%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : REL005-1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n016.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 75.37s 75.55s
% Output : CNFRefutation 75.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 14
% Syntax : Number of clauses : 126 ( 126 unt; 0 nHn; 11 RR)
% Number of literals : 126 ( 125 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 : 224 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
converse(meet(sk1,sk2)) != meet(converse(sk1),converse(sk2)),
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(c29,plain,
join(top,zero) = top,
inference(equational,[status(thm)],[c5,c27]) ).
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(c36,plain,
join(top,join(zero,X)) = join(top,X),
inference(equational,[status(thm)],[c27,c33]) ).
cnf(c38,plain,
join(top,join(X,zero)) = join(top,X),
inference(equational,[status(thm)],[c3,c36]) ).
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(c48,plain,
join(converse(X),join(converse(Y),Z)) = join(converse(join(X,Y)),Z),
inference(equational,[status(thm)],[c11,c15]) ).
cnf(c53,plain,
complement(join(meet(X,Y),complement(Z))) = meet(join(complement(X),complement(Y)),Z),
inference(equational,[status(thm)],[c26]) ).
cnf(c63,plain,
join(complement(X),join(complement(Y),meet(X,Y))) = top,
inference(equational,[status(thm)],[c5,c15,c26]) ).
cnf(c64,plain,
join(zero,join(complement(X),meet(top,X))) = top,
inference(equational,[status(thm)],[c27,c63]) ).
cnf(c65,plain,
join(zero,join(zero,meet(top,top))) = top,
inference(equational,[status(thm)],[c27,c64]) ).
cnf(c68,plain,
meet(meet(X,Y),join(complement(X),complement(Y))) = zero,
inference(equational,[status(thm)],[c7,c26,c28]) ).
cnf(c77,plain,
join(composition(X,converse(Y)),converse(Z)) = converse(join(composition(Y,converse(X)),Z)),
inference(equational,[status(thm)],[c11,c19]) ).
cnf(c81,plain,
converse(composition(join(X,converse(Y)),Z)) = composition(converse(Z),join(converse(X),Y)),
inference(equational,[status(thm)],[c9,c17]) ).
cnf(c97,plain,
join(top,join(X,join(zero,Y))) = join(X,join(top,Y)),
inference(equational,[status(thm)],[c24,c36]) ).
cnf(c102,plain,
join(complement(converse(X)),converse(join(Y,X))) = join(top,converse(Y)),
inference(equational,[status(thm)],[c3,c5,c48]) ).
cnf(c106,plain,
join(X,converse(join(complement(converse(X)),Y))) = converse(join(top,Y)),
inference(equational,[status(thm)],[c18,c33]) ).
cnf(c109,plain,
meet(meet(X,Y),join(complement(Y),complement(X))) = zero,
inference(equational,[status(thm)],[c28,c68]) ).
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(c118,plain,
complement(complement(X)) = meet(X,X),
inference(equational,[status(thm)],[c26,c116]) ).
cnf(c119,plain,
meet(top,top) = complement(zero),
inference(equational,[status(thm)],[c27,c118]) ).
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)],[c29,c38,c97,c117,c121]) ).
cnf(c123,plain,
converse(top) = top,
inference(equational,[status(thm)],[c106,c122]) ).
cnf(c126,plain,
join(zero,join(zero,X)) = join(zero,X),
inference(equational,[status(thm)],[c15,c117]) ).
cnf(c150,plain,
join(complement(X),join(Y,complement(X))) = join(Y,complement(X)),
inference(equational,[status(thm)],[c24,c116]) ).
cnf(c187,plain,
join(composition(X,Y),join(composition(Z,Y),W)) = join(composition(join(X,Z),Y),W),
inference(equational,[status(thm)],[c15,c42]) ).
cnf(c188,plain,
join(X,join(composition(Y,X),Z)) = join(composition(join(Y,one),X),Z),
inference(equational,[status(thm)],[c21,c22,c24,c187]) ).
cnf(c193,plain,
join(X,join(X,Y)) = join(composition(join(one,one),X),Y),
inference(equational,[status(thm)],[c21,c22,c188]) ).
cnf(c197,plain,
converse(join(composition(X,converse(Y)),composition(X,Z))) = composition(join(Y,converse(Z)),converse(X)),
inference(equational,[status(thm)],[c9,c42,c77]) ).
cnf(c198,plain,
composition(X,converse(join(Y,Y))) = composition(join(X,X),converse(Y)),
inference(equational,[status(thm)],[c2,c19,c42,c197]) ).
cnf(c199,plain,
composition(join(X,X),Y) = composition(X,join(Y,Y)),
inference(equational,[status(thm)],[c2,c9,c81,c198]) ).
cnf(c202,plain,
composition(join(X,X),complement(Y)) = composition(X,complement(Y)),
inference(equational,[status(thm)],[c116,c199]) ).
cnf(c225,plain,
composition(join(X,X),meet(Y,Z)) = composition(X,meet(Y,Z)),
inference(equational,[status(thm)],[c26,c202]) ).
cnf(c447,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(c448,plain,
join(meet(X,Y),complement(join(complement(X),Y))) = X,
inference(equational,[status(thm)],[c26,c447]) ).
cnf(c449,plain,
join(zero,complement(complement(X))) = X,
inference(equational,[status(thm)],[c7,c116,c448]) ).
cnf(c452,plain,
join(zero,X) = X,
inference(equational,[status(thm)],[c126,c449]) ).
cnf(c453,plain,
complement(zero) = top,
inference(equational,[status(thm)],[c65,c119,c452]) ).
cnf(c454,plain,
complement(complement(X)) = X,
inference(equational,[status(thm)],[c449,c452]) ).
cnf(c455,plain,
join(X,zero) = X,
inference(equational,[status(thm)],[c3,c452]) ).
cnf(c460,plain,
meet(top,X) = X,
inference(equational,[status(thm)],[c31,c452,c454]) ).
cnf(c461,plain,
meet(X,top) = X,
inference(equational,[status(thm)],[c28,c460]) ).
cnf(c462,plain,
join(X,meet(X,Y)) = X,
inference(equational,[status(thm)],[c3,c23,c193,c225,c448]) ).
cnf(c465,plain,
join(complement(X),complement(Y)) = complement(meet(X,Y)),
inference(equational,[status(thm)],[c26,c449,c452]) ).
cnf(c466,plain,
complement(meet(complement(X),Y)) = join(X,complement(Y)),
inference(equational,[status(thm)],[c31,c452,c460,c465]) ).
cnf(c469,plain,
join(X,complement(meet(X,Y))) = top,
inference(equational,[status(thm)],[c33,c120,c465]) ).
cnf(c471,plain,
complement(join(X,complement(Y))) = meet(complement(X),Y),
inference(equational,[status(thm)],[c31,c452,c460,c466]) ).
cnf(c472,plain,
meet(X,join(X,complement(Y))) = X,
inference(equational,[status(thm)],[c27,c448,c455,c466,c469]) ).
cnf(c473,plain,
meet(X,join(X,Y)) = X,
inference(equational,[status(thm)],[c31,c460,c472]) ).
cnf(c478,plain,
join(meet(X,Y),meet(X,complement(Y))) = X,
inference(equational,[status(thm)],[c3,c26,c448]) ).
cnf(c479,plain,
join(X,meet(Y,X)) = X,
inference(equational,[status(thm)],[c28,c462]) ).
cnf(c480,plain,
meet(X,join(Y,X)) = X,
inference(equational,[status(thm)],[c3,c473]) ).
cnf(c489,plain,
join(meet(X,Y),meet(complement(Y),X)) = X,
inference(equational,[status(thm)],[c28,c478]) ).
cnf(c490,plain,
join(X,join(X,complement(Y))) = join(X,complement(Y)),
inference(equational,[status(thm)],[c15,c116,c150,c466]) ).
cnf(c491,plain,
join(X,join(X,Y)) = join(X,Y),
inference(equational,[status(thm)],[c31,c452,c454,c460,c490]) ).
cnf(c497,plain,
join(meet(X,Y),meet(complement(X),Y)) = Y,
inference(equational,[status(thm)],[c28,c489]) ).
cnf(c498,plain,
meet(meet(X,Y),complement(meet(Y,X))) = zero,
inference(equational,[status(thm)],[c109,c465]) ).
cnf(c502,plain,
join(complement(X),join(Y,complement(Z))) = join(Y,complement(meet(X,Z))),
inference(equational,[status(thm)],[c24,c465]) ).
cnf(c503,plain,
complement(meet(X,meet(Y,Z))) = complement(meet(Y,meet(X,Z))),
inference(equational,[status(thm)],[c465,c502]) ).
cnf(c504,plain,
meet(X,meet(Y,Z)) = meet(Y,meet(X,Z)),
inference(equational,[status(thm)],[c31,c452,c454,c460,c503]) ).
cnf(c506,plain,
meet(meet(X,Y),Z) = meet(X,meet(Z,Y)),
inference(equational,[status(thm)],[c28,c504]) ).
cnf(c508,plain,
meet(X,meet(Y,Z)) = meet(Z,meet(Y,X)),
inference(equational,[status(thm)],[c28,c506]) ).
cnf(c512,plain,
meet(X,meet(Y,complement(meet(X,Y)))) = zero,
inference(equational,[status(thm)],[c453,c461,c498,c508]) ).
cnf(c513,plain,
meet(X,join(Y,complement(X))) = meet(X,Y),
inference(equational,[status(thm)],[c455,c466,c473,c489,c506,c512]) ).
cnf(c521,plain,
join(complement(X),meet(X,Y)) = join(Y,complement(X)),
inference(equational,[status(thm)],[c3,c480,c497,c513]) ).
cnf(c556,plain,
join(converse(X),complement(converse(meet(complement(Y),X)))) = top,
inference(equational,[status(thm)],[c3,c102,c122,c489]) ).
cnf(c570,plain,
meet(X,converse(complement(converse(complement(X))))) = X,
inference(equational,[status(thm)],[c27,c39,c123,c448,c455]) ).
cnf(c573,plain,
complement(meet(converse(X),converse(complement(X)))) = top,
inference(equational,[status(thm)],[c2,c454,c465,c556,c570]) ).
cnf(c574,plain,
meet(converse(X),converse(complement(X))) = zero,
inference(equational,[status(thm)],[c461,c512,c573]) ).
cnf(c576,plain,
meet(X,converse(complement(converse(X)))) = zero,
inference(equational,[status(thm)],[c2,c574]) ).
cnf(c577,plain,
converse(complement(converse(complement(X)))) = X,
inference(equational,[status(thm)],[c455,c497,c570,c576]) ).
cnf(c578,plain,
complement(converse(complement(X))) = converse(X),
inference(equational,[status(thm)],[c2,c577]) ).
cnf(c579,plain,
complement(converse(X)) = converse(complement(X)),
inference(equational,[status(thm)],[c454,c578]) ).
cnf(c593,plain,
complement(join(X,join(Y,complement(Z)))) = meet(complement(join(X,Y)),Z),
inference(equational,[status(thm)],[c15,c471]) ).
cnf(c606,plain,
meet(complement(meet(X,Y)),join(complement(X),Y)) = complement(X),
inference(equational,[status(thm)],[c53,c448,c465]) ).
cnf(c607,plain,
meet(join(X,Y),join(X,complement(Y))) = X,
inference(equational,[status(thm)],[c28,c31,c452,c454,c460,c466,c606]) ).
cnf(c612,plain,
meet(complement(meet(X,Y)),join(Y,complement(X))) = complement(X),
inference(equational,[status(thm)],[c3,c606]) ).
cnf(c619,plain,
meet(complement(X),meet(complement(Y),Z)) = meet(complement(join(X,Y)),Z),
inference(equational,[status(thm)],[c466,c471,c593]) ).
cnf(c638,plain,
join(meet(X,Y),join(Z,meet(X,complement(Y)))) = join(Z,X),
inference(equational,[status(thm)],[c24,c478]) ).
cnf(c699,plain,
join(meet(X,Y),join(Z,meet(complement(Y),X))) = join(Z,X),
inference(equational,[status(thm)],[c28,c638]) ).
cnf(c1049,plain,
join(complement(X),join(Y,meet(complement(Z),X))) = join(Y,complement(meet(X,Z))),
inference(equational,[status(thm)],[c471,c479,c506,c612,c619,c699]) ).
cnf(c1091,plain,
join(meet(X,Y),join(Z,complement(X))) = join(Z,join(Y,complement(X))),
inference(equational,[status(thm)],[c3,c454,c465,c466,c472,c521,c1049]) ).
cnf(c1111,plain,
meet(converse(join(X,Y)),converse(join(X,complement(Y)))) = converse(X),
inference(equational,[status(thm)],[c11,c579,c607]) ).
cnf(c1112,plain,
meet(converse(X),converse(join(Y,complement(X)))) = converse(meet(X,Y)),
inference(equational,[status(thm)],[c466,c489,c491,c1091,c1111]) ).
cnf(c1113,plain,
converse(meet(converse(X),Y)) = meet(X,converse(Y)),
inference(equational,[status(thm)],[c2,c17,c513,c579,c1112]) ).
cnf(c1115,plain,
meet(converse(X),converse(Y)) = converse(meet(X,Y)),
inference(equational,[status(thm)],[c2,c1113]) ).
cnf(g1,plain,
converse(meet(sk1,sk2)) = meet(converse(sk1),converse(sk2)),
inference(equational,[status(thm)],[c1115]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : REL005-1 : TPTP v9.0.0. Released v4.0.0.
% 0.12/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n016.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Jul 14 16:07:19 EDT 2025
% 0.12/0.33 % CPUTime :
% 75.37/75.55 % SZS status Unsatisfiable
% 75.37/75.55 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------