%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL050-3 : 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 : n013.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 15.61s 2.45s
% Output : CNFRefutation 15.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 14
% Syntax : Number of formulae : 162 ( 162 unt; 0 def)
% Number of atoms : 162 ( 161 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 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 : 210 ( 13 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_1810,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_1810]) ).
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_1811,plain,
zero = complement(join(complement(A),complement(complement(A)))),
inference(paramod,[status(thm)],[c_6,c_18]) ).
cnf(c_1812,plain,
zero = complement(top),
inference(paramod,[status(thm)],[c_17,c_1811]) ).
cnf(c_19,plain,
complement(top) = zero,
inference(copy,[status(thm)],[c_1812]) ).
fof(goals_17,axiom,
complement(composition(sk1,top)) != composition(complement(composition(sk1,top)),top),
file('theBenchmark.p',goals_17) ).
cnf(c_26,plain,
complement(composition(sk1,top)) != composition(complement(composition(sk1,top)),top),
inference(clausify,[status(thm)],[goals_17]) ).
cnf(c_27,plain,
composition(complement(composition(sk1,top)),top) != complement(composition(sk1,top)),
inference(copy,[status(thm)],[c_26]) ).
cnf(c_30,plain,
join(complement(join(A,complement(B))),complement(join(complement(B),complement(A)))) = B,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_31,plain,
join(complement(join(complement(A),B)),complement(join(complement(B),complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_1813,plain,
converse(A) = composition(converse(one),converse(A)),
inference(paramod,[status(thm)],[c_9,c_13]) ).
cnf(c_34,plain,
composition(converse(one),converse(A)) = converse(A),
inference(copy,[status(thm)],[c_1813]) ).
cnf(c_1814,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_1815,plain,
converse(complement(A)) = join(converse(complement(A)),composition(converse(complement(composition(B,A))),converse(converse(B)))),
inference(paramod,[status(thm)],[c_13,c_1814]) ).
cnf(c_1816,plain,
converse(complement(A)) = join(converse(complement(A)),composition(converse(complement(composition(B,A))),B)),
inference(paramod,[status(thm)],[c_11,c_1815]) ).
cnf(c_38,plain,
join(converse(complement(A)),composition(converse(complement(composition(B,A))),B)) = converse(complement(A)),
inference(copy,[status(thm)],[c_1816]) ).
cnf(c_1817,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_17,c_5]) ).
cnf(c_41,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_19,c_1817]) ).
cnf(c_1818,plain,
join(complement(join(complement(A),complement(A))),complement(top)) = A,
inference(paramod,[status(thm)],[c_17,c_5]) ).
cnf(c_1819,plain,
join(complement(join(complement(A),complement(A))),zero) = A,
inference(paramod,[status(thm)],[c_19,c_1818]) ).
cnf(c_42,plain,
join(zero,complement(join(complement(A),complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_1819]) ).
cnf(c_1820,plain,
converse(top) = join(converse(A),converse(complement(A))),
inference(paramod,[status(thm)],[c_17,c_12]) ).
cnf(c_44,plain,
join(converse(A),converse(complement(A))) = converse(top),
inference(copy,[status(thm)],[c_1820]) ).
cnf(c_1821,plain,
join(zero,composition(converse(A),complement(composition(A,top)))) = complement(top),
inference(paramod,[status(thm)],[c_19,c_15]) ).
cnf(c_47,plain,
join(zero,composition(converse(A),complement(composition(A,top)))) = zero,
inference(paramod,[status(thm)],[c_19,c_1821]) ).
cnf(c_1822,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_34]) ).
cnf(c_60,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_11,c_1822]) ).
cnf(c_1823,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_60,c_9]) ).
cnf(c_62,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_1823]) ).
cnf(c_66,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_60,c_15]) ).
cnf(c_67,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_62,c_60]) ).
cnf(c_68,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_67,c_66]) ).
cnf(c_69,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_68,c_42]) ).
cnf(c_1824,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_17,c_31]) ).
cnf(c_1825,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_1,c_1824]) ).
cnf(c_1826,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_19,c_1825]) ).
cnf(c_72,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_1,c_1826]) ).
cnf(c_73,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_72,c_41]) ).
cnf(c_74,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_73,c_72]) ).
cnf(c_75,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_73,c_69]) ).
cnf(c_76,plain,
complement(join(A,A)) = complement(A),
inference(paramod,[status(thm)],[c_75,c_74]) ).
cnf(c_78,plain,
composition(converse(A),complement(composition(A,top))) = zero,
inference(paramod,[status(thm)],[c_75,c_47]) ).
cnf(c_1827,plain,
join(complement(join(A,B)),complement(join(complement(complement(A)),complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_73,c_5]) ).
cnf(c_91,plain,
join(complement(join(A,B)),complement(join(A,complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_73,c_1827]) ).
cnf(c_1828,plain,
join(complement(join(A,B)),complement(join(complement(complement(B)),complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_73,c_30]) ).
cnf(c_93,plain,
join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_73,c_1828]) ).
cnf(c_1829,plain,
join(join(A,A),complement(A)) = top,
inference(paramod,[status(thm)],[c_76,c_17]) ).
cnf(c_1830,plain,
join(A,join(A,complement(A))) = top,
inference(paramod,[status(thm)],[c_3,c_1829]) ).
cnf(c_98,plain,
join(A,top) = top,
inference(paramod,[status(thm)],[c_17,c_1830]) ).
cnf(c_1831,plain,
complement(complement(A)) = join(A,A),
inference(paramod,[status(thm)],[c_76,c_73]) ).
cnf(c_1832,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_73,c_1831]) ).
cnf(c_99,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_1832]) ).
cnf(c_1833,plain,
top = join(top,A),
inference(paramod,[status(thm)],[c_98,c_1]) ).
cnf(c_113,plain,
join(top,A) = top,
inference(copy,[status(thm)],[c_1833]) ).
cnf(c_1834,plain,
composition(top,A) = join(composition(B,A),composition(top,A)),
inference(paramod,[status(thm)],[c_98,c_10]) ).
cnf(c_114,plain,
join(composition(A,B),composition(top,B)) = composition(top,B),
inference(copy,[status(thm)],[c_1834]) ).
cnf(c_1835,plain,
converse(top) = join(converse(A),converse(top)),
inference(paramod,[status(thm)],[c_98,c_12]) ).
cnf(c_115,plain,
join(converse(A),converse(top)) = converse(top),
inference(copy,[status(thm)],[c_1835]) ).
cnf(c_1836,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_99,c_3]) ).
cnf(c_117,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_1836]) ).
cnf(c_139,plain,
join(A,converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_11,c_115]) ).
cnf(c_142,plain,
converse(top) = top,
inference(paramod,[status(thm)],[c_139,c_113]) ).
cnf(c_144,plain,
join(converse(A),converse(complement(A))) = top,
inference(paramod,[status(thm)],[c_142,c_44]) ).
cnf(c_165,plain,
join(A,converse(complement(converse(A)))) = top,
inference(paramod,[status(thm)],[c_11,c_144]) ).
cnf(c_175,plain,
composition(top,complement(composition(top,top))) = zero,
inference(paramod,[status(thm)],[c_142,c_78]) ).
cnf(c_1837,plain,
composition(join(top,A),complement(composition(top,top))) = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_175,c_10]) ).
cnf(c_1838,plain,
composition(top,complement(composition(top,top))) = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_113,c_1837]) ).
cnf(c_1839,plain,
zero = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_175,c_1838]) ).
cnf(c_1840,plain,
zero = composition(A,complement(composition(top,top))),
inference(paramod,[status(thm)],[c_75,c_1839]) ).
cnf(c_183,plain,
composition(A,complement(composition(top,top))) = zero,
inference(copy,[status(thm)],[c_1840]) ).
cnf(c_1841,plain,
zero = complement(composition(top,top)),
inference(paramod,[status(thm)],[c_183,c_67]) ).
cnf(c_188,plain,
complement(composition(top,top)) = zero,
inference(copy,[status(thm)],[c_1841]) ).
cnf(c_1842,plain,
join(composition(top,top),zero) = top,
inference(paramod,[status(thm)],[c_188,c_17]) ).
cnf(c_1843,plain,
join(zero,composition(top,top)) = top,
inference(paramod,[status(thm)],[c_1,c_1842]) ).
cnf(c_192,plain,
composition(top,top) = top,
inference(paramod,[status(thm)],[c_75,c_1843]) ).
cnf(c_1844,plain,
composition(top,A) = composition(top,composition(top,A)),
inference(paramod,[status(thm)],[c_192,c_8]) ).
cnf(c_195,plain,
composition(top,composition(top,A)) = composition(top,A),
inference(copy,[status(thm)],[c_1844]) ).
cnf(c_209,plain,
join(A,composition(top,A)) = composition(top,A),
inference(paramod,[status(thm)],[c_67,c_114]) ).
cnf(c_1845,plain,
converse(composition(top,A)) = join(converse(A),converse(composition(top,A))),
inference(paramod,[status(thm)],[c_209,c_12]) ).
cnf(c_1846,plain,
composition(converse(A),converse(top)) = join(converse(A),converse(composition(top,A))),
inference(paramod,[status(thm)],[c_13,c_1845]) ).
cnf(c_1847,plain,
composition(converse(A),top) = join(converse(A),converse(composition(top,A))),
inference(paramod,[status(thm)],[c_142,c_1846]) ).
cnf(c_1848,plain,
composition(converse(A),top) = join(converse(A),composition(converse(A),converse(top))),
inference(paramod,[status(thm)],[c_13,c_1847]) ).
cnf(c_1849,plain,
composition(converse(A),top) = join(converse(A),composition(converse(A),top)),
inference(paramod,[status(thm)],[c_142,c_1848]) ).
cnf(c_212,plain,
join(converse(A),composition(converse(A),top)) = composition(converse(A),top),
inference(copy,[status(thm)],[c_1849]) ).
cnf(c_1850,plain,
join(complement(join(A,B)),complement(A)) = join(complement(join(A,B)),complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_91,c_117]) ).
cnf(c_1851,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_1850]) ).
cnf(c_221,plain,
join(complement(A),complement(join(A,B))) = complement(A),
inference(paramod,[status(thm)],[c_91,c_1851]) ).
cnf(c_1852,plain,
join(converse(complement(composition(top,A))),composition(converse(complement(composition(top,A))),top)) = converse(complement(composition(top,A))),
inference(paramod,[status(thm)],[c_195,c_38]) ).
cnf(c_228,plain,
composition(converse(complement(composition(top,A))),top) = converse(complement(composition(top,A))),
inference(paramod,[status(thm)],[c_212,c_1852]) ).
cnf(c_1853,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_93,c_91]) ).
cnf(c_1854,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_73,c_1853]) ).
cnf(c_1855,plain,
join(A,complement(join(complement(join(B,A)),join(A,complement(B))))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_73,c_1854]) ).
cnf(c_1856,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_1855]) ).
cnf(c_1857,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_1856]) ).
cnf(c_1858,plain,
join(A,complement(join(A,complement(B)))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_221,c_1857]) ).
cnf(c_240,plain,
join(A,complement(join(A,complement(B)))) = join(B,A),
inference(paramod,[status(thm)],[c_73,c_1858]) ).
cnf(c_1859,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_93,c_93]) ).
cnf(c_1860,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_73,c_1859]) ).
cnf(c_1861,plain,
join(A,complement(join(complement(join(A,complement(B))),join(B,A)))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_73,c_1860]) ).
cnf(c_1862,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_1861]) ).
cnf(c_1863,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_1862]) ).
cnf(c_1864,plain,
join(A,complement(join(B,join(B,A)))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_240,c_1863]) ).
cnf(c_1865,plain,
join(A,complement(join(B,A))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_117,c_1864]) ).
cnf(c_242,plain,
join(A,complement(join(B,A))) = join(A,complement(B)),
inference(paramod,[status(thm)],[c_73,c_1865]) ).
cnf(c_1866,plain,
join(converse(complement(A)),complement(top)) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_144,c_242]) ).
cnf(c_1867,plain,
join(converse(complement(A)),zero) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_19,c_1866]) ).
cnf(c_1868,plain,
join(zero,converse(complement(A))) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_1,c_1867]) ).
cnf(c_1869,plain,
converse(complement(A)) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_75,c_1868]) ).
cnf(c_1870,plain,
converse(complement(A)) = join(complement(converse(A)),converse(complement(A))),
inference(paramod,[status(thm)],[c_1,c_1869]) ).
cnf(c_373,plain,
join(complement(converse(A)),converse(complement(A))) = converse(complement(A)),
inference(copy,[status(thm)],[c_1870]) ).
cnf(c_1871,plain,
join(converse(complement(converse(A))),complement(top)) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_165,c_242]) ).
cnf(c_1872,plain,
join(converse(complement(converse(A))),zero) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_19,c_1871]) ).
cnf(c_1873,plain,
join(zero,converse(complement(converse(A)))) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_1,c_1872]) ).
cnf(c_1874,plain,
converse(complement(converse(A))) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_75,c_1873]) ).
cnf(c_1875,plain,
converse(complement(converse(A))) = join(complement(A),converse(complement(converse(A)))),
inference(paramod,[status(thm)],[c_1,c_1874]) ).
cnf(c_377,plain,
join(complement(A),converse(complement(converse(A)))) = converse(complement(converse(A))),
inference(copy,[status(thm)],[c_1875]) ).
cnf(c_1876,plain,
converse(converse(complement(A))) = join(converse(complement(converse(A))),converse(converse(complement(A)))),
inference(paramod,[status(thm)],[c_373,c_12]) ).
cnf(c_1877,plain,
complement(A) = join(converse(complement(converse(A))),converse(converse(complement(A)))),
inference(paramod,[status(thm)],[c_11,c_1876]) ).
cnf(c_1878,plain,
complement(A) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_11,c_1877]) ).
cnf(c_1879,plain,
complement(A) = join(complement(A),converse(complement(converse(A)))),
inference(paramod,[status(thm)],[c_1,c_1878]) ).
cnf(c_1880,plain,
complement(A) = converse(complement(converse(A))),
inference(paramod,[status(thm)],[c_377,c_1879]) ).
cnf(c_423,plain,
converse(complement(converse(A))) = complement(A),
inference(copy,[status(thm)],[c_1880]) ).
cnf(c_443,plain,
converse(complement(A)) = complement(converse(A)),
inference(paramod,[status(thm)],[c_423,c_11]) ).
cnf(c_1881,plain,
composition(complement(converse(composition(top,A))),top) = converse(complement(composition(top,A))),
inference(paramod,[status(thm)],[c_443,c_228]) ).
cnf(c_1882,plain,
composition(complement(composition(converse(A),converse(top))),top) = converse(complement(composition(top,A))),
inference(paramod,[status(thm)],[c_13,c_1881]) ).
cnf(c_1883,plain,
composition(complement(composition(converse(A),top)),top) = converse(complement(composition(top,A))),
inference(paramod,[status(thm)],[c_142,c_1882]) ).
cnf(c_1884,plain,
composition(complement(composition(converse(A),top)),top) = complement(converse(composition(top,A))),
inference(paramod,[status(thm)],[c_443,c_1883]) ).
cnf(c_1885,plain,
composition(complement(composition(converse(A),top)),top) = complement(composition(converse(A),converse(top))),
inference(paramod,[status(thm)],[c_13,c_1884]) ).
cnf(c_471,plain,
composition(complement(composition(converse(A),top)),top) = complement(composition(converse(A),top)),
inference(paramod,[status(thm)],[c_142,c_1885]) ).
cnf(c_1886,plain,
composition(complement(composition(A,top)),top) = complement(composition(converse(converse(A)),top)),
inference(paramod,[status(thm)],[c_11,c_471]) ).
cnf(c_1808,plain,
composition(complement(composition(A,top)),top) = complement(composition(A,top)),
inference(paramod,[status(thm)],[c_11,c_1886]) ).
cnf(c_1809,plain,
$false,
inference(resolve,[status(thm)],[c_1808,c_27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : REL050-3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n013.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Sat Sep 26 05:41:51 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.43 % Process 2054550 was started by sandbox2 on n013,
% 0.18/0.43 % Sat Sep 26 05:41:51 2026
% 0.18/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.44
% 0.18/0.44 % From the command line: assign(max_seconds, 300).
% 15.61/2.45
% 15.61/2.45 % SZS status Unsatisfiable for theBenchmark
% 15.61/2.45
% 15.61/2.45 % Proof 1 at 1.50 (+ 0.46) seconds.
% 15.61/2.45 % Length of proof is 71.
% 15.61/2.45 % Level of proof is 21.
% 15.61/2.45 % Maximum clause weight is 30.000.
% 15.61/2.45 % Given clauses 316.
% 15.61/2.45
% 15.61/2.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------