%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : REL029-10 : TPTP v9.0.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n015.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 219.41s 219.55s
% Output : CNFRefutation 219.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 16
% Syntax : Number of clauses : 241 ( 241 unt; 0 nHn; 45 RR)
% Number of literals : 241 ( 240 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 : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 352 ( 25 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
tuple(join(meet(composition(sk1,sk3),composition(sk2,sk3)),composition(meet(sk1,sk2),sk3)),join(composition(meet(sk1,sk2),sk3),meet(composition(sk1,sk3),composition(sk2,sk3)))) != tuple(composition(meet(sk1,sk2),sk3),meet(composition(sk1,sk3),composition(sk2,sk3))),
file('theBenchmark.p',goals_19) ).
cnf(c1,axiom,
composition(X,one) = X,
file('theBenchmark.p',composition_identity_6) ).
cnf(c2,axiom,
converse(converse(X)) = X,
file('theBenchmark.p',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('theBenchmark.p',maddux1_join_commutativity_1) ).
cnf(c6,plain,
join(one,sk1) = one,
inference(equational,[status(thm)],[c3,c5]) ).
cnf(c7,plain,
join(one,sk2) = one,
inference(equational,[status(thm)],[c4,c5]) ).
cnf(c8,axiom,
zero = meet(X,complement(X)),
file('theBenchmark.p',def_zero_13) ).
cnf(c9,plain,
meet(X,complement(X)) = zero,
inference(equational,[status(thm)],[c8]) ).
cnf(c10,axiom,
top = join(X,complement(X)),
file('theBenchmark.p',def_top_12) ).
cnf(c11,plain,
join(X,complement(X)) = top,
inference(equational,[status(thm)],[c10]) ).
cnf(c12,axiom,
converse(join(X,Y)) = join(converse(X),converse(Y)),
file('theBenchmark.p',converse_additivity_9) ).
cnf(c13,plain,
join(converse(X),converse(Y)) = converse(join(X,Y)),
inference(equational,[status(thm)],[c12]) ).
cnf(c14,axiom,
converse(composition(X,Y)) = composition(converse(Y),converse(X)),
file('theBenchmark.p',converse_multiplicativity_10) ).
cnf(c15,plain,
composition(converse(X),converse(Y)) = converse(composition(Y,X)),
inference(equational,[status(thm)],[c14]) ).
cnf(c16,axiom,
join(X,join(Y,Z)) = join(join(X,Y),Z),
file('theBenchmark.p',maddux2_join_associativity_2) ).
cnf(c17,plain,
join(join(X,Y),Z) = join(X,join(Y,Z)),
inference(equational,[status(thm)],[c16]) ).
cnf(c18,axiom,
composition(X,composition(Y,Z)) = composition(composition(X,Y),Z),
file('theBenchmark.p',composition_associativity_5) ).
cnf(c19,plain,
composition(composition(X,Y),Z) = composition(X,composition(Y,Z)),
inference(equational,[status(thm)],[c18]) ).
cnf(c20,plain,
composition(X,composition(one,Y)) = composition(X,Y),
inference(equational,[status(thm)],[c1,c19]) ).
cnf(c25,plain,
converse(join(X,converse(Y))) = join(converse(X),Y),
inference(equational,[status(thm)],[c2,c13]) ).
cnf(c26,plain,
converse(join(converse(X),Y)) = join(X,converse(Y)),
inference(equational,[status(thm)],[c2,c13]) ).
cnf(c27,plain,
converse(composition(converse(X),Y)) = composition(converse(Y),X),
inference(equational,[status(thm)],[c2,c15]) ).
cnf(c28,plain,
composition(converse(one),X) = X,
inference(equational,[status(thm)],[c1,c2,c27]) ).
cnf(c29,plain,
converse(one) = one,
inference(equational,[status(thm)],[c1,c28]) ).
cnf(c30,plain,
composition(one,X) = X,
inference(equational,[status(thm)],[c20,c28]) ).
cnf(c31,plain,
converse(composition(X,converse(Y))) = composition(Y,converse(X)),
inference(equational,[status(thm)],[c2,c15]) ).
cnf(c32,plain,
join(X,join(Y,Z)) = join(Y,join(X,Z)),
inference(equational,[status(thm)],[c5,c17]) ).
cnf(c33,axiom,
meet(X,Y) = complement(join(complement(X),complement(Y))),
file('theBenchmark.p',maddux4_definiton_of_meet_4) ).
cnf(c34,plain,
complement(join(complement(X),complement(Y))) = meet(X,Y),
inference(equational,[status(thm)],[c33]) ).
cnf(c35,plain,
complement(top) = zero,
inference(equational,[status(thm)],[c9,c11,c34]) ).
cnf(c36,plain,
meet(X,Y) = meet(Y,X),
inference(equational,[status(thm)],[c5,c34]) ).
cnf(c40,plain,
complement(join(zero,complement(X))) = meet(top,X),
inference(equational,[status(thm)],[c34,c35]) ).
cnf(c42,plain,
join(one,join(sk1,X)) = join(one,X),
inference(equational,[status(thm)],[c6,c17]) ).
cnf(c43,plain,
join(one,complement(sk1)) = join(top,one),
inference(equational,[status(thm)],[c5,c11,c42]) ).
cnf(c44,plain,
join(one,join(sk2,X)) = join(one,X),
inference(equational,[status(thm)],[c7,c17]) ).
cnf(c45,plain,
join(one,complement(sk2)) = join(top,one),
inference(equational,[status(thm)],[c5,c11,c44]) ).
cnf(c48,plain,
join(one,join(X,sk2)) = join(X,one),
inference(equational,[status(thm)],[c7,c32]) ).
cnf(c49,plain,
join(X,join(complement(X),Y)) = join(top,Y),
inference(equational,[status(thm)],[c11,c17]) ).
cnf(c50,plain,
join(top,complement(complement(X))) = join(X,top),
inference(equational,[status(thm)],[c11,c49]) ).
cnf(c53,plain,
join(one,converse(X)) = converse(join(one,X)),
inference(equational,[status(thm)],[c13,c29]) ).
cnf(c61,plain,
join(X,converse(complement(converse(X)))) = converse(top),
inference(equational,[status(thm)],[c11,c26]) ).
cnf(c66,plain,
join(X,join(Y,complement(X))) = join(top,Y),
inference(equational,[status(thm)],[c5,c49]) ).
cnf(c67,axiom,
composition(join(X,Y),Z) = join(composition(X,Z),composition(Y,Z)),
file('theBenchmark.p',composition_distributivity_7) ).
cnf(c68,plain,
join(composition(X,Y),composition(Z,Y)) = composition(join(X,Z),Y),
inference(equational,[status(thm)],[c67]) ).
cnf(c69,plain,
join(X,composition(Y,X)) = composition(join(one,Y),X),
inference(equational,[status(thm)],[c28,c29,c68]) ).
cnf(c70,plain,
join(X,composition(sk1,X)) = X,
inference(equational,[status(thm)],[c6,c30,c69]) ).
cnf(c71,plain,
join(X,composition(sk2,X)) = X,
inference(equational,[status(thm)],[c7,c30,c69]) ).
cnf(c72,plain,
join(X,composition(Y,X)) = composition(join(Y,one),X),
inference(equational,[status(thm)],[c5,c28,c29,c68]) ).
cnf(c74,plain,
join(X,X) = composition(join(one,one),X),
inference(equational,[status(thm)],[c30,c72]) ).
cnf(c84,plain,
join(one,composition(sk2,sk1)) = one,
inference(equational,[status(thm)],[c6,c42,c71]) ).
cnf(c85,plain,
join(X,join(Y,complement(join(X,Y)))) = top,
inference(equational,[status(thm)],[c11,c17]) ).
cnf(c89,plain,
composition(converse(X),composition(converse(Y),Z)) = composition(converse(composition(Y,X)),Z),
inference(equational,[status(thm)],[c15,c19]) ).
cnf(c90,plain,
join(converse(X),join(converse(Y),Z)) = join(converse(join(X,Y)),Z),
inference(equational,[status(thm)],[c13,c17]) ).
cnf(c92,plain,
converse(join(one,complement(converse(sk1)))) = converse(join(top,one)),
inference(equational,[status(thm)],[c5,c42,c53,c61]) ).
cnf(c93,plain,
join(one,complement(converse(sk1))) = join(top,one),
inference(equational,[status(thm)],[c2,c92]) ).
cnf(c97,plain,
meet(join(complement(X),complement(Y)),Z) = complement(join(meet(X,Y),complement(Z))),
inference(equational,[status(thm)],[c34]) ).
cnf(c102,plain,
join(X,composition(X,converse(sk2))) = X,
inference(equational,[status(thm)],[c2,c26,c31,c71]) ).
cnf(c103,plain,
join(one,join(X,complement(sk2))) = join(top,join(one,X)),
inference(equational,[status(thm)],[c32,c44,c66]) ).
cnf(c104,plain,
join(one,join(X,complement(sk1))) = join(top,join(one,X)),
inference(equational,[status(thm)],[c32,c42,c66]) ).
cnf(c139,plain,
complement(join(meet(top,X),complement(Y))) = meet(join(zero,complement(X)),Y),
inference(equational,[status(thm)],[c35,c97]) ).
cnf(c140,plain,
complement(join(meet(X,top),complement(Y))) = meet(join(zero,complement(X)),Y),
inference(equational,[status(thm)],[c5,c35,c97]) ).
cnf(c144,plain,
composition(join(X,converse(Y)),converse(Z)) = converse(composition(Z,join(converse(X),Y))),
inference(equational,[status(thm)],[c15,c26]) ).
cnf(c145,plain,
composition(converse(X),join(Y,converse(Z))) = converse(composition(join(converse(Y),Z),X)),
inference(equational,[status(thm)],[c15,c26]) ).
cnf(c158,plain,
join(composition(X,converse(Y)),converse(Z)) = converse(join(composition(Y,converse(X)),Z)),
inference(equational,[status(thm)],[c13,c31]) ).
cnf(c168,plain,
composition(X,converse(join(one,Y))) = join(X,composition(X,converse(Y))),
inference(equational,[status(thm)],[c26,c31,c69]) ).
cnf(c169,plain,
join(X,composition(X,complement(one))) = composition(X,top),
inference(equational,[status(thm)],[c2,c29,c61,c168]) ).
cnf(c170,plain,
join(converse(join(X,one)),Y) = join(one,join(converse(X),Y)),
inference(equational,[status(thm)],[c29,c32,c90]) ).
cnf(c172,plain,
join(one,join(converse(sk2),X)) = join(one,X),
inference(equational,[status(thm)],[c4,c29,c170]) ).
cnf(c218,plain,
join(complement(converse(X)),converse(join(Y,X))) = join(top,converse(Y)),
inference(equational,[status(thm)],[c5,c11,c90]) ).
cnf(c219,plain,
join(complement(X),join(Y,X)) = join(top,Y),
inference(equational,[status(thm)],[c2,c13,c218]) ).
cnf(c238,plain,
join(X,converse(join(complement(converse(X)),Y))) = converse(join(top,Y)),
inference(equational,[status(thm)],[c26,c49]) ).
cnf(c251,axiom,
join(composition(converse(X),complement(composition(X,Y))),complement(Y)) = complement(Y),
file('theBenchmark.p',converse_cancellativity_11) ).
cnf(c252,plain,
join(complement(X),composition(converse(Y),complement(composition(Y,X)))) = complement(X),
inference(equational,[status(thm)],[c5,c251]) ).
cnf(c253,plain,
join(complement(X),complement(X)) = complement(X),
inference(equational,[status(thm)],[c28,c30,c252]) ).
cnf(c254,plain,
join(zero,zero) = zero,
inference(equational,[status(thm)],[c35,c253]) ).
cnf(c256,plain,
join(top,complement(X)) = top,
inference(equational,[status(thm)],[c11,c49,c253]) ).
cnf(c257,plain,
join(X,top) = top,
inference(equational,[status(thm)],[c50,c256]) ).
cnf(c258,plain,
join(top,X) = top,
inference(equational,[status(thm)],[c35,c219,c257]) ).
cnf(c259,plain,
converse(top) = top,
inference(equational,[status(thm)],[c238,c258]) ).
cnf(c262,plain,
join(zero,join(zero,X)) = join(zero,X),
inference(equational,[status(thm)],[c17,c254]) ).
cnf(c263,plain,
join(complement(one),composition(converse(X),complement(X))) = complement(one),
inference(equational,[status(thm)],[c1,c252]) ).
cnf(c268,plain,
join(complement(one),composition(X,complement(converse(X)))) = complement(one),
inference(equational,[status(thm)],[c2,c263]) ).
cnf(c269,plain,
join(meet(X,Y),meet(X,Y)) = meet(X,Y),
inference(equational,[status(thm)],[c34,c253]) ).
cnf(c299,plain,
join(X,composition(join(Y,sk2),X)) = composition(join(Y,one),X),
inference(equational,[status(thm)],[c48,c69]) ).
cnf(c301,plain,
join(X,composition(join(sk1,Y),X)) = composition(join(one,Y),X),
inference(equational,[status(thm)],[c42,c69]) ).
cnf(c302,plain,
join(X,join(composition(sk2,X),Y)) = join(X,Y),
inference(equational,[status(thm)],[c17,c71]) ).
cnf(c303,plain,
join(X,join(composition(sk1,X),Y)) = join(X,Y),
inference(equational,[status(thm)],[c17,c70]) ).
cnf(c304,plain,
join(X,join(Y,composition(sk1,X))) = join(Y,X),
inference(equational,[status(thm)],[c32,c70]) ).
cnf(c307,plain,
join(X,join(Y,composition(sk2,X))) = join(Y,X),
inference(equational,[status(thm)],[c32,c71]) ).
cnf(c309,plain,
join(one,join(X,complement(join(sk1,X)))) = top,
inference(equational,[status(thm)],[c42,c85,c257]) ).
cnf(c311,plain,
join(one,complement(join(sk1,sk1))) = top,
inference(equational,[status(thm)],[c42,c309]) ).
cnf(c312,plain,
join(one,join(X,complement(join(sk2,X)))) = top,
inference(equational,[status(thm)],[c44,c85,c257]) ).
cnf(c313,plain,
join(one,complement(join(sk2,sk2))) = top,
inference(equational,[status(thm)],[c44,c312]) ).
cnf(c322,plain,
composition(join(one,one),meet(X,Y)) = meet(X,Y),
inference(equational,[status(thm)],[c74,c269]) ).
cnf(c334,plain,
join(X,join(one,complement(join(sk1,X)))) = top,
inference(equational,[status(thm)],[c32,c309]) ).
cnf(c336,plain,
join(converse(complement(converse(X))),join(Y,X)) = top,
inference(equational,[status(thm)],[c25,c218,c258,c259]) ).
cnf(c346,plain,
join(X,composition(sk2,composition(sk1,X))) = X,
inference(equational,[status(thm)],[c19,c30,c69,c84]) ).
cnf(c364,plain,
join(complement(one),composition(sk1,top)) = join(sk1,complement(one)),
inference(equational,[status(thm)],[c169,c304]) ).
cnf(c366,plain,
join(complement(one),composition(sk2,top)) = join(sk2,complement(one)),
inference(equational,[status(thm)],[c169,c307]) ).
cnf(c373,plain,
join(composition(X,Y),join(composition(Z,Y),W)) = join(composition(join(X,Z),Y),W),
inference(equational,[status(thm)],[c17,c68]) ).
cnf(c374,plain,
join(X,join(composition(Y,X),Z)) = join(composition(join(one,Y),X),Z),
inference(equational,[status(thm)],[c28,c29,c373]) ).
cnf(c375,plain,
join(X,join(composition(Y,X),Z)) = join(composition(join(Y,one),X),Z),
inference(equational,[status(thm)],[c28,c29,c32,c373]) ).
cnf(c380,plain,
join(X,join(X,Y)) = join(composition(join(one,one),X),Y),
inference(equational,[status(thm)],[c30,c375]) ).
cnf(c381,plain,
join(X,join(Y,composition(Z,X))) = join(composition(join(one,Z),X),Y),
inference(equational,[status(thm)],[c5,c374]) ).
cnf(c383,plain,
join(composition(X,Y),composition(Z,composition(W,Y))) = composition(join(X,composition(Z,W)),Y),
inference(equational,[status(thm)],[c19,c68]) ).
cnf(c411,plain,
converse(join(composition(X,converse(Y)),composition(X,Z))) = converse(composition(X,join(converse(Y),Z))),
inference(equational,[status(thm)],[c15,c68,c144,c158]) ).
cnf(c412,plain,
composition(X,converse(join(Y,Y))) = composition(join(X,X),converse(Y)),
inference(equational,[status(thm)],[c13,c31,c68,c411]) ).
cnf(c413,plain,
composition(join(X,X),Y) = composition(X,join(Y,Y)),
inference(equational,[status(thm)],[c2,c13,c412]) ).
cnf(c422,plain,
join(X,composition(sk1,join(X,X))) = X,
inference(equational,[status(thm)],[c6,c30,c301,c413]) ).
cnf(c423,plain,
join(X,composition(sk2,join(X,X))) = X,
inference(equational,[status(thm)],[c4,c30,c299,c413]) ).
cnf(c424,plain,
converse(join(composition(X,Y),composition(X,Z))) = converse(composition(X,join(Y,Z))),
inference(equational,[status(thm)],[c2,c411]) ).
cnf(c425,plain,
join(composition(X,Y),composition(X,Z)) = composition(X,join(Y,Z)),
inference(equational,[status(thm)],[c2,c424]) ).
cnf(c441,plain,
join(X,composition(Y,join(X,X))) = composition(join(one,join(Y,Y)),X),
inference(equational,[status(thm)],[c69,c413]) ).
cnf(c475,plain,
join(X,join(Y,X)) = join(composition(join(one,one),X),Y),
inference(equational,[status(thm)],[c28,c29,c381]) ).
cnf(c498,plain,
join(X,converse(complement(converse(composition(sk2,X))))) = top,
inference(equational,[status(thm)],[c5,c71,c336]) ).
cnf(c662,plain,
join(X,composition(sk1,join(X,Y))) = join(X,composition(sk1,Y)),
inference(equational,[status(thm)],[c303,c425]) ).
cnf(c663,plain,
join(X,composition(sk1,complement(X))) = join(X,composition(sk1,top)),
inference(equational,[status(thm)],[c11,c662]) ).
cnf(c664,plain,
join(X,composition(sk2,join(X,Y))) = join(X,composition(sk2,Y)),
inference(equational,[status(thm)],[c302,c425]) ).
cnf(c665,plain,
join(X,composition(sk2,complement(X))) = join(X,composition(sk2,top)),
inference(equational,[status(thm)],[c11,c664]) ).
cnf(c669,plain,
join(X,composition(sk2,join(Y,X))) = join(composition(sk2,Y),X),
inference(equational,[status(thm)],[c307,c425]) ).
cnf(c670,plain,
join(complement(sk1),composition(sk2,top)) = join(sk2,complement(sk1)),
inference(equational,[status(thm)],[c1,c43,c258,c669]) ).
cnf(c671,plain,
join(X,composition(sk1,join(Y,X))) = join(composition(sk1,Y),X),
inference(equational,[status(thm)],[c304,c425]) ).
cnf(c672,plain,
join(complement(sk2),composition(sk1,top)) = join(sk1,complement(sk2)),
inference(equational,[status(thm)],[c1,c45,c258,c671]) ).
cnf(c681,plain,
join(X,composition(converse(sk2),join(X,X))) = X,
inference(equational,[status(thm)],[c7,c29,c30,c53,c172,c441]) ).
cnf(c694,plain,
join(complement(one),complement(composition(X,complement(converse(X))))) = top,
inference(equational,[status(thm)],[c5,c219,c256,c268]) ).
cnf(c695,plain,
meet(one,composition(X,complement(converse(X)))) = zero,
inference(equational,[status(thm)],[c34,c35,c694]) ).
cnf(c787,plain,
join(converse(X),complement(converse(composition(sk2,X)))) = top,
inference(equational,[status(thm)],[c25,c259,c498]) ).
cnf(c932,plain,
join(X,composition(X,join(complement(one),Y))) = composition(X,top),
inference(equational,[status(thm)],[c2,c29,c168,c238,c258]) ).
cnf(c944,axiom,
X = join(complement(join(complement(X),complement(Y))),complement(join(complement(X),Y))),
file('theBenchmark.p',maddux3_a_kind_of_de_Morgan_3) ).
cnf(c945,plain,
join(meet(X,Y),complement(join(complement(X),Y))) = X,
inference(equational,[status(thm)],[c34,c944]) ).
cnf(c946,plain,
join(zero,complement(complement(X))) = X,
inference(equational,[status(thm)],[c9,c253,c945]) ).
cnf(c948,plain,
join(zero,X) = X,
inference(equational,[status(thm)],[c262,c946]) ).
cnf(c950,plain,
join(X,zero) = X,
inference(equational,[status(thm)],[c5,c948]) ).
cnf(c951,plain,
complement(complement(X)) = X,
inference(equational,[status(thm)],[c946,c948]) ).
cnf(c954,plain,
join(X,X) = X,
inference(equational,[status(thm)],[c253,c951]) ).
cnf(c955,plain,
meet(top,X) = X,
inference(equational,[status(thm)],[c40,c948,c951]) ).
cnf(c956,plain,
meet(X,top) = X,
inference(equational,[status(thm)],[c36,c955]) ).
cnf(c957,plain,
join(X,meet(X,Y)) = X,
inference(equational,[status(thm)],[c5,c322,c380,c945]) ).
cnf(c962,plain,
join(complement(X),complement(Y)) = complement(meet(X,Y)),
inference(equational,[status(thm)],[c34,c946,c948]) ).
cnf(c963,plain,
complement(meet(complement(X),Y)) = join(X,complement(Y)),
inference(equational,[status(thm)],[c40,c948,c955,c962]) ).
cnf(c964,plain,
complement(meet(X,complement(Y))) = join(complement(X),Y),
inference(equational,[status(thm)],[c40,c948,c955,c962]) ).
cnf(c965,plain,
join(X,complement(meet(Y,X))) = top,
inference(equational,[status(thm)],[c66,c256,c962]) ).
cnf(c966,plain,
join(X,complement(meet(X,Y))) = top,
inference(equational,[status(thm)],[c49,c256,c962]) ).
cnf(c967,plain,
complement(join(X,complement(Y))) = meet(complement(X),Y),
inference(equational,[status(thm)],[c946,c948,c963]) ).
cnf(c968,plain,
meet(sk2,complement(one)) = zero,
inference(equational,[status(thm)],[c35,c36,c313,c954,c967]) ).
cnf(c969,plain,
meet(one,sk2) = sk2,
inference(equational,[status(thm)],[c36,c945,c948,c951,c962,c968]) ).
cnf(c970,plain,
meet(sk1,complement(one)) = zero,
inference(equational,[status(thm)],[c35,c36,c311,c954,c967]) ).
cnf(c971,plain,
meet(one,sk1) = sk1,
inference(equational,[status(thm)],[c36,c945,c948,c951,c962,c970]) ).
cnf(c972,plain,
meet(X,join(complement(Y),X)) = X,
inference(equational,[status(thm)],[c35,c945,c950,c964,c965]) ).
cnf(c973,plain,
meet(X,join(Y,X)) = X,
inference(equational,[status(thm)],[c40,c955,c972]) ).
cnf(c974,plain,
meet(X,join(X,complement(Y))) = X,
inference(equational,[status(thm)],[c35,c945,c950,c963,c966]) ).
cnf(c975,plain,
meet(X,join(X,Y)) = X,
inference(equational,[status(thm)],[c40,c955,c974]) ).
cnf(c978,plain,
meet(X,meet(X,Y)) = meet(X,Y),
inference(equational,[status(thm)],[c36,c945,c974]) ).
cnf(c982,plain,
meet(complement(one),converse(sk1)) = zero,
inference(equational,[status(thm)],[c35,c93,c258,c967]) ).
cnf(c983,plain,
join(meet(X,Y),meet(X,complement(Y))) = X,
inference(equational,[status(thm)],[c5,c34,c945]) ).
cnf(c984,plain,
join(X,meet(Y,X)) = X,
inference(equational,[status(thm)],[c36,c957]) ).
cnf(c992,plain,
meet(X,composition(X,top)) = X,
inference(equational,[status(thm)],[c932,c975]) ).
cnf(c995,plain,
join(one,complement(meet(X,sk1))) = top,
inference(equational,[status(thm)],[c104,c258,c962]) ).
cnf(c996,plain,
join(one,complement(meet(X,sk2))) = top,
inference(equational,[status(thm)],[c103,c258,c962]) ).
cnf(c998,plain,
complement(join(complement(X),Y)) = meet(complement(Y),X),
inference(equational,[status(thm)],[c5,c967]) ).
cnf(c1003,plain,
join(X,join(Y,X)) = join(X,Y),
inference(equational,[status(thm)],[c30,c475,c954]) ).
cnf(c1013,plain,
join(meet(X,Y),meet(complement(Y),X)) = X,
inference(equational,[status(thm)],[c36,c983]) ).
cnf(c1014,plain,
meet(one,converse(sk1)) = converse(sk1),
inference(equational,[status(thm)],[c36,c950,c982,c1013]) ).
cnf(c1016,plain,
join(meet(X,Y),meet(Y,complement(X))) = Y,
inference(equational,[status(thm)],[c36,c983]) ).
cnf(c1019,plain,
meet(X,composition(sk2,X)) = composition(sk2,X),
inference(equational,[status(thm)],[c36,c423,c954,c973]) ).
cnf(c1020,plain,
meet(X,composition(sk1,X)) = composition(sk1,X),
inference(equational,[status(thm)],[c36,c422,c954,c973]) ).
cnf(c1021,plain,
meet(complement(one),meet(X,sk2)) = zero,
inference(equational,[status(thm)],[c35,c967,c996]) ).
cnf(c1023,plain,
meet(complement(one),meet(X,sk1)) = zero,
inference(equational,[status(thm)],[c35,c967,c995]) ).
cnf(c1025,plain,
meet(one,meet(X,sk1)) = meet(X,sk1),
inference(equational,[status(thm)],[c36,c950,c1013,c1023]) ).
cnf(c1027,plain,
meet(one,meet(X,sk2)) = meet(X,sk2),
inference(equational,[status(thm)],[c36,c950,c1013,c1021]) ).
cnf(c1040,plain,
join(meet(X,Y),meet(complement(X),Y)) = Y,
inference(equational,[status(thm)],[c36,c1016]) ).
cnf(c1052,plain,
meet(one,meet(sk1,X)) = meet(X,sk1),
inference(equational,[status(thm)],[c36,c1025]) ).
cnf(c1053,plain,
join(complement(X),join(complement(Y),Z)) = join(complement(meet(X,Y)),Z),
inference(equational,[status(thm)],[c17,c962]) ).
cnf(c1054,plain,
complement(meet(meet(X,Y),Z)) = complement(meet(X,meet(Y,Z))),
inference(equational,[status(thm)],[c962,c1053]) ).
cnf(c1055,plain,
meet(meet(X,Y),Z) = meet(X,meet(Y,Z)),
inference(equational,[status(thm)],[c946,c948,c951,c1054]) ).
cnf(c1056,plain,
meet(X,meet(Y,Z)) = meet(Y,meet(X,Z)),
inference(equational,[status(thm)],[c36,c1055]) ).
cnf(c1063,plain,
join(meet(complement(X),Y),complement(Z)) = complement(meet(join(X,complement(Y)),Z)),
inference(equational,[status(thm)],[c139,c948,c955,c962]) ).
cnf(c1091,plain,
meet(X,composition(X,converse(sk2))) = composition(X,converse(sk2)),
inference(equational,[status(thm)],[c36,c102,c973]) ).
cnf(c1099,plain,
join(X,converse(meet(converse(X),Y))) = X,
inference(equational,[status(thm)],[c2,c26,c957]) ).
cnf(c1139,plain,
meet(complement(X),meet(complement(Y),Z)) = complement(join(X,join(Y,complement(Z)))),
inference(equational,[status(thm)],[c140,c948,c956,c963]) ).
cnf(c1157,plain,
join(X,join(meet(X,Y),Z)) = join(X,Z),
inference(equational,[status(thm)],[c17,c957]) ).
cnf(c1158,plain,
join(X,meet(complement(X),Y)) = join(X,Y),
inference(equational,[status(thm)],[c1040,c1157]) ).
cnf(c1165,plain,
join(X,join(Y,meet(X,Z))) = join(Y,X),
inference(equational,[status(thm)],[c32,c957]) ).
cnf(c1166,plain,
join(complement(X),meet(Y,X)) = join(complement(X),Y),
inference(equational,[status(thm)],[c5,c1013,c1165]) ).
cnf(c1168,plain,
join(converse(X),complement(converse(meet(X,complement(Y))))) = top,
inference(equational,[status(thm)],[c5,c218,c258,c983]) ).
cnf(c1169,plain,
join(converse(X),complement(converse(meet(X,Y)))) = top,
inference(equational,[status(thm)],[c40,c955,c1168]) ).
cnf(c1193,plain,
meet(X,composition(converse(sk2),X)) = composition(converse(sk2),X),
inference(equational,[status(thm)],[c36,c681,c954,c973]) ).
cnf(c1196,plain,
meet(complement(converse(X)),converse(meet(X,Y))) = zero,
inference(equational,[status(thm)],[c35,c967,c1169]) ).
cnf(c1212,plain,
join(X,converse(meet(Y,converse(X)))) = X,
inference(equational,[status(thm)],[c2,c26,c984]) ).
cnf(c1242,plain,
meet(one,meet(converse(sk1),X)) = meet(converse(sk1),X),
inference(equational,[status(thm)],[c1014,c1055]) ).
cnf(c1257,plain,
meet(converse(X),converse(meet(X,Y))) = converse(meet(X,Y)),
inference(equational,[status(thm)],[c948,c951,c1040,c1196]) ).
cnf(c1259,plain,
meet(one,converse(meet(X,sk2))) = converse(meet(X,sk2)),
inference(equational,[status(thm)],[c29,c1027,c1257]) ).
cnf(c1297,plain,
meet(X,meet(complement(Y),join(complement(X),Y))) = zero,
inference(equational,[status(thm)],[c9,c964,c1055]) ).
cnf(c1298,plain,
meet(complement(X),join(complement(Y),X)) = complement(join(Y,X)),
inference(equational,[status(thm)],[c948,c998,c1003,c1040,c1139,c1158,c1297]) ).
cnf(c1299,plain,
meet(X,complement(meet(Y,X))) = meet(complement(Y),X),
inference(equational,[status(thm)],[c40,c948,c955,c962,c967,c1298]) ).
cnf(c1300,plain,
meet(complement(X),join(Y,X)) = meet(complement(X),Y),
inference(equational,[status(thm)],[c40,c948,c955,c998,c1298]) ).
cnf(c1302,plain,
meet(X,join(Y,complement(X))) = meet(Y,X),
inference(equational,[status(thm)],[c951,c963,c1299]) ).
cnf(c1305,plain,
meet(complement(X),join(X,Y)) = meet(complement(X),Y),
inference(equational,[status(thm)],[c5,c1300]) ).
cnf(c1306,plain,
meet(one,composition(sk2,top)) = sk2,
inference(equational,[status(thm)],[c36,c366,c951,c969,c1302,c1305]) ).
cnf(c1307,plain,
meet(sk1,composition(sk2,top)) = meet(sk1,sk2),
inference(equational,[status(thm)],[c36,c670,c951,c1302,c1305]) ).
cnf(c1308,plain,
meet(one,composition(sk1,top)) = sk1,
inference(equational,[status(thm)],[c36,c364,c951,c971,c1302,c1305]) ).
cnf(c1309,plain,
meet(sk2,composition(sk1,top)) = meet(sk1,sk2),
inference(equational,[status(thm)],[c672,c951,c1302,c1305]) ).
cnf(c1313,plain,
meet(X,join(complement(X),Y)) = meet(X,Y),
inference(equational,[status(thm)],[c951,c1305]) ).
cnf(c1314,plain,
meet(X,composition(sk1,top)) = composition(sk1,X),
inference(equational,[status(thm)],[c663,c951,c1020,c1313]) ).
cnf(c1316,plain,
composition(sk1,sk2) = meet(sk1,sk2),
inference(equational,[status(thm)],[c1309,c1314]) ).
cnf(c1317,plain,
meet(X,composition(sk2,top)) = composition(sk2,X),
inference(equational,[status(thm)],[c665,c951,c1019,c1313]) ).
cnf(c1319,plain,
composition(sk2,sk1) = meet(sk1,sk2),
inference(equational,[status(thm)],[c1307,c1317]) ).
cnf(c1401,plain,
complement(meet(join(X,Y),join(X,complement(Y)))) = complement(X),
inference(equational,[status(thm)],[c36,c945,c951,c1063]) ).
cnf(c1402,plain,
meet(join(X,Y),join(X,complement(Y))) = X,
inference(equational,[status(thm)],[c946,c948,c951,c1401]) ).
cnf(c1465,plain,
meet(X,meet(Y,composition(X,top))) = meet(Y,X),
inference(equational,[status(thm)],[c992,c1056]) ).
cnf(c1466,plain,
meet(sk1,composition(sk1,X)) = meet(X,sk1),
inference(equational,[status(thm)],[c36,c1025,c1052,c1314,c1465]) ).
cnf(c1469,plain,
composition(sk1,converse(sk2)) = meet(sk1,converse(sk2)),
inference(equational,[status(thm)],[c36,c1091,c1466]) ).
cnf(c1529,plain,
join(X,meet(complement(one),join(sk1,X))) = X,
inference(equational,[status(thm)],[c334,c955,c967,c1402]) ).
cnf(c1617,plain,
join(meet(X,Y),join(meet(complement(Y),X),Z)) = join(X,Z),
inference(equational,[status(thm)],[c17,c945,c998]) ).
cnf(c1618,plain,
join(meet(X,Y),join(Z,meet(complement(Y),X))) = join(X,Z),
inference(equational,[status(thm)],[c5,c1617]) ).
cnf(c1621,plain,
join(X,meet(one,join(sk1,X))) = join(sk1,X),
inference(equational,[status(thm)],[c5,c17,c36,c954,c1529,c1618]) ).
cnf(c1623,plain,
meet(X,meet(Y,meet(X,Z))) = meet(X,meet(Y,Z)),
inference(equational,[status(thm)],[c978,c1056]) ).
cnf(c1624,plain,
meet(one,composition(sk1,X)) = meet(X,sk1),
inference(equational,[status(thm)],[c1025,c1308,c1314,c1623]) ).
cnf(c1625,plain,
meet(one,composition(sk2,X)) = meet(X,sk2),
inference(equational,[status(thm)],[c1027,c1306,c1317,c1623]) ).
cnf(c1626,plain,
meet(sk1,complement(converse(sk1))) = zero,
inference(equational,[status(thm)],[c36,c695,c1624]) ).
cnf(c1627,plain,
meet(sk1,converse(sk1)) = sk1,
inference(equational,[status(thm)],[c36,c950,c1016,c1626]) ).
cnf(c1628,plain,
join(sk1,converse(sk1)) = converse(sk1),
inference(equational,[status(thm)],[c5,c950,c951,c1166,c1626]) ).
cnf(c1629,plain,
meet(sk2,complement(converse(sk2))) = zero,
inference(equational,[status(thm)],[c36,c695,c1625]) ).
cnf(c1631,plain,
join(sk2,converse(sk2)) = converse(sk2),
inference(equational,[status(thm)],[c5,c950,c951,c1166,c1629]) ).
cnf(c1632,plain,
converse(sk2) = sk2,
inference(equational,[status(thm)],[c2,c5,c25,c1631]) ).
cnf(c1633,plain,
converse(sk1) = sk1,
inference(equational,[status(thm)],[c1212,c1627,c1628]) ).
cnf(c1651,plain,
meet(X,composition(sk2,Y)) = meet(Y,composition(sk2,X)),
inference(equational,[status(thm)],[c1056,c1317]) ).
cnf(c1689,plain,
meet(converse(X),converse(composition(sk2,X))) = converse(composition(sk2,X)),
inference(equational,[status(thm)],[c36,c787,c951,c956,c1300]) ).
cnf(c1691,plain,
meet(sk1,converse(meet(sk1,sk2))) = converse(meet(sk1,sk2)),
inference(equational,[status(thm)],[c1242,c1259,c1319,c1633,c1689]) ).
cnf(c1692,plain,
join(sk1,converse(meet(sk1,sk2))) = sk1,
inference(equational,[status(thm)],[c5,c1013,c1158,c1691]) ).
cnf(c1693,plain,
composition(converse(X),sk1) = converse(composition(sk1,X)),
inference(equational,[status(thm)],[c145,c957,c1633,c1692]) ).
cnf(c1696,plain,
converse(meet(sk1,sk2)) = meet(sk1,sk2),
inference(equational,[status(thm)],[c1193,c1316,c1319,c1632,c1691,c1693]) ).
cnf(c1732,plain,
join(sk1,converse(meet(sk1,X))) = sk1,
inference(equational,[status(thm)],[c5,c971,c1099,c1621,c1633]) ).
cnf(c1749,plain,
composition(converse(composition(join(X,converse(Y)),Z)),W) = composition(converse(Z),composition(join(converse(X),Y),W)),
inference(equational,[status(thm)],[c25,c89]) ).
cnf(c2073,plain,
meet(X,composition(sk2,composition(sk1,X))) = composition(sk2,composition(sk1,X)),
inference(equational,[status(thm)],[c36,c346,c973]) ).
cnf(c2830,plain,
composition(converse(composition(sk1,X)),Y) = composition(converse(X),composition(sk1,Y)),
inference(equational,[status(thm)],[c957,c1633,c1732,c1749]) ).
cnf(c2831,plain,
composition(meet(sk1,sk2),X) = composition(sk2,composition(sk1,X)),
inference(equational,[status(thm)],[c1469,c1632,c1696,c2830]) ).
cnf(g1,plain,
tuple(join(meet(composition(sk1,sk3),composition(sk2,sk3)),composition(meet(sk1,sk2),sk3)),join(composition(meet(sk1,sk2),sk3),meet(composition(sk1,sk3),composition(sk2,sk3)))) = tuple(composition(meet(sk1,sk2),sk3),meet(composition(sk1,sk3),composition(sk2,sk3))),
inference(equational,[status(thm)],[c5,c269,c383,c1319,c1651,c2073,c2831]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : REL029-10 : TPTP v9.0.0. Released v7.3.0.
% 0.07/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.32 % Computer : n015.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 16:13:04 EDT 2025
% 0.12/0.33 % CPUTime :
% 219.41/219.55 % SZS status Unsatisfiable
% 219.41/219.55 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------