%------------------------------------------------------------------------------
% 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 : n002.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 5.05s 1.15s
% Output : CNFRefutation 5.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 14
% Syntax : Number of formulae : 187 ( 177 unt; 0 def)
% Number of atoms : 197 ( 196 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 28 ( 18 ~; 8 |; 2 &)
% ( 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 : 230 ( 14 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(composition(complement(composition(X0,top)),top),complement(composition(X0,top))) = complement(composition(X0,top))
& join(complement(composition(X0,top)),composition(complement(composition(X0,top)),top)) = composition(complement(composition(X0,top)),top) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0] :
( join(composition(complement(composition(X0,top)),top),complement(composition(X0,top))) = complement(composition(X0,top))
& join(complement(composition(X0,top)),composition(complement(composition(X0,top)),top)) = composition(complement(composition(X0,top)),top) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_15,plain,
join(A,B) = join(B,A),
inference(clausify,[status(thm)],[maddux1_join_commutativity]) ).
cnf(c_16,plain,
join(join(A,B),C) = join(A,join(B,C)),
inference(clausify,[status(thm)],[maddux2_join_associativity]) ).
cnf(c_17,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_18,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = A,
inference(paramod,[status(thm)],[c_15,c_17]) ).
cnf(c_19,plain,
meet(A,B) = complement(join(complement(A),complement(B))),
inference(clausify,[status(thm)],[maddux4_definiton_of_meet]) ).
cnf(c_20,plain,
composition(composition(A,B),C) = composition(A,composition(B,C)),
inference(clausify,[status(thm)],[composition_associativity]) ).
cnf(c_21,plain,
composition(A,one) = A,
inference(clausify,[status(thm)],[composition_identity]) ).
cnf(c_22,plain,
composition(join(A,B),C) = join(composition(A,C),composition(B,C)),
inference(clausify,[status(thm)],[composition_distributivity]) ).
cnf(c_23,plain,
converse(converse(A)) = A,
inference(clausify,[status(thm)],[converse_idempotence]) ).
cnf(c_24,plain,
converse(join(A,B)) = join(converse(A),converse(B)),
inference(clausify,[status(thm)],[converse_additivity]) ).
cnf(c_25,plain,
converse(composition(A,B)) = composition(converse(B),converse(A)),
inference(clausify,[status(thm)],[converse_multiplicativity]) ).
cnf(c_26,plain,
complement(A) = join(composition(converse(B),complement(composition(B,A))),complement(A)),
inference(clausify,[status(thm)],[converse_cancellativity]) ).
cnf(c_1754,plain,
complement(A) = join(complement(A),composition(converse(B),complement(composition(B,A)))),
inference(paramod,[status(thm)],[c_15,c_26]) ).
cnf(c_27,plain,
join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A),
inference(copy,[status(thm)],[c_1754]) ).
cnf(c_28,plain,
join(A,complement(A)) = top,
inference(clausify,[status(thm)],[def_top]) ).
cnf(c_29,plain,
meet(A,complement(A)) = zero,
inference(clausify,[status(thm)],[def_zero]) ).
cnf(c_1755,plain,
complement(join(complement(A),complement(complement(A)))) = zero,
inference(paramod,[status(thm)],[c_19,c_29]) ).
cnf(c_30,plain,
complement(top) = zero,
inference(paramod,[status(thm)],[c_28,c_1755]) ).
fof(nnf_14,plain,
? [X0] :
( complement(composition(X0,top)) != join(composition(complement(composition(X0,top)),top),complement(composition(X0,top)))
| composition(complement(composition(X0,top)),top) != join(complement(composition(X0,top)),composition(complement(composition(X0,top)),top)) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( complement(composition(sK0,top)) != join(composition(complement(composition(sK0,top)),top),complement(composition(sK0,top)))
| composition(complement(composition(sK0,top)),top) != join(complement(composition(sK0,top)),composition(complement(composition(sK0,top)),top)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[nnf_14]) ).
cnf(c_31,negated_conjecture,
( complement(composition(sK0,top)) != join(composition(complement(composition(sK0,top)),top),complement(composition(sK0,top)))
| composition(complement(composition(sK0,top)),top) != join(complement(composition(sK0,top)),composition(complement(composition(sK0,top)),top)) ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_1756,negated_conjecture,
( complement(composition(sK0,top)) != join(complement(composition(sK0,top)),composition(complement(composition(sK0,top)),top))
| composition(complement(composition(sK0,top)),top) != join(complement(composition(sK0,top)),composition(complement(composition(sK0,top)),top)) ),
inference(paramod,[status(thm)],[c_15,c_31]) ).
cnf(c_1757,negated_conjecture,
( complement(composition(sK0,top)) != join(complement(composition(sK0,top)),composition(complement(composition(sK0,top)),top))
| join(complement(composition(sK0,top)),composition(complement(composition(sK0,top)),top)) != composition(complement(composition(sK0,top)),top) ),
inference(copy,[status(thm)],[c_1756]) ).
cnf(c_32,negated_conjecture,
( join(complement(composition(sK0,top)),composition(complement(composition(sK0,top)),top)) != complement(composition(sK0,top))
| join(complement(composition(sK0,top)),composition(complement(composition(sK0,top)),top)) != composition(complement(composition(sK0,top)),top) ),
inference(copy,[status(thm)],[c_1757]) ).
cnf(c_35,plain,
join(complement(join(A,complement(B))),complement(join(complement(B),complement(A)))) = B,
inference(paramod,[status(thm)],[c_15,c_18]) ).
cnf(c_36,plain,
join(complement(join(complement(A),B)),complement(join(complement(B),complement(A)))) = A,
inference(paramod,[status(thm)],[c_15,c_18]) ).
cnf(c_1758,plain,
converse(A) = composition(converse(one),converse(A)),
inference(paramod,[status(thm)],[c_21,c_25]) ).
cnf(c_39,plain,
composition(converse(one),converse(A)) = converse(A),
inference(copy,[status(thm)],[c_1758]) ).
cnf(c_1759,plain,
converse(complement(A)) = join(converse(complement(A)),converse(composition(converse(B),complement(composition(B,A))))),
inference(paramod,[status(thm)],[c_27,c_24]) ).
cnf(c_1760,plain,
converse(complement(A)) = join(converse(complement(A)),composition(converse(complement(composition(B,A))),converse(converse(B)))),
inference(paramod,[status(thm)],[c_25,c_1759]) ).
cnf(c_1761,plain,
converse(complement(A)) = join(converse(complement(A)),composition(converse(complement(composition(B,A))),B)),
inference(paramod,[status(thm)],[c_23,c_1760]) ).
cnf(c_43,plain,
join(converse(complement(A)),composition(converse(complement(composition(B,A))),B)) = converse(complement(A)),
inference(copy,[status(thm)],[c_1761]) ).
cnf(c_1762,plain,
join(top,A) = join(B,join(complement(B),A)),
inference(paramod,[status(thm)],[c_28,c_16]) ).
cnf(c_44,plain,
join(A,join(complement(A),B)) = join(top,B),
inference(copy,[status(thm)],[c_1762]) ).
cnf(c_1763,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_28,c_18]) ).
cnf(c_46,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_30,c_1763]) ).
cnf(c_1764,plain,
join(complement(join(complement(A),complement(A))),complement(top)) = A,
inference(paramod,[status(thm)],[c_28,c_18]) ).
cnf(c_1765,plain,
join(complement(join(complement(A),complement(A))),zero) = A,
inference(paramod,[status(thm)],[c_30,c_1764]) ).
cnf(c_47,plain,
join(zero,complement(join(complement(A),complement(A)))) = A,
inference(paramod,[status(thm)],[c_15,c_1765]) ).
cnf(c_1766,plain,
converse(top) = join(converse(A),converse(complement(A))),
inference(paramod,[status(thm)],[c_28,c_24]) ).
cnf(c_49,plain,
join(converse(A),converse(complement(A))) = converse(top),
inference(copy,[status(thm)],[c_1766]) ).
cnf(c_1767,plain,
join(zero,composition(converse(A),complement(composition(A,top)))) = complement(top),
inference(paramod,[status(thm)],[c_30,c_27]) ).
cnf(c_52,plain,
join(zero,composition(converse(A),complement(composition(A,top)))) = zero,
inference(paramod,[status(thm)],[c_30,c_1767]) ).
cnf(c_1768,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_23,c_39]) ).
cnf(c_65,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_23,c_1768]) ).
cnf(c_1769,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_65,c_21]) ).
cnf(c_67,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_1769]) ).
cnf(c_71,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_65,c_27]) ).
cnf(c_72,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_67,c_65]) ).
cnf(c_73,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_72,c_71]) ).
cnf(c_74,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_73,c_47]) ).
cnf(c_1770,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_28,c_36]) ).
cnf(c_1771,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_15,c_1770]) ).
cnf(c_1772,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_30,c_1771]) ).
cnf(c_77,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_15,c_1772]) ).
cnf(c_78,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_77,c_46]) ).
cnf(c_79,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_78,c_77]) ).
cnf(c_80,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_78,c_74]) ).
cnf(c_81,plain,
complement(join(A,A)) = complement(A),
inference(paramod,[status(thm)],[c_80,c_79]) ).
cnf(c_83,plain,
composition(converse(A),complement(composition(A,top))) = zero,
inference(paramod,[status(thm)],[c_80,c_52]) ).
cnf(c_1773,plain,
join(complement(join(A,B)),complement(join(complement(complement(A)),complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_78,c_18]) ).
cnf(c_96,plain,
join(complement(join(A,B)),complement(join(A,complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_78,c_1773]) ).
cnf(c_1774,plain,
join(complement(join(A,B)),complement(join(complement(complement(B)),complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_78,c_35]) ).
cnf(c_98,plain,
join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_78,c_1774]) ).
cnf(c_1775,plain,
join(join(A,A),complement(A)) = top,
inference(paramod,[status(thm)],[c_81,c_28]) ).
cnf(c_1776,plain,
join(A,join(A,complement(A))) = top,
inference(paramod,[status(thm)],[c_16,c_1775]) ).
cnf(c_103,plain,
join(A,top) = top,
inference(paramod,[status(thm)],[c_28,c_1776]) ).
cnf(c_1777,plain,
complement(complement(A)) = join(A,A),
inference(paramod,[status(thm)],[c_81,c_78]) ).
cnf(c_1778,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_78,c_1777]) ).
cnf(c_104,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_1778]) ).
cnf(c_1779,plain,
top = join(top,A),
inference(paramod,[status(thm)],[c_103,c_15]) ).
cnf(c_118,plain,
join(top,A) = top,
inference(copy,[status(thm)],[c_1779]) ).
cnf(c_1780,plain,
composition(top,A) = join(composition(B,A),composition(top,A)),
inference(paramod,[status(thm)],[c_103,c_22]) ).
cnf(c_119,plain,
join(composition(A,B),composition(top,B)) = composition(top,B),
inference(copy,[status(thm)],[c_1780]) ).
cnf(c_1781,plain,
converse(top) = join(converse(A),converse(top)),
inference(paramod,[status(thm)],[c_103,c_24]) ).
cnf(c_120,plain,
join(converse(A),converse(top)) = converse(top),
inference(copy,[status(thm)],[c_1781]) ).
cnf(c_121,plain,
join(A,join(complement(A),B)) = top,
inference(paramod,[status(thm)],[c_118,c_44]) ).
cnf(c_1782,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_104,c_16]) ).
cnf(c_122,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_1782]) ).
cnf(c_144,plain,
join(A,converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_23,c_120]) ).
cnf(c_147,plain,
converse(top) = top,
inference(paramod,[status(thm)],[c_144,c_118]) ).
cnf(c_149,plain,
join(converse(A),converse(complement(A))) = top,
inference(paramod,[status(thm)],[c_147,c_49]) ).
cnf(c_170,plain,
join(A,converse(complement(converse(A)))) = top,
inference(paramod,[status(thm)],[c_23,c_149]) ).
cnf(c_180,plain,
composition(top,complement(composition(top,top))) = zero,
inference(paramod,[status(thm)],[c_147,c_83]) ).
cnf(c_1783,plain,
composition(join(top,A),complement(composition(top,top))) = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_180,c_22]) ).
cnf(c_1784,plain,
composition(top,complement(composition(top,top))) = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_118,c_1783]) ).
cnf(c_1785,plain,
zero = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_180,c_1784]) ).
cnf(c_1786,plain,
zero = composition(A,complement(composition(top,top))),
inference(paramod,[status(thm)],[c_80,c_1785]) ).
cnf(c_188,plain,
composition(A,complement(composition(top,top))) = zero,
inference(copy,[status(thm)],[c_1786]) ).
cnf(c_1787,plain,
zero = complement(composition(top,top)),
inference(paramod,[status(thm)],[c_188,c_72]) ).
cnf(c_192,plain,
complement(composition(top,top)) = zero,
inference(copy,[status(thm)],[c_1787]) ).
cnf(c_1788,plain,
join(composition(top,top),zero) = top,
inference(paramod,[status(thm)],[c_192,c_28]) ).
cnf(c_1789,plain,
join(zero,composition(top,top)) = top,
inference(paramod,[status(thm)],[c_15,c_1788]) ).
cnf(c_196,plain,
composition(top,top) = top,
inference(paramod,[status(thm)],[c_80,c_1789]) ).
cnf(c_1790,plain,
composition(top,A) = composition(top,composition(top,A)),
inference(paramod,[status(thm)],[c_196,c_20]) ).
cnf(c_199,plain,
composition(top,composition(top,A)) = composition(top,A),
inference(copy,[status(thm)],[c_1790]) ).
cnf(c_212,plain,
join(A,composition(top,A)) = composition(top,A),
inference(paramod,[status(thm)],[c_72,c_119]) ).
cnf(c_1791,plain,
converse(composition(top,A)) = join(converse(A),converse(composition(top,A))),
inference(paramod,[status(thm)],[c_212,c_24]) ).
cnf(c_1792,plain,
composition(converse(A),converse(top)) = join(converse(A),converse(composition(top,A))),
inference(paramod,[status(thm)],[c_25,c_1791]) ).
cnf(c_1793,plain,
composition(converse(A),top) = join(converse(A),converse(composition(top,A))),
inference(paramod,[status(thm)],[c_147,c_1792]) ).
cnf(c_1794,plain,
composition(converse(A),top) = join(converse(A),composition(converse(A),converse(top))),
inference(paramod,[status(thm)],[c_25,c_1793]) ).
cnf(c_1795,plain,
composition(converse(A),top) = join(converse(A),composition(converse(A),top)),
inference(paramod,[status(thm)],[c_147,c_1794]) ).
cnf(c_215,plain,
join(converse(A),composition(converse(A),top)) = composition(converse(A),top),
inference(copy,[status(thm)],[c_1795]) ).
cnf(c_1796,plain,
join(complement(join(A,B)),complement(A)) = join(complement(join(A,B)),complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_96,c_122]) ).
cnf(c_1797,plain,
join(complement(A),complement(join(A,B))) = join(complement(join(A,B)),complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_15,c_1796]) ).
cnf(c_224,plain,
join(complement(A),complement(join(A,B))) = complement(A),
inference(paramod,[status(thm)],[c_96,c_1797]) ).
cnf(c_1798,plain,
join(converse(complement(composition(top,A))),composition(converse(complement(composition(top,A))),top)) = converse(complement(composition(top,A))),
inference(paramod,[status(thm)],[c_199,c_43]) ).
cnf(c_231,plain,
composition(converse(complement(composition(top,A))),top) = converse(complement(composition(top,A))),
inference(paramod,[status(thm)],[c_215,c_1798]) ).
cnf(c_1799,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_98,c_96]) ).
cnf(c_1800,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_78,c_1799]) ).
cnf(c_1801,plain,
join(A,complement(join(complement(join(B,A)),join(A,complement(B))))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_78,c_1800]) ).
cnf(c_1802,plain,
join(A,complement(join(join(A,complement(B)),complement(join(B,A))))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_15,c_1801]) ).
cnf(c_1803,plain,
join(A,complement(join(A,join(complement(B),complement(join(B,A)))))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_16,c_1802]) ).
cnf(c_1804,plain,
join(A,complement(join(A,complement(B)))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_224,c_1803]) ).
cnf(c_243,plain,
join(A,complement(join(A,complement(B)))) = join(B,A),
inference(paramod,[status(thm)],[c_78,c_1804]) ).
cnf(c_1805,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_98,c_98]) ).
cnf(c_1806,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_78,c_1805]) ).
cnf(c_1807,plain,
join(A,complement(join(complement(join(A,complement(B))),join(B,A)))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_78,c_1806]) ).
cnf(c_1808,plain,
join(A,complement(join(join(B,A),complement(join(A,complement(B)))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_15,c_1807]) ).
cnf(c_1809,plain,
join(A,complement(join(B,join(A,complement(join(A,complement(B))))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_16,c_1808]) ).
cnf(c_1810,plain,
join(A,complement(join(B,join(B,A)))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_243,c_1809]) ).
cnf(c_1811,plain,
join(A,complement(join(B,A))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_122,c_1810]) ).
cnf(c_245,plain,
join(A,complement(join(B,A))) = join(A,complement(B)),
inference(paramod,[status(thm)],[c_78,c_1811]) ).
cnf(c_258,plain,
join(A,composition(top,complement(A))) = top,
inference(paramod,[status(thm)],[c_212,c_121]) ).
cnf(c_265,plain,
join(complement(A),composition(top,A)) = top,
inference(paramod,[status(thm)],[c_78,c_258]) ).
cnf(c_1812,plain,
converse(top) = join(converse(complement(A)),converse(composition(top,A))),
inference(paramod,[status(thm)],[c_265,c_24]) ).
cnf(c_1813,plain,
top = join(converse(complement(A)),converse(composition(top,A))),
inference(paramod,[status(thm)],[c_147,c_1812]) ).
cnf(c_1814,plain,
top = join(converse(complement(A)),composition(converse(A),converse(top))),
inference(paramod,[status(thm)],[c_25,c_1813]) ).
cnf(c_1815,plain,
top = join(converse(complement(A)),composition(converse(A),top)),
inference(paramod,[status(thm)],[c_147,c_1814]) ).
cnf(c_1816,plain,
top = join(composition(converse(A),top),converse(complement(A))),
inference(paramod,[status(thm)],[c_15,c_1815]) ).
cnf(c_268,plain,
join(composition(converse(A),top),converse(complement(A))) = top,
inference(copy,[status(thm)],[c_1816]) ).
cnf(c_332,plain,
join(composition(A,top),converse(complement(converse(A)))) = top,
inference(paramod,[status(thm)],[c_23,c_268]) ).
cnf(c_1817,plain,
join(converse(complement(A)),complement(top)) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_149,c_245]) ).
cnf(c_1818,plain,
join(converse(complement(A)),zero) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_30,c_1817]) ).
cnf(c_1819,plain,
join(zero,converse(complement(A))) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_15,c_1818]) ).
cnf(c_1820,plain,
converse(complement(A)) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_80,c_1819]) ).
cnf(c_1821,plain,
converse(complement(A)) = join(complement(converse(A)),converse(complement(A))),
inference(paramod,[status(thm)],[c_15,c_1820]) ).
cnf(c_374,plain,
join(complement(converse(A)),converse(complement(A))) = converse(complement(A)),
inference(copy,[status(thm)],[c_1821]) ).
cnf(c_1822,plain,
join(converse(complement(converse(A))),complement(top)) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_170,c_245]) ).
cnf(c_1823,plain,
join(converse(complement(converse(A))),zero) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_30,c_1822]) ).
cnf(c_1824,plain,
join(zero,converse(complement(converse(A)))) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_15,c_1823]) ).
cnf(c_1825,plain,
converse(complement(converse(A))) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_80,c_1824]) ).
cnf(c_1826,plain,
converse(complement(converse(A))) = join(complement(A),converse(complement(converse(A)))),
inference(paramod,[status(thm)],[c_15,c_1825]) ).
cnf(c_378,plain,
join(complement(A),converse(complement(converse(A)))) = converse(complement(converse(A))),
inference(copy,[status(thm)],[c_1826]) ).
cnf(c_1827,plain,
converse(converse(complement(A))) = join(converse(complement(converse(A))),converse(converse(complement(A)))),
inference(paramod,[status(thm)],[c_374,c_24]) ).
cnf(c_1828,plain,
complement(A) = join(converse(complement(converse(A))),converse(converse(complement(A)))),
inference(paramod,[status(thm)],[c_23,c_1827]) ).
cnf(c_1829,plain,
complement(A) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_23,c_1828]) ).
cnf(c_1830,plain,
complement(A) = join(complement(A),converse(complement(converse(A)))),
inference(paramod,[status(thm)],[c_15,c_1829]) ).
cnf(c_1831,plain,
complement(A) = converse(complement(converse(A))),
inference(paramod,[status(thm)],[c_378,c_1830]) ).
cnf(c_424,plain,
converse(complement(converse(A))) = complement(A),
inference(copy,[status(thm)],[c_1831]) ).
cnf(c_1832,plain,
join(composition(A,top),complement(A)) = top,
inference(paramod,[status(thm)],[c_424,c_332]) ).
cnf(c_429,plain,
join(complement(A),composition(A,top)) = top,
inference(paramod,[status(thm)],[c_15,c_1832]) ).
cnf(c_1833,plain,
join(composition(A,top),complement(top)) = join(composition(A,top),complement(complement(A))),
inference(paramod,[status(thm)],[c_429,c_245]) ).
cnf(c_1834,plain,
join(composition(A,top),zero) = join(composition(A,top),complement(complement(A))),
inference(paramod,[status(thm)],[c_30,c_1833]) ).
cnf(c_1835,plain,
join(zero,composition(A,top)) = join(composition(A,top),complement(complement(A))),
inference(paramod,[status(thm)],[c_15,c_1834]) ).
cnf(c_1836,plain,
composition(A,top) = join(composition(A,top),complement(complement(A))),
inference(paramod,[status(thm)],[c_80,c_1835]) ).
cnf(c_1837,plain,
composition(A,top) = join(composition(A,top),A),
inference(paramod,[status(thm)],[c_78,c_1836]) ).
cnf(c_1838,plain,
composition(A,top) = join(A,composition(A,top)),
inference(paramod,[status(thm)],[c_15,c_1837]) ).
cnf(c_439,plain,
join(A,composition(A,top)) = composition(A,top),
inference(copy,[status(thm)],[c_1838]) ).
cnf(c_1839,negated_conjecture,
( join(complement(composition(sK0,top)),composition(complement(composition(sK0,top)),top)) != complement(composition(sK0,top))
| composition(complement(composition(sK0,top)),top) != composition(complement(composition(sK0,top)),top) ),
inference(paramod,[status(thm)],[c_439,c_32]) ).
cnf(c_1840,negated_conjecture,
( composition(complement(composition(sK0,top)),top) != complement(composition(sK0,top))
| composition(complement(composition(sK0,top)),top) != composition(complement(composition(sK0,top)),top) ),
inference(paramod,[status(thm)],[c_439,c_1839]) ).
cnf(c_441,negated_conjecture,
composition(complement(composition(sK0,top)),top) != complement(composition(sK0,top)),
inference(copy,[status(thm)],[c_1840]) ).
cnf(c_445,plain,
converse(complement(A)) = complement(converse(A)),
inference(paramod,[status(thm)],[c_424,c_23]) ).
cnf(c_1841,plain,
composition(complement(converse(composition(top,A))),top) = converse(complement(composition(top,A))),
inference(paramod,[status(thm)],[c_445,c_231]) ).
cnf(c_1842,plain,
composition(complement(composition(converse(A),converse(top))),top) = converse(complement(composition(top,A))),
inference(paramod,[status(thm)],[c_25,c_1841]) ).
cnf(c_1843,plain,
composition(complement(composition(converse(A),top)),top) = converse(complement(composition(top,A))),
inference(paramod,[status(thm)],[c_147,c_1842]) ).
cnf(c_1844,plain,
composition(complement(composition(converse(A),top)),top) = complement(converse(composition(top,A))),
inference(paramod,[status(thm)],[c_445,c_1843]) ).
cnf(c_1845,plain,
composition(complement(composition(converse(A),top)),top) = complement(composition(converse(A),converse(top))),
inference(paramod,[status(thm)],[c_25,c_1844]) ).
cnf(c_473,plain,
composition(complement(composition(converse(A),top)),top) = complement(composition(converse(A),top)),
inference(paramod,[status(thm)],[c_147,c_1845]) ).
cnf(c_1846,plain,
composition(complement(composition(A,top)),top) = complement(composition(converse(converse(A)),top)),
inference(paramod,[status(thm)],[c_23,c_473]) ).
cnf(c_1752,plain,
composition(complement(composition(A,top)),top) = complement(composition(A,top)),
inference(paramod,[status(thm)],[c_23,c_1846]) ).
cnf(c_1753,plain,
$false,
inference(resolve,[status(thm)],[c_1752,c_441]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL050+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n002.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 05:44:50 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 955947 was started by sandbox2 on n002,
% 0.10/0.37 % Sat Sep 26 05:44:50 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 5.05/1.15
% 5.05/1.15 % SZS status Theorem for theBenchmark
% 5.05/1.15
% 5.05/1.15 % Proof 1 at 0.54 (+ 0.21) seconds.
% 5.05/1.15 % Length of proof is 91.
% 5.05/1.15 % Level of proof is 22.
% 5.05/1.15 % Maximum clause weight is 44.000.
% 5.05/1.15 % Given clauses 308.
% 5.05/1.15
% 5.05/1.15 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------