%------------------------------------------------------------------------------
% 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/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 : Theorem 11.06s 1.86s
% Output : CNFRefutation 11.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 82
% Number of leaves : 14
% Syntax : Number of formulae : 315 ( 311 unt; 0 def)
% Number of atoms : 319 ( 318 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 12 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 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 : 285 ( 17 sgn 27 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(maddux1_join_commutativity,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('theBenchmark.p',maddux1_join_commutativity) ).
fof(maddux2_join_associativity,axiom,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('theBenchmark.p',maddux2_join_associativity) ).
fof(maddux3_a_kind_of_de_Morgan,axiom,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
file('theBenchmark.p',maddux3_a_kind_of_de_Morgan) ).
fof(maddux4_definiton_of_meet,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
file('theBenchmark.p',maddux4_definiton_of_meet) ).
fof(composition_associativity,axiom,
! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
file('theBenchmark.p',composition_associativity) ).
fof(composition_identity,axiom,
! [X0] : composition(X0,one) = X0,
file('theBenchmark.p',composition_identity) ).
fof(composition_distributivity,axiom,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('theBenchmark.p',composition_distributivity) ).
fof(converse_idempotence,axiom,
! [X0] : converse(converse(X0)) = X0,
file('theBenchmark.p',converse_idempotence) ).
fof(converse_additivity,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('theBenchmark.p',converse_additivity) ).
fof(converse_multiplicativity,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('theBenchmark.p',converse_multiplicativity) ).
fof(converse_cancellativity,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
file('theBenchmark.p',converse_cancellativity) ).
fof(def_top,axiom,
! [X0] : top = join(X0,complement(X0)),
file('theBenchmark.p',def_top) ).
fof(def_zero,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('theBenchmark.p',def_zero) ).
fof(goals,conjecture,
! [X0] :
( join(X0,one) = one
=> meet(complement(composition(X0,top)),one) = meet(complement(X0),one) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0] :
( join(X0,one) = one
=> meet(complement(composition(X0,top)),one) = meet(complement(X0),one) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_18,plain,
join(A,B) = join(B,A),
inference(clausify,[status(thm)],[maddux1_join_commutativity]) ).
cnf(c_19,plain,
join(join(A,B),C) = join(A,join(B,C)),
inference(clausify,[status(thm)],[maddux2_join_associativity]) ).
cnf(c_20,plain,
join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) = A,
inference(clausify,[status(thm)],[maddux3_a_kind_of_de_Morgan]) ).
cnf(c_21,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = A,
inference(paramod,[status(thm)],[c_18,c_20]) ).
cnf(c_22,plain,
meet(A,B) = complement(join(complement(A),complement(B))),
inference(clausify,[status(thm)],[maddux4_definiton_of_meet]) ).
cnf(c_23,plain,
composition(composition(A,B),C) = composition(A,composition(B,C)),
inference(clausify,[status(thm)],[composition_associativity]) ).
cnf(c_24,plain,
composition(A,one) = A,
inference(clausify,[status(thm)],[composition_identity]) ).
cnf(c_25,plain,
composition(join(A,B),C) = join(composition(A,C),composition(B,C)),
inference(clausify,[status(thm)],[composition_distributivity]) ).
cnf(c_26,plain,
converse(converse(A)) = A,
inference(clausify,[status(thm)],[converse_idempotence]) ).
cnf(c_27,plain,
converse(join(A,B)) = join(converse(A),converse(B)),
inference(clausify,[status(thm)],[converse_additivity]) ).
cnf(c_28,plain,
converse(composition(A,B)) = composition(converse(B),converse(A)),
inference(clausify,[status(thm)],[converse_multiplicativity]) ).
cnf(c_29,plain,
complement(A) = join(composition(converse(B),complement(composition(B,A))),complement(A)),
inference(clausify,[status(thm)],[converse_cancellativity]) ).
cnf(c_1783,plain,
complement(A) = join(complement(A),composition(converse(B),complement(composition(B,A)))),
inference(paramod,[status(thm)],[c_18,c_29]) ).
cnf(c_30,plain,
join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A),
inference(copy,[status(thm)],[c_1783]) ).
cnf(c_31,plain,
join(A,complement(A)) = top,
inference(clausify,[status(thm)],[def_top]) ).
cnf(c_32,plain,
meet(A,complement(A)) = zero,
inference(clausify,[status(thm)],[def_zero]) ).
cnf(c_1784,plain,
complement(join(complement(A),complement(complement(A)))) = zero,
inference(paramod,[status(thm)],[c_22,c_32]) ).
cnf(c_33,plain,
complement(top) = zero,
inference(paramod,[status(thm)],[c_31,c_1784]) ).
fof(nnf_17,plain,
? [X0] :
( meet(complement(composition(X0,top)),one) != meet(complement(X0),one)
& join(X0,one) = one ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( meet(complement(composition(sK0,top)),one) != meet(complement(sK0),one)
& join(sK0,one) = one ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[nnf_17]) ).
cnf(c_40,negated_conjecture,
join(sK0,one) = one,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_41,negated_conjecture,
join(one,sK0) = one,
inference(paramod,[status(thm)],[c_18,c_40]) ).
cnf(c_42,negated_conjecture,
meet(complement(composition(sK0,top)),one) != meet(complement(sK0),one),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_1785,negated_conjecture,
complement(join(complement(complement(composition(sK0,top))),complement(one))) != meet(complement(sK0),one),
inference(paramod,[status(thm)],[c_22,c_42]) ).
cnf(c_1786,negated_conjecture,
complement(join(complement(one),complement(complement(composition(sK0,top))))) != meet(complement(sK0),one),
inference(paramod,[status(thm)],[c_18,c_1785]) ).
cnf(c_1787,negated_conjecture,
complement(join(complement(one),complement(complement(composition(sK0,top))))) != complement(join(complement(complement(sK0)),complement(one))),
inference(paramod,[status(thm)],[c_22,c_1786]) ).
cnf(c_43,negated_conjecture,
complement(join(complement(one),complement(complement(composition(sK0,top))))) != complement(join(complement(one),complement(complement(sK0)))),
inference(paramod,[status(thm)],[c_18,c_1787]) ).
cnf(c_1788,plain,
join(join(A,B),C) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_18,c_19]) ).
cnf(c_45,plain,
join(A,join(B,C)) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_19,c_1788]) ).
cnf(c_46,plain,
join(complement(join(A,complement(B))),complement(join(complement(B),complement(A)))) = B,
inference(paramod,[status(thm)],[c_18,c_21]) ).
cnf(c_47,plain,
join(complement(join(complement(A),B)),complement(join(complement(B),complement(A)))) = A,
inference(paramod,[status(thm)],[c_18,c_21]) ).
cnf(c_1789,plain,
converse(A) = join(converse(complement(join(complement(A),B))),converse(complement(join(complement(A),complement(B))))),
inference(paramod,[status(thm)],[c_21,c_27]) ).
cnf(c_49,plain,
join(converse(complement(join(complement(A),B))),converse(complement(join(complement(A),complement(B))))) = converse(A),
inference(copy,[status(thm)],[c_1789]) ).
cnf(c_1790,plain,
converse(A) = composition(converse(one),converse(A)),
inference(paramod,[status(thm)],[c_24,c_28]) ).
cnf(c_50,plain,
composition(converse(one),converse(A)) = converse(A),
inference(copy,[status(thm)],[c_1790]) ).
cnf(c_52,plain,
join(complement(one),composition(converse(A),complement(A))) = complement(one),
inference(paramod,[status(thm)],[c_24,c_30]) ).
cnf(c_1791,plain,
converse(complement(A)) = join(converse(complement(A)),converse(composition(converse(B),complement(composition(B,A))))),
inference(paramod,[status(thm)],[c_30,c_27]) ).
cnf(c_1792,plain,
converse(complement(A)) = join(converse(complement(A)),composition(converse(complement(composition(B,A))),converse(converse(B)))),
inference(paramod,[status(thm)],[c_28,c_1791]) ).
cnf(c_1793,plain,
converse(complement(A)) = join(converse(complement(A)),composition(converse(complement(composition(B,A))),B)),
inference(paramod,[status(thm)],[c_26,c_1792]) ).
cnf(c_54,plain,
join(converse(complement(A)),composition(converse(complement(composition(B,A))),B)) = converse(complement(A)),
inference(copy,[status(thm)],[c_1793]) ).
cnf(c_1794,plain,
join(top,A) = join(B,join(complement(B),A)),
inference(paramod,[status(thm)],[c_31,c_19]) ).
cnf(c_55,plain,
join(A,join(complement(A),B)) = join(top,B),
inference(copy,[status(thm)],[c_1794]) ).
cnf(c_1795,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_31,c_21]) ).
cnf(c_57,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_33,c_1795]) ).
cnf(c_1796,plain,
join(complement(join(complement(A),complement(A))),complement(top)) = A,
inference(paramod,[status(thm)],[c_31,c_21]) ).
cnf(c_1797,plain,
join(complement(join(complement(A),complement(A))),zero) = A,
inference(paramod,[status(thm)],[c_33,c_1796]) ).
cnf(c_58,plain,
join(zero,complement(join(complement(A),complement(A)))) = A,
inference(paramod,[status(thm)],[c_18,c_1797]) ).
cnf(c_1798,plain,
composition(top,A) = join(composition(B,A),composition(complement(B),A)),
inference(paramod,[status(thm)],[c_31,c_25]) ).
cnf(c_59,plain,
join(composition(A,B),composition(complement(A),B)) = composition(top,B),
inference(copy,[status(thm)],[c_1798]) ).
cnf(c_1799,plain,
converse(top) = join(converse(A),converse(complement(A))),
inference(paramod,[status(thm)],[c_31,c_27]) ).
cnf(c_60,plain,
join(converse(A),converse(complement(A))) = converse(top),
inference(copy,[status(thm)],[c_1799]) ).
cnf(c_1800,plain,
join(zero,composition(converse(A),complement(composition(A,top)))) = complement(top),
inference(paramod,[status(thm)],[c_33,c_30]) ).
cnf(c_63,plain,
join(zero,composition(converse(A),complement(composition(A,top)))) = zero,
inference(paramod,[status(thm)],[c_33,c_1800]) ).
cnf(c_1801,plain,
join(one,A) = join(one,join(sK0,A)),
inference(paramod,[status(thm)],[c_41,c_19]) ).
cnf(c_65,plain,
join(one,join(sK0,A)) = join(one,A),
inference(copy,[status(thm)],[c_1801]) ).
cnf(c_1802,plain,
composition(one,A) = join(composition(one,A),composition(sK0,A)),
inference(paramod,[status(thm)],[c_41,c_25]) ).
cnf(c_67,plain,
join(composition(one,A),composition(sK0,A)) = composition(one,A),
inference(copy,[status(thm)],[c_1802]) ).
cnf(c_1803,plain,
converse(one) = join(converse(one),converse(sK0)),
inference(paramod,[status(thm)],[c_41,c_27]) ).
cnf(c_68,plain,
join(converse(one),converse(sK0)) = converse(one),
inference(copy,[status(thm)],[c_1803]) ).
cnf(c_1804,plain,
A = join(complement(join(complement(A),complement(B))),complement(join(B,complement(A)))),
inference(paramod,[status(thm)],[c_46,c_18]) ).
cnf(c_71,plain,
join(complement(join(complement(A),complement(B))),complement(join(B,complement(A)))) = A,
inference(copy,[status(thm)],[c_1804]) ).
cnf(c_1805,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_26,c_50]) ).
cnf(c_81,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_26,c_1805]) ).
cnf(c_1806,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_81,c_24]) ).
cnf(c_83,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_1806]) ).
cnf(c_87,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_81,c_30]) ).
cnf(c_88,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_83,c_81]) ).
cnf(c_1807,plain,
join(one,converse(sK0)) = converse(one),
inference(paramod,[status(thm)],[c_83,c_68]) ).
cnf(c_89,plain,
join(one,converse(sK0)) = one,
inference(paramod,[status(thm)],[c_83,c_1807]) ).
cnf(c_1808,plain,
join(A,composition(sK0,A)) = composition(one,A),
inference(paramod,[status(thm)],[c_88,c_67]) ).
cnf(c_90,plain,
join(A,composition(sK0,A)) = A,
inference(paramod,[status(thm)],[c_88,c_1808]) ).
cnf(c_91,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_88,c_87]) ).
cnf(c_92,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_91,c_58]) ).
cnf(c_1809,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_31,c_47]) ).
cnf(c_1810,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_18,c_1809]) ).
cnf(c_1811,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_33,c_1810]) ).
cnf(c_95,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_18,c_1811]) ).
cnf(c_96,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_95,c_57]) ).
cnf(c_97,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_96,c_95]) ).
cnf(c_98,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_96,c_92]) ).
cnf(c_1812,negated_conjecture,
complement(join(complement(one),composition(sK0,top))) != complement(join(complement(one),complement(complement(sK0)))),
inference(paramod,[status(thm)],[c_96,c_43]) ).
cnf(c_1813,negated_conjecture,
complement(join(complement(one),composition(sK0,top))) != complement(join(complement(one),sK0)),
inference(paramod,[status(thm)],[c_96,c_1812]) ).
cnf(c_99,negated_conjecture,
complement(join(complement(one),composition(sK0,top))) != complement(join(sK0,complement(one))),
inference(paramod,[status(thm)],[c_18,c_1813]) ).
cnf(c_100,plain,
complement(join(A,A)) = complement(A),
inference(paramod,[status(thm)],[c_98,c_97]) ).
cnf(c_102,plain,
composition(converse(A),complement(composition(A,top))) = zero,
inference(paramod,[status(thm)],[c_98,c_63]) ).
cnf(c_1814,plain,
join(converse(complement(top)),converse(complement(join(complement(A),complement(complement(complement(A))))))) = converse(A),
inference(paramod,[status(thm)],[c_31,c_49]) ).
cnf(c_1815,plain,
join(converse(zero),converse(complement(join(complement(A),complement(complement(complement(A))))))) = converse(A),
inference(paramod,[status(thm)],[c_33,c_1814]) ).
cnf(c_1816,plain,
join(converse(zero),converse(complement(join(complement(A),complement(A))))) = converse(A),
inference(paramod,[status(thm)],[c_96,c_1815]) ).
cnf(c_1817,plain,
join(converse(zero),converse(complement(complement(A)))) = converse(A),
inference(paramod,[status(thm)],[c_91,c_1816]) ).
cnf(c_104,plain,
join(converse(zero),converse(A)) = converse(A),
inference(paramod,[status(thm)],[c_96,c_1817]) ).
cnf(c_1818,plain,
A = join(A,zero),
inference(paramod,[status(thm)],[c_98,c_18]) ).
cnf(c_107,plain,
join(A,zero) = A,
inference(copy,[status(thm)],[c_1818]) ).
cnf(c_1819,plain,
composition(one,A) = join(composition(one,A),composition(converse(sK0),A)),
inference(paramod,[status(thm)],[c_89,c_25]) ).
cnf(c_1820,plain,
A = join(composition(one,A),composition(converse(sK0),A)),
inference(paramod,[status(thm)],[c_88,c_1819]) ).
cnf(c_1821,plain,
A = join(A,composition(converse(sK0),A)),
inference(paramod,[status(thm)],[c_88,c_1820]) ).
cnf(c_116,plain,
join(A,composition(converse(sK0),A)) = A,
inference(copy,[status(thm)],[c_1821]) ).
cnf(c_1822,plain,
join(complement(join(A,B)),complement(join(complement(complement(A)),complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_96,c_21]) ).
cnf(c_138,plain,
join(complement(join(A,B)),complement(join(A,complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_96,c_1822]) ).
cnf(c_1823,plain,
join(complement(join(A,B)),complement(join(complement(complement(B)),complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_96,c_46]) ).
cnf(c_140,plain,
join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_96,c_1823]) ).
cnf(c_143,plain,
join(complement(one),composition(converse(complement(A)),A)) = complement(one),
inference(paramod,[status(thm)],[c_96,c_52]) ).
cnf(c_1824,plain,
join(join(A,A),complement(A)) = top,
inference(paramod,[status(thm)],[c_100,c_31]) ).
cnf(c_1825,plain,
join(A,join(A,complement(A))) = top,
inference(paramod,[status(thm)],[c_19,c_1824]) ).
cnf(c_146,plain,
join(A,top) = top,
inference(paramod,[status(thm)],[c_31,c_1825]) ).
cnf(c_1826,plain,
complement(complement(A)) = join(A,A),
inference(paramod,[status(thm)],[c_100,c_96]) ).
cnf(c_1827,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_96,c_1826]) ).
cnf(c_147,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_1827]) ).
cnf(c_1828,plain,
top = join(top,A),
inference(paramod,[status(thm)],[c_146,c_18]) ).
cnf(c_149,plain,
join(top,A) = top,
inference(copy,[status(thm)],[c_1828]) ).
cnf(c_1829,plain,
composition(top,A) = join(composition(B,A),composition(top,A)),
inference(paramod,[status(thm)],[c_146,c_25]) ).
cnf(c_150,plain,
join(composition(A,B),composition(top,B)) = composition(top,B),
inference(copy,[status(thm)],[c_1829]) ).
cnf(c_1830,plain,
converse(top) = join(converse(A),converse(top)),
inference(paramod,[status(thm)],[c_146,c_27]) ).
cnf(c_151,plain,
join(converse(A),converse(top)) = converse(top),
inference(copy,[status(thm)],[c_1830]) ).
cnf(c_152,plain,
join(A,join(complement(A),B)) = top,
inference(paramod,[status(thm)],[c_149,c_55]) ).
cnf(c_1831,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_147,c_19]) ).
cnf(c_153,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_1831]) ).
cnf(c_1832,plain,
join(converse(zero),composition(converse(complement(composition(A,top))),A)) = converse(complement(top)),
inference(paramod,[status(thm)],[c_33,c_54]) ).
cnf(c_158,plain,
join(converse(zero),composition(converse(complement(composition(A,top))),A)) = converse(zero),
inference(paramod,[status(thm)],[c_33,c_1832]) ).
cnf(c_1833,plain,
join(converse(zero),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_26,c_104]) ).
cnf(c_166,plain,
join(converse(zero),A) = A,
inference(paramod,[status(thm)],[c_26,c_1833]) ).
cnf(c_168,plain,
composition(converse(complement(composition(A,top))),A) = converse(zero),
inference(paramod,[status(thm)],[c_166,c_158]) ).
cnf(c_1834,plain,
zero = converse(zero),
inference(paramod,[status(thm)],[c_166,c_107]) ).
cnf(c_172,plain,
converse(zero) = zero,
inference(copy,[status(thm)],[c_1834]) ).
cnf(c_173,plain,
composition(converse(complement(composition(A,top))),A) = zero,
inference(paramod,[status(thm)],[c_172,c_168]) ).
cnf(c_1835,plain,
join(A,composition(top,B)) = join(composition(C,B),join(A,composition(complement(C),B))),
inference(paramod,[status(thm)],[c_59,c_45]) ).
cnf(c_187,plain,
join(composition(A,B),join(C,composition(complement(A),B))) = join(C,composition(top,B)),
inference(copy,[status(thm)],[c_1835]) ).
cnf(c_192,plain,
join(A,converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_26,c_151]) ).
cnf(c_195,plain,
converse(top) = top,
inference(paramod,[status(thm)],[c_192,c_149]) ).
cnf(c_200,plain,
join(converse(A),converse(complement(A))) = top,
inference(paramod,[status(thm)],[c_195,c_60]) ).
cnf(c_1836,plain,
join(one,top) = join(one,complement(sK0)),
inference(paramod,[status(thm)],[c_31,c_65]) ).
cnf(c_1837,plain,
top = join(one,complement(sK0)),
inference(paramod,[status(thm)],[c_146,c_1836]) ).
cnf(c_209,plain,
join(one,complement(sK0)) = top,
inference(copy,[status(thm)],[c_1837]) ).
cnf(c_1838,plain,
converse(A) = join(converse(A),converse(composition(converse(sK0),A))),
inference(paramod,[status(thm)],[c_116,c_27]) ).
cnf(c_1839,plain,
converse(A) = join(converse(A),composition(converse(A),converse(converse(sK0)))),
inference(paramod,[status(thm)],[c_28,c_1838]) ).
cnf(c_1840,plain,
converse(A) = join(converse(A),composition(converse(A),sK0)),
inference(paramod,[status(thm)],[c_26,c_1839]) ).
cnf(c_231,plain,
join(converse(A),composition(converse(A),sK0)) = converse(A),
inference(copy,[status(thm)],[c_1840]) ).
cnf(c_1841,plain,
join(complement(join(complement(sK0),complement(one))),complement(top)) = sK0,
inference(paramod,[status(thm)],[c_209,c_71]) ).
cnf(c_1842,plain,
join(complement(join(complement(one),complement(sK0))),complement(top)) = sK0,
inference(paramod,[status(thm)],[c_18,c_1841]) ).
cnf(c_1843,plain,
join(complement(join(complement(one),complement(sK0))),zero) = sK0,
inference(paramod,[status(thm)],[c_33,c_1842]) ).
cnf(c_1844,plain,
join(zero,complement(join(complement(one),complement(sK0)))) = sK0,
inference(paramod,[status(thm)],[c_18,c_1843]) ).
cnf(c_238,plain,
complement(join(complement(one),complement(sK0))) = sK0,
inference(paramod,[status(thm)],[c_98,c_1844]) ).
cnf(c_250,plain,
join(A,converse(complement(converse(A)))) = top,
inference(paramod,[status(thm)],[c_26,c_200]) ).
cnf(c_253,plain,
join(one,converse(complement(one))) = top,
inference(paramod,[status(thm)],[c_83,c_200]) ).
cnf(c_1845,plain,
complement(sK0) = join(complement(one),complement(sK0)),
inference(paramod,[status(thm)],[c_238,c_96]) ).
cnf(c_265,plain,
join(complement(one),complement(sK0)) = complement(sK0),
inference(copy,[status(thm)],[c_1845]) ).
cnf(c_274,plain,
composition(top,complement(composition(top,top))) = zero,
inference(paramod,[status(thm)],[c_195,c_102]) ).
cnf(c_1846,plain,
composition(join(top,A),complement(composition(top,top))) = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_274,c_25]) ).
cnf(c_1847,plain,
composition(top,complement(composition(top,top))) = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_149,c_1846]) ).
cnf(c_1848,plain,
zero = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_274,c_1847]) ).
cnf(c_1849,plain,
zero = composition(A,complement(composition(top,top))),
inference(paramod,[status(thm)],[c_98,c_1848]) ).
cnf(c_289,plain,
composition(A,complement(composition(top,top))) = zero,
inference(copy,[status(thm)],[c_1849]) ).
cnf(c_1850,plain,
zero = complement(composition(top,top)),
inference(paramod,[status(thm)],[c_289,c_88]) ).
cnf(c_294,plain,
complement(composition(top,top)) = zero,
inference(copy,[status(thm)],[c_1850]) ).
cnf(c_1851,plain,
join(composition(top,top),zero) = top,
inference(paramod,[status(thm)],[c_294,c_31]) ).
cnf(c_1852,plain,
join(zero,composition(top,top)) = top,
inference(paramod,[status(thm)],[c_18,c_1851]) ).
cnf(c_300,plain,
composition(top,top) = top,
inference(paramod,[status(thm)],[c_98,c_1852]) ).
cnf(c_1853,plain,
composition(top,A) = composition(top,composition(top,A)),
inference(paramod,[status(thm)],[c_300,c_23]) ).
cnf(c_309,plain,
composition(top,composition(top,A)) = composition(top,A),
inference(copy,[status(thm)],[c_1853]) ).
cnf(c_318,plain,
join(A,composition(top,A)) = composition(top,A),
inference(paramod,[status(thm)],[c_88,c_150]) ).
cnf(c_1854,plain,
join(complement(composition(top,A)),composition(converse(top),complement(composition(top,A)))) = complement(composition(top,A)),
inference(paramod,[status(thm)],[c_309,c_30]) ).
cnf(c_1855,plain,
join(complement(composition(top,A)),composition(top,complement(composition(top,A)))) = complement(composition(top,A)),
inference(paramod,[status(thm)],[c_195,c_1854]) ).
cnf(c_365,plain,
composition(top,complement(composition(top,A))) = complement(composition(top,A)),
inference(paramod,[status(thm)],[c_318,c_1855]) ).
cnf(c_402,plain,
join(A,composition(top,complement(A))) = top,
inference(paramod,[status(thm)],[c_318,c_152]) ).
cnf(c_408,plain,
join(complement(A),composition(top,A)) = top,
inference(paramod,[status(thm)],[c_96,c_402]) ).
cnf(c_1856,plain,
converse(top) = join(converse(complement(A)),converse(composition(top,A))),
inference(paramod,[status(thm)],[c_408,c_27]) ).
cnf(c_1857,plain,
top = join(converse(complement(A)),converse(composition(top,A))),
inference(paramod,[status(thm)],[c_195,c_1856]) ).
cnf(c_1858,plain,
top = join(converse(complement(A)),composition(converse(A),converse(top))),
inference(paramod,[status(thm)],[c_28,c_1857]) ).
cnf(c_1859,plain,
top = join(converse(complement(A)),composition(converse(A),top)),
inference(paramod,[status(thm)],[c_195,c_1858]) ).
cnf(c_1860,plain,
top = join(composition(converse(A),top),converse(complement(A))),
inference(paramod,[status(thm)],[c_18,c_1859]) ).
cnf(c_414,plain,
join(composition(converse(A),top),converse(complement(A))) = top,
inference(copy,[status(thm)],[c_1860]) ).
cnf(c_1861,plain,
join(A,composition(converse(converse(A)),sK0)) = converse(converse(A)),
inference(paramod,[status(thm)],[c_26,c_231]) ).
cnf(c_1862,plain,
join(A,composition(A,sK0)) = converse(converse(A)),
inference(paramod,[status(thm)],[c_26,c_1861]) ).
cnf(c_460,plain,
join(A,composition(A,sK0)) = A,
inference(paramod,[status(thm)],[c_26,c_1862]) ).
cnf(c_510,plain,
join(composition(A,top),converse(complement(converse(A)))) = top,
inference(paramod,[status(thm)],[c_26,c_414]) ).
cnf(c_1863,plain,
join(complement(join(A,B)),complement(A)) = join(complement(join(A,B)),complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_138,c_153]) ).
cnf(c_1864,plain,
join(complement(A),complement(join(A,B))) = join(complement(join(A,B)),complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_18,c_1863]) ).
cnf(c_528,plain,
join(complement(A),complement(join(A,B))) = complement(A),
inference(paramod,[status(thm)],[c_138,c_1864]) ).
cnf(c_544,plain,
join(complement(A),complement(join(B,A))) = complement(A),
inference(paramod,[status(thm)],[c_18,c_528]) ).
cnf(c_1865,plain,
join(A,complement(join(B,complement(A)))) = complement(complement(A)),
inference(paramod,[status(thm)],[c_96,c_544]) ).
cnf(c_565,plain,
join(A,complement(join(B,complement(A)))) = A,
inference(paramod,[status(thm)],[c_96,c_1865]) ).
cnf(c_1866,plain,
join(complement(top),complement(join(converse(complement(one)),complement(one)))) = complement(converse(complement(one))),
inference(paramod,[status(thm)],[c_253,c_140]) ).
cnf(c_1867,plain,
join(zero,complement(join(converse(complement(one)),complement(one)))) = complement(converse(complement(one))),
inference(paramod,[status(thm)],[c_33,c_1866]) ).
cnf(c_1868,plain,
join(zero,complement(join(complement(one),converse(complement(one))))) = complement(converse(complement(one))),
inference(paramod,[status(thm)],[c_18,c_1867]) ).
cnf(c_612,plain,
complement(join(complement(one),converse(complement(one)))) = complement(converse(complement(one))),
inference(paramod,[status(thm)],[c_98,c_1868]) ).
cnf(c_1869,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_138,c_140]) ).
cnf(c_1870,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_96,c_1869]) ).
cnf(c_1871,plain,
join(A,complement(join(complement(join(A,complement(B))),join(A,B)))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_96,c_1870]) ).
cnf(c_1872,plain,
join(A,complement(join(join(A,B),complement(join(A,complement(B)))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_18,c_1871]) ).
cnf(c_1873,plain,
join(A,complement(join(A,join(B,complement(join(A,complement(B))))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_19,c_1872]) ).
cnf(c_1874,plain,
join(A,complement(join(A,B))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_565,c_1873]) ).
cnf(c_623,plain,
join(A,complement(join(A,B))) = join(A,complement(B)),
inference(paramod,[status(thm)],[c_96,c_1874]) ).
cnf(c_1875,plain,
join(zero,composition(complement(converse(complement(composition(A,top)))),A)) = composition(top,A),
inference(paramod,[status(thm)],[c_173,c_59]) ).
cnf(c_637,plain,
composition(complement(converse(complement(composition(A,top)))),A) = composition(top,A),
inference(paramod,[status(thm)],[c_98,c_1875]) ).
cnf(c_703,plain,
join(complement(one),converse(complement(one))) = complement(one),
inference(paramod,[status(thm)],[c_24,c_143]) ).
cnf(c_1876,plain,
complement(complement(one)) = complement(converse(complement(one))),
inference(paramod,[status(thm)],[c_703,c_612]) ).
cnf(c_1877,plain,
one = complement(converse(complement(one))),
inference(paramod,[status(thm)],[c_96,c_1876]) ).
cnf(c_707,plain,
complement(converse(complement(one))) = one,
inference(copy,[status(thm)],[c_1877]) ).
cnf(c_1878,plain,
complement(one) = converse(complement(one)),
inference(paramod,[status(thm)],[c_707,c_96]) ).
cnf(c_715,plain,
converse(complement(one)) = complement(one),
inference(copy,[status(thm)],[c_1878]) ).
cnf(c_816,plain,
join(A,complement(join(B,A))) = join(A,complement(B)),
inference(paramod,[status(thm)],[c_18,c_623]) ).
cnf(c_1879,plain,
join(composition(A,sK0),complement(A)) = join(complement(A),composition(top,sK0)),
inference(paramod,[status(thm)],[c_460,c_187]) ).
cnf(c_1880,plain,
join(complement(A),composition(A,sK0)) = join(complement(A),composition(top,sK0)),
inference(paramod,[status(thm)],[c_18,c_1879]) ).
cnf(c_858,plain,
join(complement(A),composition(top,sK0)) = join(complement(A),composition(A,sK0)),
inference(copy,[status(thm)],[c_1880]) ).
cnf(c_1881,plain,
join(converse(complement(A)),complement(top)) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_200,c_816]) ).
cnf(c_1882,plain,
join(converse(complement(A)),zero) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_33,c_1881]) ).
cnf(c_1883,plain,
join(zero,converse(complement(A))) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_18,c_1882]) ).
cnf(c_1884,plain,
converse(complement(A)) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_98,c_1883]) ).
cnf(c_1885,plain,
converse(complement(A)) = join(complement(converse(A)),converse(complement(A))),
inference(paramod,[status(thm)],[c_18,c_1884]) ).
cnf(c_884,plain,
join(complement(converse(A)),converse(complement(A))) = converse(complement(A)),
inference(copy,[status(thm)],[c_1885]) ).
cnf(c_1886,plain,
join(converse(complement(converse(A))),complement(top)) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_250,c_816]) ).
cnf(c_1887,plain,
join(converse(complement(converse(A))),zero) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_33,c_1886]) ).
cnf(c_1888,plain,
join(zero,converse(complement(converse(A)))) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_18,c_1887]) ).
cnf(c_1889,plain,
converse(complement(converse(A))) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_98,c_1888]) ).
cnf(c_1890,plain,
converse(complement(converse(A))) = join(complement(A),converse(complement(converse(A)))),
inference(paramod,[status(thm)],[c_18,c_1889]) ).
cnf(c_887,plain,
join(complement(A),converse(complement(converse(A)))) = converse(complement(converse(A))),
inference(copy,[status(thm)],[c_1890]) ).
cnf(c_1891,plain,
join(complement(one),composition(top,sK0)) = join(complement(one),sK0),
inference(paramod,[status(thm)],[c_88,c_858]) ).
cnf(c_930,plain,
join(complement(one),composition(top,sK0)) = join(sK0,complement(one)),
inference(paramod,[status(thm)],[c_18,c_1891]) ).
cnf(c_1892,plain,
converse(join(sK0,complement(one))) = join(converse(complement(one)),converse(composition(top,sK0))),
inference(paramod,[status(thm)],[c_930,c_27]) ).
cnf(c_1893,plain,
join(converse(sK0),converse(complement(one))) = join(converse(complement(one)),converse(composition(top,sK0))),
inference(paramod,[status(thm)],[c_27,c_1892]) ).
cnf(c_1894,plain,
join(converse(sK0),complement(one)) = join(converse(complement(one)),converse(composition(top,sK0))),
inference(paramod,[status(thm)],[c_715,c_1893]) ).
cnf(c_1895,plain,
join(complement(one),converse(sK0)) = join(converse(complement(one)),converse(composition(top,sK0))),
inference(paramod,[status(thm)],[c_18,c_1894]) ).
cnf(c_1896,plain,
join(complement(one),converse(sK0)) = join(complement(one),converse(composition(top,sK0))),
inference(paramod,[status(thm)],[c_715,c_1895]) ).
cnf(c_1897,plain,
join(complement(one),converse(sK0)) = join(complement(one),composition(converse(sK0),converse(top))),
inference(paramod,[status(thm)],[c_28,c_1896]) ).
cnf(c_1898,plain,
join(complement(one),converse(sK0)) = join(complement(one),composition(converse(sK0),top)),
inference(paramod,[status(thm)],[c_195,c_1897]) ).
cnf(c_960,plain,
join(complement(one),composition(converse(sK0),top)) = join(complement(one),converse(sK0)),
inference(copy,[status(thm)],[c_1898]) ).
cnf(c_1899,plain,
join(complement(one),complement(join(sK0,complement(one)))) = join(complement(one),complement(composition(top,sK0))),
inference(paramod,[status(thm)],[c_930,c_623]) ).
cnf(c_1900,plain,
join(complement(one),complement(sK0)) = join(complement(one),complement(composition(top,sK0))),
inference(paramod,[status(thm)],[c_816,c_1899]) ).
cnf(c_1901,plain,
complement(sK0) = join(complement(one),complement(composition(top,sK0))),
inference(paramod,[status(thm)],[c_265,c_1900]) ).
cnf(c_967,plain,
join(complement(one),complement(composition(top,sK0))) = complement(sK0),
inference(copy,[status(thm)],[c_1901]) ).
cnf(c_1902,plain,
join(complement(sK0),A) = join(complement(one),join(complement(composition(top,sK0)),A)),
inference(paramod,[status(thm)],[c_967,c_19]) ).
cnf(c_969,plain,
join(complement(one),join(complement(composition(top,sK0)),A)) = join(complement(sK0),A),
inference(copy,[status(thm)],[c_1902]) ).
cnf(c_1903,plain,
converse(complement(sK0)) = join(converse(complement(one)),converse(complement(composition(top,sK0)))),
inference(paramod,[status(thm)],[c_967,c_27]) ).
cnf(c_1904,plain,
converse(complement(sK0)) = join(complement(one),converse(complement(composition(top,sK0)))),
inference(paramod,[status(thm)],[c_715,c_1903]) ).
cnf(c_971,plain,
join(complement(one),converse(complement(composition(top,sK0)))) = converse(complement(sK0)),
inference(copy,[status(thm)],[c_1904]) ).
cnf(c_1905,plain,
converse(converse(complement(A))) = join(converse(complement(converse(A))),converse(converse(complement(A)))),
inference(paramod,[status(thm)],[c_884,c_27]) ).
cnf(c_1906,plain,
complement(A) = join(converse(complement(converse(A))),converse(converse(complement(A)))),
inference(paramod,[status(thm)],[c_26,c_1905]) ).
cnf(c_1907,plain,
complement(A) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_26,c_1906]) ).
cnf(c_1908,plain,
complement(A) = join(complement(A),converse(complement(converse(A)))),
inference(paramod,[status(thm)],[c_18,c_1907]) ).
cnf(c_1909,plain,
complement(A) = converse(complement(converse(A))),
inference(paramod,[status(thm)],[c_887,c_1908]) ).
cnf(c_977,plain,
converse(complement(converse(A))) = complement(A),
inference(copy,[status(thm)],[c_1909]) ).
cnf(c_1910,plain,
join(composition(A,top),complement(A)) = top,
inference(paramod,[status(thm)],[c_977,c_510]) ).
cnf(c_983,plain,
join(complement(A),composition(A,top)) = top,
inference(paramod,[status(thm)],[c_18,c_1910]) ).
cnf(c_1911,plain,
join(complement(A),complement(top)) = join(complement(A),complement(composition(A,top))),
inference(paramod,[status(thm)],[c_983,c_623]) ).
cnf(c_1912,plain,
join(complement(A),zero) = join(complement(A),complement(composition(A,top))),
inference(paramod,[status(thm)],[c_33,c_1911]) ).
cnf(c_1913,plain,
join(zero,complement(A)) = join(complement(A),complement(composition(A,top))),
inference(paramod,[status(thm)],[c_18,c_1912]) ).
cnf(c_1914,plain,
complement(A) = join(complement(A),complement(composition(A,top))),
inference(paramod,[status(thm)],[c_98,c_1913]) ).
cnf(c_1005,plain,
join(complement(A),complement(composition(A,top))) = complement(A),
inference(copy,[status(thm)],[c_1914]) ).
cnf(c_1007,plain,
converse(complement(A)) = complement(converse(A)),
inference(paramod,[status(thm)],[c_977,c_26]) ).
cnf(c_1915,plain,
join(complement(one),complement(converse(composition(top,sK0)))) = converse(complement(sK0)),
inference(paramod,[status(thm)],[c_1007,c_971]) ).
cnf(c_1916,plain,
join(complement(one),complement(composition(converse(sK0),converse(top)))) = converse(complement(sK0)),
inference(paramod,[status(thm)],[c_28,c_1915]) ).
cnf(c_1917,plain,
join(complement(one),complement(composition(converse(sK0),top))) = converse(complement(sK0)),
inference(paramod,[status(thm)],[c_195,c_1916]) ).
cnf(c_1028,plain,
join(complement(one),complement(composition(converse(sK0),top))) = complement(converse(sK0)),
inference(paramod,[status(thm)],[c_1007,c_1917]) ).
cnf(c_1918,plain,
composition(complement(complement(converse(composition(A,top)))),A) = composition(top,A),
inference(paramod,[status(thm)],[c_1007,c_637]) ).
cnf(c_1919,plain,
composition(complement(complement(composition(converse(top),converse(A)))),A) = composition(top,A),
inference(paramod,[status(thm)],[c_28,c_1918]) ).
cnf(c_1920,plain,
composition(complement(complement(composition(top,converse(A)))),A) = composition(top,A),
inference(paramod,[status(thm)],[c_195,c_1919]) ).
cnf(c_1921,plain,
composition(composition(top,converse(A)),A) = composition(top,A),
inference(paramod,[status(thm)],[c_96,c_1920]) ).
cnf(c_1046,plain,
composition(top,composition(converse(A),A)) = composition(top,A),
inference(paramod,[status(thm)],[c_23,c_1921]) ).
cnf(c_1922,plain,
converse(composition(top,A)) = composition(converse(composition(converse(A),A)),converse(top)),
inference(paramod,[status(thm)],[c_1046,c_28]) ).
cnf(c_1923,plain,
composition(converse(A),converse(top)) = composition(converse(composition(converse(A),A)),converse(top)),
inference(paramod,[status(thm)],[c_28,c_1922]) ).
cnf(c_1924,plain,
composition(converse(A),top) = composition(converse(composition(converse(A),A)),converse(top)),
inference(paramod,[status(thm)],[c_195,c_1923]) ).
cnf(c_1925,plain,
composition(converse(A),top) = composition(composition(converse(A),converse(converse(A))),converse(top)),
inference(paramod,[status(thm)],[c_28,c_1924]) ).
cnf(c_1926,plain,
composition(converse(A),top) = composition(composition(converse(A),A),converse(top)),
inference(paramod,[status(thm)],[c_26,c_1925]) ).
cnf(c_1927,plain,
composition(converse(A),top) = composition(composition(converse(A),A),top),
inference(paramod,[status(thm)],[c_195,c_1926]) ).
cnf(c_1928,plain,
composition(converse(A),top) = composition(converse(A),composition(A,top)),
inference(paramod,[status(thm)],[c_23,c_1927]) ).
cnf(c_1375,plain,
composition(converse(A),composition(A,top)) = composition(converse(A),top),
inference(copy,[status(thm)],[c_1928]) ).
cnf(c_1929,plain,
composition(A,composition(converse(A),top)) = composition(converse(converse(A)),top),
inference(paramod,[status(thm)],[c_26,c_1375]) ).
cnf(c_1381,plain,
composition(A,composition(converse(A),top)) = composition(A,top),
inference(paramod,[status(thm)],[c_26,c_1929]) ).
cnf(c_1382,plain,
join(composition(sK0,top),composition(converse(sK0),top)) = composition(sK0,top),
inference(paramod,[status(thm)],[c_1375,c_116]) ).
cnf(c_1930,plain,
join(composition(converse(sK0),top),composition(sK0,top)) = composition(converse(sK0),top),
inference(paramod,[status(thm)],[c_1381,c_90]) ).
cnf(c_1931,plain,
join(composition(sK0,top),composition(converse(sK0),top)) = composition(converse(sK0),top),
inference(paramod,[status(thm)],[c_18,c_1930]) ).
cnf(c_1932,plain,
composition(sK0,top) = composition(converse(sK0),top),
inference(paramod,[status(thm)],[c_1382,c_1931]) ).
cnf(c_1714,plain,
composition(converse(sK0),top) = composition(sK0,top),
inference(copy,[status(thm)],[c_1932]) ).
cnf(c_1933,plain,
join(complement(one),complement(composition(sK0,top))) = complement(converse(sK0)),
inference(paramod,[status(thm)],[c_1714,c_1028]) ).
cnf(c_1727,plain,
complement(converse(sK0)) = join(complement(one),complement(composition(sK0,top))),
inference(copy,[status(thm)],[c_1933]) ).
cnf(c_1934,plain,
join(complement(one),composition(sK0,top)) = join(complement(one),converse(sK0)),
inference(paramod,[status(thm)],[c_1714,c_960]) ).
cnf(c_1728,plain,
join(complement(one),converse(sK0)) = join(complement(one),composition(sK0,top)),
inference(copy,[status(thm)],[c_1934]) ).
cnf(c_1935,plain,
converse(composition(sK0,top)) = composition(converse(top),converse(converse(sK0))),
inference(paramod,[status(thm)],[c_1714,c_28]) ).
cnf(c_1936,plain,
composition(converse(top),converse(sK0)) = composition(converse(top),converse(converse(sK0))),
inference(paramod,[status(thm)],[c_28,c_1935]) ).
cnf(c_1937,plain,
composition(top,converse(sK0)) = composition(converse(top),converse(converse(sK0))),
inference(paramod,[status(thm)],[c_195,c_1936]) ).
cnf(c_1938,plain,
composition(top,converse(sK0)) = composition(top,converse(converse(sK0))),
inference(paramod,[status(thm)],[c_195,c_1937]) ).
cnf(c_1734,plain,
composition(top,converse(sK0)) = composition(top,sK0),
inference(paramod,[status(thm)],[c_26,c_1938]) ).
cnf(c_1939,plain,
join(complement(converse(sK0)),composition(converse(top),complement(composition(top,sK0)))) = complement(converse(sK0)),
inference(paramod,[status(thm)],[c_1734,c_30]) ).
cnf(c_1940,plain,
join(join(complement(one),complement(composition(sK0,top))),composition(converse(top),complement(composition(top,sK0)))) = complement(converse(sK0)),
inference(paramod,[status(thm)],[c_1727,c_1939]) ).
cnf(c_1941,plain,
join(join(complement(one),complement(composition(sK0,top))),composition(top,complement(composition(top,sK0)))) = complement(converse(sK0)),
inference(paramod,[status(thm)],[c_195,c_1940]) ).
cnf(c_1942,plain,
join(join(complement(one),complement(composition(sK0,top))),complement(composition(top,sK0))) = complement(converse(sK0)),
inference(paramod,[status(thm)],[c_365,c_1941]) ).
cnf(c_1943,plain,
join(complement(composition(top,sK0)),join(complement(one),complement(composition(sK0,top)))) = complement(converse(sK0)),
inference(paramod,[status(thm)],[c_18,c_1942]) ).
cnf(c_1944,plain,
join(complement(one),join(complement(composition(top,sK0)),complement(composition(sK0,top)))) = complement(converse(sK0)),
inference(paramod,[status(thm)],[c_45,c_1943]) ).
cnf(c_1945,plain,
join(complement(sK0),complement(composition(sK0,top))) = complement(converse(sK0)),
inference(paramod,[status(thm)],[c_969,c_1944]) ).
cnf(c_1946,plain,
complement(sK0) = complement(converse(sK0)),
inference(paramod,[status(thm)],[c_1005,c_1945]) ).
cnf(c_1947,plain,
complement(sK0) = join(complement(one),complement(composition(sK0,top))),
inference(paramod,[status(thm)],[c_1727,c_1946]) ).
cnf(c_1753,plain,
join(complement(one),complement(composition(sK0,top))) = complement(sK0),
inference(copy,[status(thm)],[c_1947]) ).
cnf(c_1765,plain,
complement(converse(sK0)) = complement(sK0),
inference(paramod,[status(thm)],[c_1753,c_1727]) ).
cnf(c_1948,plain,
complement(complement(sK0)) = converse(sK0),
inference(paramod,[status(thm)],[c_1765,c_96]) ).
cnf(c_1949,plain,
sK0 = converse(sK0),
inference(paramod,[status(thm)],[c_96,c_1948]) ).
cnf(c_1769,plain,
converse(sK0) = sK0,
inference(copy,[status(thm)],[c_1949]) ).
cnf(c_1950,plain,
join(complement(one),sK0) = join(complement(one),composition(sK0,top)),
inference(paramod,[status(thm)],[c_1769,c_1728]) ).
cnf(c_1951,plain,
join(sK0,complement(one)) = join(complement(one),composition(sK0,top)),
inference(paramod,[status(thm)],[c_18,c_1950]) ).
cnf(c_1774,plain,
join(complement(one),composition(sK0,top)) = join(sK0,complement(one)),
inference(copy,[status(thm)],[c_1951]) ).
cnf(c_1952,negated_conjecture,
complement(join(sK0,complement(one))) != complement(join(sK0,complement(one))),
inference(paramod,[status(thm)],[c_1774,c_99]) ).
cnf(c_1782,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_1952]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL027+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n003.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sat Sep 26 05:34:53 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.35 % Process 2125941 was started by sandbox2 on n003,
% 0.07/0.35 % Sat Sep 26 05:34:53 2026
% 0.07/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.07/0.36
% 0.07/0.36 % From the command line: assign(max_seconds, 300).
% 11.06/1.86
% 11.06/1.86 % SZS status Theorem for theBenchmark
% 11.06/1.86
% 11.06/1.86 % Proof 1 at 0.91 (+ 0.33) seconds.
% 11.06/1.86 % Length of proof is 142.
% 11.06/1.86 % Level of proof is 29.
% 11.06/1.86 % Maximum clause weight is 33.000.
% 11.06/1.86 % Given clauses 303.
% 11.06/1.86
% 11.06/1.86 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------