%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL025+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 : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:24:53 AM UTC 2026
% Result : Theorem 7.77s 1.71s
% Output : CNFRefutation 7.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 84
% Number of leaves : 14
% Syntax : Number of formulae : 303 ( 290 unt; 0 def)
% Number of atoms : 325 ( 324 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 46 ( 24 ~; 11 |; 7 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 285 ( 17 sgn 27 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(maddux1_join_commutativity,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('theBenchmark.p',maddux1_join_commutativity) ).
fof(maddux2_join_associativity,axiom,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('theBenchmark.p',maddux2_join_associativity) ).
fof(maddux3_a_kind_of_de_Morgan,axiom,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
file('theBenchmark.p',maddux3_a_kind_of_de_Morgan) ).
fof(maddux4_definiton_of_meet,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
file('theBenchmark.p',maddux4_definiton_of_meet) ).
fof(composition_associativity,axiom,
! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
file('theBenchmark.p',composition_associativity) ).
fof(composition_identity,axiom,
! [X0] : composition(X0,one) = X0,
file('theBenchmark.p',composition_identity) ).
fof(composition_distributivity,axiom,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('theBenchmark.p',composition_distributivity) ).
fof(converse_idempotence,axiom,
! [X0] : converse(converse(X0)) = X0,
file('theBenchmark.p',converse_idempotence) ).
fof(converse_additivity,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('theBenchmark.p',converse_additivity) ).
fof(converse_multiplicativity,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('theBenchmark.p',converse_multiplicativity) ).
fof(converse_cancellativity,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
file('theBenchmark.p',converse_cancellativity) ).
fof(def_top,axiom,
! [X0] : top = join(X0,complement(X0)),
file('theBenchmark.p',def_top) ).
fof(def_zero,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('theBenchmark.p',def_zero) ).
fof(goals,conjecture,
! [X0] :
( ( join(X0,one) = one
=> join(X0,converse(X0)) = converse(X0) )
& ( join(X0,one) = one
=> join(converse(X0),X0) = X0 ) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0] :
( ( join(X0,one) = one
=> join(X0,converse(X0)) = converse(X0) )
& ( join(X0,one) = one
=> join(converse(X0),X0) = X0 ) ),
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_1752,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_1752]) ).
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_1753,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_1753]) ).
fof(nnf_14,plain,
? [X0] :
( ( converse(X0) != join(X0,converse(X0))
& join(X0,one) = one )
| ( join(converse(X0),X0) != X0
& join(X0,one) = one ) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg_sk,plain,
( ( converse(sK0) != join(sK0,converse(sK0))
& join(sK0,one) = one )
| ( join(converse(sK0),sK0) != sK0
& join(sK0,one) = one ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[nnf_14]) ).
fof(sk_goals_neg,plain,
( ( converse(sK0) != join(sK0,converse(sK0))
| join(converse(sK0),sK0) != sK0 )
& join(sK0,one) = one ),
inference(cnf_transformation,[status(thm)],[sk_goals_neg_sk]) ).
cnf(c_31,negated_conjecture,
join(sK0,one) = one,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_32,negated_conjecture,
join(one,sK0) = one,
inference(paramod,[status(thm)],[c_15,c_31]) ).
cnf(c_33,negated_conjecture,
( converse(sK0) != join(sK0,converse(sK0))
| join(converse(sK0),sK0) != sK0 ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_1754,negated_conjecture,
( converse(sK0) != join(sK0,converse(sK0))
| join(sK0,converse(sK0)) != sK0 ),
inference(paramod,[status(thm)],[c_15,c_33]) ).
cnf(c_34,negated_conjecture,
( join(sK0,converse(sK0)) != converse(sK0)
| join(sK0,converse(sK0)) != sK0 ),
inference(copy,[status(thm)],[c_1754]) ).
cnf(c_1755,plain,
join(join(A,B),C) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_15,c_16]) ).
cnf(c_36,plain,
join(A,join(B,C)) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_16,c_1755]) ).
cnf(c_37,plain,
join(complement(join(A,complement(B))),complement(join(complement(B),complement(A)))) = B,
inference(paramod,[status(thm)],[c_15,c_18]) ).
cnf(c_38,plain,
join(complement(join(complement(A),B)),complement(join(complement(B),complement(A)))) = A,
inference(paramod,[status(thm)],[c_15,c_18]) ).
cnf(c_1756,plain,
converse(A) = join(converse(complement(join(complement(A),B))),converse(complement(join(complement(A),complement(B))))),
inference(paramod,[status(thm)],[c_18,c_24]) ).
cnf(c_40,plain,
join(converse(complement(join(complement(A),B))),converse(complement(join(complement(A),complement(B))))) = converse(A),
inference(copy,[status(thm)],[c_1756]) ).
cnf(c_1757,plain,
converse(A) = composition(converse(one),converse(A)),
inference(paramod,[status(thm)],[c_21,c_25]) ).
cnf(c_41,plain,
composition(converse(one),converse(A)) = converse(A),
inference(copy,[status(thm)],[c_1757]) ).
cnf(c_43,plain,
join(complement(one),composition(converse(A),complement(A))) = complement(one),
inference(paramod,[status(thm)],[c_21,c_27]) ).
cnf(c_1758,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_1759,plain,
converse(complement(A)) = join(converse(complement(A)),composition(converse(complement(composition(B,A))),converse(converse(B)))),
inference(paramod,[status(thm)],[c_25,c_1758]) ).
cnf(c_1760,plain,
converse(complement(A)) = join(converse(complement(A)),composition(converse(complement(composition(B,A))),B)),
inference(paramod,[status(thm)],[c_23,c_1759]) ).
cnf(c_45,plain,
join(converse(complement(A)),composition(converse(complement(composition(B,A))),B)) = converse(complement(A)),
inference(copy,[status(thm)],[c_1760]) ).
cnf(c_1761,plain,
join(top,A) = join(B,join(complement(B),A)),
inference(paramod,[status(thm)],[c_28,c_16]) ).
cnf(c_46,plain,
join(A,join(complement(A),B)) = join(top,B),
inference(copy,[status(thm)],[c_1761]) ).
cnf(c_1762,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_28,c_18]) ).
cnf(c_48,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_30,c_1762]) ).
cnf(c_1763,plain,
join(complement(join(complement(A),complement(A))),complement(top)) = A,
inference(paramod,[status(thm)],[c_28,c_18]) ).
cnf(c_1764,plain,
join(complement(join(complement(A),complement(A))),zero) = A,
inference(paramod,[status(thm)],[c_30,c_1763]) ).
cnf(c_49,plain,
join(zero,complement(join(complement(A),complement(A)))) = A,
inference(paramod,[status(thm)],[c_15,c_1764]) ).
cnf(c_1765,plain,
composition(top,A) = join(composition(B,A),composition(complement(B),A)),
inference(paramod,[status(thm)],[c_28,c_22]) ).
cnf(c_50,plain,
join(composition(A,B),composition(complement(A),B)) = composition(top,B),
inference(copy,[status(thm)],[c_1765]) ).
cnf(c_1766,plain,
converse(top) = join(converse(A),converse(complement(A))),
inference(paramod,[status(thm)],[c_28,c_24]) ).
cnf(c_51,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_54,plain,
join(zero,composition(converse(A),complement(composition(A,top)))) = zero,
inference(paramod,[status(thm)],[c_30,c_1767]) ).
cnf(c_1768,plain,
join(one,A) = join(one,join(sK0,A)),
inference(paramod,[status(thm)],[c_32,c_16]) ).
cnf(c_56,plain,
join(one,join(sK0,A)) = join(one,A),
inference(copy,[status(thm)],[c_1768]) ).
cnf(c_1769,plain,
composition(one,A) = join(composition(one,A),composition(sK0,A)),
inference(paramod,[status(thm)],[c_32,c_22]) ).
cnf(c_58,plain,
join(composition(one,A),composition(sK0,A)) = composition(one,A),
inference(copy,[status(thm)],[c_1769]) ).
cnf(c_1770,plain,
converse(one) = join(converse(one),converse(sK0)),
inference(paramod,[status(thm)],[c_32,c_24]) ).
cnf(c_59,plain,
join(converse(one),converse(sK0)) = converse(one),
inference(copy,[status(thm)],[c_1770]) ).
cnf(c_1771,plain,
A = join(complement(join(complement(A),complement(B))),complement(join(B,complement(A)))),
inference(paramod,[status(thm)],[c_37,c_15]) ).
cnf(c_62,plain,
join(complement(join(complement(A),complement(B))),complement(join(B,complement(A)))) = A,
inference(copy,[status(thm)],[c_1771]) ).
cnf(c_1772,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_23,c_41]) ).
cnf(c_72,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_23,c_1772]) ).
cnf(c_1773,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_72,c_21]) ).
cnf(c_74,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_1773]) ).
cnf(c_78,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_72,c_27]) ).
cnf(c_79,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_74,c_72]) ).
cnf(c_1774,plain,
join(one,converse(sK0)) = converse(one),
inference(paramod,[status(thm)],[c_74,c_59]) ).
cnf(c_80,plain,
join(one,converse(sK0)) = one,
inference(paramod,[status(thm)],[c_74,c_1774]) ).
cnf(c_1775,plain,
join(A,composition(sK0,A)) = composition(one,A),
inference(paramod,[status(thm)],[c_79,c_58]) ).
cnf(c_81,plain,
join(A,composition(sK0,A)) = A,
inference(paramod,[status(thm)],[c_79,c_1775]) ).
cnf(c_82,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_79,c_78]) ).
cnf(c_83,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_82,c_49]) ).
cnf(c_1776,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_28,c_38]) ).
cnf(c_1777,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_15,c_1776]) ).
cnf(c_1778,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_30,c_1777]) ).
cnf(c_86,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_15,c_1778]) ).
cnf(c_87,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_86,c_48]) ).
cnf(c_88,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_87,c_86]) ).
cnf(c_89,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_87,c_83]) ).
cnf(c_90,plain,
complement(join(A,A)) = complement(A),
inference(paramod,[status(thm)],[c_89,c_88]) ).
cnf(c_92,plain,
composition(converse(A),complement(composition(A,top))) = zero,
inference(paramod,[status(thm)],[c_89,c_54]) ).
cnf(c_1779,plain,
join(converse(complement(top)),converse(complement(join(complement(A),complement(complement(complement(A))))))) = converse(A),
inference(paramod,[status(thm)],[c_28,c_40]) ).
cnf(c_1780,plain,
join(converse(zero),converse(complement(join(complement(A),complement(complement(complement(A))))))) = converse(A),
inference(paramod,[status(thm)],[c_30,c_1779]) ).
cnf(c_1781,plain,
join(converse(zero),converse(complement(join(complement(A),complement(A))))) = converse(A),
inference(paramod,[status(thm)],[c_87,c_1780]) ).
cnf(c_1782,plain,
join(converse(zero),converse(complement(complement(A)))) = converse(A),
inference(paramod,[status(thm)],[c_82,c_1781]) ).
cnf(c_94,plain,
join(converse(zero),converse(A)) = converse(A),
inference(paramod,[status(thm)],[c_87,c_1782]) ).
cnf(c_1783,plain,
A = join(A,zero),
inference(paramod,[status(thm)],[c_89,c_15]) ).
cnf(c_97,plain,
join(A,zero) = A,
inference(copy,[status(thm)],[c_1783]) ).
cnf(c_1784,plain,
composition(one,A) = join(composition(one,A),composition(converse(sK0),A)),
inference(paramod,[status(thm)],[c_80,c_22]) ).
cnf(c_1785,plain,
A = join(composition(one,A),composition(converse(sK0),A)),
inference(paramod,[status(thm)],[c_79,c_1784]) ).
cnf(c_1786,plain,
A = join(A,composition(converse(sK0),A)),
inference(paramod,[status(thm)],[c_79,c_1785]) ).
cnf(c_106,plain,
join(A,composition(converse(sK0),A)) = A,
inference(copy,[status(thm)],[c_1786]) ).
cnf(c_1787,plain,
join(complement(join(A,B)),complement(join(complement(complement(A)),complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_87,c_18]) ).
cnf(c_128,plain,
join(complement(join(A,B)),complement(join(A,complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_87,c_1787]) ).
cnf(c_1788,plain,
join(complement(join(A,B)),complement(join(complement(complement(B)),complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_87,c_37]) ).
cnf(c_130,plain,
join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_87,c_1788]) ).
cnf(c_133,plain,
join(complement(one),composition(converse(complement(A)),A)) = complement(one),
inference(paramod,[status(thm)],[c_87,c_43]) ).
cnf(c_1789,plain,
join(join(A,A),complement(A)) = top,
inference(paramod,[status(thm)],[c_90,c_28]) ).
cnf(c_1790,plain,
join(A,join(A,complement(A))) = top,
inference(paramod,[status(thm)],[c_16,c_1789]) ).
cnf(c_136,plain,
join(A,top) = top,
inference(paramod,[status(thm)],[c_28,c_1790]) ).
cnf(c_1791,plain,
complement(complement(A)) = join(A,A),
inference(paramod,[status(thm)],[c_90,c_87]) ).
cnf(c_1792,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_87,c_1791]) ).
cnf(c_137,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_1792]) ).
cnf(c_1793,plain,
top = join(top,A),
inference(paramod,[status(thm)],[c_136,c_15]) ).
cnf(c_139,plain,
join(top,A) = top,
inference(copy,[status(thm)],[c_1793]) ).
cnf(c_1794,plain,
composition(top,A) = join(composition(B,A),composition(top,A)),
inference(paramod,[status(thm)],[c_136,c_22]) ).
cnf(c_140,plain,
join(composition(A,B),composition(top,B)) = composition(top,B),
inference(copy,[status(thm)],[c_1794]) ).
cnf(c_1795,plain,
converse(top) = join(converse(A),converse(top)),
inference(paramod,[status(thm)],[c_136,c_24]) ).
cnf(c_141,plain,
join(converse(A),converse(top)) = converse(top),
inference(copy,[status(thm)],[c_1795]) ).
cnf(c_142,plain,
join(A,join(complement(A),B)) = top,
inference(paramod,[status(thm)],[c_139,c_46]) ).
cnf(c_1796,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_137,c_16]) ).
cnf(c_143,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_1796]) ).
cnf(c_1797,plain,
join(converse(zero),composition(converse(complement(composition(A,top))),A)) = converse(complement(top)),
inference(paramod,[status(thm)],[c_30,c_45]) ).
cnf(c_148,plain,
join(converse(zero),composition(converse(complement(composition(A,top))),A)) = converse(zero),
inference(paramod,[status(thm)],[c_30,c_1797]) ).
cnf(c_1798,plain,
join(converse(zero),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_23,c_94]) ).
cnf(c_156,plain,
join(converse(zero),A) = A,
inference(paramod,[status(thm)],[c_23,c_1798]) ).
cnf(c_158,plain,
composition(converse(complement(composition(A,top))),A) = converse(zero),
inference(paramod,[status(thm)],[c_156,c_148]) ).
cnf(c_1799,plain,
zero = converse(zero),
inference(paramod,[status(thm)],[c_156,c_97]) ).
cnf(c_162,plain,
converse(zero) = zero,
inference(copy,[status(thm)],[c_1799]) ).
cnf(c_163,plain,
composition(converse(complement(composition(A,top))),A) = zero,
inference(paramod,[status(thm)],[c_162,c_158]) ).
cnf(c_1800,plain,
join(A,composition(top,B)) = join(composition(C,B),join(A,composition(complement(C),B))),
inference(paramod,[status(thm)],[c_50,c_36]) ).
cnf(c_177,plain,
join(composition(A,B),join(C,composition(complement(A),B))) = join(C,composition(top,B)),
inference(copy,[status(thm)],[c_1800]) ).
cnf(c_182,plain,
join(A,converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_23,c_141]) ).
cnf(c_185,plain,
converse(top) = top,
inference(paramod,[status(thm)],[c_182,c_139]) ).
cnf(c_190,plain,
join(converse(A),converse(complement(A))) = top,
inference(paramod,[status(thm)],[c_185,c_51]) ).
cnf(c_1801,plain,
join(one,top) = join(one,complement(sK0)),
inference(paramod,[status(thm)],[c_28,c_56]) ).
cnf(c_1802,plain,
top = join(one,complement(sK0)),
inference(paramod,[status(thm)],[c_136,c_1801]) ).
cnf(c_199,plain,
join(one,complement(sK0)) = top,
inference(copy,[status(thm)],[c_1802]) ).
cnf(c_1803,plain,
converse(A) = join(converse(A),converse(composition(converse(sK0),A))),
inference(paramod,[status(thm)],[c_106,c_24]) ).
cnf(c_1804,plain,
converse(A) = join(converse(A),composition(converse(A),converse(converse(sK0)))),
inference(paramod,[status(thm)],[c_25,c_1803]) ).
cnf(c_1805,plain,
converse(A) = join(converse(A),composition(converse(A),sK0)),
inference(paramod,[status(thm)],[c_23,c_1804]) ).
cnf(c_221,plain,
join(converse(A),composition(converse(A),sK0)) = converse(A),
inference(copy,[status(thm)],[c_1805]) ).
cnf(c_1806,plain,
join(complement(join(complement(sK0),complement(one))),complement(top)) = sK0,
inference(paramod,[status(thm)],[c_199,c_62]) ).
cnf(c_1807,plain,
join(complement(join(complement(one),complement(sK0))),complement(top)) = sK0,
inference(paramod,[status(thm)],[c_15,c_1806]) ).
cnf(c_1808,plain,
join(complement(join(complement(one),complement(sK0))),zero) = sK0,
inference(paramod,[status(thm)],[c_30,c_1807]) ).
cnf(c_1809,plain,
join(zero,complement(join(complement(one),complement(sK0)))) = sK0,
inference(paramod,[status(thm)],[c_15,c_1808]) ).
cnf(c_228,plain,
complement(join(complement(one),complement(sK0))) = sK0,
inference(paramod,[status(thm)],[c_89,c_1809]) ).
cnf(c_240,plain,
join(A,converse(complement(converse(A)))) = top,
inference(paramod,[status(thm)],[c_23,c_190]) ).
cnf(c_243,plain,
join(one,converse(complement(one))) = top,
inference(paramod,[status(thm)],[c_74,c_190]) ).
cnf(c_1810,plain,
complement(sK0) = join(complement(one),complement(sK0)),
inference(paramod,[status(thm)],[c_228,c_87]) ).
cnf(c_255,plain,
join(complement(one),complement(sK0)) = complement(sK0),
inference(copy,[status(thm)],[c_1810]) ).
cnf(c_264,plain,
composition(top,complement(composition(top,top))) = zero,
inference(paramod,[status(thm)],[c_185,c_92]) ).
cnf(c_1811,plain,
composition(join(top,A),complement(composition(top,top))) = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_264,c_22]) ).
cnf(c_1812,plain,
composition(top,complement(composition(top,top))) = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_139,c_1811]) ).
cnf(c_1813,plain,
zero = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_264,c_1812]) ).
cnf(c_1814,plain,
zero = composition(A,complement(composition(top,top))),
inference(paramod,[status(thm)],[c_89,c_1813]) ).
cnf(c_279,plain,
composition(A,complement(composition(top,top))) = zero,
inference(copy,[status(thm)],[c_1814]) ).
cnf(c_1815,plain,
zero = complement(composition(top,top)),
inference(paramod,[status(thm)],[c_279,c_79]) ).
cnf(c_283,plain,
complement(composition(top,top)) = zero,
inference(copy,[status(thm)],[c_1815]) ).
cnf(c_1816,plain,
join(composition(top,top),zero) = top,
inference(paramod,[status(thm)],[c_283,c_28]) ).
cnf(c_1817,plain,
join(zero,composition(top,top)) = top,
inference(paramod,[status(thm)],[c_15,c_1816]) ).
cnf(c_289,plain,
composition(top,top) = top,
inference(paramod,[status(thm)],[c_89,c_1817]) ).
cnf(c_1818,plain,
composition(top,A) = composition(top,composition(top,A)),
inference(paramod,[status(thm)],[c_289,c_20]) ).
cnf(c_298,plain,
composition(top,composition(top,A)) = composition(top,A),
inference(copy,[status(thm)],[c_1818]) ).
cnf(c_306,plain,
join(A,composition(top,A)) = composition(top,A),
inference(paramod,[status(thm)],[c_79,c_140]) ).
cnf(c_1819,plain,
join(complement(composition(top,A)),composition(converse(top),complement(composition(top,A)))) = complement(composition(top,A)),
inference(paramod,[status(thm)],[c_298,c_27]) ).
cnf(c_1820,plain,
join(complement(composition(top,A)),composition(top,complement(composition(top,A)))) = complement(composition(top,A)),
inference(paramod,[status(thm)],[c_185,c_1819]) ).
cnf(c_353,plain,
composition(top,complement(composition(top,A))) = complement(composition(top,A)),
inference(paramod,[status(thm)],[c_306,c_1820]) ).
cnf(c_390,plain,
join(A,composition(top,complement(A))) = top,
inference(paramod,[status(thm)],[c_306,c_142]) ).
cnf(c_396,plain,
join(complement(A),composition(top,A)) = top,
inference(paramod,[status(thm)],[c_87,c_390]) ).
cnf(c_1821,plain,
converse(top) = join(converse(complement(A)),converse(composition(top,A))),
inference(paramod,[status(thm)],[c_396,c_24]) ).
cnf(c_1822,plain,
top = join(converse(complement(A)),converse(composition(top,A))),
inference(paramod,[status(thm)],[c_185,c_1821]) ).
cnf(c_1823,plain,
top = join(converse(complement(A)),composition(converse(A),converse(top))),
inference(paramod,[status(thm)],[c_25,c_1822]) ).
cnf(c_1824,plain,
top = join(converse(complement(A)),composition(converse(A),top)),
inference(paramod,[status(thm)],[c_185,c_1823]) ).
cnf(c_1825,plain,
top = join(composition(converse(A),top),converse(complement(A))),
inference(paramod,[status(thm)],[c_15,c_1824]) ).
cnf(c_402,plain,
join(composition(converse(A),top),converse(complement(A))) = top,
inference(copy,[status(thm)],[c_1825]) ).
cnf(c_1826,plain,
join(A,composition(converse(converse(A)),sK0)) = converse(converse(A)),
inference(paramod,[status(thm)],[c_23,c_221]) ).
cnf(c_1827,plain,
join(A,composition(A,sK0)) = converse(converse(A)),
inference(paramod,[status(thm)],[c_23,c_1826]) ).
cnf(c_448,plain,
join(A,composition(A,sK0)) = A,
inference(paramod,[status(thm)],[c_23,c_1827]) ).
cnf(c_498,plain,
join(composition(A,top),converse(complement(converse(A)))) = top,
inference(paramod,[status(thm)],[c_23,c_402]) ).
cnf(c_1828,plain,
join(complement(join(A,B)),complement(A)) = join(complement(join(A,B)),complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_128,c_143]) ).
cnf(c_1829,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_1828]) ).
cnf(c_516,plain,
join(complement(A),complement(join(A,B))) = complement(A),
inference(paramod,[status(thm)],[c_128,c_1829]) ).
cnf(c_532,plain,
join(complement(A),complement(join(B,A))) = complement(A),
inference(paramod,[status(thm)],[c_15,c_516]) ).
cnf(c_1830,plain,
join(A,complement(join(B,complement(A)))) = complement(complement(A)),
inference(paramod,[status(thm)],[c_87,c_532]) ).
cnf(c_553,plain,
join(A,complement(join(B,complement(A)))) = A,
inference(paramod,[status(thm)],[c_87,c_1830]) ).
cnf(c_1831,plain,
join(complement(top),complement(join(converse(complement(one)),complement(one)))) = complement(converse(complement(one))),
inference(paramod,[status(thm)],[c_243,c_130]) ).
cnf(c_1832,plain,
join(zero,complement(join(converse(complement(one)),complement(one)))) = complement(converse(complement(one))),
inference(paramod,[status(thm)],[c_30,c_1831]) ).
cnf(c_1833,plain,
join(zero,complement(join(complement(one),converse(complement(one))))) = complement(converse(complement(one))),
inference(paramod,[status(thm)],[c_15,c_1832]) ).
cnf(c_600,plain,
complement(join(complement(one),converse(complement(one)))) = complement(converse(complement(one))),
inference(paramod,[status(thm)],[c_89,c_1833]) ).
cnf(c_1834,plain,
join(complement(complement(A)),complement(join(complement(join(A,complement(B))),complement(complement(join(A,B)))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_128,c_130]) ).
cnf(c_1835,plain,
join(A,complement(join(complement(join(A,complement(B))),complement(complement(join(A,B)))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_87,c_1834]) ).
cnf(c_1836,plain,
join(A,complement(join(complement(join(A,complement(B))),join(A,B)))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_87,c_1835]) ).
cnf(c_1837,plain,
join(A,complement(join(join(A,B),complement(join(A,complement(B)))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_15,c_1836]) ).
cnf(c_1838,plain,
join(A,complement(join(A,join(B,complement(join(A,complement(B))))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_16,c_1837]) ).
cnf(c_1839,plain,
join(A,complement(join(A,B))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_553,c_1838]) ).
cnf(c_611,plain,
join(A,complement(join(A,B))) = join(A,complement(B)),
inference(paramod,[status(thm)],[c_87,c_1839]) ).
cnf(c_1840,plain,
join(zero,composition(complement(converse(complement(composition(A,top)))),A)) = composition(top,A),
inference(paramod,[status(thm)],[c_163,c_50]) ).
cnf(c_623,plain,
composition(complement(converse(complement(composition(A,top)))),A) = composition(top,A),
inference(paramod,[status(thm)],[c_89,c_1840]) ).
cnf(c_689,plain,
join(complement(one),converse(complement(one))) = complement(one),
inference(paramod,[status(thm)],[c_21,c_133]) ).
cnf(c_1841,plain,
complement(complement(one)) = complement(converse(complement(one))),
inference(paramod,[status(thm)],[c_689,c_600]) ).
cnf(c_1842,plain,
one = complement(converse(complement(one))),
inference(paramod,[status(thm)],[c_87,c_1841]) ).
cnf(c_693,plain,
complement(converse(complement(one))) = one,
inference(copy,[status(thm)],[c_1842]) ).
cnf(c_1843,plain,
complement(one) = converse(complement(one)),
inference(paramod,[status(thm)],[c_693,c_87]) ).
cnf(c_701,plain,
converse(complement(one)) = complement(one),
inference(copy,[status(thm)],[c_1843]) ).
cnf(c_802,plain,
join(A,complement(join(B,A))) = join(A,complement(B)),
inference(paramod,[status(thm)],[c_15,c_611]) ).
cnf(c_1844,plain,
join(composition(A,sK0),complement(A)) = join(complement(A),composition(top,sK0)),
inference(paramod,[status(thm)],[c_448,c_177]) ).
cnf(c_1845,plain,
join(complement(A),composition(A,sK0)) = join(complement(A),composition(top,sK0)),
inference(paramod,[status(thm)],[c_15,c_1844]) ).
cnf(c_844,plain,
join(complement(A),composition(top,sK0)) = join(complement(A),composition(A,sK0)),
inference(copy,[status(thm)],[c_1845]) ).
cnf(c_1846,plain,
join(converse(complement(A)),complement(top)) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_190,c_802]) ).
cnf(c_1847,plain,
join(converse(complement(A)),zero) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_30,c_1846]) ).
cnf(c_1848,plain,
join(zero,converse(complement(A))) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_15,c_1847]) ).
cnf(c_1849,plain,
converse(complement(A)) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_89,c_1848]) ).
cnf(c_1850,plain,
converse(complement(A)) = join(complement(converse(A)),converse(complement(A))),
inference(paramod,[status(thm)],[c_15,c_1849]) ).
cnf(c_870,plain,
join(complement(converse(A)),converse(complement(A))) = converse(complement(A)),
inference(copy,[status(thm)],[c_1850]) ).
cnf(c_1851,plain,
join(converse(complement(converse(A))),complement(top)) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_240,c_802]) ).
cnf(c_1852,plain,
join(converse(complement(converse(A))),zero) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_30,c_1851]) ).
cnf(c_1853,plain,
join(zero,converse(complement(converse(A)))) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_15,c_1852]) ).
cnf(c_1854,plain,
converse(complement(converse(A))) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_89,c_1853]) ).
cnf(c_1855,plain,
converse(complement(converse(A))) = join(complement(A),converse(complement(converse(A)))),
inference(paramod,[status(thm)],[c_15,c_1854]) ).
cnf(c_873,plain,
join(complement(A),converse(complement(converse(A)))) = converse(complement(converse(A))),
inference(copy,[status(thm)],[c_1855]) ).
cnf(c_1856,plain,
join(complement(one),composition(top,sK0)) = join(complement(one),sK0),
inference(paramod,[status(thm)],[c_79,c_844]) ).
cnf(c_916,plain,
join(complement(one),composition(top,sK0)) = join(sK0,complement(one)),
inference(paramod,[status(thm)],[c_15,c_1856]) ).
cnf(c_1857,plain,
join(complement(one),complement(join(sK0,complement(one)))) = join(complement(one),complement(composition(top,sK0))),
inference(paramod,[status(thm)],[c_916,c_611]) ).
cnf(c_1858,plain,
join(complement(one),complement(sK0)) = join(complement(one),complement(composition(top,sK0))),
inference(paramod,[status(thm)],[c_802,c_1857]) ).
cnf(c_1859,plain,
complement(sK0) = join(complement(one),complement(composition(top,sK0))),
inference(paramod,[status(thm)],[c_255,c_1858]) ).
cnf(c_953,plain,
join(complement(one),complement(composition(top,sK0))) = complement(sK0),
inference(copy,[status(thm)],[c_1859]) ).
cnf(c_1860,plain,
join(complement(sK0),A) = join(complement(one),join(complement(composition(top,sK0)),A)),
inference(paramod,[status(thm)],[c_953,c_16]) ).
cnf(c_955,plain,
join(complement(one),join(complement(composition(top,sK0)),A)) = join(complement(sK0),A),
inference(copy,[status(thm)],[c_1860]) ).
cnf(c_1861,plain,
converse(complement(sK0)) = join(converse(complement(one)),converse(complement(composition(top,sK0)))),
inference(paramod,[status(thm)],[c_953,c_24]) ).
cnf(c_1862,plain,
converse(complement(sK0)) = join(complement(one),converse(complement(composition(top,sK0)))),
inference(paramod,[status(thm)],[c_701,c_1861]) ).
cnf(c_957,plain,
join(complement(one),converse(complement(composition(top,sK0)))) = converse(complement(sK0)),
inference(copy,[status(thm)],[c_1862]) ).
cnf(c_1863,plain,
converse(converse(complement(A))) = join(converse(complement(converse(A))),converse(converse(complement(A)))),
inference(paramod,[status(thm)],[c_870,c_24]) ).
cnf(c_1864,plain,
complement(A) = join(converse(complement(converse(A))),converse(converse(complement(A)))),
inference(paramod,[status(thm)],[c_23,c_1863]) ).
cnf(c_1865,plain,
complement(A) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_23,c_1864]) ).
cnf(c_1866,plain,
complement(A) = join(complement(A),converse(complement(converse(A)))),
inference(paramod,[status(thm)],[c_15,c_1865]) ).
cnf(c_1867,plain,
complement(A) = converse(complement(converse(A))),
inference(paramod,[status(thm)],[c_873,c_1866]) ).
cnf(c_963,plain,
converse(complement(converse(A))) = complement(A),
inference(copy,[status(thm)],[c_1867]) ).
cnf(c_1868,plain,
join(composition(A,top),complement(A)) = top,
inference(paramod,[status(thm)],[c_963,c_498]) ).
cnf(c_969,plain,
join(complement(A),composition(A,top)) = top,
inference(paramod,[status(thm)],[c_15,c_1868]) ).
cnf(c_1869,plain,
join(complement(A),complement(top)) = join(complement(A),complement(composition(A,top))),
inference(paramod,[status(thm)],[c_969,c_611]) ).
cnf(c_1870,plain,
join(complement(A),zero) = join(complement(A),complement(composition(A,top))),
inference(paramod,[status(thm)],[c_30,c_1869]) ).
cnf(c_1871,plain,
join(zero,complement(A)) = join(complement(A),complement(composition(A,top))),
inference(paramod,[status(thm)],[c_15,c_1870]) ).
cnf(c_1872,plain,
complement(A) = join(complement(A),complement(composition(A,top))),
inference(paramod,[status(thm)],[c_89,c_1871]) ).
cnf(c_991,plain,
join(complement(A),complement(composition(A,top))) = complement(A),
inference(copy,[status(thm)],[c_1872]) ).
cnf(c_993,plain,
converse(complement(A)) = complement(converse(A)),
inference(paramod,[status(thm)],[c_963,c_23]) ).
cnf(c_1873,plain,
join(complement(one),complement(converse(composition(top,sK0)))) = converse(complement(sK0)),
inference(paramod,[status(thm)],[c_993,c_957]) ).
cnf(c_1874,plain,
join(complement(one),complement(composition(converse(sK0),converse(top)))) = converse(complement(sK0)),
inference(paramod,[status(thm)],[c_25,c_1873]) ).
cnf(c_1875,plain,
join(complement(one),complement(composition(converse(sK0),top))) = converse(complement(sK0)),
inference(paramod,[status(thm)],[c_185,c_1874]) ).
cnf(c_1014,plain,
join(complement(one),complement(composition(converse(sK0),top))) = complement(converse(sK0)),
inference(paramod,[status(thm)],[c_993,c_1875]) ).
cnf(c_1876,plain,
composition(complement(complement(converse(composition(A,top)))),A) = composition(top,A),
inference(paramod,[status(thm)],[c_993,c_623]) ).
cnf(c_1877,plain,
composition(complement(complement(composition(converse(top),converse(A)))),A) = composition(top,A),
inference(paramod,[status(thm)],[c_25,c_1876]) ).
cnf(c_1878,plain,
composition(complement(complement(composition(top,converse(A)))),A) = composition(top,A),
inference(paramod,[status(thm)],[c_185,c_1877]) ).
cnf(c_1879,plain,
composition(composition(top,converse(A)),A) = composition(top,A),
inference(paramod,[status(thm)],[c_87,c_1878]) ).
cnf(c_1032,plain,
composition(top,composition(converse(A),A)) = composition(top,A),
inference(paramod,[status(thm)],[c_20,c_1879]) ).
cnf(c_1880,plain,
converse(composition(top,A)) = composition(converse(composition(converse(A),A)),converse(top)),
inference(paramod,[status(thm)],[c_1032,c_25]) ).
cnf(c_1881,plain,
composition(converse(A),converse(top)) = composition(converse(composition(converse(A),A)),converse(top)),
inference(paramod,[status(thm)],[c_25,c_1880]) ).
cnf(c_1882,plain,
composition(converse(A),top) = composition(converse(composition(converse(A),A)),converse(top)),
inference(paramod,[status(thm)],[c_185,c_1881]) ).
cnf(c_1883,plain,
composition(converse(A),top) = composition(composition(converse(A),converse(converse(A))),converse(top)),
inference(paramod,[status(thm)],[c_25,c_1882]) ).
cnf(c_1884,plain,
composition(converse(A),top) = composition(composition(converse(A),A),converse(top)),
inference(paramod,[status(thm)],[c_23,c_1883]) ).
cnf(c_1885,plain,
composition(converse(A),top) = composition(composition(converse(A),A),top),
inference(paramod,[status(thm)],[c_185,c_1884]) ).
cnf(c_1886,plain,
composition(converse(A),top) = composition(converse(A),composition(A,top)),
inference(paramod,[status(thm)],[c_20,c_1885]) ).
cnf(c_1356,plain,
composition(converse(A),composition(A,top)) = composition(converse(A),top),
inference(copy,[status(thm)],[c_1886]) ).
cnf(c_1887,plain,
composition(A,composition(converse(A),top)) = composition(converse(converse(A)),top),
inference(paramod,[status(thm)],[c_23,c_1356]) ).
cnf(c_1362,plain,
composition(A,composition(converse(A),top)) = composition(A,top),
inference(paramod,[status(thm)],[c_23,c_1887]) ).
cnf(c_1363,plain,
join(composition(sK0,top),composition(converse(sK0),top)) = composition(sK0,top),
inference(paramod,[status(thm)],[c_1356,c_106]) ).
cnf(c_1888,plain,
join(composition(converse(sK0),top),composition(sK0,top)) = composition(converse(sK0),top),
inference(paramod,[status(thm)],[c_1362,c_81]) ).
cnf(c_1889,plain,
join(composition(sK0,top),composition(converse(sK0),top)) = composition(converse(sK0),top),
inference(paramod,[status(thm)],[c_15,c_1888]) ).
cnf(c_1890,plain,
composition(sK0,top) = composition(converse(sK0),top),
inference(paramod,[status(thm)],[c_1363,c_1889]) ).
cnf(c_1684,plain,
composition(converse(sK0),top) = composition(sK0,top),
inference(copy,[status(thm)],[c_1890]) ).
cnf(c_1891,plain,
join(complement(one),complement(composition(sK0,top))) = complement(converse(sK0)),
inference(paramod,[status(thm)],[c_1684,c_1014]) ).
cnf(c_1697,plain,
complement(converse(sK0)) = join(complement(one),complement(composition(sK0,top))),
inference(copy,[status(thm)],[c_1891]) ).
cnf(c_1892,plain,
converse(composition(sK0,top)) = composition(converse(top),converse(converse(sK0))),
inference(paramod,[status(thm)],[c_1684,c_25]) ).
cnf(c_1893,plain,
composition(converse(top),converse(sK0)) = composition(converse(top),converse(converse(sK0))),
inference(paramod,[status(thm)],[c_25,c_1892]) ).
cnf(c_1894,plain,
composition(top,converse(sK0)) = composition(converse(top),converse(converse(sK0))),
inference(paramod,[status(thm)],[c_185,c_1893]) ).
cnf(c_1895,plain,
composition(top,converse(sK0)) = composition(top,converse(converse(sK0))),
inference(paramod,[status(thm)],[c_185,c_1894]) ).
cnf(c_1704,plain,
composition(top,converse(sK0)) = composition(top,sK0),
inference(paramod,[status(thm)],[c_23,c_1895]) ).
cnf(c_1896,plain,
join(complement(converse(sK0)),composition(converse(top),complement(composition(top,sK0)))) = complement(converse(sK0)),
inference(paramod,[status(thm)],[c_1704,c_27]) ).
cnf(c_1897,plain,
join(join(complement(one),complement(composition(sK0,top))),composition(converse(top),complement(composition(top,sK0)))) = complement(converse(sK0)),
inference(paramod,[status(thm)],[c_1697,c_1896]) ).
cnf(c_1898,plain,
join(join(complement(one),complement(composition(sK0,top))),composition(top,complement(composition(top,sK0)))) = complement(converse(sK0)),
inference(paramod,[status(thm)],[c_185,c_1897]) ).
cnf(c_1899,plain,
join(join(complement(one),complement(composition(sK0,top))),complement(composition(top,sK0))) = complement(converse(sK0)),
inference(paramod,[status(thm)],[c_353,c_1898]) ).
cnf(c_1900,plain,
join(complement(composition(top,sK0)),join(complement(one),complement(composition(sK0,top)))) = complement(converse(sK0)),
inference(paramod,[status(thm)],[c_15,c_1899]) ).
cnf(c_1901,plain,
join(complement(one),join(complement(composition(top,sK0)),complement(composition(sK0,top)))) = complement(converse(sK0)),
inference(paramod,[status(thm)],[c_36,c_1900]) ).
cnf(c_1902,plain,
join(complement(sK0),complement(composition(sK0,top))) = complement(converse(sK0)),
inference(paramod,[status(thm)],[c_955,c_1901]) ).
cnf(c_1903,plain,
complement(sK0) = complement(converse(sK0)),
inference(paramod,[status(thm)],[c_991,c_1902]) ).
cnf(c_1904,plain,
complement(sK0) = join(complement(one),complement(composition(sK0,top))),
inference(paramod,[status(thm)],[c_1697,c_1903]) ).
cnf(c_1720,plain,
join(complement(one),complement(composition(sK0,top))) = complement(sK0),
inference(copy,[status(thm)],[c_1904]) ).
cnf(c_1731,plain,
complement(converse(sK0)) = complement(sK0),
inference(paramod,[status(thm)],[c_1720,c_1697]) ).
cnf(c_1905,plain,
complement(complement(sK0)) = converse(sK0),
inference(paramod,[status(thm)],[c_1731,c_87]) ).
cnf(c_1906,plain,
sK0 = converse(sK0),
inference(paramod,[status(thm)],[c_87,c_1905]) ).
cnf(c_1738,plain,
converse(sK0) = sK0,
inference(copy,[status(thm)],[c_1906]) ).
cnf(c_1907,negated_conjecture,
( join(sK0,converse(sK0)) != converse(sK0)
| join(sK0,sK0) != sK0 ),
inference(paramod,[status(thm)],[c_1738,c_34]) ).
cnf(c_1908,negated_conjecture,
( join(sK0,converse(sK0)) != converse(sK0)
| sK0 != sK0 ),
inference(paramod,[status(thm)],[c_137,c_1907]) ).
cnf(c_1909,negated_conjecture,
( join(sK0,sK0) != converse(sK0)
| sK0 != sK0 ),
inference(paramod,[status(thm)],[c_1738,c_1908]) ).
cnf(c_1910,negated_conjecture,
( sK0 != converse(sK0)
| sK0 != sK0 ),
inference(paramod,[status(thm)],[c_137,c_1909]) ).
cnf(c_1911,negated_conjecture,
( sK0 != sK0
| sK0 != sK0 ),
inference(paramod,[status(thm)],[c_1738,c_1910]) ).
cnf(c_1912,negated_conjecture,
sK0 != sK0,
inference(copy,[status(thm)],[c_1911]) ).
cnf(c_1751,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_1912]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL025+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n020.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 05:33:03 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 741051 was started by sandbox2 on n020,
% 0.11/0.37 % Sat Sep 26 05:33:03 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.37
% 0.11/0.37 % From the command line: assign(max_seconds, 300).
% 7.77/1.71
% 7.77/1.71 % SZS status Theorem for theBenchmark
% 7.77/1.71
% 7.77/1.71 % Proof 1 at 0.93 (+ 0.34) seconds.
% 7.77/1.71 % Length of proof is 138.
% 7.77/1.71 % Level of proof is 28.
% 7.77/1.71 % Maximum clause weight is 30.000.
% 7.77/1.71 % Given clauses 298.
% 7.77/1.71
% 7.77/1.71 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------