%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : REL004-2 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n006.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 07:41:15 AM UTC 2025
% Result : Unsatisfiable 66.21s 66.26s
% Output : CNFRefutation 66.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 13
% Syntax : Number of clauses : 82 ( 82 unt; 0 nHn; 6 RR)
% Number of literals : 82 ( 81 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 : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 132 ( 9 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
converse(complement(sk1)) != complement(converse(sk1)),
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(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(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(c22,plain,
composition(one,X) = X,
inference(equational,[status(thm)],[c16,c20]) ).
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(c31,plain,
complement(join(zero,complement(X))) = meet(top,X),
inference(equational,[status(thm)],[c26,c27]) ).
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(c47,plain,
join(X,join(Y,complement(join(X,Y)))) = top,
inference(equational,[status(thm)],[c5,c15]) ).
cnf(c49,plain,
join(converse(X),join(converse(Y),Z)) = join(converse(join(X,Y)),Z),
inference(equational,[status(thm)],[c11,c15]) ).
cnf(c57,plain,
join(X,join(Y,complement(join(Y,X)))) = top,
inference(equational,[status(thm)],[c24,c47]) ).
cnf(c110,plain,
join(complement(converse(X)),converse(join(Y,X))) = join(top,converse(Y)),
inference(equational,[status(thm)],[c3,c5,c49]) ).
cnf(c114,plain,
join(X,converse(join(complement(converse(X)),Y))) = converse(join(top,Y)),
inference(equational,[status(thm)],[c18,c33]) ).
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(c124,plain,
join(zero,zero) = zero,
inference(equational,[status(thm)],[c27,c123]) ).
cnf(c125,plain,
meet(X,X) = complement(complement(X)),
inference(equational,[status(thm)],[c26,c123]) ).
cnf(c126,plain,
join(top,complement(X)) = top,
inference(equational,[status(thm)],[c5,c33,c123]) ).
cnf(c127,plain,
join(X,top) = top,
inference(equational,[status(thm)],[c34,c126]) ).
cnf(c128,plain,
join(top,X) = top,
inference(equational,[status(thm)],[c3,c127]) ).
cnf(c129,plain,
converse(top) = top,
inference(equational,[status(thm)],[c114,c128]) ).
cnf(c132,plain,
join(zero,join(zero,X)) = join(zero,X),
inference(equational,[status(thm)],[c15,c124]) ).
cnf(c474,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(c475,plain,
join(meet(X,Y),complement(join(complement(X),Y))) = X,
inference(equational,[status(thm)],[c26,c474]) ).
cnf(c476,plain,
join(zero,complement(complement(X))) = X,
inference(equational,[status(thm)],[c7,c123,c475]) ).
cnf(c478,plain,
join(zero,X) = X,
inference(equational,[status(thm)],[c132,c476]) ).
cnf(c480,plain,
join(X,zero) = X,
inference(equational,[status(thm)],[c3,c478]) ).
cnf(c481,plain,
complement(complement(X)) = X,
inference(equational,[status(thm)],[c476,c478]) ).
cnf(c483,plain,
meet(top,X) = X,
inference(equational,[status(thm)],[c31,c478,c481]) ).
cnf(c484,plain,
meet(X,top) = X,
inference(equational,[status(thm)],[c28,c483]) ).
cnf(c488,plain,
join(complement(X),complement(Y)) = complement(meet(X,Y)),
inference(equational,[status(thm)],[c26,c476,c478]) ).
cnf(c489,plain,
complement(meet(complement(X),Y)) = join(X,complement(Y)),
inference(equational,[status(thm)],[c31,c478,c483,c488]) ).
cnf(c490,plain,
complement(meet(X,complement(Y))) = join(complement(X),Y),
inference(equational,[status(thm)],[c31,c478,c483,c488]) ).
cnf(c492,plain,
join(X,complement(meet(X,Y))) = top,
inference(equational,[status(thm)],[c33,c126,c488]) ).
cnf(c497,plain,
meet(X,join(X,complement(Y))) = X,
inference(equational,[status(thm)],[c27,c475,c480,c489,c492]) ).
cnf(c498,plain,
meet(X,join(X,Y)) = X,
inference(equational,[status(thm)],[c31,c483,c497]) ).
cnf(c508,plain,
join(meet(X,Y),meet(X,complement(Y))) = X,
inference(equational,[status(thm)],[c3,c26,c475]) ).
cnf(c510,plain,
meet(X,join(Y,X)) = X,
inference(equational,[status(thm)],[c3,c498]) ).
cnf(c521,plain,
join(meet(X,Y),meet(Y,complement(X))) = Y,
inference(equational,[status(thm)],[c28,c508]) ).
cnf(c522,plain,
join(meet(X,Y),meet(complement(Y),X)) = X,
inference(equational,[status(thm)],[c28,c508]) ).
cnf(c528,plain,
join(meet(X,Y),meet(complement(X),Y)) = Y,
inference(equational,[status(thm)],[c28,c521]) ).
cnf(c534,plain,
join(complement(X),join(Y,complement(Z))) = join(Y,complement(meet(X,Z))),
inference(equational,[status(thm)],[c24,c488]) ).
cnf(c535,plain,
complement(meet(X,meet(Y,Z))) = complement(meet(Y,meet(X,Z))),
inference(equational,[status(thm)],[c488,c534]) ).
cnf(c536,plain,
meet(X,meet(Y,Z)) = meet(Y,meet(X,Z)),
inference(equational,[status(thm)],[c31,c478,c481,c483,c535]) ).
cnf(c538,plain,
meet(meet(X,Y),Z) = meet(X,meet(Z,Y)),
inference(equational,[status(thm)],[c28,c536]) ).
cnf(c563,plain,
join(X,complement(meet(Y,join(complement(Y),X)))) = top,
inference(equational,[status(thm)],[c57,c488]) ).
cnf(c565,plain,
meet(X,meet(Y,complement(meet(Y,X)))) = zero,
inference(equational,[status(thm)],[c26,c27,c488,c563]) ).
cnf(c566,plain,
meet(X,join(complement(X),Y)) = meet(X,Y),
inference(equational,[status(thm)],[c480,c490,c510,c522,c538,c565]) ).
cnf(c576,plain,
meet(X,converse(complement(converse(complement(X))))) = X,
inference(equational,[status(thm)],[c39,c129,c484,c566]) ).
cnf(c586,plain,
join(converse(X),complement(converse(meet(complement(Y),X)))) = top,
inference(equational,[status(thm)],[c3,c110,c128,c522]) ).
cnf(c587,plain,
join(converse(X),complement(converse(meet(Y,X)))) = top,
inference(equational,[status(thm)],[c31,c483,c586]) ).
cnf(c640,plain,
complement(meet(converse(X),converse(complement(X)))) = top,
inference(equational,[status(thm)],[c2,c28,c488,c576,c587]) ).
cnf(c641,plain,
meet(converse(X),converse(complement(X))) = zero,
inference(equational,[status(thm)],[c28,c484,c565,c640]) ).
cnf(c661,plain,
meet(X,converse(complement(converse(X)))) = zero,
inference(equational,[status(thm)],[c2,c641]) ).
cnf(c662,plain,
converse(complement(converse(complement(X)))) = X,
inference(equational,[status(thm)],[c480,c528,c576,c661]) ).
cnf(c663,plain,
complement(converse(complement(X))) = converse(X),
inference(equational,[status(thm)],[c2,c662]) ).
cnf(c664,plain,
converse(complement(X)) = complement(converse(X)),
inference(equational,[status(thm)],[c2,c125,c576,c663]) ).
cnf(g1,plain,
converse(complement(sk1)) = complement(converse(sk1)),
inference(equational,[status(thm)],[c664]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : REL004-2 : TPTP v9.0.0. Released v4.0.0.
% 0.08/0.13 % Command : run_Leo-III %s %d THM
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Jul 14 16:07:19 EDT 2025
% 0.13/0.34 % CPUTime :
% 66.21/66.26 % SZS status Unsatisfiable
% 66.21/66.26 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------