%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : REL026-1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n013.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 07:41:22 AM UTC 2025
% Result : Unsatisfiable 65.89s 65.98s
% Output : CNFRefutation 65.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 15
% 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 : 180 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
meet(composition(sk1,top),sk2) != composition(sk1,sk2),
file('theBenchmark.p',goals_15) ).
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(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(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,
converse(composition(converse(X),Y)) = composition(converse(Y),X),
inference(equational,[status(thm)],[c2,c13]) ).
cnf(c22,plain,
composition(converse(one),X) = X,
inference(equational,[status(thm)],[c1,c2,c21]) ).
cnf(c23,plain,
converse(one) = one,
inference(equational,[status(thm)],[c1,c22]) ).
cnf(c24,plain,
composition(one,X) = X,
inference(equational,[status(thm)],[c18,c22]) ).
cnf(c25,plain,
converse(composition(X,converse(Y))) = composition(Y,converse(X)),
inference(equational,[status(thm)],[c2,c13]) ).
cnf(c26,plain,
converse(join(converse(X),Y)) = join(X,converse(Y)),
inference(equational,[status(thm)],[c2,c11]) ).
cnf(c27,plain,
converse(join(X,converse(Y))) = join(converse(X),Y),
inference(equational,[status(thm)],[c2,c11]) ).
cnf(c28,plain,
join(X,join(Y,Z)) = join(Y,join(X,Z)),
inference(equational,[status(thm)],[c4,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)],[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)],[c5,c15]) ).
cnf(c41,plain,
join(X,join(complement(X),Y)) = join(top,Y),
inference(equational,[status(thm)],[c7,c15]) ).
cnf(c42,plain,
join(top,complement(complement(X))) = join(X,top),
inference(equational,[status(thm)],[c7,c41]) ).
cnf(c45,plain,
join(one,converse(X)) = converse(join(one,X)),
inference(equational,[status(thm)],[c11,c23]) ).
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)],[c22,c23,c58]) ).
cnf(c62,plain,
join(X,join(Y,complement(join(X,Y)))) = top,
inference(equational,[status(thm)],[c7,c15]) ).
cnf(c70,plain,
complement(join(complement(X),meet(Y,Z))) = meet(X,join(complement(Y),complement(Z))),
inference(equational,[status(thm)],[c30]) ).
cnf(c71,plain,
complement(join(meet(X,Y),complement(Z))) = meet(join(complement(X),complement(Y)),Z),
inference(equational,[status(thm)],[c30]) ).
cnf(c74,plain,
join(X,join(Y,complement(join(Y,X)))) = top,
inference(equational,[status(thm)],[c28,c62]) ).
cnf(c94,plain,
join(complement(X),join(complement(Y),meet(X,Y))) = top,
inference(equational,[status(thm)],[c7,c15,c30]) ).
cnf(c95,plain,
join(zero,join(complement(X),meet(X,top))) = top,
inference(equational,[status(thm)],[c28,c31,c94]) ).
cnf(c96,plain,
join(zero,join(zero,meet(top,top))) = top,
inference(equational,[status(thm)],[c31,c95]) ).
cnf(c107,plain,
composition(join(converse(X),Y),converse(Z)) = converse(composition(Z,join(X,converse(Y)))),
inference(equational,[status(thm)],[c13,c27]) ).
cnf(c111,plain,
join(converse(X),composition(Y,converse(Z))) = converse(join(X,composition(Z,converse(Y)))),
inference(equational,[status(thm)],[c25,c27]) ).
cnf(c117,plain,
join(X,composition(X,converse(Y))) = composition(X,converse(join(one,Y))),
inference(equational,[status(thm)],[c25,c26,c59]) ).
cnf(c118,plain,
join(X,composition(X,Y)) = composition(X,join(one,Y)),
inference(equational,[status(thm)],[c2,c45,c117]) ).
cnf(c119,plain,
composition(join(one,X),X) = composition(X,join(one,X)),
inference(equational,[status(thm)],[c59,c118]) ).
cnf(c164,plain,
join(X,converse(join(complement(converse(X)),Y))) = converse(join(top,Y)),
inference(equational,[status(thm)],[c26,c41]) ).
cnf(c173,axiom,
join(composition(converse(X),complement(composition(X,Y))),complement(Y)) = complement(Y),
file('REL001-0.ax',converse_cancellativity_11) ).
cnf(c174,plain,
join(complement(X),composition(converse(Y),complement(composition(Y,X)))) = complement(X),
inference(equational,[status(thm)],[c4,c173]) ).
cnf(c175,plain,
join(complement(X),complement(X)) = complement(X),
inference(equational,[status(thm)],[c22,c24,c174]) ).
cnf(c176,plain,
join(zero,zero) = zero,
inference(equational,[status(thm)],[c31,c175]) ).
cnf(c177,plain,
complement(complement(X)) = meet(X,X),
inference(equational,[status(thm)],[c30,c175]) ).
cnf(c178,plain,
meet(top,top) = complement(zero),
inference(equational,[status(thm)],[c31,c177]) ).
cnf(c179,plain,
join(top,complement(X)) = top,
inference(equational,[status(thm)],[c4,c7,c62,c175]) ).
cnf(c180,plain,
join(X,top) = top,
inference(equational,[status(thm)],[c42,c179]) ).
cnf(c181,plain,
join(top,X) = top,
inference(equational,[status(thm)],[c4,c180]) ).
cnf(c182,plain,
converse(top) = top,
inference(equational,[status(thm)],[c164,c181]) ).
cnf(c185,plain,
join(zero,join(zero,X)) = join(zero,X),
inference(equational,[status(thm)],[c15,c176]) ).
cnf(c190,plain,
composition(join(one,X),top) = top,
inference(equational,[status(thm)],[c59,c181]) ).
cnf(c191,plain,
composition(top,top) = top,
inference(equational,[status(thm)],[c119,c180,c190]) ).
cnf(c192,plain,
composition(top,zero) = zero,
inference(equational,[status(thm)],[c31,c59,c174,c180,c182,c191]) ).
cnf(c224,plain,
join(one,join(X,complement(join(X,sk1)))) = top,
inference(equational,[status(thm)],[c37,c74,c180]) ).
cnf(c237,plain,
join(X,join(one,complement(join(X,sk1)))) = top,
inference(equational,[status(thm)],[c28,c224]) ).
cnf(c256,plain,
join(composition(X,Y),join(composition(Z,Y),W)) = join(composition(join(X,Z),Y),W),
inference(equational,[status(thm)],[c15,c58]) ).
cnf(c257,plain,
join(X,join(composition(Y,X),Z)) = join(composition(join(one,Y),X),Z),
inference(equational,[status(thm)],[c22,c23,c256]) ).
cnf(c258,plain,
join(X,join(composition(sk1,X),Y)) = join(X,Y),
inference(equational,[status(thm)],[c5,c24,c257]) ).
cnf(c259,plain,
join(X,complement(composition(sk1,X))) = top,
inference(equational,[status(thm)],[c7,c180,c258]) ).
cnf(c262,plain,
meet(X,composition(sk1,complement(X))) = zero,
inference(equational,[status(thm)],[c30,c31,c259]) ).
cnf(c263,plain,
join(X,join(composition(Y,X),Z)) = join(composition(join(Y,one),X),Z),
inference(equational,[status(thm)],[c22,c23,c28,c256]) ).
cnf(c271,plain,
join(X,join(X,Y)) = join(composition(join(one,one),X),Y),
inference(equational,[status(thm)],[c22,c23,c263]) ).
cnf(c275,plain,
join(X,join(composition(Y,X),Z)) = join(Z,composition(join(one,Y),X)),
inference(equational,[status(thm)],[c4,c257]) ).
cnf(c285,plain,
join(X,join(composition(top,X),Y)) = join(Y,composition(top,X)),
inference(equational,[status(thm)],[c5,c7,c237,c275]) ).
cnf(c288,plain,
converse(join(composition(X,Y),composition(X,converse(Z)))) = converse(composition(X,join(Y,converse(Z)))),
inference(equational,[status(thm)],[c13,c58,c107,c111]) ).
cnf(c289,plain,
composition(X,converse(join(Y,Y))) = composition(join(X,X),converse(Y)),
inference(equational,[status(thm)],[c11,c25,c58,c288]) ).
cnf(c290,plain,
composition(join(X,X),Y) = composition(X,join(Y,Y)),
inference(equational,[status(thm)],[c2,c11,c289]) ).
cnf(c293,plain,
composition(join(X,X),complement(Y)) = composition(X,complement(Y)),
inference(equational,[status(thm)],[c175,c290]) ).
cnf(c301,plain,
converse(join(composition(X,Y),composition(X,Z))) = converse(composition(X,join(Y,Z))),
inference(equational,[status(thm)],[c2,c288]) ).
cnf(c302,plain,
join(composition(X,Y),composition(X,Z)) = composition(X,join(Y,Z)),
inference(equational,[status(thm)],[c2,c301]) ).
cnf(c310,plain,
composition(join(X,X),meet(Y,Z)) = composition(X,meet(Y,Z)),
inference(equational,[status(thm)],[c30,c293]) ).
cnf(c325,plain,
join(X,composition(sk1,join(X,Y))) = join(X,composition(sk1,Y)),
inference(equational,[status(thm)],[c258,c302]) ).
cnf(c326,plain,
join(X,composition(sk1,complement(X))) = join(X,composition(sk1,top)),
inference(equational,[status(thm)],[c7,c325]) ).
cnf(c640,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(c641,plain,
join(meet(X,Y),complement(join(complement(X),Y))) = X,
inference(equational,[status(thm)],[c30,c640]) ).
cnf(c642,plain,
join(zero,complement(complement(X))) = X,
inference(equational,[status(thm)],[c9,c175,c641]) ).
cnf(c645,plain,
join(zero,X) = X,
inference(equational,[status(thm)],[c185,c642]) ).
cnf(c646,plain,
complement(zero) = top,
inference(equational,[status(thm)],[c96,c178,c645]) ).
cnf(c647,plain,
join(X,zero) = X,
inference(equational,[status(thm)],[c192,c285,c645]) ).
cnf(c648,plain,
complement(complement(X)) = X,
inference(equational,[status(thm)],[c642,c645]) ).
cnf(c651,plain,
meet(X,X) = X,
inference(equational,[status(thm)],[c7,c31,c641,c647,c648]) ).
cnf(c653,plain,
complement(join(X,complement(Y))) = meet(complement(X),Y),
inference(equational,[status(thm)],[c71,c175,c651]) ).
cnf(c654,plain,
meet(zero,complement(X)) = zero,
inference(equational,[status(thm)],[c31,c42,c180,c653]) ).
cnf(c655,plain,
meet(top,X) = X,
inference(equational,[status(thm)],[c71,c181,c645,c646,c648,c654]) ).
cnf(c661,plain,
complement(join(complement(X),Y)) = meet(X,complement(Y)),
inference(equational,[status(thm)],[c70,c175,c651]) ).
cnf(c662,plain,
complement(meet(X,complement(Y))) = join(complement(X),Y),
inference(equational,[status(thm)],[c35,c645,c655,c661]) ).
cnf(c666,plain,
join(X,meet(X,Y)) = X,
inference(equational,[status(thm)],[c4,c24,c271,c310,c641]) ).
cnf(c669,plain,
complement(meet(complement(X),Y)) = join(complement(Y),X),
inference(equational,[status(thm)],[c32,c662]) ).
cnf(c679,plain,
join(X,meet(Y,X)) = X,
inference(equational,[status(thm)],[c32,c666]) ).
cnf(c680,plain,
join(meet(X,Y),meet(X,complement(Y))) = X,
inference(equational,[status(thm)],[c4,c30,c641]) ).
cnf(c691,plain,
join(meet(X,Y),meet(complement(Y),X)) = X,
inference(equational,[status(thm)],[c32,c680]) ).
cnf(c712,plain,
meet(X,composition(sk1,X)) = composition(sk1,X),
inference(equational,[status(thm)],[c32,c262,c647,c648,c691]) ).
cnf(c743,plain,
complement(join(X,meet(complement(Y),Z))) = meet(complement(X),join(Y,complement(Z))),
inference(equational,[status(thm)],[c653]) ).
cnf(c744,plain,
meet(join(X,Y),join(complement(Y),X)) = X,
inference(equational,[status(thm)],[c32,c648,c669,c680,c743]) ).
cnf(c745,plain,
meet(X,join(complement(X),Y)) = meet(X,Y),
inference(equational,[status(thm)],[c15,c662,c679,c680,c744]) ).
cnf(c748,plain,
meet(X,composition(sk1,top)) = composition(sk1,X),
inference(equational,[status(thm)],[c326,c648,c712,c745]) ).
cnf(g1,plain,
meet(composition(sk1,top),sk2) = composition(sk1,sk2),
inference(equational,[status(thm)],[c32,c748]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : REL026-1 : TPTP v9.0.0. Released v4.0.0.
% 0.04/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n013.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
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Jul 14 16:11:19 EDT 2025
% 0.11/0.33 % CPUTime :
% 65.89/65.98 % SZS status Unsatisfiable
% 65.89/65.98 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------