%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : REL030-1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n007.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 07:41:24 AM UTC 2025
% Result : Unsatisfiable 69.76s 69.93s
% Output : CNFRefutation 69.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 15
% Syntax : Number of clauses : 117 ( 117 unt; 0 nHn; 14 RR)
% Number of literals : 117 ( 116 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 : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 191 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
meet(composition(sk1,sk2),complement(sk3)) != meet(composition(sk1,sk2),complement(composition(sk1,sk3))),
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(sk1,one) = one,
file('theBenchmark.p',goals_14) ).
cnf(c4,axiom,
join(X,Y) = join(Y,X),
file('REL001-0.ax',maddux1_join_commutativity_1) ).
cnf(c5,plain,
join(one,sk1) = one,
inference(equational,[status(thm)],[c3,c4]) ).
cnf(c6,axiom,
top = join(X,complement(X)),
file('REL001-0.ax',def_top_12) ).
cnf(c7,plain,
join(X,complement(X)) = top,
inference(equational,[status(thm)],[c6]) ).
cnf(c8,axiom,
zero = meet(X,complement(X)),
file('REL001-0.ax',def_zero_13) ).
cnf(c9,plain,
meet(X,complement(X)) = zero,
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,
converse(composition(X,Y)) = composition(converse(Y),converse(X)),
file('REL001-0.ax',converse_multiplicativity_10) ).
cnf(c13,plain,
composition(converse(X),converse(Y)) = converse(composition(Y,X)),
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,axiom,
composition(X,composition(Y,Z)) = composition(composition(X,Y),Z),
file('REL001-0.ax',composition_associativity_5) ).
cnf(c17,plain,
composition(composition(X,Y),Z) = composition(X,composition(Y,Z)),
inference(equational,[status(thm)],[c16]) ).
cnf(c18,plain,
composition(X,composition(one,Y)) = composition(X,Y),
inference(equational,[status(thm)],[c1,c17]) ).
cnf(c21,plain,
converse(composition(converse(X),Y)) = composition(converse(Y),X),
inference(equational,[status(thm)],[c2,c13]) ).
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)],[c18,c22]) ).
cnf(c25,plain,
converse(composition(X,converse(Y))) = composition(Y,converse(X)),
inference(equational,[status(thm)],[c2,c13]) ).
cnf(c26,plain,
converse(join(converse(X),Y)) = join(X,converse(Y)),
inference(equational,[status(thm)],[c2,c11]) ).
cnf(c28,plain,
join(X,join(Y,Z)) = join(Y,join(X,Z)),
inference(equational,[status(thm)],[c4,c15]) ).
cnf(c29,axiom,
meet(X,Y) = complement(join(complement(X),complement(Y))),
file('REL001-0.ax',maddux4_definiton_of_meet_4) ).
cnf(c30,plain,
complement(join(complement(X),complement(Y))) = meet(X,Y),
inference(equational,[status(thm)],[c29]) ).
cnf(c31,plain,
complement(top) = zero,
inference(equational,[status(thm)],[c7,c9,c30]) ).
cnf(c32,plain,
meet(X,Y) = meet(Y,X),
inference(equational,[status(thm)],[c4,c30]) ).
cnf(c33,plain,
join(top,zero) = top,
inference(equational,[status(thm)],[c7,c31]) ).
cnf(c35,plain,
complement(join(zero,complement(X))) = meet(top,X),
inference(equational,[status(thm)],[c30,c31]) ).
cnf(c36,plain,
complement(join(zero,zero)) = meet(top,top),
inference(equational,[status(thm)],[c31,c35]) ).
cnf(c41,plain,
join(X,join(complement(X),Y)) = join(top,Y),
inference(equational,[status(thm)],[c7,c15]) ).
cnf(c42,plain,
join(top,complement(complement(X))) = join(X,top),
inference(equational,[status(thm)],[c7,c41]) ).
cnf(c44,plain,
join(top,join(zero,X)) = join(top,X),
inference(equational,[status(thm)],[c31,c41]) ).
cnf(c47,plain,
join(top,join(X,zero)) = join(top,X),
inference(equational,[status(thm)],[c4,c44]) ).
cnf(c54,axiom,
composition(join(X,Y),Z) = join(composition(X,Z),composition(Y,Z)),
file('REL001-0.ax',composition_distributivity_7) ).
cnf(c55,plain,
join(composition(X,Y),composition(Z,Y)) = composition(join(X,Z),Y),
inference(equational,[status(thm)],[c54]) ).
cnf(c56,plain,
join(X,composition(Y,X)) = composition(join(one,Y),X),
inference(equational,[status(thm)],[c22,c23,c55]) ).
cnf(c68,plain,
complement(join(meet(X,Y),complement(Z))) = meet(join(complement(X),complement(Y)),Z),
inference(equational,[status(thm)],[c30]) ).
cnf(c69,plain,
complement(join(complement(X),meet(Y,Z))) = meet(X,join(complement(Y),complement(Z))),
inference(equational,[status(thm)],[c30]) ).
cnf(c90,plain,
join(complement(X),join(complement(Y),meet(X,Y))) = top,
inference(equational,[status(thm)],[c7,c15,c30]) ).
cnf(c91,plain,
join(zero,join(complement(X),meet(top,X))) = top,
inference(equational,[status(thm)],[c31,c90]) ).
cnf(c92,plain,
join(zero,join(zero,meet(top,top))) = top,
inference(equational,[status(thm)],[c31,c91]) ).
cnf(c96,plain,
meet(top,join(complement(X),complement(Y))) = complement(join(zero,meet(X,Y))),
inference(equational,[status(thm)],[c31,c69]) ).
cnf(c101,plain,
join(composition(X,converse(Y)),converse(Z)) = converse(join(composition(Y,converse(X)),Z)),
inference(equational,[status(thm)],[c25,c26]) ).
cnf(c108,plain,
composition(join(X,converse(Y)),converse(Z)) = converse(composition(Z,join(converse(X),Y))),
inference(equational,[status(thm)],[c13,c26]) ).
cnf(c133,plain,
join(top,join(X,join(zero,Y))) = join(X,join(top,Y)),
inference(equational,[status(thm)],[c28,c44]) ).
cnf(c158,axiom,
join(composition(converse(X),complement(composition(X,Y))),complement(Y)) = complement(Y),
file('REL001-0.ax',converse_cancellativity_11) ).
cnf(c159,plain,
join(complement(X),composition(converse(Y),complement(composition(Y,X)))) = complement(X),
inference(equational,[status(thm)],[c4,c158]) ).
cnf(c160,plain,
join(complement(X),complement(X)) = complement(X),
inference(equational,[status(thm)],[c22,c24,c159]) ).
cnf(c161,plain,
join(zero,zero) = zero,
inference(equational,[status(thm)],[c31,c160]) ).
cnf(c162,plain,
complement(complement(X)) = meet(X,X),
inference(equational,[status(thm)],[c30,c160]) ).
cnf(c163,plain,
meet(top,top) = complement(zero),
inference(equational,[status(thm)],[c31,c162]) ).
cnf(c164,plain,
join(top,complement(X)) = top,
inference(equational,[status(thm)],[c7,c41,c160]) ).
cnf(c165,plain,
join(X,top) = top,
inference(equational,[status(thm)],[c42,c164]) ).
cnf(c166,plain,
join(top,X) = top,
inference(equational,[status(thm)],[c33,c47,c133,c161,c165]) ).
cnf(c170,plain,
join(zero,join(zero,X)) = join(zero,X),
inference(equational,[status(thm)],[c15,c161]) ).
cnf(c241,plain,
join(composition(X,Y),join(composition(Z,Y),W)) = join(composition(join(X,Z),Y),W),
inference(equational,[status(thm)],[c15,c55]) ).
cnf(c242,plain,
join(X,join(composition(Y,X),Z)) = join(composition(join(one,Y),X),Z),
inference(equational,[status(thm)],[c22,c23,c241]) ).
cnf(c243,plain,
join(X,join(composition(sk1,X),Y)) = join(X,Y),
inference(equational,[status(thm)],[c5,c24,c242]) ).
cnf(c244,plain,
join(X,complement(composition(sk1,X))) = top,
inference(equational,[status(thm)],[c7,c165,c243]) ).
cnf(c247,plain,
meet(X,composition(sk1,complement(X))) = zero,
inference(equational,[status(thm)],[c30,c31,c244]) ).
cnf(c274,plain,
converse(join(composition(X,converse(Y)),composition(X,Z))) = converse(composition(X,join(converse(Y),Z))),
inference(equational,[status(thm)],[c13,c55,c101,c108]) ).
cnf(c289,plain,
converse(join(composition(X,Y),composition(X,Z))) = converse(composition(X,join(Y,Z))),
inference(equational,[status(thm)],[c2,c274]) ).
cnf(c290,plain,
join(composition(X,Y),composition(X,Z)) = composition(X,join(Y,Z)),
inference(equational,[status(thm)],[c2,c289]) ).
cnf(c313,plain,
join(X,composition(sk1,join(X,Y))) = join(X,composition(sk1,Y)),
inference(equational,[status(thm)],[c243,c290]) ).
cnf(c314,plain,
join(X,composition(sk1,complement(X))) = join(X,composition(sk1,top)),
inference(equational,[status(thm)],[c7,c313]) ).
cnf(c626,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(c627,plain,
join(meet(X,Y),complement(join(complement(X),Y))) = X,
inference(equational,[status(thm)],[c30,c626]) ).
cnf(c628,plain,
join(zero,complement(complement(X))) = X,
inference(equational,[status(thm)],[c9,c160,c627]) ).
cnf(c631,plain,
join(zero,X) = X,
inference(equational,[status(thm)],[c170,c628]) ).
cnf(c632,plain,
complement(zero) = top,
inference(equational,[status(thm)],[c92,c163,c631]) ).
cnf(c633,plain,
complement(complement(X)) = X,
inference(equational,[status(thm)],[c628,c631]) ).
cnf(c634,plain,
join(X,zero) = X,
inference(equational,[status(thm)],[c4,c631]) ).
cnf(c638,plain,
meet(X,X) = X,
inference(equational,[status(thm)],[c7,c31,c627,c633,c634]) ).
cnf(c639,plain,
complement(join(complement(X),Y)) = meet(X,complement(Y)),
inference(equational,[status(thm)],[c69,c160,c638]) ).
cnf(c640,plain,
meet(zero,complement(X)) = zero,
inference(equational,[status(thm)],[c31,c36,c161,c163,c166,c632,c639]) ).
cnf(c642,plain,
meet(top,X) = X,
inference(equational,[status(thm)],[c68,c166,c631,c632,c633,c640]) ).
cnf(c645,plain,
complement(join(X,complement(Y))) = meet(complement(X),Y),
inference(equational,[status(thm)],[c68,c160,c638]) ).
cnf(c648,plain,
complement(meet(X,complement(Y))) = join(complement(X),Y),
inference(equational,[status(thm)],[c628,c631,c639]) ).
cnf(c649,plain,
meet(complement(X),complement(Y)) = complement(join(X,Y)),
inference(equational,[status(thm)],[c35,c631,c642,c645]) ).
cnf(c653,plain,
meet(X,complement(join(X,Y))) = zero,
inference(equational,[status(thm)],[c31,c41,c166,c633,c639]) ).
cnf(c654,plain,
meet(X,join(X,Y)) = X,
inference(equational,[status(thm)],[c30,c627,c631,c653]) ).
cnf(c655,plain,
meet(X,join(Y,X)) = X,
inference(equational,[status(thm)],[c4,c654]) ).
cnf(c659,plain,
complement(meet(complement(X),Y)) = join(complement(Y),X),
inference(equational,[status(thm)],[c32,c648]) ).
cnf(c661,plain,
meet(X,meet(X,Y)) = meet(X,Y),
inference(equational,[status(thm)],[c32,c627,c654]) ).
cnf(c667,plain,
join(meet(X,Y),meet(X,complement(Y))) = X,
inference(equational,[status(thm)],[c4,c30,c627]) ).
cnf(c676,plain,
meet(X,meet(Y,X)) = meet(X,Y),
inference(equational,[status(thm)],[c32,c661]) ).
cnf(c677,plain,
join(meet(X,Y),meet(Y,complement(X))) = Y,
inference(equational,[status(thm)],[c32,c667]) ).
cnf(c678,plain,
join(meet(X,Y),meet(complement(Y),X)) = X,
inference(equational,[status(thm)],[c32,c667]) ).
cnf(c687,plain,
meet(meet(X,Y),complement(Z)) = meet(X,meet(Y,complement(Z))),
inference(equational,[status(thm)],[c15,c30,c639,c649]) ).
cnf(c688,plain,
meet(meet(X,Y),Z) = meet(X,meet(Y,Z)),
inference(equational,[status(thm)],[c35,c631,c633,c642,c687]) ).
cnf(c690,plain,
meet(X,meet(Y,Z)) = meet(Y,meet(X,Z)),
inference(equational,[status(thm)],[c32,c688]) ).
cnf(c693,plain,
join(meet(X,Y),meet(complement(X),Y)) = Y,
inference(equational,[status(thm)],[c32,c677]) ).
cnf(c695,plain,
meet(X,composition(sk1,X)) = composition(sk1,X),
inference(equational,[status(thm)],[c247,c633,c634,c693]) ).
cnf(c729,plain,
join(complement(X),meet(complement(Y),Z)) = complement(meet(X,join(Y,complement(Z)))),
inference(equational,[status(thm)],[c96,c631,c642,c645]) ).
cnf(c730,plain,
complement(join(meet(X,complement(Y)),Z)) = meet(join(complement(X),Y),complement(Z)),
inference(equational,[status(thm)],[c639]) ).
cnf(c731,plain,
meet(join(X,Y),join(complement(X),Y)) = Y,
inference(equational,[status(thm)],[c32,c633,c649,c693,c730]) ).
cnf(c733,plain,
meet(X,complement(meet(X,Y))) = meet(complement(Y),X),
inference(equational,[status(thm)],[c654,c678,c688,c729,c731]) ).
cnf(c734,plain,
meet(X,join(complement(X),Y)) = meet(X,Y),
inference(equational,[status(thm)],[c633,c659,c676,c688,c733]) ).
cnf(c736,plain,
meet(X,composition(sk1,top)) = composition(sk1,X),
inference(equational,[status(thm)],[c314,c633,c695,c734]) ).
cnf(c743,plain,
join(X,complement(join(Y,X))) = join(complement(Y),X),
inference(equational,[status(thm)],[c649,c655,c659,c693,c733]) ).
cnf(c767,plain,
meet(composition(sk1,top),X) = composition(sk1,X),
inference(equational,[status(thm)],[c32,c736]) ).
cnf(c790,plain,
composition(sk1,composition(sk1,top)) = composition(sk1,top),
inference(equational,[status(thm)],[c638,c736]) ).
cnf(c805,plain,
meet(X,composition(sk1,Y)) = meet(Y,composition(sk1,X)),
inference(equational,[status(thm)],[c690,c736]) ).
cnf(c811,plain,
join(X,complement(join(X,Y))) = join(complement(Y),X),
inference(equational,[status(thm)],[c4,c743]) ).
cnf(c851,plain,
complement(composition(join(one,X),complement(Y))) = meet(Y,complement(composition(X,complement(Y)))),
inference(equational,[status(thm)],[c56,c639]) ).
cnf(c852,plain,
meet(X,complement(composition(sk1,complement(X)))) = X,
inference(equational,[status(thm)],[c5,c24,c633,c851]) ).
cnf(c853,plain,
join(complement(composition(sk1,top)),X) = complement(composition(sk1,complement(X))),
inference(equational,[status(thm)],[c314,c649,c693,c811,c852]) ).
cnf(c868,plain,
composition(sk1,composition(sk1,X)) = composition(sk1,X),
inference(equational,[status(thm)],[c736,c767,c790,c805]) ).
cnf(c916,plain,
meet(composition(sk1,X),Y) = meet(X,composition(sk1,Y)),
inference(equational,[status(thm)],[c32,c805]) ).
cnf(c1106,plain,
composition(sk1,complement(composition(sk1,complement(X)))) = composition(sk1,X),
inference(equational,[status(thm)],[c734,c767,c853]) ).
cnf(c1107,plain,
composition(sk1,complement(composition(sk1,X))) = composition(sk1,complement(X)),
inference(equational,[status(thm)],[c868,c1106]) ).
cnf(g1,plain,
meet(composition(sk1,sk2),complement(sk3)) = meet(composition(sk1,sk2),complement(composition(sk1,sk3))),
inference(equational,[status(thm)],[c32,c805,c916,c1107]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : REL030-1 : TPTP v9.0.0. Released v4.0.0.
% 0.08/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.33 % Computer : n007.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 16:13:34 EDT 2025
% 0.11/0.33 % CPUTime :
% 69.76/69.93 % SZS status Unsatisfiable
% 69.76/69.93 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------