%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL050-2 : 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 : n009.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 08:25:08 AM UTC 2026
% Result : Unsatisfiable 15.87s 2.73s
% Output : CNFRefutation 15.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 14
% Syntax : Number of formulae : 186 ( 181 unt; 0 def)
% Number of atoms : 191 ( 190 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 11 ~; 5 |; 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 : 234 ( 14 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_1743,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_1743]) ).
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_1744,plain,
zero = complement(join(complement(A),complement(complement(A)))),
inference(paramod,[status(thm)],[c_6,c_18]) ).
cnf(c_1745,plain,
zero = complement(top),
inference(paramod,[status(thm)],[c_17,c_1744]) ).
cnf(c_19,plain,
complement(top) = zero,
inference(copy,[status(thm)],[c_1745]) ).
fof(goals_14,axiom,
( join(composition(complement(composition(sk1,top)),top),complement(composition(sk1,top))) != complement(composition(sk1,top))
| join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)) != composition(complement(composition(sk1,top)),top) ),
file('theBenchmark.p',goals_14) ).
cnf(c_20,plain,
( join(composition(complement(composition(sk1,top)),top),complement(composition(sk1,top))) != complement(composition(sk1,top))
| join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)) != composition(complement(composition(sk1,top)),top) ),
inference(clausify,[status(thm)],[goals_14]) ).
cnf(c_21,plain,
( join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)) != complement(composition(sk1,top))
| join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)) != composition(complement(composition(sk1,top)),top) ),
inference(paramod,[status(thm)],[c_1,c_20]) ).
cnf(c_24,plain,
join(complement(join(A,complement(B))),complement(join(complement(B),complement(A)))) = B,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_25,plain,
join(complement(join(complement(A),B)),complement(join(complement(B),complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_1746,plain,
converse(A) = composition(converse(one),converse(A)),
inference(paramod,[status(thm)],[c_9,c_13]) ).
cnf(c_28,plain,
composition(converse(one),converse(A)) = converse(A),
inference(copy,[status(thm)],[c_1746]) ).
cnf(c_1747,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_1748,plain,
converse(complement(A)) = join(converse(complement(A)),composition(converse(complement(composition(B,A))),converse(converse(B)))),
inference(paramod,[status(thm)],[c_13,c_1747]) ).
cnf(c_1749,plain,
converse(complement(A)) = join(converse(complement(A)),composition(converse(complement(composition(B,A))),B)),
inference(paramod,[status(thm)],[c_11,c_1748]) ).
cnf(c_32,plain,
join(converse(complement(A)),composition(converse(complement(composition(B,A))),B)) = converse(complement(A)),
inference(copy,[status(thm)],[c_1749]) ).
cnf(c_1750,plain,
join(top,A) = join(B,join(complement(B),A)),
inference(paramod,[status(thm)],[c_17,c_3]) ).
cnf(c_33,plain,
join(A,join(complement(A),B)) = join(top,B),
inference(copy,[status(thm)],[c_1750]) ).
cnf(c_1751,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_17,c_5]) ).
cnf(c_35,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_19,c_1751]) ).
cnf(c_1752,plain,
join(complement(join(complement(A),complement(A))),complement(top)) = A,
inference(paramod,[status(thm)],[c_17,c_5]) ).
cnf(c_1753,plain,
join(complement(join(complement(A),complement(A))),zero) = A,
inference(paramod,[status(thm)],[c_19,c_1752]) ).
cnf(c_36,plain,
join(zero,complement(join(complement(A),complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_1753]) ).
cnf(c_1754,plain,
converse(top) = join(converse(A),converse(complement(A))),
inference(paramod,[status(thm)],[c_17,c_12]) ).
cnf(c_38,plain,
join(converse(A),converse(complement(A))) = converse(top),
inference(copy,[status(thm)],[c_1754]) ).
cnf(c_1755,plain,
join(zero,composition(converse(A),complement(composition(A,top)))) = complement(top),
inference(paramod,[status(thm)],[c_19,c_15]) ).
cnf(c_41,plain,
join(zero,composition(converse(A),complement(composition(A,top)))) = zero,
inference(paramod,[status(thm)],[c_19,c_1755]) ).
cnf(c_1756,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_28]) ).
cnf(c_54,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_11,c_1756]) ).
cnf(c_1757,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_54,c_9]) ).
cnf(c_56,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_1757]) ).
cnf(c_60,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_54,c_15]) ).
cnf(c_61,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_56,c_54]) ).
cnf(c_62,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_61,c_60]) ).
cnf(c_63,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_62,c_36]) ).
cnf(c_1758,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_17,c_25]) ).
cnf(c_1759,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_1,c_1758]) ).
cnf(c_1760,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_19,c_1759]) ).
cnf(c_66,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_1,c_1760]) ).
cnf(c_67,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_66,c_35]) ).
cnf(c_68,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_67,c_66]) ).
cnf(c_69,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_67,c_63]) ).
cnf(c_70,plain,
complement(join(A,A)) = complement(A),
inference(paramod,[status(thm)],[c_69,c_68]) ).
cnf(c_72,plain,
composition(converse(A),complement(composition(A,top))) = zero,
inference(paramod,[status(thm)],[c_69,c_41]) ).
cnf(c_1761,plain,
join(complement(join(A,B)),complement(join(complement(complement(A)),complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_67,c_5]) ).
cnf(c_85,plain,
join(complement(join(A,B)),complement(join(A,complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_67,c_1761]) ).
cnf(c_1762,plain,
join(complement(join(A,B)),complement(join(complement(complement(B)),complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_67,c_24]) ).
cnf(c_87,plain,
join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_67,c_1762]) ).
cnf(c_1763,plain,
join(join(A,A),complement(A)) = top,
inference(paramod,[status(thm)],[c_70,c_17]) ).
cnf(c_1764,plain,
join(A,join(A,complement(A))) = top,
inference(paramod,[status(thm)],[c_3,c_1763]) ).
cnf(c_92,plain,
join(A,top) = top,
inference(paramod,[status(thm)],[c_17,c_1764]) ).
cnf(c_1765,plain,
complement(complement(A)) = join(A,A),
inference(paramod,[status(thm)],[c_70,c_67]) ).
cnf(c_1766,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_67,c_1765]) ).
cnf(c_93,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_1766]) ).
cnf(c_1767,plain,
top = join(top,A),
inference(paramod,[status(thm)],[c_92,c_1]) ).
cnf(c_107,plain,
join(top,A) = top,
inference(copy,[status(thm)],[c_1767]) ).
cnf(c_1768,plain,
composition(top,A) = join(composition(B,A),composition(top,A)),
inference(paramod,[status(thm)],[c_92,c_10]) ).
cnf(c_108,plain,
join(composition(A,B),composition(top,B)) = composition(top,B),
inference(copy,[status(thm)],[c_1768]) ).
cnf(c_1769,plain,
converse(top) = join(converse(A),converse(top)),
inference(paramod,[status(thm)],[c_92,c_12]) ).
cnf(c_109,plain,
join(converse(A),converse(top)) = converse(top),
inference(copy,[status(thm)],[c_1769]) ).
cnf(c_110,plain,
join(A,join(complement(A),B)) = top,
inference(paramod,[status(thm)],[c_107,c_33]) ).
cnf(c_1770,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_93,c_3]) ).
cnf(c_111,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_1770]) ).
cnf(c_133,plain,
join(A,converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_11,c_109]) ).
cnf(c_136,plain,
converse(top) = top,
inference(paramod,[status(thm)],[c_133,c_107]) ).
cnf(c_138,plain,
join(converse(A),converse(complement(A))) = top,
inference(paramod,[status(thm)],[c_136,c_38]) ).
cnf(c_159,plain,
join(A,converse(complement(converse(A)))) = top,
inference(paramod,[status(thm)],[c_11,c_138]) ).
cnf(c_169,plain,
composition(top,complement(composition(top,top))) = zero,
inference(paramod,[status(thm)],[c_136,c_72]) ).
cnf(c_1771,plain,
composition(join(top,A),complement(composition(top,top))) = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_169,c_10]) ).
cnf(c_1772,plain,
composition(top,complement(composition(top,top))) = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_107,c_1771]) ).
cnf(c_1773,plain,
zero = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_169,c_1772]) ).
cnf(c_1774,plain,
zero = composition(A,complement(composition(top,top))),
inference(paramod,[status(thm)],[c_69,c_1773]) ).
cnf(c_177,plain,
composition(A,complement(composition(top,top))) = zero,
inference(copy,[status(thm)],[c_1774]) ).
cnf(c_1775,plain,
zero = complement(composition(top,top)),
inference(paramod,[status(thm)],[c_177,c_61]) ).
cnf(c_181,plain,
complement(composition(top,top)) = zero,
inference(copy,[status(thm)],[c_1775]) ).
cnf(c_1776,plain,
join(composition(top,top),zero) = top,
inference(paramod,[status(thm)],[c_181,c_17]) ).
cnf(c_1777,plain,
join(zero,composition(top,top)) = top,
inference(paramod,[status(thm)],[c_1,c_1776]) ).
cnf(c_185,plain,
composition(top,top) = top,
inference(paramod,[status(thm)],[c_69,c_1777]) ).
cnf(c_1778,plain,
composition(top,A) = composition(top,composition(top,A)),
inference(paramod,[status(thm)],[c_185,c_8]) ).
cnf(c_188,plain,
composition(top,composition(top,A)) = composition(top,A),
inference(copy,[status(thm)],[c_1778]) ).
cnf(c_201,plain,
join(A,composition(top,A)) = composition(top,A),
inference(paramod,[status(thm)],[c_61,c_108]) ).
cnf(c_1779,plain,
converse(composition(top,A)) = join(converse(A),converse(composition(top,A))),
inference(paramod,[status(thm)],[c_201,c_12]) ).
cnf(c_1780,plain,
composition(converse(A),converse(top)) = join(converse(A),converse(composition(top,A))),
inference(paramod,[status(thm)],[c_13,c_1779]) ).
cnf(c_1781,plain,
composition(converse(A),top) = join(converse(A),converse(composition(top,A))),
inference(paramod,[status(thm)],[c_136,c_1780]) ).
cnf(c_1782,plain,
composition(converse(A),top) = join(converse(A),composition(converse(A),converse(top))),
inference(paramod,[status(thm)],[c_13,c_1781]) ).
cnf(c_1783,plain,
composition(converse(A),top) = join(converse(A),composition(converse(A),top)),
inference(paramod,[status(thm)],[c_136,c_1782]) ).
cnf(c_204,plain,
join(converse(A),composition(converse(A),top)) = composition(converse(A),top),
inference(copy,[status(thm)],[c_1783]) ).
cnf(c_1784,plain,
join(complement(join(A,B)),complement(A)) = join(complement(join(A,B)),complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_85,c_111]) ).
cnf(c_1785,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_1784]) ).
cnf(c_213,plain,
join(complement(A),complement(join(A,B))) = complement(A),
inference(paramod,[status(thm)],[c_85,c_1785]) ).
cnf(c_1786,plain,
join(converse(complement(composition(top,A))),composition(converse(complement(composition(top,A))),top)) = converse(complement(composition(top,A))),
inference(paramod,[status(thm)],[c_188,c_32]) ).
cnf(c_220,plain,
composition(converse(complement(composition(top,A))),top) = converse(complement(composition(top,A))),
inference(paramod,[status(thm)],[c_204,c_1786]) ).
cnf(c_1787,plain,
join(complement(complement(A)),complement(join(complement(join(B,A)),complement(complement(join(A,complement(B))))))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_87,c_85]) ).
cnf(c_1788,plain,
join(A,complement(join(complement(join(B,A)),complement(complement(join(A,complement(B))))))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_67,c_1787]) ).
cnf(c_1789,plain,
join(A,complement(join(complement(join(B,A)),join(A,complement(B))))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_67,c_1788]) ).
cnf(c_1790,plain,
join(A,complement(join(join(A,complement(B)),complement(join(B,A))))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_1,c_1789]) ).
cnf(c_1791,plain,
join(A,complement(join(A,join(complement(B),complement(join(B,A)))))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_3,c_1790]) ).
cnf(c_1792,plain,
join(A,complement(join(A,complement(B)))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_213,c_1791]) ).
cnf(c_232,plain,
join(A,complement(join(A,complement(B)))) = join(B,A),
inference(paramod,[status(thm)],[c_67,c_1792]) ).
cnf(c_1793,plain,
join(complement(complement(A)),complement(join(complement(join(A,complement(B))),complement(complement(join(B,A)))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_87,c_87]) ).
cnf(c_1794,plain,
join(A,complement(join(complement(join(A,complement(B))),complement(complement(join(B,A)))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_67,c_1793]) ).
cnf(c_1795,plain,
join(A,complement(join(complement(join(A,complement(B))),join(B,A)))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_67,c_1794]) ).
cnf(c_1796,plain,
join(A,complement(join(join(B,A),complement(join(A,complement(B)))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_1,c_1795]) ).
cnf(c_1797,plain,
join(A,complement(join(B,join(A,complement(join(A,complement(B))))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_3,c_1796]) ).
cnf(c_1798,plain,
join(A,complement(join(B,join(B,A)))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_232,c_1797]) ).
cnf(c_1799,plain,
join(A,complement(join(B,A))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_111,c_1798]) ).
cnf(c_234,plain,
join(A,complement(join(B,A))) = join(A,complement(B)),
inference(paramod,[status(thm)],[c_67,c_1799]) ).
cnf(c_247,plain,
join(A,composition(top,complement(A))) = top,
inference(paramod,[status(thm)],[c_201,c_110]) ).
cnf(c_254,plain,
join(complement(A),composition(top,A)) = top,
inference(paramod,[status(thm)],[c_67,c_247]) ).
cnf(c_1800,plain,
converse(top) = join(converse(complement(A)),converse(composition(top,A))),
inference(paramod,[status(thm)],[c_254,c_12]) ).
cnf(c_1801,plain,
top = join(converse(complement(A)),converse(composition(top,A))),
inference(paramod,[status(thm)],[c_136,c_1800]) ).
cnf(c_1802,plain,
top = join(converse(complement(A)),composition(converse(A),converse(top))),
inference(paramod,[status(thm)],[c_13,c_1801]) ).
cnf(c_1803,plain,
top = join(converse(complement(A)),composition(converse(A),top)),
inference(paramod,[status(thm)],[c_136,c_1802]) ).
cnf(c_1804,plain,
top = join(composition(converse(A),top),converse(complement(A))),
inference(paramod,[status(thm)],[c_1,c_1803]) ).
cnf(c_257,plain,
join(composition(converse(A),top),converse(complement(A))) = top,
inference(copy,[status(thm)],[c_1804]) ).
cnf(c_321,plain,
join(composition(A,top),converse(complement(converse(A)))) = top,
inference(paramod,[status(thm)],[c_11,c_257]) ).
cnf(c_1805,plain,
join(converse(complement(A)),complement(top)) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_138,c_234]) ).
cnf(c_1806,plain,
join(converse(complement(A)),zero) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_19,c_1805]) ).
cnf(c_1807,plain,
join(zero,converse(complement(A))) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_1,c_1806]) ).
cnf(c_1808,plain,
converse(complement(A)) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_69,c_1807]) ).
cnf(c_1809,plain,
converse(complement(A)) = join(complement(converse(A)),converse(complement(A))),
inference(paramod,[status(thm)],[c_1,c_1808]) ).
cnf(c_363,plain,
join(complement(converse(A)),converse(complement(A))) = converse(complement(A)),
inference(copy,[status(thm)],[c_1809]) ).
cnf(c_1810,plain,
join(converse(complement(converse(A))),complement(top)) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_159,c_234]) ).
cnf(c_1811,plain,
join(converse(complement(converse(A))),zero) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_19,c_1810]) ).
cnf(c_1812,plain,
join(zero,converse(complement(converse(A)))) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_1,c_1811]) ).
cnf(c_1813,plain,
converse(complement(converse(A))) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_69,c_1812]) ).
cnf(c_1814,plain,
converse(complement(converse(A))) = join(complement(A),converse(complement(converse(A)))),
inference(paramod,[status(thm)],[c_1,c_1813]) ).
cnf(c_367,plain,
join(complement(A),converse(complement(converse(A)))) = converse(complement(converse(A))),
inference(copy,[status(thm)],[c_1814]) ).
cnf(c_1815,plain,
converse(converse(complement(A))) = join(converse(complement(converse(A))),converse(converse(complement(A)))),
inference(paramod,[status(thm)],[c_363,c_12]) ).
cnf(c_1816,plain,
complement(A) = join(converse(complement(converse(A))),converse(converse(complement(A)))),
inference(paramod,[status(thm)],[c_11,c_1815]) ).
cnf(c_1817,plain,
complement(A) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_11,c_1816]) ).
cnf(c_1818,plain,
complement(A) = join(complement(A),converse(complement(converse(A)))),
inference(paramod,[status(thm)],[c_1,c_1817]) ).
cnf(c_1819,plain,
complement(A) = converse(complement(converse(A))),
inference(paramod,[status(thm)],[c_367,c_1818]) ).
cnf(c_413,plain,
converse(complement(converse(A))) = complement(A),
inference(copy,[status(thm)],[c_1819]) ).
cnf(c_1820,plain,
join(composition(A,top),complement(A)) = top,
inference(paramod,[status(thm)],[c_413,c_321]) ).
cnf(c_418,plain,
join(complement(A),composition(A,top)) = top,
inference(paramod,[status(thm)],[c_1,c_1820]) ).
cnf(c_1821,plain,
join(composition(A,top),complement(top)) = join(composition(A,top),complement(complement(A))),
inference(paramod,[status(thm)],[c_418,c_234]) ).
cnf(c_1822,plain,
join(composition(A,top),zero) = join(composition(A,top),complement(complement(A))),
inference(paramod,[status(thm)],[c_19,c_1821]) ).
cnf(c_1823,plain,
join(zero,composition(A,top)) = join(composition(A,top),complement(complement(A))),
inference(paramod,[status(thm)],[c_1,c_1822]) ).
cnf(c_1824,plain,
composition(A,top) = join(composition(A,top),complement(complement(A))),
inference(paramod,[status(thm)],[c_69,c_1823]) ).
cnf(c_1825,plain,
composition(A,top) = join(composition(A,top),A),
inference(paramod,[status(thm)],[c_67,c_1824]) ).
cnf(c_1826,plain,
composition(A,top) = join(A,composition(A,top)),
inference(paramod,[status(thm)],[c_1,c_1825]) ).
cnf(c_428,plain,
join(A,composition(A,top)) = composition(A,top),
inference(copy,[status(thm)],[c_1826]) ).
cnf(c_1827,plain,
( join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)) != complement(composition(sk1,top))
| composition(complement(composition(sk1,top)),top) != composition(complement(composition(sk1,top)),top) ),
inference(paramod,[status(thm)],[c_428,c_21]) ).
cnf(c_1828,plain,
( composition(complement(composition(sk1,top)),top) != complement(composition(sk1,top))
| composition(complement(composition(sk1,top)),top) != composition(complement(composition(sk1,top)),top) ),
inference(paramod,[status(thm)],[c_428,c_1827]) ).
cnf(c_430,plain,
composition(complement(composition(sk1,top)),top) != complement(composition(sk1,top)),
inference(copy,[status(thm)],[c_1828]) ).
cnf(c_434,plain,
converse(complement(A)) = complement(converse(A)),
inference(paramod,[status(thm)],[c_413,c_11]) ).
cnf(c_1829,plain,
composition(complement(converse(composition(top,A))),top) = converse(complement(composition(top,A))),
inference(paramod,[status(thm)],[c_434,c_220]) ).
cnf(c_1830,plain,
composition(complement(composition(converse(A),converse(top))),top) = converse(complement(composition(top,A))),
inference(paramod,[status(thm)],[c_13,c_1829]) ).
cnf(c_1831,plain,
composition(complement(composition(converse(A),top)),top) = converse(complement(composition(top,A))),
inference(paramod,[status(thm)],[c_136,c_1830]) ).
cnf(c_1832,plain,
composition(complement(composition(converse(A),top)),top) = complement(converse(composition(top,A))),
inference(paramod,[status(thm)],[c_434,c_1831]) ).
cnf(c_1833,plain,
composition(complement(composition(converse(A),top)),top) = complement(composition(converse(A),converse(top))),
inference(paramod,[status(thm)],[c_13,c_1832]) ).
cnf(c_462,plain,
composition(complement(composition(converse(A),top)),top) = complement(composition(converse(A),top)),
inference(paramod,[status(thm)],[c_136,c_1833]) ).
cnf(c_1834,plain,
composition(complement(composition(A,top)),top) = complement(composition(converse(converse(A)),top)),
inference(paramod,[status(thm)],[c_11,c_462]) ).
cnf(c_1741,plain,
composition(complement(composition(A,top)),top) = complement(composition(A,top)),
inference(paramod,[status(thm)],[c_11,c_1834]) ).
cnf(c_1742,plain,
$false,
inference(resolve,[status(thm)],[c_1741,c_430]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : REL050-2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n009.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Sat Sep 26 05:42:29 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.45 % Process 3488115 was started by sandbox2 on n009,
% 0.19/0.45 % Sat Sep 26 05:42:29 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.45
% 0.19/0.45 % From the command line: assign(max_seconds, 300).
% 15.87/2.73
% 15.87/2.73 % SZS status Unsatisfiable for theBenchmark
% 15.87/2.73
% 15.87/2.73 % Proof 1 at 1.41 (+ 0.59) seconds.
% 15.87/2.73 % Length of proof is 80.
% 15.87/2.73 % Level of proof is 21.
% 15.87/2.73 % Maximum clause weight is 44.000.
% 15.87/2.73 % Given clauses 308.
% 15.87/2.73
% 15.87/2.73 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------