%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : REL024-2 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n011.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 07:41:21 AM UTC 2025
% Result : Unsatisfiable 65.72s 65.74s
% Output : CNFRefutation 65.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of clauses : 46 ( 46 unt; 0 nHn; 4 RR)
% Number of literals : 46 ( 45 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 : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 93 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
join(composition(meet(sk1,converse(sk2)),meet(sk2,sk3)),composition(meet(sk1,converse(sk2)),sk3)) != composition(meet(sk1,converse(sk2)),sk3),
file('theBenchmark.p',goals_17) ).
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(X,Y) = join(Y,X),
file('REL001-0.ax',maddux1_join_commutativity_1) ).
cnf(c8,axiom,
converse(composition(X,Y)) = composition(converse(Y),converse(X)),
file('REL001-0.ax',converse_multiplicativity_10) ).
cnf(c9,plain,
composition(converse(X),converse(Y)) = converse(composition(Y,X)),
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,
composition(X,composition(Y,Z)) = composition(composition(X,Y),Z),
file('REL001-0.ax',composition_associativity_5) ).
cnf(c13,plain,
composition(composition(X,Y),Z) = composition(X,composition(Y,Z)),
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,plain,
composition(X,composition(one,Y)) = composition(X,Y),
inference(equational,[status(thm)],[c1,c13]) ).
cnf(c17,plain,
converse(join(X,converse(Y))) = join(converse(X),Y),
inference(equational,[status(thm)],[c2,c11]) ).
cnf(c18,plain,
converse(join(converse(X),Y)) = join(X,converse(Y)),
inference(equational,[status(thm)],[c2,c11]) ).
cnf(c19,plain,
converse(composition(converse(X),Y)) = composition(converse(Y),X),
inference(equational,[status(thm)],[c2,c9]) ).
cnf(c20,plain,
composition(converse(one),X) = X,
inference(equational,[status(thm)],[c1,c2,c19]) ).
cnf(c21,plain,
converse(one) = one,
inference(equational,[status(thm)],[c1,c20]) ).
cnf(c22,plain,
composition(one,X) = X,
inference(equational,[status(thm)],[c16,c20]) ).
cnf(c23,plain,
converse(composition(X,converse(Y))) = composition(Y,converse(X)),
inference(equational,[status(thm)],[c2,c9]) ).
cnf(c24,plain,
join(X,join(Y,Z)) = join(Y,join(X,Z)),
inference(equational,[status(thm)],[c3,c15]) ).
cnf(c25,axiom,
meet(X,Y) = complement(join(complement(X),complement(Y))),
file('REL001-0.ax',maddux4_definiton_of_meet_4) ).
cnf(c26,plain,
complement(join(complement(X),complement(Y))) = meet(X,Y),
inference(equational,[status(thm)],[c25]) ).
cnf(c28,plain,
meet(X,Y) = meet(Y,X),
inference(equational,[status(thm)],[c3,c26]) ).
cnf(c41,axiom,
composition(join(X,Y),Z) = join(composition(X,Z),composition(Y,Z)),
file('REL001-0.ax',composition_distributivity_7) ).
cnf(c42,plain,
join(composition(X,Y),composition(Z,Y)) = composition(join(X,Z),Y),
inference(equational,[status(thm)],[c41]) ).
cnf(c44,plain,
join(X,composition(Y,X)) = composition(join(Y,one),X),
inference(equational,[status(thm)],[c3,c20,c21,c42]) ).
cnf(c46,plain,
join(X,X) = composition(join(one,one),X),
inference(equational,[status(thm)],[c20,c21,c44]) ).
cnf(c80,plain,
composition(join(X,converse(Y)),converse(Z)) = converse(composition(Z,join(converse(X),Y))),
inference(equational,[status(thm)],[c17,c23]) ).
cnf(c83,plain,
join(composition(X,converse(Y)),converse(Z)) = converse(join(composition(Y,converse(X)),Z)),
inference(equational,[status(thm)],[c18,c23]) ).
cnf(c121,axiom,
join(composition(converse(X),complement(composition(X,Y))),complement(Y)) = complement(Y),
file('REL001-0.ax',converse_cancellativity_11) ).
cnf(c122,plain,
join(complement(X),composition(converse(Y),complement(composition(Y,X)))) = complement(X),
inference(equational,[status(thm)],[c3,c121]) ).
cnf(c123,plain,
join(complement(X),complement(X)) = complement(X),
inference(equational,[status(thm)],[c20,c22,c122]) ).
cnf(c141,plain,
join(meet(X,Y),meet(X,Y)) = meet(X,Y),
inference(equational,[status(thm)],[c26,c123]) ).
cnf(c180,plain,
composition(join(one,one),meet(X,Y)) = meet(X,Y),
inference(equational,[status(thm)],[c46,c141]) ).
cnf(c192,plain,
join(composition(X,Y),join(composition(Z,Y),W)) = join(composition(join(X,Z),Y),W),
inference(equational,[status(thm)],[c15,c42]) ).
cnf(c193,plain,
join(X,join(composition(Y,X),Z)) = join(composition(join(Y,one),X),Z),
inference(equational,[status(thm)],[c20,c21,c24,c192]) ).
cnf(c197,plain,
join(X,join(X,Y)) = join(composition(join(one,one),X),Y),
inference(equational,[status(thm)],[c20,c21,c193]) ).
cnf(c216,plain,
converse(join(composition(X,converse(Y)),composition(X,Z))) = converse(composition(X,join(converse(Y),Z))),
inference(equational,[status(thm)],[c9,c42,c80,c83]) ).
cnf(c227,plain,
converse(join(composition(X,Y),composition(X,Z))) = converse(composition(X,join(Y,Z))),
inference(equational,[status(thm)],[c2,c216]) ).
cnf(c228,plain,
join(composition(X,Y),composition(X,Z)) = composition(X,join(Y,Z)),
inference(equational,[status(thm)],[c2,c227]) ).
cnf(c499,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(c500,plain,
join(meet(X,Y),complement(join(complement(X),Y))) = X,
inference(equational,[status(thm)],[c26,c499]) ).
cnf(c513,plain,
join(X,meet(X,Y)) = X,
inference(equational,[status(thm)],[c3,c180,c197,c500]) ).
cnf(g1,plain,
join(composition(meet(sk1,converse(sk2)),meet(sk2,sk3)),composition(meet(sk1,converse(sk2)),sk3)) = composition(meet(sk1,converse(sk2)),sk3),
inference(equational,[status(thm)],[c3,c28,c228,c513]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : REL024-2 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.33 % Computer : n011.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Mon Jul 14 16:11:34 EDT 2025
% 0.11/0.33 % CPUTime :
% 65.72/65.74 % SZS status Unsatisfiable
% 65.72/65.74 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------