%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : REL007-1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n014.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 07:41:16 AM UTC 2025
% Result : Unsatisfiable 64.60s 64.72s
% Output : CNFRefutation 64.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 15
% Syntax : Number of clauses : 117 ( 117 unt; 0 nHn; 20 RR)
% Number of literals : 117 ( 116 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 : 190 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
meet(converse(sk1),sk2) != zero,
file('theBenchmark.p',goals_15) ).
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,
meet(sk1,converse(sk2)) = zero,
file('theBenchmark.p',goals_14) ).
cnf(c9,axiom,
converse(composition(X,Y)) = composition(converse(Y),converse(X)),
file('REL001-0.ax',converse_multiplicativity_10) ).
cnf(c10,plain,
composition(converse(X),converse(Y)) = converse(composition(Y,X)),
inference(equational,[status(thm)],[c9]) ).
cnf(c11,axiom,
converse(join(X,Y)) = join(converse(X),converse(Y)),
file('REL001-0.ax',converse_additivity_9) ).
cnf(c12,plain,
join(converse(X),converse(Y)) = converse(join(X,Y)),
inference(equational,[status(thm)],[c11]) ).
cnf(c13,axiom,
composition(X,composition(Y,Z)) = composition(composition(X,Y),Z),
file('REL001-0.ax',composition_associativity_5) ).
cnf(c14,plain,
composition(composition(X,Y),Z) = composition(X,composition(Y,Z)),
inference(equational,[status(thm)],[c13]) ).
cnf(c15,axiom,
join(X,join(Y,Z)) = join(join(X,Y),Z),
file('REL001-0.ax',maddux2_join_associativity_2) ).
cnf(c16,plain,
join(join(X,Y),Z) = join(X,join(Y,Z)),
inference(equational,[status(thm)],[c15]) ).
cnf(c17,plain,
composition(X,composition(one,Y)) = composition(X,Y),
inference(equational,[status(thm)],[c1,c14]) ).
cnf(c19,plain,
converse(join(converse(X),Y)) = join(X,converse(Y)),
inference(equational,[status(thm)],[c2,c12]) ).
cnf(c20,plain,
converse(composition(X,converse(Y))) = composition(Y,converse(X)),
inference(equational,[status(thm)],[c2,c10]) ).
cnf(c21,plain,
converse(composition(converse(X),Y)) = composition(converse(Y),X),
inference(equational,[status(thm)],[c2,c10]) ).
cnf(c22,plain,
composition(converse(one),X) = X,
inference(equational,[status(thm)],[c1,c2,c21]) ).
cnf(c23,plain,
converse(one) = one,
inference(equational,[status(thm)],[c1,c22]) ).
cnf(c24,plain,
composition(one,X) = X,
inference(equational,[status(thm)],[c17,c22]) ).
cnf(c25,plain,
join(X,join(Y,Z)) = join(Y,join(X,Z)),
inference(equational,[status(thm)],[c3,c16]) ).
cnf(c26,axiom,
meet(X,Y) = complement(join(complement(X),complement(Y))),
file('REL001-0.ax',maddux4_definiton_of_meet_4) ).
cnf(c27,plain,
complement(join(complement(X),complement(Y))) = meet(X,Y),
inference(equational,[status(thm)],[c26]) ).
cnf(c28,plain,
complement(top) = zero,
inference(equational,[status(thm)],[c5,c7,c27]) ).
cnf(c29,plain,
meet(X,Y) = meet(Y,X),
inference(equational,[status(thm)],[c3,c27]) ).
cnf(c30,plain,
join(top,zero) = top,
inference(equational,[status(thm)],[c5,c28]) ).
cnf(c32,plain,
complement(join(zero,complement(X))) = meet(top,X),
inference(equational,[status(thm)],[c27,c28]) ).
cnf(c34,plain,
join(X,join(complement(X),Y)) = join(top,Y),
inference(equational,[status(thm)],[c5,c16]) ).
cnf(c35,plain,
join(top,complement(complement(X))) = join(X,top),
inference(equational,[status(thm)],[c5,c34]) ).
cnf(c37,plain,
join(top,join(zero,X)) = join(top,X),
inference(equational,[status(thm)],[c28,c34]) ).
cnf(c39,plain,
join(top,join(X,zero)) = join(top,X),
inference(equational,[status(thm)],[c3,c37]) ).
cnf(c40,plain,
join(X,converse(complement(converse(X)))) = converse(top),
inference(equational,[status(thm)],[c5,c19]) ).
cnf(c41,plain,
join(X,join(Y,complement(X))) = join(Y,top),
inference(equational,[status(thm)],[c5,c25]) ).
cnf(c42,axiom,
composition(join(X,Y),Z) = join(composition(X,Z),composition(Y,Z)),
file('REL001-0.ax',composition_distributivity_7) ).
cnf(c43,plain,
join(composition(X,Y),composition(Z,Y)) = composition(join(X,Z),Y),
inference(equational,[status(thm)],[c42]) ).
cnf(c47,plain,
join(X,join(Y,complement(join(X,Y)))) = top,
inference(equational,[status(thm)],[c5,c16]) ).
cnf(c49,plain,
join(converse(X),join(converse(Y),Z)) = join(converse(join(X,Y)),Z),
inference(equational,[status(thm)],[c12,c16]) ).
cnf(c56,plain,
join(X,join(Y,complement(join(Y,X)))) = top,
inference(equational,[status(thm)],[c25,c47]) ).
cnf(c62,plain,
converse(join(X,join(converse(Y),Z))) = join(Y,converse(join(X,Z))),
inference(equational,[status(thm)],[c19,c25]) ).
cnf(c64,plain,
join(complement(X),join(complement(Y),meet(X,Y))) = top,
inference(equational,[status(thm)],[c5,c16,c27]) ).
cnf(c65,plain,
join(zero,join(complement(X),meet(top,X))) = top,
inference(equational,[status(thm)],[c28,c64]) ).
cnf(c66,plain,
join(zero,join(zero,meet(top,top))) = top,
inference(equational,[status(thm)],[c28,c65]) ).
cnf(c69,plain,
meet(meet(X,Y),join(complement(X),complement(Y))) = zero,
inference(equational,[status(thm)],[c7,c27,c29]) ).
cnf(c77,plain,
composition(join(converse(X),Y),converse(Z)) = converse(composition(Z,join(X,converse(Y)))),
inference(equational,[status(thm)],[c19,c20]) ).
cnf(c78,plain,
join(converse(X),composition(Y,converse(Z))) = converse(join(X,composition(Z,converse(Y)))),
inference(equational,[status(thm)],[c12,c20]) ).
cnf(c102,plain,
join(top,join(X,join(zero,Y))) = join(X,join(top,Y)),
inference(equational,[status(thm)],[c25,c37]) ).
cnf(c106,plain,
join(X,converse(join(complement(converse(X)),Y))) = converse(join(top,Y)),
inference(equational,[status(thm)],[c19,c34]) ).
cnf(c114,plain,
meet(meet(X,Y),join(complement(Y),complement(X))) = zero,
inference(equational,[status(thm)],[c29,c69]) ).
cnf(c119,axiom,
join(composition(converse(X),complement(composition(X,Y))),complement(Y)) = complement(Y),
file('REL001-0.ax',converse_cancellativity_11) ).
cnf(c120,plain,
join(complement(X),composition(converse(Y),complement(composition(Y,X)))) = complement(X),
inference(equational,[status(thm)],[c3,c119]) ).
cnf(c121,plain,
join(complement(X),complement(X)) = complement(X),
inference(equational,[status(thm)],[c22,c24,c120]) ).
cnf(c122,plain,
join(zero,zero) = zero,
inference(equational,[status(thm)],[c28,c121]) ).
cnf(c123,plain,
complement(complement(X)) = meet(X,X),
inference(equational,[status(thm)],[c27,c121]) ).
cnf(c124,plain,
meet(top,top) = complement(zero),
inference(equational,[status(thm)],[c28,c123]) ).
cnf(c125,plain,
join(top,complement(X)) = top,
inference(equational,[status(thm)],[c3,c5,c41,c121]) ).
cnf(c126,plain,
join(X,top) = top,
inference(equational,[status(thm)],[c35,c125]) ).
cnf(c128,plain,
join(top,X) = top,
inference(equational,[status(thm)],[c30,c39,c102,c122,c126]) ).
cnf(c129,plain,
converse(top) = top,
inference(equational,[status(thm)],[c106,c128]) ).
cnf(c131,plain,
join(zero,join(zero,X)) = join(zero,X),
inference(equational,[status(thm)],[c16,c122]) ).
cnf(c171,plain,
join(X,join(converse(complement(converse(X))),Y)) = top,
inference(equational,[status(thm)],[c16,c40,c128,c129]) ).
cnf(c175,plain,
join(complement(converse(X)),converse(join(X,Y))) = top,
inference(equational,[status(thm)],[c62,c129,c171]) ).
cnf(c192,plain,
join(composition(X,Y),join(composition(Z,Y),W)) = join(composition(join(X,Z),Y),W),
inference(equational,[status(thm)],[c16,c43]) ).
cnf(c193,plain,
join(X,join(composition(Y,X),Z)) = join(composition(join(Y,one),X),Z),
inference(equational,[status(thm)],[c22,c23,c25,c192]) ).
cnf(c198,plain,
join(X,join(X,Y)) = join(composition(join(one,one),X),Y),
inference(equational,[status(thm)],[c22,c23,c193]) ).
cnf(c202,plain,
converse(join(composition(X,Y),composition(X,converse(Z)))) = converse(composition(X,join(Y,converse(Z)))),
inference(equational,[status(thm)],[c10,c43,c77,c78]) ).
cnf(c203,plain,
composition(X,converse(join(Y,Y))) = composition(join(X,X),converse(Y)),
inference(equational,[status(thm)],[c12,c20,c43,c202]) ).
cnf(c204,plain,
composition(join(X,X),Y) = composition(X,join(Y,Y)),
inference(equational,[status(thm)],[c2,c12,c203]) ).
cnf(c207,plain,
composition(join(X,X),complement(Y)) = composition(X,complement(Y)),
inference(equational,[status(thm)],[c121,c204]) ).
cnf(c230,plain,
composition(join(X,X),meet(Y,Z)) = composition(X,meet(Y,Z)),
inference(equational,[status(thm)],[c27,c207]) ).
cnf(c308,plain,
join(X,converse(join(Y,complement(join(converse(X),Y))))) = top,
inference(equational,[status(thm)],[c19,c47,c129]) ).
cnf(c373,plain,
join(converse(join(X,Y)),complement(converse(join(Y,X)))) = top,
inference(equational,[status(thm)],[c12,c49,c56]) ).
cnf(c380,plain,
join(X,converse(join(Y,complement(join(Y,converse(X)))))) = top,
inference(equational,[status(thm)],[c3,c308]) ).
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)],[c27,c447]) ).
cnf(c449,plain,
join(zero,complement(complement(X))) = X,
inference(equational,[status(thm)],[c7,c121,c448]) ).
cnf(c452,plain,
join(zero,X) = X,
inference(equational,[status(thm)],[c131,c449]) ).
cnf(c453,plain,
complement(zero) = top,
inference(equational,[status(thm)],[c66,c124,c452]) ).
cnf(c454,plain,
join(X,zero) = X,
inference(equational,[status(thm)],[c3,c452]) ).
cnf(c455,plain,
complement(complement(X)) = X,
inference(equational,[status(thm)],[c449,c452]) ).
cnf(c460,plain,
meet(top,X) = X,
inference(equational,[status(thm)],[c32,c452,c455]) ).
cnf(c461,plain,
meet(X,top) = X,
inference(equational,[status(thm)],[c29,c460]) ).
cnf(c462,plain,
join(X,meet(X,Y)) = X,
inference(equational,[status(thm)],[c3,c24,c198,c230,c448]) ).
cnf(c465,plain,
join(complement(X),complement(Y)) = complement(meet(X,Y)),
inference(equational,[status(thm)],[c27,c449,c452]) ).
cnf(c466,plain,
complement(meet(complement(X),Y)) = join(X,complement(Y)),
inference(equational,[status(thm)],[c32,c452,c460,c465]) ).
cnf(c467,plain,
complement(meet(X,complement(Y))) = join(complement(X),Y),
inference(equational,[status(thm)],[c32,c452,c460,c465]) ).
cnf(c470,plain,
complement(join(X,complement(Y))) = meet(complement(X),Y),
inference(equational,[status(thm)],[c449,c452,c466]) ).
cnf(c471,plain,
complement(join(complement(X),Y)) = meet(X,complement(Y)),
inference(equational,[status(thm)],[c32,c452,c460,c467]) ).
cnf(c478,plain,
join(meet(X,Y),meet(X,complement(Y))) = X,
inference(equational,[status(thm)],[c3,c27,c448]) ).
cnf(c479,plain,
meet(sk1,complement(converse(sk2))) = sk1,
inference(equational,[status(thm)],[c8,c452,c478]) ).
cnf(c480,plain,
join(converse(sk2),complement(sk1)) = complement(sk1),
inference(equational,[status(thm)],[c3,c467,c479]) ).
cnf(c481,plain,
join(X,meet(Y,X)) = X,
inference(equational,[status(thm)],[c29,c462]) ).
cnf(c486,plain,
meet(complement(X),complement(Y)) = complement(join(X,Y)),
inference(equational,[status(thm)],[c32,c452,c460,c470]) ).
cnf(c495,plain,
join(meet(X,Y),meet(Y,complement(X))) = Y,
inference(equational,[status(thm)],[c29,c478]) ).
cnf(c502,plain,
join(complement(sk2),converse(complement(sk1))) = top,
inference(equational,[status(thm)],[c2,c175,c480]) ).
cnf(c506,plain,
meet(meet(X,Y),complement(meet(Y,X))) = zero,
inference(equational,[status(thm)],[c114,c465]) ).
cnf(c513,plain,
join(complement(X),join(Y,complement(Z))) = join(Y,complement(meet(X,Z))),
inference(equational,[status(thm)],[c25,c465]) ).
cnf(c514,plain,
complement(meet(X,meet(Y,Z))) = complement(meet(Y,meet(X,Z))),
inference(equational,[status(thm)],[c465,c513]) ).
cnf(c515,plain,
meet(X,meet(Y,Z)) = meet(Y,meet(X,Z)),
inference(equational,[status(thm)],[c32,c452,c455,c460,c514]) ).
cnf(c516,plain,
meet(X,meet(Y,Z)) = meet(Z,meet(X,Y)),
inference(equational,[status(thm)],[c29,c515]) ).
cnf(c517,plain,
meet(meet(X,Y),Z) = meet(X,meet(Z,Y)),
inference(equational,[status(thm)],[c29,c515]) ).
cnf(c521,plain,
join(complement(sk1),converse(complement(sk2))) = top,
inference(equational,[status(thm)],[c28,c380,c454,c502]) ).
cnf(c523,plain,
meet(X,meet(Y,Z)) = meet(Z,meet(Y,X)),
inference(equational,[status(thm)],[c29,c516]) ).
cnf(c526,plain,
meet(X,meet(Y,complement(meet(Y,X)))) = zero,
inference(equational,[status(thm)],[c69,c453,c461,c465,c506,c523]) ).
cnf(c528,plain,
meet(X,complement(meet(X,Y))) = meet(X,complement(Y)),
inference(equational,[status(thm)],[c452,c481,c486,c495,c517,c526]) ).
cnf(c531,plain,
join(X,meet(complement(X),Y)) = join(X,Y),
inference(equational,[status(thm)],[c455,c466,c470,c486,c528]) ).
cnf(c532,plain,
join(complement(X),meet(X,Y)) = join(complement(X),Y),
inference(equational,[status(thm)],[c467,c528]) ).
cnf(c553,plain,
meet(sk1,complement(converse(complement(sk2)))) = zero,
inference(equational,[status(thm)],[c28,c471,c521]) ).
cnf(c554,plain,
join(X,meet(Y,complement(X))) = join(X,Y),
inference(equational,[status(thm)],[c29,c531]) ).
cnf(c555,plain,
join(sk1,converse(complement(sk2))) = converse(complement(sk2)),
inference(equational,[status(thm)],[c3,c454,c553,c554]) ).
cnf(c560,plain,
complement(meet(sk2,converse(sk1))) = top,
inference(equational,[status(thm)],[c2,c19,c373,c465,c471,c532,c555]) ).
cnf(c561,plain,
meet(sk2,converse(sk1)) = zero,
inference(equational,[status(thm)],[c29,c461,c526,c560]) ).
cnf(g1,plain,
meet(converse(sk1),sk2) = zero,
inference(equational,[status(thm)],[c29,c561]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : REL007-1 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.13 % Command : run_Leo-III %s %d THM
% 0.12/0.34 % Computer : n014.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Jul 14 16:07:34 EDT 2025
% 0.12/0.34 % CPUTime :
% 64.60/64.72 % SZS status Unsatisfiable
% 64.60/64.72 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------