%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL027-3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:24:56 AM UTC 2026
% Result : Unsatisfiable 5.86s 1.77s
% Output : CNFRefutation 5.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 82
% Number of leaves : 15
% Syntax : Number of formulae : 317 ( 317 unt; 0 def)
% Number of atoms : 317 ( 316 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 10 ( 10 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 8 ( 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 : 289 ( 17 sgn 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(maddux1_join_commutativity_1,axiom,
! [VAR_0,VAR_1] : join(VAR_0,VAR_1) = join(VAR_1,VAR_0),
file('theBenchmark.p',maddux1_join_commutativity_1) ).
cnf(c_1,plain,
join(A,B) = join(B,A),
inference(clausify,[status(thm)],[maddux1_join_commutativity_1]) ).
fof(maddux2_join_associativity_2,axiom,
! [VAR_0,VAR_1,VAR_2] : join(VAR_0,join(VAR_1,VAR_2)) = join(join(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',maddux2_join_associativity_2) ).
cnf(c_2,plain,
join(A,join(B,C)) = join(join(A,B),C),
inference(clausify,[status(thm)],[maddux2_join_associativity_2]) ).
cnf(c_3,plain,
join(join(A,B),C) = join(A,join(B,C)),
inference(copy,[status(thm)],[c_2]) ).
fof(maddux3_a_kind_of_de_Morgan_3,axiom,
! [VAR_0,VAR_1] : VAR_0 = join(complement(join(complement(VAR_0),complement(VAR_1))),complement(join(complement(VAR_0),VAR_1))),
file('theBenchmark.p',maddux3_a_kind_of_de_Morgan_3) ).
cnf(c_4,plain,
A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))),
inference(clausify,[status(thm)],[maddux3_a_kind_of_de_Morgan_3]) ).
cnf(c_1770,plain,
A = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),
inference(paramod,[status(thm)],[c_1,c_4]) ).
cnf(c_5,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = A,
inference(copy,[status(thm)],[c_1770]) ).
fof(maddux4_definiton_of_meet_4,axiom,
! [VAR_0,VAR_1] : meet(VAR_0,VAR_1) = complement(join(complement(VAR_0),complement(VAR_1))),
file('theBenchmark.p',maddux4_definiton_of_meet_4) ).
cnf(c_6,plain,
meet(A,B) = complement(join(complement(A),complement(B))),
inference(clausify,[status(thm)],[maddux4_definiton_of_meet_4]) ).
fof(composition_associativity_5,axiom,
! [VAR_0,VAR_1,VAR_2] : composition(VAR_0,composition(VAR_1,VAR_2)) = composition(composition(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',composition_associativity_5) ).
cnf(c_7,plain,
composition(A,composition(B,C)) = composition(composition(A,B),C),
inference(clausify,[status(thm)],[composition_associativity_5]) ).
cnf(c_8,plain,
composition(composition(A,B),C) = composition(A,composition(B,C)),
inference(copy,[status(thm)],[c_7]) ).
fof(composition_identity_6,axiom,
! [VAR_0] : composition(VAR_0,one) = VAR_0,
file('theBenchmark.p',composition_identity_6) ).
cnf(c_9,plain,
composition(A,one) = A,
inference(clausify,[status(thm)],[composition_identity_6]) ).
fof(composition_distributivity_7,axiom,
! [VAR_0,VAR_1,VAR_2] : composition(join(VAR_0,VAR_1),VAR_2) = join(composition(VAR_0,VAR_2),composition(VAR_1,VAR_2)),
file('theBenchmark.p',composition_distributivity_7) ).
cnf(c_10,plain,
composition(join(A,B),C) = join(composition(A,C),composition(B,C)),
inference(clausify,[status(thm)],[composition_distributivity_7]) ).
fof(converse_idempotence_8,axiom,
! [VAR_0] : converse(converse(VAR_0)) = VAR_0,
file('theBenchmark.p',converse_idempotence_8) ).
cnf(c_11,plain,
converse(converse(A)) = A,
inference(clausify,[status(thm)],[converse_idempotence_8]) ).
fof(converse_additivity_9,axiom,
! [VAR_0,VAR_1] : converse(join(VAR_0,VAR_1)) = join(converse(VAR_0),converse(VAR_1)),
file('theBenchmark.p',converse_additivity_9) ).
cnf(c_12,plain,
converse(join(A,B)) = join(converse(A),converse(B)),
inference(clausify,[status(thm)],[converse_additivity_9]) ).
fof(converse_multiplicativity_10,axiom,
! [VAR_0,VAR_1] : converse(composition(VAR_0,VAR_1)) = composition(converse(VAR_1),converse(VAR_0)),
file('theBenchmark.p',converse_multiplicativity_10) ).
cnf(c_13,plain,
converse(composition(A,B)) = composition(converse(B),converse(A)),
inference(clausify,[status(thm)],[converse_multiplicativity_10]) ).
fof(converse_cancellativity_11,axiom,
! [VAR_0,VAR_1] : join(composition(converse(VAR_0),complement(composition(VAR_0,VAR_1))),complement(VAR_1)) = complement(VAR_1),
file('theBenchmark.p',converse_cancellativity_11) ).
cnf(c_14,plain,
join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B),
inference(clausify,[status(thm)],[converse_cancellativity_11]) ).
cnf(c_15,plain,
join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A),
inference(paramod,[status(thm)],[c_1,c_14]) ).
fof(def_top_12,axiom,
! [VAR_0] : top = join(VAR_0,complement(VAR_0)),
file('theBenchmark.p',def_top_12) ).
cnf(c_16,plain,
top = join(A,complement(A)),
inference(clausify,[status(thm)],[def_top_12]) ).
cnf(c_17,plain,
join(A,complement(A)) = top,
inference(copy,[status(thm)],[c_16]) ).
fof(def_zero_13,axiom,
! [VAR_0] : zero = meet(VAR_0,complement(VAR_0)),
file('theBenchmark.p',def_zero_13) ).
cnf(c_18,plain,
zero = meet(A,complement(A)),
inference(clausify,[status(thm)],[def_zero_13]) ).
cnf(c_1771,plain,
zero = complement(join(complement(A),complement(complement(A)))),
inference(paramod,[status(thm)],[c_6,c_18]) ).
cnf(c_1772,plain,
zero = complement(top),
inference(paramod,[status(thm)],[c_17,c_1771]) ).
cnf(c_19,plain,
complement(top) = zero,
inference(copy,[status(thm)],[c_1772]) ).
fof(goals_17,axiom,
join(sk1,one) = one,
file('theBenchmark.p',goals_17) ).
cnf(c_26,plain,
join(sk1,one) = one,
inference(clausify,[status(thm)],[goals_17]) ).
cnf(c_27,plain,
join(one,sk1) = one,
inference(paramod,[status(thm)],[c_1,c_26]) ).
fof(goals_18,axiom,
meet(complement(composition(sk1,top)),one) != meet(complement(sk1),one),
file('theBenchmark.p',goals_18) ).
cnf(c_28,plain,
meet(complement(composition(sk1,top)),one) != meet(complement(sk1),one),
inference(clausify,[status(thm)],[goals_18]) ).
cnf(c_1773,plain,
complement(join(complement(complement(composition(sk1,top))),complement(one))) != meet(complement(sk1),one),
inference(paramod,[status(thm)],[c_6,c_28]) ).
cnf(c_1774,plain,
complement(join(complement(one),complement(complement(composition(sk1,top))))) != meet(complement(sk1),one),
inference(paramod,[status(thm)],[c_1,c_1773]) ).
cnf(c_1775,plain,
complement(join(complement(one),complement(complement(composition(sk1,top))))) != complement(join(complement(complement(sk1)),complement(one))),
inference(paramod,[status(thm)],[c_6,c_1774]) ).
cnf(c_29,plain,
complement(join(complement(one),complement(complement(composition(sk1,top))))) != complement(join(complement(one),complement(complement(sk1)))),
inference(paramod,[status(thm)],[c_1,c_1775]) ).
cnf(c_1776,plain,
join(join(A,B),C) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_31,plain,
join(A,join(B,C)) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_3,c_1776]) ).
cnf(c_32,plain,
join(complement(join(A,complement(B))),complement(join(complement(B),complement(A)))) = B,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_33,plain,
join(complement(join(complement(A),B)),complement(join(complement(B),complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_1777,plain,
converse(A) = join(converse(complement(join(complement(A),B))),converse(complement(join(complement(A),complement(B))))),
inference(paramod,[status(thm)],[c_5,c_12]) ).
cnf(c_35,plain,
join(converse(complement(join(complement(A),B))),converse(complement(join(complement(A),complement(B))))) = converse(A),
inference(copy,[status(thm)],[c_1777]) ).
cnf(c_1778,plain,
converse(A) = composition(converse(one),converse(A)),
inference(paramod,[status(thm)],[c_9,c_13]) ).
cnf(c_36,plain,
composition(converse(one),converse(A)) = converse(A),
inference(copy,[status(thm)],[c_1778]) ).
cnf(c_38,plain,
join(complement(one),composition(converse(A),complement(A))) = complement(one),
inference(paramod,[status(thm)],[c_9,c_15]) ).
cnf(c_1779,plain,
converse(complement(A)) = join(converse(complement(A)),converse(composition(converse(B),complement(composition(B,A))))),
inference(paramod,[status(thm)],[c_15,c_12]) ).
cnf(c_1780,plain,
converse(complement(A)) = join(converse(complement(A)),composition(converse(complement(composition(B,A))),converse(converse(B)))),
inference(paramod,[status(thm)],[c_13,c_1779]) ).
cnf(c_1781,plain,
converse(complement(A)) = join(converse(complement(A)),composition(converse(complement(composition(B,A))),B)),
inference(paramod,[status(thm)],[c_11,c_1780]) ).
cnf(c_40,plain,
join(converse(complement(A)),composition(converse(complement(composition(B,A))),B)) = converse(complement(A)),
inference(copy,[status(thm)],[c_1781]) ).
cnf(c_1782,plain,
join(top,A) = join(B,join(complement(B),A)),
inference(paramod,[status(thm)],[c_17,c_3]) ).
cnf(c_41,plain,
join(A,join(complement(A),B)) = join(top,B),
inference(copy,[status(thm)],[c_1782]) ).
cnf(c_1783,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_17,c_5]) ).
cnf(c_43,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_19,c_1783]) ).
cnf(c_1784,plain,
join(complement(join(complement(A),complement(A))),complement(top)) = A,
inference(paramod,[status(thm)],[c_17,c_5]) ).
cnf(c_1785,plain,
join(complement(join(complement(A),complement(A))),zero) = A,
inference(paramod,[status(thm)],[c_19,c_1784]) ).
cnf(c_44,plain,
join(zero,complement(join(complement(A),complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_1785]) ).
cnf(c_1786,plain,
composition(top,A) = join(composition(B,A),composition(complement(B),A)),
inference(paramod,[status(thm)],[c_17,c_10]) ).
cnf(c_45,plain,
join(composition(A,B),composition(complement(A),B)) = composition(top,B),
inference(copy,[status(thm)],[c_1786]) ).
cnf(c_1787,plain,
converse(top) = join(converse(A),converse(complement(A))),
inference(paramod,[status(thm)],[c_17,c_12]) ).
cnf(c_46,plain,
join(converse(A),converse(complement(A))) = converse(top),
inference(copy,[status(thm)],[c_1787]) ).
cnf(c_1788,plain,
join(zero,composition(converse(A),complement(composition(A,top)))) = complement(top),
inference(paramod,[status(thm)],[c_19,c_15]) ).
cnf(c_49,plain,
join(zero,composition(converse(A),complement(composition(A,top)))) = zero,
inference(paramod,[status(thm)],[c_19,c_1788]) ).
cnf(c_1789,plain,
join(one,A) = join(one,join(sk1,A)),
inference(paramod,[status(thm)],[c_27,c_3]) ).
cnf(c_51,plain,
join(one,join(sk1,A)) = join(one,A),
inference(copy,[status(thm)],[c_1789]) ).
cnf(c_1790,plain,
composition(one,A) = join(composition(one,A),composition(sk1,A)),
inference(paramod,[status(thm)],[c_27,c_10]) ).
cnf(c_53,plain,
join(composition(one,A),composition(sk1,A)) = composition(one,A),
inference(copy,[status(thm)],[c_1790]) ).
cnf(c_1791,plain,
converse(one) = join(converse(one),converse(sk1)),
inference(paramod,[status(thm)],[c_27,c_12]) ).
cnf(c_54,plain,
join(converse(one),converse(sk1)) = converse(one),
inference(copy,[status(thm)],[c_1791]) ).
cnf(c_1792,plain,
A = join(complement(join(complement(A),complement(B))),complement(join(B,complement(A)))),
inference(paramod,[status(thm)],[c_32,c_1]) ).
cnf(c_57,plain,
join(complement(join(complement(A),complement(B))),complement(join(B,complement(A)))) = A,
inference(copy,[status(thm)],[c_1792]) ).
cnf(c_1793,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_36]) ).
cnf(c_67,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_11,c_1793]) ).
cnf(c_1794,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_67,c_9]) ).
cnf(c_69,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_1794]) ).
cnf(c_73,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_67,c_15]) ).
cnf(c_74,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_69,c_67]) ).
cnf(c_1795,plain,
join(one,converse(sk1)) = converse(one),
inference(paramod,[status(thm)],[c_69,c_54]) ).
cnf(c_75,plain,
join(one,converse(sk1)) = one,
inference(paramod,[status(thm)],[c_69,c_1795]) ).
cnf(c_1796,plain,
join(A,composition(sk1,A)) = composition(one,A),
inference(paramod,[status(thm)],[c_74,c_53]) ).
cnf(c_76,plain,
join(A,composition(sk1,A)) = A,
inference(paramod,[status(thm)],[c_74,c_1796]) ).
cnf(c_77,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_74,c_73]) ).
cnf(c_78,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_77,c_44]) ).
cnf(c_1797,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_17,c_33]) ).
cnf(c_1798,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_1,c_1797]) ).
cnf(c_1799,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_19,c_1798]) ).
cnf(c_81,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_1,c_1799]) ).
cnf(c_82,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_81,c_43]) ).
cnf(c_83,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_82,c_81]) ).
cnf(c_84,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_82,c_78]) ).
cnf(c_1800,plain,
complement(join(complement(one),composition(sk1,top))) != complement(join(complement(one),complement(complement(sk1)))),
inference(paramod,[status(thm)],[c_82,c_29]) ).
cnf(c_1801,plain,
complement(join(complement(one),composition(sk1,top))) != complement(join(complement(one),sk1)),
inference(paramod,[status(thm)],[c_82,c_1800]) ).
cnf(c_85,plain,
complement(join(complement(one),composition(sk1,top))) != complement(join(sk1,complement(one))),
inference(paramod,[status(thm)],[c_1,c_1801]) ).
cnf(c_86,plain,
complement(join(A,A)) = complement(A),
inference(paramod,[status(thm)],[c_84,c_83]) ).
cnf(c_88,plain,
composition(converse(A),complement(composition(A,top))) = zero,
inference(paramod,[status(thm)],[c_84,c_49]) ).
cnf(c_1802,plain,
join(converse(complement(top)),converse(complement(join(complement(A),complement(complement(complement(A))))))) = converse(A),
inference(paramod,[status(thm)],[c_17,c_35]) ).
cnf(c_1803,plain,
join(converse(zero),converse(complement(join(complement(A),complement(complement(complement(A))))))) = converse(A),
inference(paramod,[status(thm)],[c_19,c_1802]) ).
cnf(c_1804,plain,
join(converse(zero),converse(complement(join(complement(A),complement(A))))) = converse(A),
inference(paramod,[status(thm)],[c_82,c_1803]) ).
cnf(c_1805,plain,
join(converse(zero),converse(complement(complement(A)))) = converse(A),
inference(paramod,[status(thm)],[c_77,c_1804]) ).
cnf(c_90,plain,
join(converse(zero),converse(A)) = converse(A),
inference(paramod,[status(thm)],[c_82,c_1805]) ).
cnf(c_1806,plain,
A = join(A,zero),
inference(paramod,[status(thm)],[c_84,c_1]) ).
cnf(c_93,plain,
join(A,zero) = A,
inference(copy,[status(thm)],[c_1806]) ).
cnf(c_1807,plain,
composition(one,A) = join(composition(one,A),composition(converse(sk1),A)),
inference(paramod,[status(thm)],[c_75,c_10]) ).
cnf(c_1808,plain,
A = join(composition(one,A),composition(converse(sk1),A)),
inference(paramod,[status(thm)],[c_74,c_1807]) ).
cnf(c_1809,plain,
A = join(A,composition(converse(sk1),A)),
inference(paramod,[status(thm)],[c_74,c_1808]) ).
cnf(c_102,plain,
join(A,composition(converse(sk1),A)) = A,
inference(copy,[status(thm)],[c_1809]) ).
cnf(c_1810,plain,
join(complement(join(A,B)),complement(join(complement(complement(A)),complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_82,c_5]) ).
cnf(c_124,plain,
join(complement(join(A,B)),complement(join(A,complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_82,c_1810]) ).
cnf(c_1811,plain,
join(complement(join(A,B)),complement(join(complement(complement(B)),complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_82,c_32]) ).
cnf(c_126,plain,
join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_82,c_1811]) ).
cnf(c_129,plain,
join(complement(one),composition(converse(complement(A)),A)) = complement(one),
inference(paramod,[status(thm)],[c_82,c_38]) ).
cnf(c_1812,plain,
join(join(A,A),complement(A)) = top,
inference(paramod,[status(thm)],[c_86,c_17]) ).
cnf(c_1813,plain,
join(A,join(A,complement(A))) = top,
inference(paramod,[status(thm)],[c_3,c_1812]) ).
cnf(c_132,plain,
join(A,top) = top,
inference(paramod,[status(thm)],[c_17,c_1813]) ).
cnf(c_1814,plain,
complement(complement(A)) = join(A,A),
inference(paramod,[status(thm)],[c_86,c_82]) ).
cnf(c_1815,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_82,c_1814]) ).
cnf(c_133,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_1815]) ).
cnf(c_1816,plain,
top = join(top,A),
inference(paramod,[status(thm)],[c_132,c_1]) ).
cnf(c_135,plain,
join(top,A) = top,
inference(copy,[status(thm)],[c_1816]) ).
cnf(c_1817,plain,
composition(top,A) = join(composition(B,A),composition(top,A)),
inference(paramod,[status(thm)],[c_132,c_10]) ).
cnf(c_136,plain,
join(composition(A,B),composition(top,B)) = composition(top,B),
inference(copy,[status(thm)],[c_1817]) ).
cnf(c_1818,plain,
converse(top) = join(converse(A),converse(top)),
inference(paramod,[status(thm)],[c_132,c_12]) ).
cnf(c_137,plain,
join(converse(A),converse(top)) = converse(top),
inference(copy,[status(thm)],[c_1818]) ).
cnf(c_138,plain,
join(A,join(complement(A),B)) = top,
inference(paramod,[status(thm)],[c_135,c_41]) ).
cnf(c_1819,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_133,c_3]) ).
cnf(c_139,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_1819]) ).
cnf(c_1820,plain,
join(converse(zero),composition(converse(complement(composition(A,top))),A)) = converse(complement(top)),
inference(paramod,[status(thm)],[c_19,c_40]) ).
cnf(c_144,plain,
join(converse(zero),composition(converse(complement(composition(A,top))),A)) = converse(zero),
inference(paramod,[status(thm)],[c_19,c_1820]) ).
cnf(c_1821,plain,
join(converse(zero),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_90]) ).
cnf(c_152,plain,
join(converse(zero),A) = A,
inference(paramod,[status(thm)],[c_11,c_1821]) ).
cnf(c_154,plain,
composition(converse(complement(composition(A,top))),A) = converse(zero),
inference(paramod,[status(thm)],[c_152,c_144]) ).
cnf(c_1822,plain,
zero = converse(zero),
inference(paramod,[status(thm)],[c_152,c_93]) ).
cnf(c_158,plain,
converse(zero) = zero,
inference(copy,[status(thm)],[c_1822]) ).
cnf(c_159,plain,
composition(converse(complement(composition(A,top))),A) = zero,
inference(paramod,[status(thm)],[c_158,c_154]) ).
cnf(c_1823,plain,
join(A,composition(top,B)) = join(composition(C,B),join(A,composition(complement(C),B))),
inference(paramod,[status(thm)],[c_45,c_31]) ).
cnf(c_173,plain,
join(composition(A,B),join(C,composition(complement(A),B))) = join(C,composition(top,B)),
inference(copy,[status(thm)],[c_1823]) ).
cnf(c_178,plain,
join(A,converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_11,c_137]) ).
cnf(c_181,plain,
converse(top) = top,
inference(paramod,[status(thm)],[c_178,c_135]) ).
cnf(c_186,plain,
join(converse(A),converse(complement(A))) = top,
inference(paramod,[status(thm)],[c_181,c_46]) ).
cnf(c_1824,plain,
join(one,top) = join(one,complement(sk1)),
inference(paramod,[status(thm)],[c_17,c_51]) ).
cnf(c_1825,plain,
top = join(one,complement(sk1)),
inference(paramod,[status(thm)],[c_132,c_1824]) ).
cnf(c_195,plain,
join(one,complement(sk1)) = top,
inference(copy,[status(thm)],[c_1825]) ).
cnf(c_1826,plain,
converse(A) = join(converse(A),converse(composition(converse(sk1),A))),
inference(paramod,[status(thm)],[c_102,c_12]) ).
cnf(c_1827,plain,
converse(A) = join(converse(A),composition(converse(A),converse(converse(sk1)))),
inference(paramod,[status(thm)],[c_13,c_1826]) ).
cnf(c_1828,plain,
converse(A) = join(converse(A),composition(converse(A),sk1)),
inference(paramod,[status(thm)],[c_11,c_1827]) ).
cnf(c_217,plain,
join(converse(A),composition(converse(A),sk1)) = converse(A),
inference(copy,[status(thm)],[c_1828]) ).
cnf(c_1829,plain,
join(complement(join(complement(sk1),complement(one))),complement(top)) = sk1,
inference(paramod,[status(thm)],[c_195,c_57]) ).
cnf(c_1830,plain,
join(complement(join(complement(one),complement(sk1))),complement(top)) = sk1,
inference(paramod,[status(thm)],[c_1,c_1829]) ).
cnf(c_1831,plain,
join(complement(join(complement(one),complement(sk1))),zero) = sk1,
inference(paramod,[status(thm)],[c_19,c_1830]) ).
cnf(c_1832,plain,
join(zero,complement(join(complement(one),complement(sk1)))) = sk1,
inference(paramod,[status(thm)],[c_1,c_1831]) ).
cnf(c_224,plain,
complement(join(complement(one),complement(sk1))) = sk1,
inference(paramod,[status(thm)],[c_84,c_1832]) ).
cnf(c_236,plain,
join(A,converse(complement(converse(A)))) = top,
inference(paramod,[status(thm)],[c_11,c_186]) ).
cnf(c_239,plain,
join(one,converse(complement(one))) = top,
inference(paramod,[status(thm)],[c_69,c_186]) ).
cnf(c_1833,plain,
complement(sk1) = join(complement(one),complement(sk1)),
inference(paramod,[status(thm)],[c_224,c_82]) ).
cnf(c_251,plain,
join(complement(one),complement(sk1)) = complement(sk1),
inference(copy,[status(thm)],[c_1833]) ).
cnf(c_260,plain,
composition(top,complement(composition(top,top))) = zero,
inference(paramod,[status(thm)],[c_181,c_88]) ).
cnf(c_1834,plain,
composition(join(top,A),complement(composition(top,top))) = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_260,c_10]) ).
cnf(c_1835,plain,
composition(top,complement(composition(top,top))) = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_135,c_1834]) ).
cnf(c_1836,plain,
zero = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_260,c_1835]) ).
cnf(c_1837,plain,
zero = composition(A,complement(composition(top,top))),
inference(paramod,[status(thm)],[c_84,c_1836]) ).
cnf(c_275,plain,
composition(A,complement(composition(top,top))) = zero,
inference(copy,[status(thm)],[c_1837]) ).
cnf(c_1838,plain,
zero = complement(composition(top,top)),
inference(paramod,[status(thm)],[c_275,c_74]) ).
cnf(c_280,plain,
complement(composition(top,top)) = zero,
inference(copy,[status(thm)],[c_1838]) ).
cnf(c_1839,plain,
join(composition(top,top),zero) = top,
inference(paramod,[status(thm)],[c_280,c_17]) ).
cnf(c_1840,plain,
join(zero,composition(top,top)) = top,
inference(paramod,[status(thm)],[c_1,c_1839]) ).
cnf(c_286,plain,
composition(top,top) = top,
inference(paramod,[status(thm)],[c_84,c_1840]) ).
cnf(c_1841,plain,
composition(top,A) = composition(top,composition(top,A)),
inference(paramod,[status(thm)],[c_286,c_8]) ).
cnf(c_295,plain,
composition(top,composition(top,A)) = composition(top,A),
inference(copy,[status(thm)],[c_1841]) ).
cnf(c_304,plain,
join(A,composition(top,A)) = composition(top,A),
inference(paramod,[status(thm)],[c_74,c_136]) ).
cnf(c_1842,plain,
join(complement(composition(top,A)),composition(converse(top),complement(composition(top,A)))) = complement(composition(top,A)),
inference(paramod,[status(thm)],[c_295,c_15]) ).
cnf(c_1843,plain,
join(complement(composition(top,A)),composition(top,complement(composition(top,A)))) = complement(composition(top,A)),
inference(paramod,[status(thm)],[c_181,c_1842]) ).
cnf(c_351,plain,
composition(top,complement(composition(top,A))) = complement(composition(top,A)),
inference(paramod,[status(thm)],[c_304,c_1843]) ).
cnf(c_388,plain,
join(A,composition(top,complement(A))) = top,
inference(paramod,[status(thm)],[c_304,c_138]) ).
cnf(c_394,plain,
join(complement(A),composition(top,A)) = top,
inference(paramod,[status(thm)],[c_82,c_388]) ).
cnf(c_1844,plain,
converse(top) = join(converse(complement(A)),converse(composition(top,A))),
inference(paramod,[status(thm)],[c_394,c_12]) ).
cnf(c_1845,plain,
top = join(converse(complement(A)),converse(composition(top,A))),
inference(paramod,[status(thm)],[c_181,c_1844]) ).
cnf(c_1846,plain,
top = join(converse(complement(A)),composition(converse(A),converse(top))),
inference(paramod,[status(thm)],[c_13,c_1845]) ).
cnf(c_1847,plain,
top = join(converse(complement(A)),composition(converse(A),top)),
inference(paramod,[status(thm)],[c_181,c_1846]) ).
cnf(c_1848,plain,
top = join(composition(converse(A),top),converse(complement(A))),
inference(paramod,[status(thm)],[c_1,c_1847]) ).
cnf(c_400,plain,
join(composition(converse(A),top),converse(complement(A))) = top,
inference(copy,[status(thm)],[c_1848]) ).
cnf(c_1849,plain,
join(A,composition(converse(converse(A)),sk1)) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_217]) ).
cnf(c_1850,plain,
join(A,composition(A,sk1)) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_1849]) ).
cnf(c_446,plain,
join(A,composition(A,sk1)) = A,
inference(paramod,[status(thm)],[c_11,c_1850]) ).
cnf(c_496,plain,
join(composition(A,top),converse(complement(converse(A)))) = top,
inference(paramod,[status(thm)],[c_11,c_400]) ).
cnf(c_1851,plain,
join(complement(join(A,B)),complement(A)) = join(complement(join(A,B)),complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_124,c_139]) ).
cnf(c_1852,plain,
join(complement(A),complement(join(A,B))) = join(complement(join(A,B)),complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_1,c_1851]) ).
cnf(c_514,plain,
join(complement(A),complement(join(A,B))) = complement(A),
inference(paramod,[status(thm)],[c_124,c_1852]) ).
cnf(c_530,plain,
join(complement(A),complement(join(B,A))) = complement(A),
inference(paramod,[status(thm)],[c_1,c_514]) ).
cnf(c_1853,plain,
join(A,complement(join(B,complement(A)))) = complement(complement(A)),
inference(paramod,[status(thm)],[c_82,c_530]) ).
cnf(c_551,plain,
join(A,complement(join(B,complement(A)))) = A,
inference(paramod,[status(thm)],[c_82,c_1853]) ).
cnf(c_1854,plain,
join(complement(top),complement(join(converse(complement(one)),complement(one)))) = complement(converse(complement(one))),
inference(paramod,[status(thm)],[c_239,c_126]) ).
cnf(c_1855,plain,
join(zero,complement(join(converse(complement(one)),complement(one)))) = complement(converse(complement(one))),
inference(paramod,[status(thm)],[c_19,c_1854]) ).
cnf(c_1856,plain,
join(zero,complement(join(complement(one),converse(complement(one))))) = complement(converse(complement(one))),
inference(paramod,[status(thm)],[c_1,c_1855]) ).
cnf(c_598,plain,
complement(join(complement(one),converse(complement(one)))) = complement(converse(complement(one))),
inference(paramod,[status(thm)],[c_84,c_1856]) ).
cnf(c_1857,plain,
join(complement(complement(A)),complement(join(complement(join(A,complement(B))),complement(complement(join(A,B)))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_124,c_126]) ).
cnf(c_1858,plain,
join(A,complement(join(complement(join(A,complement(B))),complement(complement(join(A,B)))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_82,c_1857]) ).
cnf(c_1859,plain,
join(A,complement(join(complement(join(A,complement(B))),join(A,B)))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_82,c_1858]) ).
cnf(c_1860,plain,
join(A,complement(join(join(A,B),complement(join(A,complement(B)))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_1,c_1859]) ).
cnf(c_1861,plain,
join(A,complement(join(A,join(B,complement(join(A,complement(B))))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_3,c_1860]) ).
cnf(c_1862,plain,
join(A,complement(join(A,B))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_551,c_1861]) ).
cnf(c_609,plain,
join(A,complement(join(A,B))) = join(A,complement(B)),
inference(paramod,[status(thm)],[c_82,c_1862]) ).
cnf(c_1863,plain,
join(zero,composition(complement(converse(complement(composition(A,top)))),A)) = composition(top,A),
inference(paramod,[status(thm)],[c_159,c_45]) ).
cnf(c_623,plain,
composition(complement(converse(complement(composition(A,top)))),A) = composition(top,A),
inference(paramod,[status(thm)],[c_84,c_1863]) ).
cnf(c_689,plain,
join(complement(one),converse(complement(one))) = complement(one),
inference(paramod,[status(thm)],[c_9,c_129]) ).
cnf(c_1864,plain,
complement(complement(one)) = complement(converse(complement(one))),
inference(paramod,[status(thm)],[c_689,c_598]) ).
cnf(c_1865,plain,
one = complement(converse(complement(one))),
inference(paramod,[status(thm)],[c_82,c_1864]) ).
cnf(c_693,plain,
complement(converse(complement(one))) = one,
inference(copy,[status(thm)],[c_1865]) ).
cnf(c_1866,plain,
complement(one) = converse(complement(one)),
inference(paramod,[status(thm)],[c_693,c_82]) ).
cnf(c_701,plain,
converse(complement(one)) = complement(one),
inference(copy,[status(thm)],[c_1866]) ).
cnf(c_802,plain,
join(A,complement(join(B,A))) = join(A,complement(B)),
inference(paramod,[status(thm)],[c_1,c_609]) ).
cnf(c_1867,plain,
join(composition(A,sk1),complement(A)) = join(complement(A),composition(top,sk1)),
inference(paramod,[status(thm)],[c_446,c_173]) ).
cnf(c_1868,plain,
join(complement(A),composition(A,sk1)) = join(complement(A),composition(top,sk1)),
inference(paramod,[status(thm)],[c_1,c_1867]) ).
cnf(c_844,plain,
join(complement(A),composition(top,sk1)) = join(complement(A),composition(A,sk1)),
inference(copy,[status(thm)],[c_1868]) ).
cnf(c_1869,plain,
join(converse(complement(A)),complement(top)) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_186,c_802]) ).
cnf(c_1870,plain,
join(converse(complement(A)),zero) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_19,c_1869]) ).
cnf(c_1871,plain,
join(zero,converse(complement(A))) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_1,c_1870]) ).
cnf(c_1872,plain,
converse(complement(A)) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_84,c_1871]) ).
cnf(c_1873,plain,
converse(complement(A)) = join(complement(converse(A)),converse(complement(A))),
inference(paramod,[status(thm)],[c_1,c_1872]) ).
cnf(c_870,plain,
join(complement(converse(A)),converse(complement(A))) = converse(complement(A)),
inference(copy,[status(thm)],[c_1873]) ).
cnf(c_1874,plain,
join(converse(complement(converse(A))),complement(top)) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_236,c_802]) ).
cnf(c_1875,plain,
join(converse(complement(converse(A))),zero) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_19,c_1874]) ).
cnf(c_1876,plain,
join(zero,converse(complement(converse(A)))) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_1,c_1875]) ).
cnf(c_1877,plain,
converse(complement(converse(A))) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_84,c_1876]) ).
cnf(c_1878,plain,
converse(complement(converse(A))) = join(complement(A),converse(complement(converse(A)))),
inference(paramod,[status(thm)],[c_1,c_1877]) ).
cnf(c_873,plain,
join(complement(A),converse(complement(converse(A)))) = converse(complement(converse(A))),
inference(copy,[status(thm)],[c_1878]) ).
cnf(c_1879,plain,
join(complement(one),composition(top,sk1)) = join(complement(one),sk1),
inference(paramod,[status(thm)],[c_74,c_844]) ).
cnf(c_916,plain,
join(complement(one),composition(top,sk1)) = join(sk1,complement(one)),
inference(paramod,[status(thm)],[c_1,c_1879]) ).
cnf(c_1880,plain,
converse(join(sk1,complement(one))) = join(converse(complement(one)),converse(composition(top,sk1))),
inference(paramod,[status(thm)],[c_916,c_12]) ).
cnf(c_1881,plain,
join(converse(sk1),converse(complement(one))) = join(converse(complement(one)),converse(composition(top,sk1))),
inference(paramod,[status(thm)],[c_12,c_1880]) ).
cnf(c_1882,plain,
join(converse(sk1),complement(one)) = join(converse(complement(one)),converse(composition(top,sk1))),
inference(paramod,[status(thm)],[c_701,c_1881]) ).
cnf(c_1883,plain,
join(complement(one),converse(sk1)) = join(converse(complement(one)),converse(composition(top,sk1))),
inference(paramod,[status(thm)],[c_1,c_1882]) ).
cnf(c_1884,plain,
join(complement(one),converse(sk1)) = join(complement(one),converse(composition(top,sk1))),
inference(paramod,[status(thm)],[c_701,c_1883]) ).
cnf(c_1885,plain,
join(complement(one),converse(sk1)) = join(complement(one),composition(converse(sk1),converse(top))),
inference(paramod,[status(thm)],[c_13,c_1884]) ).
cnf(c_1886,plain,
join(complement(one),converse(sk1)) = join(complement(one),composition(converse(sk1),top)),
inference(paramod,[status(thm)],[c_181,c_1885]) ).
cnf(c_946,plain,
join(complement(one),composition(converse(sk1),top)) = join(complement(one),converse(sk1)),
inference(copy,[status(thm)],[c_1886]) ).
cnf(c_1887,plain,
join(complement(one),complement(join(sk1,complement(one)))) = join(complement(one),complement(composition(top,sk1))),
inference(paramod,[status(thm)],[c_916,c_609]) ).
cnf(c_1888,plain,
join(complement(one),complement(sk1)) = join(complement(one),complement(composition(top,sk1))),
inference(paramod,[status(thm)],[c_802,c_1887]) ).
cnf(c_1889,plain,
complement(sk1) = join(complement(one),complement(composition(top,sk1))),
inference(paramod,[status(thm)],[c_251,c_1888]) ).
cnf(c_953,plain,
join(complement(one),complement(composition(top,sk1))) = complement(sk1),
inference(copy,[status(thm)],[c_1889]) ).
cnf(c_1890,plain,
converse(complement(sk1)) = join(converse(complement(one)),converse(complement(composition(top,sk1)))),
inference(paramod,[status(thm)],[c_953,c_12]) ).
cnf(c_1891,plain,
converse(complement(sk1)) = join(complement(one),converse(complement(composition(top,sk1)))),
inference(paramod,[status(thm)],[c_701,c_1890]) ).
cnf(c_957,plain,
join(complement(one),converse(complement(composition(top,sk1)))) = converse(complement(sk1)),
inference(copy,[status(thm)],[c_1891]) ).
cnf(c_1892,plain,
join(A,complement(sk1)) = join(complement(one),join(A,complement(composition(top,sk1)))),
inference(paramod,[status(thm)],[c_953,c_31]) ).
cnf(c_958,plain,
join(complement(one),join(A,complement(composition(top,sk1)))) = join(A,complement(sk1)),
inference(copy,[status(thm)],[c_1892]) ).
cnf(c_1893,plain,
converse(converse(complement(A))) = join(converse(complement(converse(A))),converse(converse(complement(A)))),
inference(paramod,[status(thm)],[c_870,c_12]) ).
cnf(c_1894,plain,
complement(A) = join(converse(complement(converse(A))),converse(converse(complement(A)))),
inference(paramod,[status(thm)],[c_11,c_1893]) ).
cnf(c_1895,plain,
complement(A) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_11,c_1894]) ).
cnf(c_1896,plain,
complement(A) = join(complement(A),converse(complement(converse(A)))),
inference(paramod,[status(thm)],[c_1,c_1895]) ).
cnf(c_1897,plain,
complement(A) = converse(complement(converse(A))),
inference(paramod,[status(thm)],[c_873,c_1896]) ).
cnf(c_963,plain,
converse(complement(converse(A))) = complement(A),
inference(copy,[status(thm)],[c_1897]) ).
cnf(c_1898,plain,
join(composition(A,top),complement(A)) = top,
inference(paramod,[status(thm)],[c_963,c_496]) ).
cnf(c_969,plain,
join(complement(A),composition(A,top)) = top,
inference(paramod,[status(thm)],[c_1,c_1898]) ).
cnf(c_1899,plain,
join(complement(A),complement(top)) = join(complement(A),complement(composition(A,top))),
inference(paramod,[status(thm)],[c_969,c_609]) ).
cnf(c_1900,plain,
join(complement(A),zero) = join(complement(A),complement(composition(A,top))),
inference(paramod,[status(thm)],[c_19,c_1899]) ).
cnf(c_1901,plain,
join(zero,complement(A)) = join(complement(A),complement(composition(A,top))),
inference(paramod,[status(thm)],[c_1,c_1900]) ).
cnf(c_1902,plain,
complement(A) = join(complement(A),complement(composition(A,top))),
inference(paramod,[status(thm)],[c_84,c_1901]) ).
cnf(c_991,plain,
join(complement(A),complement(composition(A,top))) = complement(A),
inference(copy,[status(thm)],[c_1902]) ).
cnf(c_993,plain,
converse(complement(A)) = complement(converse(A)),
inference(paramod,[status(thm)],[c_963,c_11]) ).
cnf(c_1903,plain,
join(complement(one),complement(converse(composition(top,sk1)))) = converse(complement(sk1)),
inference(paramod,[status(thm)],[c_993,c_957]) ).
cnf(c_1904,plain,
join(complement(one),complement(composition(converse(sk1),converse(top)))) = converse(complement(sk1)),
inference(paramod,[status(thm)],[c_13,c_1903]) ).
cnf(c_1905,plain,
join(complement(one),complement(composition(converse(sk1),top))) = converse(complement(sk1)),
inference(paramod,[status(thm)],[c_181,c_1904]) ).
cnf(c_1014,plain,
join(complement(one),complement(composition(converse(sk1),top))) = complement(converse(sk1)),
inference(paramod,[status(thm)],[c_993,c_1905]) ).
cnf(c_1906,plain,
composition(complement(complement(converse(composition(A,top)))),A) = composition(top,A),
inference(paramod,[status(thm)],[c_993,c_623]) ).
cnf(c_1907,plain,
composition(complement(complement(composition(converse(top),converse(A)))),A) = composition(top,A),
inference(paramod,[status(thm)],[c_13,c_1906]) ).
cnf(c_1908,plain,
composition(complement(complement(composition(top,converse(A)))),A) = composition(top,A),
inference(paramod,[status(thm)],[c_181,c_1907]) ).
cnf(c_1909,plain,
composition(composition(top,converse(A)),A) = composition(top,A),
inference(paramod,[status(thm)],[c_82,c_1908]) ).
cnf(c_1032,plain,
composition(top,composition(converse(A),A)) = composition(top,A),
inference(paramod,[status(thm)],[c_8,c_1909]) ).
cnf(c_1910,plain,
converse(composition(top,A)) = composition(converse(composition(converse(A),A)),converse(top)),
inference(paramod,[status(thm)],[c_1032,c_13]) ).
cnf(c_1911,plain,
composition(converse(A),converse(top)) = composition(converse(composition(converse(A),A)),converse(top)),
inference(paramod,[status(thm)],[c_13,c_1910]) ).
cnf(c_1912,plain,
composition(converse(A),top) = composition(converse(composition(converse(A),A)),converse(top)),
inference(paramod,[status(thm)],[c_181,c_1911]) ).
cnf(c_1913,plain,
composition(converse(A),top) = composition(composition(converse(A),converse(converse(A))),converse(top)),
inference(paramod,[status(thm)],[c_13,c_1912]) ).
cnf(c_1914,plain,
composition(converse(A),top) = composition(composition(converse(A),A),converse(top)),
inference(paramod,[status(thm)],[c_11,c_1913]) ).
cnf(c_1915,plain,
composition(converse(A),top) = composition(composition(converse(A),A),top),
inference(paramod,[status(thm)],[c_181,c_1914]) ).
cnf(c_1916,plain,
composition(converse(A),top) = composition(converse(A),composition(A,top)),
inference(paramod,[status(thm)],[c_8,c_1915]) ).
cnf(c_1361,plain,
composition(converse(A),composition(A,top)) = composition(converse(A),top),
inference(copy,[status(thm)],[c_1916]) ).
cnf(c_1917,plain,
composition(A,composition(converse(A),top)) = composition(converse(converse(A)),top),
inference(paramod,[status(thm)],[c_11,c_1361]) ).
cnf(c_1367,plain,
composition(A,composition(converse(A),top)) = composition(A,top),
inference(paramod,[status(thm)],[c_11,c_1917]) ).
cnf(c_1368,plain,
join(composition(sk1,top),composition(converse(sk1),top)) = composition(sk1,top),
inference(paramod,[status(thm)],[c_1361,c_102]) ).
cnf(c_1918,plain,
join(composition(converse(sk1),top),composition(sk1,top)) = composition(converse(sk1),top),
inference(paramod,[status(thm)],[c_1367,c_76]) ).
cnf(c_1919,plain,
join(composition(sk1,top),composition(converse(sk1),top)) = composition(converse(sk1),top),
inference(paramod,[status(thm)],[c_1,c_1918]) ).
cnf(c_1920,plain,
composition(sk1,top) = composition(converse(sk1),top),
inference(paramod,[status(thm)],[c_1368,c_1919]) ).
cnf(c_1700,plain,
composition(converse(sk1),top) = composition(sk1,top),
inference(copy,[status(thm)],[c_1920]) ).
cnf(c_1921,plain,
join(complement(one),complement(composition(sk1,top))) = complement(converse(sk1)),
inference(paramod,[status(thm)],[c_1700,c_1014]) ).
cnf(c_1713,plain,
complement(converse(sk1)) = join(complement(one),complement(composition(sk1,top))),
inference(copy,[status(thm)],[c_1921]) ).
cnf(c_1922,plain,
join(complement(one),composition(sk1,top)) = join(complement(one),converse(sk1)),
inference(paramod,[status(thm)],[c_1700,c_946]) ).
cnf(c_1714,plain,
join(complement(one),converse(sk1)) = join(complement(one),composition(sk1,top)),
inference(copy,[status(thm)],[c_1922]) ).
cnf(c_1923,plain,
converse(composition(sk1,top)) = composition(converse(top),converse(converse(sk1))),
inference(paramod,[status(thm)],[c_1700,c_13]) ).
cnf(c_1924,plain,
composition(converse(top),converse(sk1)) = composition(converse(top),converse(converse(sk1))),
inference(paramod,[status(thm)],[c_13,c_1923]) ).
cnf(c_1925,plain,
composition(top,converse(sk1)) = composition(converse(top),converse(converse(sk1))),
inference(paramod,[status(thm)],[c_181,c_1924]) ).
cnf(c_1926,plain,
composition(top,converse(sk1)) = composition(top,converse(converse(sk1))),
inference(paramod,[status(thm)],[c_181,c_1925]) ).
cnf(c_1720,plain,
composition(top,converse(sk1)) = composition(top,sk1),
inference(paramod,[status(thm)],[c_11,c_1926]) ).
cnf(c_1927,plain,
join(complement(converse(sk1)),composition(converse(top),complement(composition(top,sk1)))) = complement(converse(sk1)),
inference(paramod,[status(thm)],[c_1720,c_15]) ).
cnf(c_1928,plain,
join(join(complement(one),complement(composition(sk1,top))),composition(converse(top),complement(composition(top,sk1)))) = complement(converse(sk1)),
inference(paramod,[status(thm)],[c_1713,c_1927]) ).
cnf(c_1929,plain,
join(join(complement(one),complement(composition(sk1,top))),composition(top,complement(composition(top,sk1)))) = complement(converse(sk1)),
inference(paramod,[status(thm)],[c_181,c_1928]) ).
cnf(c_1930,plain,
join(join(complement(one),complement(composition(sk1,top))),complement(composition(top,sk1))) = complement(converse(sk1)),
inference(paramod,[status(thm)],[c_351,c_1929]) ).
cnf(c_1931,plain,
join(complement(one),join(complement(composition(sk1,top)),complement(composition(top,sk1)))) = complement(converse(sk1)),
inference(paramod,[status(thm)],[c_3,c_1930]) ).
cnf(c_1932,plain,
join(complement(composition(sk1,top)),complement(sk1)) = complement(converse(sk1)),
inference(paramod,[status(thm)],[c_958,c_1931]) ).
cnf(c_1933,plain,
join(complement(sk1),complement(composition(sk1,top))) = complement(converse(sk1)),
inference(paramod,[status(thm)],[c_1,c_1932]) ).
cnf(c_1934,plain,
complement(sk1) = complement(converse(sk1)),
inference(paramod,[status(thm)],[c_991,c_1933]) ).
cnf(c_1935,plain,
complement(sk1) = join(complement(one),complement(composition(sk1,top))),
inference(paramod,[status(thm)],[c_1713,c_1934]) ).
cnf(c_1739,plain,
join(complement(one),complement(composition(sk1,top))) = complement(sk1),
inference(copy,[status(thm)],[c_1935]) ).
cnf(c_1751,plain,
complement(converse(sk1)) = complement(sk1),
inference(paramod,[status(thm)],[c_1739,c_1713]) ).
cnf(c_1936,plain,
complement(complement(sk1)) = converse(sk1),
inference(paramod,[status(thm)],[c_1751,c_82]) ).
cnf(c_1937,plain,
sk1 = converse(sk1),
inference(paramod,[status(thm)],[c_82,c_1936]) ).
cnf(c_1755,plain,
converse(sk1) = sk1,
inference(copy,[status(thm)],[c_1937]) ).
cnf(c_1938,plain,
join(complement(one),sk1) = join(complement(one),composition(sk1,top)),
inference(paramod,[status(thm)],[c_1755,c_1714]) ).
cnf(c_1939,plain,
join(sk1,complement(one)) = join(complement(one),composition(sk1,top)),
inference(paramod,[status(thm)],[c_1,c_1938]) ).
cnf(c_1760,plain,
join(complement(one),composition(sk1,top)) = join(sk1,complement(one)),
inference(copy,[status(thm)],[c_1939]) ).
cnf(c_1940,plain,
complement(join(sk1,complement(one))) != complement(join(sk1,complement(one))),
inference(paramod,[status(thm)],[c_1760,c_85]) ).
cnf(c_1769,plain,
$false,
inference(copy,[status(thm)],[c_1940]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL027-3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n001.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 05:38:56 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 1009958 was started by sandbox on n001,
% 0.09/0.36 % Sat Sep 26 05:38:56 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 5.86/1.77
% 5.86/1.77 % SZS status Unsatisfiable for theBenchmark
% 5.86/1.77
% 5.86/1.77 % Proof 1 at 0.55 (+ 0.17) seconds.
% 5.86/1.77 % Length of proof is 131.
% 5.86/1.77 % Level of proof is 28.
% 5.86/1.77 % Maximum clause weight is 33.000.
% 5.86/1.77 % Given clauses 303.
% 5.86/1.77
% 5.86/1.77 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------