%------------------------------------------------------------------------------
% 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 : n026.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 : Theorem 10.61s 1.87s
% Output : CNFRefutation 10.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 14
% Syntax : Number of formulae : 160 ( 160 unt; 0 def)
% Number of atoms : 160 ( 159 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 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 : 206 ( 13 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] : complement(composition(X0,top)) = composition(complement(composition(X0,top)),top),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0] : complement(composition(X0,top)) = composition(complement(composition(X0,top)),top),
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_1823,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_1823]) ).
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_1824,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_1824]) ).
fof(nnf_17,plain,
? [X0] : composition(complement(composition(X0,top)),top) != complement(composition(X0,top)),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
composition(complement(composition(sK0,top)),top) != complement(composition(sK0,top)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[nnf_17]) ).
cnf(c_40,negated_conjecture,
composition(complement(composition(sK0,top)),top) != complement(composition(sK0,top)),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_43,plain,
join(complement(join(A,complement(B))),complement(join(complement(B),complement(A)))) = B,
inference(paramod,[status(thm)],[c_18,c_21]) ).
cnf(c_44,plain,
join(complement(join(complement(A),B)),complement(join(complement(B),complement(A)))) = A,
inference(paramod,[status(thm)],[c_18,c_21]) ).
cnf(c_1825,plain,
converse(A) = composition(converse(one),converse(A)),
inference(paramod,[status(thm)],[c_24,c_28]) ).
cnf(c_47,plain,
composition(converse(one),converse(A)) = converse(A),
inference(copy,[status(thm)],[c_1825]) ).
cnf(c_1826,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_1827,plain,
converse(complement(A)) = join(converse(complement(A)),composition(converse(complement(composition(B,A))),converse(converse(B)))),
inference(paramod,[status(thm)],[c_28,c_1826]) ).
cnf(c_1828,plain,
converse(complement(A)) = join(converse(complement(A)),composition(converse(complement(composition(B,A))),B)),
inference(paramod,[status(thm)],[c_26,c_1827]) ).
cnf(c_51,plain,
join(converse(complement(A)),composition(converse(complement(composition(B,A))),B)) = converse(complement(A)),
inference(copy,[status(thm)],[c_1828]) ).
cnf(c_1829,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_31,c_21]) ).
cnf(c_54,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_33,c_1829]) ).
cnf(c_1830,plain,
join(complement(join(complement(A),complement(A))),complement(top)) = A,
inference(paramod,[status(thm)],[c_31,c_21]) ).
cnf(c_1831,plain,
join(complement(join(complement(A),complement(A))),zero) = A,
inference(paramod,[status(thm)],[c_33,c_1830]) ).
cnf(c_55,plain,
join(zero,complement(join(complement(A),complement(A)))) = A,
inference(paramod,[status(thm)],[c_18,c_1831]) ).
cnf(c_1832,plain,
converse(top) = join(converse(A),converse(complement(A))),
inference(paramod,[status(thm)],[c_31,c_27]) ).
cnf(c_57,plain,
join(converse(A),converse(complement(A))) = converse(top),
inference(copy,[status(thm)],[c_1832]) ).
cnf(c_1833,plain,
join(zero,composition(converse(A),complement(composition(A,top)))) = complement(top),
inference(paramod,[status(thm)],[c_33,c_30]) ).
cnf(c_60,plain,
join(zero,composition(converse(A),complement(composition(A,top)))) = zero,
inference(paramod,[status(thm)],[c_33,c_1833]) ).
cnf(c_1834,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_26,c_47]) ).
cnf(c_73,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_26,c_1834]) ).
cnf(c_1835,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_73,c_24]) ).
cnf(c_75,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_1835]) ).
cnf(c_79,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_73,c_30]) ).
cnf(c_80,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_75,c_73]) ).
cnf(c_81,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_80,c_79]) ).
cnf(c_82,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_81,c_55]) ).
cnf(c_1836,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_31,c_44]) ).
cnf(c_1837,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_18,c_1836]) ).
cnf(c_1838,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_33,c_1837]) ).
cnf(c_85,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_18,c_1838]) ).
cnf(c_86,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_85,c_54]) ).
cnf(c_87,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_86,c_85]) ).
cnf(c_88,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_86,c_82]) ).
cnf(c_89,plain,
complement(join(A,A)) = complement(A),
inference(paramod,[status(thm)],[c_88,c_87]) ).
cnf(c_91,plain,
composition(converse(A),complement(composition(A,top))) = zero,
inference(paramod,[status(thm)],[c_88,c_60]) ).
cnf(c_1839,plain,
join(complement(join(A,B)),complement(join(complement(complement(A)),complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_86,c_21]) ).
cnf(c_104,plain,
join(complement(join(A,B)),complement(join(A,complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_86,c_1839]) ).
cnf(c_1840,plain,
join(complement(join(A,B)),complement(join(complement(complement(B)),complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_86,c_43]) ).
cnf(c_106,plain,
join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_86,c_1840]) ).
cnf(c_1841,plain,
join(join(A,A),complement(A)) = top,
inference(paramod,[status(thm)],[c_89,c_31]) ).
cnf(c_1842,plain,
join(A,join(A,complement(A))) = top,
inference(paramod,[status(thm)],[c_19,c_1841]) ).
cnf(c_111,plain,
join(A,top) = top,
inference(paramod,[status(thm)],[c_31,c_1842]) ).
cnf(c_1843,plain,
complement(complement(A)) = join(A,A),
inference(paramod,[status(thm)],[c_89,c_86]) ).
cnf(c_1844,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_86,c_1843]) ).
cnf(c_112,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_1844]) ).
cnf(c_1845,plain,
top = join(top,A),
inference(paramod,[status(thm)],[c_111,c_18]) ).
cnf(c_126,plain,
join(top,A) = top,
inference(copy,[status(thm)],[c_1845]) ).
cnf(c_1846,plain,
composition(top,A) = join(composition(B,A),composition(top,A)),
inference(paramod,[status(thm)],[c_111,c_25]) ).
cnf(c_127,plain,
join(composition(A,B),composition(top,B)) = composition(top,B),
inference(copy,[status(thm)],[c_1846]) ).
cnf(c_1847,plain,
converse(top) = join(converse(A),converse(top)),
inference(paramod,[status(thm)],[c_111,c_27]) ).
cnf(c_128,plain,
join(converse(A),converse(top)) = converse(top),
inference(copy,[status(thm)],[c_1847]) ).
cnf(c_1848,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_112,c_19]) ).
cnf(c_130,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_1848]) ).
cnf(c_152,plain,
join(A,converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_26,c_128]) ).
cnf(c_155,plain,
converse(top) = top,
inference(paramod,[status(thm)],[c_152,c_126]) ).
cnf(c_157,plain,
join(converse(A),converse(complement(A))) = top,
inference(paramod,[status(thm)],[c_155,c_57]) ).
cnf(c_178,plain,
join(A,converse(complement(converse(A)))) = top,
inference(paramod,[status(thm)],[c_26,c_157]) ).
cnf(c_188,plain,
composition(top,complement(composition(top,top))) = zero,
inference(paramod,[status(thm)],[c_155,c_91]) ).
cnf(c_1849,plain,
composition(join(top,A),complement(composition(top,top))) = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_188,c_25]) ).
cnf(c_1850,plain,
composition(top,complement(composition(top,top))) = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_126,c_1849]) ).
cnf(c_1851,plain,
zero = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_188,c_1850]) ).
cnf(c_1852,plain,
zero = composition(A,complement(composition(top,top))),
inference(paramod,[status(thm)],[c_88,c_1851]) ).
cnf(c_196,plain,
composition(A,complement(composition(top,top))) = zero,
inference(copy,[status(thm)],[c_1852]) ).
cnf(c_1853,plain,
zero = complement(composition(top,top)),
inference(paramod,[status(thm)],[c_196,c_80]) ).
cnf(c_201,plain,
complement(composition(top,top)) = zero,
inference(copy,[status(thm)],[c_1853]) ).
cnf(c_1854,plain,
join(composition(top,top),zero) = top,
inference(paramod,[status(thm)],[c_201,c_31]) ).
cnf(c_1855,plain,
join(zero,composition(top,top)) = top,
inference(paramod,[status(thm)],[c_18,c_1854]) ).
cnf(c_205,plain,
composition(top,top) = top,
inference(paramod,[status(thm)],[c_88,c_1855]) ).
cnf(c_1856,plain,
composition(top,A) = composition(top,composition(top,A)),
inference(paramod,[status(thm)],[c_205,c_23]) ).
cnf(c_208,plain,
composition(top,composition(top,A)) = composition(top,A),
inference(copy,[status(thm)],[c_1856]) ).
cnf(c_222,plain,
join(A,composition(top,A)) = composition(top,A),
inference(paramod,[status(thm)],[c_80,c_127]) ).
cnf(c_1857,plain,
converse(composition(top,A)) = join(converse(A),converse(composition(top,A))),
inference(paramod,[status(thm)],[c_222,c_27]) ).
cnf(c_1858,plain,
composition(converse(A),converse(top)) = join(converse(A),converse(composition(top,A))),
inference(paramod,[status(thm)],[c_28,c_1857]) ).
cnf(c_1859,plain,
composition(converse(A),top) = join(converse(A),converse(composition(top,A))),
inference(paramod,[status(thm)],[c_155,c_1858]) ).
cnf(c_1860,plain,
composition(converse(A),top) = join(converse(A),composition(converse(A),converse(top))),
inference(paramod,[status(thm)],[c_28,c_1859]) ).
cnf(c_1861,plain,
composition(converse(A),top) = join(converse(A),composition(converse(A),top)),
inference(paramod,[status(thm)],[c_155,c_1860]) ).
cnf(c_225,plain,
join(converse(A),composition(converse(A),top)) = composition(converse(A),top),
inference(copy,[status(thm)],[c_1861]) ).
cnf(c_1862,plain,
join(complement(join(A,B)),complement(A)) = join(complement(join(A,B)),complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_104,c_130]) ).
cnf(c_1863,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_1862]) ).
cnf(c_234,plain,
join(complement(A),complement(join(A,B))) = complement(A),
inference(paramod,[status(thm)],[c_104,c_1863]) ).
cnf(c_1864,plain,
join(converse(complement(composition(top,A))),composition(converse(complement(composition(top,A))),top)) = converse(complement(composition(top,A))),
inference(paramod,[status(thm)],[c_208,c_51]) ).
cnf(c_241,plain,
composition(converse(complement(composition(top,A))),top) = converse(complement(composition(top,A))),
inference(paramod,[status(thm)],[c_225,c_1864]) ).
cnf(c_1865,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_106,c_104]) ).
cnf(c_1866,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_86,c_1865]) ).
cnf(c_1867,plain,
join(A,complement(join(complement(join(B,A)),join(A,complement(B))))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_86,c_1866]) ).
cnf(c_1868,plain,
join(A,complement(join(join(A,complement(B)),complement(join(B,A))))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_18,c_1867]) ).
cnf(c_1869,plain,
join(A,complement(join(A,join(complement(B),complement(join(B,A)))))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_19,c_1868]) ).
cnf(c_1870,plain,
join(A,complement(join(A,complement(B)))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_234,c_1869]) ).
cnf(c_253,plain,
join(A,complement(join(A,complement(B)))) = join(B,A),
inference(paramod,[status(thm)],[c_86,c_1870]) ).
cnf(c_1871,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_106,c_106]) ).
cnf(c_1872,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_86,c_1871]) ).
cnf(c_1873,plain,
join(A,complement(join(complement(join(A,complement(B))),join(B,A)))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_86,c_1872]) ).
cnf(c_1874,plain,
join(A,complement(join(join(B,A),complement(join(A,complement(B)))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_18,c_1873]) ).
cnf(c_1875,plain,
join(A,complement(join(B,join(A,complement(join(A,complement(B))))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_19,c_1874]) ).
cnf(c_1876,plain,
join(A,complement(join(B,join(B,A)))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_253,c_1875]) ).
cnf(c_1877,plain,
join(A,complement(join(B,A))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_130,c_1876]) ).
cnf(c_255,plain,
join(A,complement(join(B,A))) = join(A,complement(B)),
inference(paramod,[status(thm)],[c_86,c_1877]) ).
cnf(c_1878,plain,
join(converse(complement(A)),complement(top)) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_157,c_255]) ).
cnf(c_1879,plain,
join(converse(complement(A)),zero) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_33,c_1878]) ).
cnf(c_1880,plain,
join(zero,converse(complement(A))) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_18,c_1879]) ).
cnf(c_1881,plain,
converse(complement(A)) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_88,c_1880]) ).
cnf(c_1882,plain,
converse(complement(A)) = join(complement(converse(A)),converse(complement(A))),
inference(paramod,[status(thm)],[c_18,c_1881]) ).
cnf(c_386,plain,
join(complement(converse(A)),converse(complement(A))) = converse(complement(A)),
inference(copy,[status(thm)],[c_1882]) ).
cnf(c_1883,plain,
join(converse(complement(converse(A))),complement(top)) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_178,c_255]) ).
cnf(c_1884,plain,
join(converse(complement(converse(A))),zero) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_33,c_1883]) ).
cnf(c_1885,plain,
join(zero,converse(complement(converse(A)))) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_18,c_1884]) ).
cnf(c_1886,plain,
converse(complement(converse(A))) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_88,c_1885]) ).
cnf(c_1887,plain,
converse(complement(converse(A))) = join(complement(A),converse(complement(converse(A)))),
inference(paramod,[status(thm)],[c_18,c_1886]) ).
cnf(c_390,plain,
join(complement(A),converse(complement(converse(A)))) = converse(complement(converse(A))),
inference(copy,[status(thm)],[c_1887]) ).
cnf(c_1888,plain,
converse(converse(complement(A))) = join(converse(complement(converse(A))),converse(converse(complement(A)))),
inference(paramod,[status(thm)],[c_386,c_27]) ).
cnf(c_1889,plain,
complement(A) = join(converse(complement(converse(A))),converse(converse(complement(A)))),
inference(paramod,[status(thm)],[c_26,c_1888]) ).
cnf(c_1890,plain,
complement(A) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_26,c_1889]) ).
cnf(c_1891,plain,
complement(A) = join(complement(A),converse(complement(converse(A)))),
inference(paramod,[status(thm)],[c_18,c_1890]) ).
cnf(c_1892,plain,
complement(A) = converse(complement(converse(A))),
inference(paramod,[status(thm)],[c_390,c_1891]) ).
cnf(c_436,plain,
converse(complement(converse(A))) = complement(A),
inference(copy,[status(thm)],[c_1892]) ).
cnf(c_456,plain,
converse(complement(A)) = complement(converse(A)),
inference(paramod,[status(thm)],[c_436,c_26]) ).
cnf(c_1893,plain,
composition(complement(converse(composition(top,A))),top) = converse(complement(composition(top,A))),
inference(paramod,[status(thm)],[c_456,c_241]) ).
cnf(c_1894,plain,
composition(complement(composition(converse(A),converse(top))),top) = converse(complement(composition(top,A))),
inference(paramod,[status(thm)],[c_28,c_1893]) ).
cnf(c_1895,plain,
composition(complement(composition(converse(A),top)),top) = converse(complement(composition(top,A))),
inference(paramod,[status(thm)],[c_155,c_1894]) ).
cnf(c_1896,plain,
composition(complement(composition(converse(A),top)),top) = complement(converse(composition(top,A))),
inference(paramod,[status(thm)],[c_456,c_1895]) ).
cnf(c_1897,plain,
composition(complement(composition(converse(A),top)),top) = complement(composition(converse(A),converse(top))),
inference(paramod,[status(thm)],[c_28,c_1896]) ).
cnf(c_484,plain,
composition(complement(composition(converse(A),top)),top) = complement(composition(converse(A),top)),
inference(paramod,[status(thm)],[c_155,c_1897]) ).
cnf(c_1898,plain,
composition(complement(composition(A,top)),top) = complement(composition(converse(converse(A)),top)),
inference(paramod,[status(thm)],[c_26,c_484]) ).
cnf(c_1821,plain,
composition(complement(composition(A,top)),top) = complement(composition(A,top)),
inference(paramod,[status(thm)],[c_26,c_1898]) ).
cnf(c_1822,plain,
$false,
inference(resolve,[status(thm)],[c_1821,c_40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL050+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n026.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sat Sep 26 05:45:10 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 214590 was started by sandbox2 on n026,
% 0.11/0.37 % Sat Sep 26 05:45:10 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.03/0.38
% 0.03/0.38 % From the command line: assign(max_seconds, 300).
% 10.61/1.87
% 10.61/1.87 % SZS status Theorem for theBenchmark
% 10.61/1.87
% 10.61/1.87 % Proof 1 at 0.97 (+ 0.28) seconds.
% 10.61/1.87 % Length of proof is 81.
% 10.61/1.87 % Level of proof is 22.
% 10.61/1.87 % Maximum clause weight is 30.000.
% 10.61/1.87 % Given clauses 316.
% 10.61/1.87
% 10.61/1.87 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------