,plain,
composition(complement(sk1),top) = complement(sk1),
inference(equational,[status(thm)],[c103,c162,c265,c832]) ).
cnf(c835,plain,
complement(composition(converse(complement(sk2)),sk2)) = top,
inference(equational,[status(thm)],[c33,c467,c784,c809,c826]) ).
cnf(c836,plain,
composition(complement(sk2),top) = complement(sk2),
inference(equational,[status(thm)],[c103,c162,c265,c835]) ).
cnf(c843,plain,
meet(meet(X,Y),complement(meet(Y,X))) = zero,
inference(equational,[status(thm)],[c152,c797]) ).
cnf(c846,plain,
join(complement(X),join(Y,complement(Z))) = join(Y,complement(meet(X,Z))),
inference(equational,[status(thm)],[c28,c797]) ).
cnf(c847,plain,
complement(meet(X,meet(Y,Z))) = complement(meet(Y,meet(X,Z))),
inference(equational,[status(thm)],[c797,c846]) ).
cnf(c848,plain,
meet(X,meet(Y,Z)) = meet(Y,meet(X,Z)),
inference(equational,[status(thm)],[c35,c784,c786,c792,c847]) ).
cnf(c850,plain,
meet(meet(X,Y),Z) = meet(X,meet(Z,Y)),
inference(equational,[status(thm)],[c32,c848]) ).
cnf(c852,plain,
meet(X,meet(Y,Z)) = meet(Z,meet(Y,X)),
inference(equational,[status(thm)],[c32,c850]) ).
cnf(c859,plain,
meet(X,meet(Y,complement(meet(Y,X)))) = zero,
inference(equational,[status(thm)],[c85,c785,c793,c797,c843,c852]) ).
cnf(c860,plain,
meet(X,join(complement(X),Y)) = meet(X,Y),
inference(equational,[status(thm)],[c787,c799,c805,c825,c850,c859]) ).
cnf(c886,plain,
meet(X,converse(complement(converse(complement(X))))) = X,
inference(equational,[status(thm)],[c43,c164,c793,c860]) ).
cnf(c952,plain,
join(X,complement(converse(complement(converse(X))))) = X,
inference(equational,[status(thm)],[c786,c798,c886]) ).
cnf(c970,plain,
meet(complement(meet(X,Y)),join(complement(X),Y)) = complement(X),
inference(equational,[status(thm)],[c66,c780,c797]) ).
cnf(c971,plain,
meet(join(X,Y),join(X,complement(Y))) = X,
inference(equational,[status(thm)],[c32,c35,c784,c786,c792,c798,c970]) ).
cnf(c972,plain,
meet(join(X,Y),join(complement(Y),X)) = X,
inference(equational,[status(thm)],[c5,c971]) ).
cnf(c983,plain,
join(X,converse(complement(converse(complement(X))))) = converse(complement(converse(complement(X)))),
inference(equational,[status(thm)],[c5,c43,c164,c793,c972]) ).
cnf(c984,plain,
complement(converse(complement(converse(X)))) = X,
inference(equational,[status(thm)],[c2,c22,c952,c983]) ).
cnf(c985,plain,
converse(complement(converse(X))) = complement(X),
inference(equational,[status(thm)],[c781,c784,c984]) ).
cnf(c986,plain,
complement(converse(X)) = converse(complement(X)),
inference(equational,[status(thm)],[c2,c985]) ).
cnf(c1061,plain,
join(complement(sk1),composition(X,top)) = composition(join(complement(sk1),X),top),
inference(equational,[status(thm)],[c49,c833]) ).
cnf(c1108,plain,
composition(complement(meet(sk1,sk2)),top) = complement(meet(sk1,sk2)),
inference(equational,[status(thm)],[c797,c836,c1061]) ).
cnf(c1218,plain,
converse(join(complement(X),composition(complement(composition(X,Y)),converse(Y)))) = converse(complement(X)),
inference(equational,[status(thm)],[c2,c11,c92,c156,c986]) ).
cnf(c1223,plain,
join(complement(X),composition(complement(composition(X,Y)),converse(Y))) = complement(X),
inference(equational,[status(thm)],[c2,c1218]) ).
cnf(c1226,plain,
composition(meet(sk1,sk2),top) = meet(sk1,sk2),
inference(equational,[status(thm)],[c103,c162,c164,c786,c1108,c1223]) ).
cnf(g1,plain,
composition(meet(sk1,sk2),top) = meet(sk1,sk2),
inference(equational,[status(thm)],[c1226]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : REL019-1 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.13/0.33 % Computer : n001.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Jul 14 16:09:49 EDT 2025
% 0.13/0.34 % CPUTime :
% 71.00/71.20 % SZS status Unsatisfiable
% 71.00/71.20 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------