%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : REL012-1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n002.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 07:41:18 AM UTC 2025
% Result : Unsatisfiable 66.27s 66.53s
% Output : CNFRefutation 66.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 14
% Syntax : Number of clauses : 87 ( 87 unt; 0 nHn; 7 RR)
% Number of literals : 87 ( 86 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 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 : 150 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
join(composition(complement(composition(sk1,sk2)),converse(sk2)),complement(sk1)) != complement(sk1),
file('theBenchmark.p',goals_14) ).
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(c4,axiom,
top = join(X,complement(X)),
file('REL001-0.ax',def_top_12) ).
cnf(c5,plain,
join(X,complement(X)) = top,
inference(equational,[status(thm)],[c4]) ).
cnf(c6,axiom,
zero = meet(X,complement(X)),
file('REL001-0.ax',def_zero_13) ).
cnf(c7,plain,
meet(X,complement(X)) = zero,
inference(equational,[status(thm)],[c6]) ).
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(X,converse(Y))) = composition(Y,converse(X)),
inference(equational,[status(thm)],[c2,c9]) ).
cnf(c20,plain,
converse(composition(converse(X),Y)) = composition(converse(Y),X),
inference(equational,[status(thm)],[c2,c9]) ).
cnf(c21,plain,
composition(converse(one),X) = X,
inference(equational,[status(thm)],[c1,c2,c20]) ).
cnf(c22,plain,
converse(one) = one,
inference(equational,[status(thm)],[c1,c21]) ).
cnf(c23,plain,
composition(one,X) = X,
inference(equational,[status(thm)],[c16,c21]) ).
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(c27,plain,
complement(top) = zero,
inference(equational,[status(thm)],[c5,c7,c26]) ).
cnf(c28,plain,
meet(X,Y) = meet(Y,X),
inference(equational,[status(thm)],[c3,c26]) ).
cnf(c33,plain,
join(X,join(complement(X),Y)) = join(top,Y),
inference(equational,[status(thm)],[c5,c15]) ).
cnf(c34,plain,
join(top,complement(complement(X))) = join(X,top),
inference(equational,[status(thm)],[c5,c33]) ).
cnf(c39,plain,
join(X,converse(complement(converse(X)))) = converse(top),
inference(equational,[status(thm)],[c5,c18]) ).
cnf(c40,plain,
join(X,join(Y,complement(X))) = join(Y,top),
inference(equational,[status(thm)],[c5,c24]) ).
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(c52,plain,
complement(join(complement(X),meet(Y,Z))) = meet(X,join(complement(Y),complement(Z))),
inference(equational,[status(thm)],[c26]) ).
cnf(c53,plain,
complement(join(meet(X,Y),complement(Z))) = meet(join(complement(X),complement(Y)),Z),
inference(equational,[status(thm)],[c26]) ).
cnf(c75,plain,
join(converse(X),composition(Y,converse(Z))) = converse(join(X,composition(Z,converse(Y)))),
inference(equational,[status(thm)],[c17,c19]) ).
cnf(c76,plain,
composition(join(converse(X),Y),converse(Z)) = converse(composition(Z,join(X,converse(Y)))),
inference(equational,[status(thm)],[c18,c19]) ).
cnf(c102,plain,
join(X,converse(join(complement(converse(X)),Y))) = converse(join(top,Y)),
inference(equational,[status(thm)],[c18,c33]) ).
cnf(c114,axiom,
join(composition(converse(X),complement(composition(X,Y))),complement(Y)) = complement(Y),
file('REL001-0.ax',converse_cancellativity_11) ).
cnf(c115,plain,
join(complement(X),composition(converse(Y),complement(composition(Y,X)))) = complement(X),
inference(equational,[status(thm)],[c3,c114]) ).
cnf(c116,plain,
join(complement(X),complement(X)) = complement(X),
inference(equational,[status(thm)],[c21,c23,c115]) ).
cnf(c117,plain,
join(zero,zero) = zero,
inference(equational,[status(thm)],[c27,c116]) ).
cnf(c120,plain,
join(top,complement(X)) = top,
inference(equational,[status(thm)],[c3,c5,c40,c116]) ).
cnf(c121,plain,
join(X,top) = top,
inference(equational,[status(thm)],[c34,c120]) ).
cnf(c122,plain,
join(top,X) = top,
inference(equational,[status(thm)],[c3,c121]) ).
cnf(c123,plain,
converse(top) = top,
inference(equational,[status(thm)],[c102,c122]) ).
cnf(c126,plain,
join(zero,join(zero,X)) = join(zero,X),
inference(equational,[status(thm)],[c15,c117]) ).
cnf(c181,plain,
join(composition(X,Y),join(composition(Z,Y),W)) = join(composition(join(X,Z),Y),W),
inference(equational,[status(thm)],[c15,c42]) ).
cnf(c182,plain,
join(X,join(composition(Y,X),Z)) = join(composition(join(Y,one),X),Z),
inference(equational,[status(thm)],[c21,c22,c24,c181]) ).
cnf(c187,plain,
join(X,join(X,Y)) = join(composition(join(one,one),X),Y),
inference(equational,[status(thm)],[c21,c22,c182]) ).
cnf(c195,plain,
converse(join(composition(X,Y),composition(X,converse(Z)))) = converse(composition(X,join(Y,converse(Z)))),
inference(equational,[status(thm)],[c9,c42,c75,c76]) ).
cnf(c196,plain,
composition(X,converse(join(Y,Y))) = composition(join(X,X),converse(Y)),
inference(equational,[status(thm)],[c11,c19,c42,c195]) ).
cnf(c197,plain,
composition(join(X,X),Y) = composition(X,join(Y,Y)),
inference(equational,[status(thm)],[c2,c11,c196]) ).
cnf(c201,plain,
composition(join(X,X),complement(Y)) = composition(X,complement(Y)),
inference(equational,[status(thm)],[c116,c197]) ).
cnf(c217,plain,
composition(join(X,X),meet(Y,Z)) = composition(X,meet(Y,Z)),
inference(equational,[status(thm)],[c26,c201]) ).
cnf(c436,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(c437,plain,
join(meet(X,Y),complement(join(complement(X),Y))) = X,
inference(equational,[status(thm)],[c26,c436]) ).
cnf(c438,plain,
join(zero,complement(complement(X))) = X,
inference(equational,[status(thm)],[c7,c116,c437]) ).
cnf(c441,plain,
join(zero,X) = X,
inference(equational,[status(thm)],[c126,c438]) ).
cnf(c443,plain,
join(X,zero) = X,
inference(equational,[status(thm)],[c3,c441]) ).
cnf(c444,plain,
complement(complement(X)) = X,
inference(equational,[status(thm)],[c438,c441]) ).
cnf(c448,plain,
meet(X,X) = X,
inference(equational,[status(thm)],[c5,c27,c437,c443,c444]) ).
cnf(c449,plain,
complement(join(X,complement(Y))) = meet(complement(X),Y),
inference(equational,[status(thm)],[c53,c116,c448]) ).
cnf(c455,plain,
complement(join(complement(X),Y)) = meet(X,complement(Y)),
inference(equational,[status(thm)],[c52,c116,c448]) ).
cnf(c456,plain,
complement(meet(complement(X),Y)) = join(X,complement(Y)),
inference(equational,[status(thm)],[c438,c441,c449]) ).
cnf(c462,plain,
join(X,meet(X,Y)) = X,
inference(equational,[status(thm)],[c3,c23,c187,c217,c437]) ).
cnf(c469,plain,
join(meet(X,Y),meet(X,complement(Y))) = X,
inference(equational,[status(thm)],[c3,c26,c437]) ).
cnf(c470,plain,
join(X,meet(Y,X)) = X,
inference(equational,[status(thm)],[c28,c462]) ).
cnf(c478,plain,
join(meet(X,Y),meet(Y,complement(X))) = Y,
inference(equational,[status(thm)],[c28,c469]) ).
cnf(c479,plain,
join(meet(X,Y),meet(complement(Y),X)) = X,
inference(equational,[status(thm)],[c28,c469]) ).
cnf(c501,plain,
meet(X,complement(converse(complement(converse(complement(X)))))) = zero,
inference(equational,[status(thm)],[c27,c39,c123,c455]) ).
cnf(c502,plain,
meet(X,converse(complement(converse(complement(X))))) = X,
inference(equational,[status(thm)],[c28,c443,c478,c501]) ).
cnf(c505,plain,
join(X,complement(converse(complement(converse(X))))) = X,
inference(equational,[status(thm)],[c444,c456,c502]) ).
cnf(c509,plain,
complement(join(X,meet(Y,complement(Z)))) = meet(complement(X),join(complement(Y),Z)),
inference(equational,[status(thm)],[c449,c455]) ).
cnf(c510,plain,
meet(join(X,Y),join(Y,complement(X))) = Y,
inference(equational,[status(thm)],[c28,c444,c456,c479,c509]) ).
cnf(c512,plain,
meet(X,join(complement(X),Y)) = meet(X,Y),
inference(equational,[status(thm)],[c15,c28,c437,c470,c510]) ).
cnf(c514,plain,
meet(X,join(Y,complement(X))) = meet(X,Y),
inference(equational,[status(thm)],[c3,c512]) ).
cnf(c546,plain,
join(X,converse(complement(converse(complement(X))))) = X,
inference(equational,[status(thm)],[c2,c18,c505]) ).
cnf(c547,plain,
converse(complement(converse(complement(X)))) = X,
inference(equational,[status(thm)],[c502,c510,c514,c546]) ).
cnf(c548,plain,
complement(converse(complement(X))) = converse(X),
inference(equational,[status(thm)],[c2,c547]) ).
cnf(c549,plain,
complement(converse(X)) = converse(complement(X)),
inference(equational,[status(thm)],[c444,c548]) ).
cnf(c751,plain,
converse(join(complement(X),composition(complement(composition(X,Y)),converse(Y)))) = converse(complement(X)),
inference(equational,[status(thm)],[c2,c9,c75,c115,c549]) ).
cnf(c752,plain,
join(complement(X),composition(complement(composition(X,Y)),converse(Y))) = complement(X),
inference(equational,[status(thm)],[c2,c751]) ).
cnf(g1,plain,
join(composition(complement(composition(sk1,sk2)),converse(sk2)),complement(sk1)) = complement(sk1),
inference(equational,[status(thm)],[c3,c752]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : REL012-1 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.11 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n002.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 16:08:34 EDT 2025
% 0.11/0.32 % CPUTime :
% 66.27/66.53 % SZS status Unsatisfiable
% 66.27/66.53 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------