%------------------------------------------------------------------------------
% 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 : n015.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 08:24:54 AM UTC 2026
% Result : Unsatisfiable 6.86s 1.37s
% Output : CNFRefutation 6.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 84
% Number of leaves : 15
% Syntax : Number of formulae : 303 ( 295 unt; 0 def)
% Number of atoms : 311 ( 310 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 25 ( 17 ~; 8 |; 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 : 289 ( 17 sgn 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(maddux1_join_commutativity_1,axiom,
! [VAR_0,VAR_1] : join(VAR_0,VAR_1) = join(VAR_1,VAR_0),
file('theBenchmark.p',maddux1_join_commutativity_1) ).
cnf(c_1,plain,
join(A,B) = join(B,A),
inference(clausify,[status(thm)],[maddux1_join_commutativity_1]) ).
fof(maddux2_join_associativity_2,axiom,
! [VAR_0,VAR_1,VAR_2] : join(VAR_0,join(VAR_1,VAR_2)) = join(join(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',maddux2_join_associativity_2) ).
cnf(c_2,plain,
join(A,join(B,C)) = join(join(A,B),C),
inference(clausify,[status(thm)],[maddux2_join_associativity_2]) ).
cnf(c_3,plain,
join(join(A,B),C) = join(A,join(B,C)),
inference(copy,[status(thm)],[c_2]) ).
fof(maddux3_a_kind_of_de_Morgan_3,axiom,
! [VAR_0,VAR_1] : VAR_0 = join(complement(join(complement(VAR_0),complement(VAR_1))),complement(join(complement(VAR_0),VAR_1))),
file('theBenchmark.p',maddux3_a_kind_of_de_Morgan_3) ).
cnf(c_4,plain,
A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))),
inference(clausify,[status(thm)],[maddux3_a_kind_of_de_Morgan_3]) ).
cnf(c_1742,plain,
A = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),
inference(paramod,[status(thm)],[c_1,c_4]) ).
cnf(c_5,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = A,
inference(copy,[status(thm)],[c_1742]) ).
fof(maddux4_definiton_of_meet_4,axiom,
! [VAR_0,VAR_1] : meet(VAR_0,VAR_1) = complement(join(complement(VAR_0),complement(VAR_1))),
file('theBenchmark.p',maddux4_definiton_of_meet_4) ).
cnf(c_6,plain,
meet(A,B) = complement(join(complement(A),complement(B))),
inference(clausify,[status(thm)],[maddux4_definiton_of_meet_4]) ).
fof(composition_associativity_5,axiom,
! [VAR_0,VAR_1,VAR_2] : composition(VAR_0,composition(VAR_1,VAR_2)) = composition(composition(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',composition_associativity_5) ).
cnf(c_7,plain,
composition(A,composition(B,C)) = composition(composition(A,B),C),
inference(clausify,[status(thm)],[composition_associativity_5]) ).
cnf(c_8,plain,
composition(composition(A,B),C) = composition(A,composition(B,C)),
inference(copy,[status(thm)],[c_7]) ).
fof(composition_identity_6,axiom,
! [VAR_0] : composition(VAR_0,one) = VAR_0,
file('theBenchmark.p',composition_identity_6) ).
cnf(c_9,plain,
composition(A,one) = A,
inference(clausify,[status(thm)],[composition_identity_6]) ).
fof(composition_distributivity_7,axiom,
! [VAR_0,VAR_1,VAR_2] : composition(join(VAR_0,VAR_1),VAR_2) = join(composition(VAR_0,VAR_2),composition(VAR_1,VAR_2)),
file('theBenchmark.p',composition_distributivity_7) ).
cnf(c_10,plain,
composition(join(A,B),C) = join(composition(A,C),composition(B,C)),
inference(clausify,[status(thm)],[composition_distributivity_7]) ).
fof(converse_idempotence_8,axiom,
! [VAR_0] : converse(converse(VAR_0)) = VAR_0,
file('theBenchmark.p',converse_idempotence_8) ).
cnf(c_11,plain,
converse(converse(A)) = A,
inference(clausify,[status(thm)],[converse_idempotence_8]) ).
fof(converse_additivity_9,axiom,
! [VAR_0,VAR_1] : converse(join(VAR_0,VAR_1)) = join(converse(VAR_0),converse(VAR_1)),
file('theBenchmark.p',converse_additivity_9) ).
cnf(c_12,plain,
converse(join(A,B)) = join(converse(A),converse(B)),
inference(clausify,[status(thm)],[converse_additivity_9]) ).
fof(converse_multiplicativity_10,axiom,
! [VAR_0,VAR_1] : converse(composition(VAR_0,VAR_1)) = composition(converse(VAR_1),converse(VAR_0)),
file('theBenchmark.p',converse_multiplicativity_10) ).
cnf(c_13,plain,
converse(composition(A,B)) = composition(converse(B),converse(A)),
inference(clausify,[status(thm)],[converse_multiplicativity_10]) ).
fof(converse_cancellativity_11,axiom,
! [VAR_0,VAR_1] : join(composition(converse(VAR_0),complement(composition(VAR_0,VAR_1))),complement(VAR_1)) = complement(VAR_1),
file('theBenchmark.p',converse_cancellativity_11) ).
cnf(c_14,plain,
join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B),
inference(clausify,[status(thm)],[converse_cancellativity_11]) ).
cnf(c_15,plain,
join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A),
inference(paramod,[status(thm)],[c_1,c_14]) ).
fof(def_top_12,axiom,
! [VAR_0] : top = join(VAR_0,complement(VAR_0)),
file('theBenchmark.p',def_top_12) ).
cnf(c_16,plain,
top = join(A,complement(A)),
inference(clausify,[status(thm)],[def_top_12]) ).
cnf(c_17,plain,
join(A,complement(A)) = top,
inference(copy,[status(thm)],[c_16]) ).
fof(def_zero_13,axiom,
! [VAR_0] : zero = meet(VAR_0,complement(VAR_0)),
file('theBenchmark.p',def_zero_13) ).
cnf(c_18,plain,
zero = meet(A,complement(A)),
inference(clausify,[status(thm)],[def_zero_13]) ).
cnf(c_1743,plain,
zero = complement(join(complement(A),complement(complement(A)))),
inference(paramod,[status(thm)],[c_6,c_18]) ).
cnf(c_1744,plain,
zero = complement(top),
inference(paramod,[status(thm)],[c_17,c_1743]) ).
cnf(c_19,plain,
complement(top) = zero,
inference(copy,[status(thm)],[c_1744]) ).
fof(goals_14,axiom,
join(sk1,one) = one,
file('theBenchmark.p',goals_14) ).
cnf(c_20,plain,
join(sk1,one) = one,
inference(clausify,[status(thm)],[goals_14]) ).
cnf(c_21,plain,
join(one,sk1) = one,
inference(paramod,[status(thm)],[c_1,c_20]) ).
fof(goals_17,axiom,
( join(converse(sk1),sk1) != sk1
| join(sk1,converse(sk1)) != converse(sk1) ),
file('theBenchmark.p',goals_17) ).
cnf(c_22,plain,
( join(converse(sk1),sk1) != sk1
| join(sk1,converse(sk1)) != converse(sk1) ),
inference(clausify,[status(thm)],[goals_17]) ).
cnf(c_23,plain,
( join(sk1,converse(sk1)) != sk1
| join(sk1,converse(sk1)) != converse(sk1) ),
inference(paramod,[status(thm)],[c_1,c_22]) ).
cnf(c_1745,plain,
join(join(A,B),C) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_25,plain,
join(A,join(B,C)) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_3,c_1745]) ).
cnf(c_26,plain,
join(complement(join(A,complement(B))),complement(join(complement(B),complement(A)))) = B,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_27,plain,
join(complement(join(complement(A),B)),complement(join(complement(B),complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_1746,plain,
converse(A) = join(converse(complement(join(complement(A),B))),converse(complement(join(complement(A),complement(B))))),
inference(paramod,[status(thm)],[c_5,c_12]) ).
cnf(c_29,plain,
join(converse(complement(join(complement(A),B))),converse(complement(join(complement(A),complement(B))))) = converse(A),
inference(copy,[status(thm)],[c_1746]) ).
cnf(c_1747,plain,
converse(A) = composition(converse(one),converse(A)),
inference(paramod,[status(thm)],[c_9,c_13]) ).
cnf(c_30,plain,
composition(converse(one),converse(A)) = converse(A),
inference(copy,[status(thm)],[c_1747]) ).
cnf(c_32,plain,
join(complement(one),composition(converse(A),complement(A))) = complement(one),
inference(paramod,[status(thm)],[c_9,c_15]) ).
cnf(c_1748,plain,
converse(complement(A)) = join(converse(complement(A)),converse(composition(converse(B),complement(composition(B,A))))),
inference(paramod,[status(thm)],[c_15,c_12]) ).
cnf(c_1749,plain,
converse(complement(A)) = join(converse(complement(A)),composition(converse(complement(composition(B,A))),converse(converse(B)))),
inference(paramod,[status(thm)],[c_13,c_1748]) ).
cnf(c_1750,plain,
converse(complement(A)) = join(converse(complement(A)),composition(converse(complement(composition(B,A))),B)),
inference(paramod,[status(thm)],[c_11,c_1749]) ).
cnf(c_34,plain,
join(converse(complement(A)),composition(converse(complement(composition(B,A))),B)) = converse(complement(A)),
inference(copy,[status(thm)],[c_1750]) ).
cnf(c_1751,plain,
join(top,A) = join(B,join(complement(B),A)),
inference(paramod,[status(thm)],[c_17,c_3]) ).
cnf(c_35,plain,
join(A,join(complement(A),B)) = join(top,B),
inference(copy,[status(thm)],[c_1751]) ).
cnf(c_1752,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_17,c_5]) ).
cnf(c_37,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_19,c_1752]) ).
cnf(c_1753,plain,
join(complement(join(complement(A),complement(A))),complement(top)) = A,
inference(paramod,[status(thm)],[c_17,c_5]) ).
cnf(c_1754,plain,
join(complement(join(complement(A),complement(A))),zero) = A,
inference(paramod,[status(thm)],[c_19,c_1753]) ).
cnf(c_38,plain,
join(zero,complement(join(complement(A),complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_1754]) ).
cnf(c_1755,plain,
composition(top,A) = join(composition(B,A),composition(complement(B),A)),
inference(paramod,[status(thm)],[c_17,c_10]) ).
cnf(c_39,plain,
join(composition(A,B),composition(complement(A),B)) = composition(top,B),
inference(copy,[status(thm)],[c_1755]) ).
cnf(c_1756,plain,
converse(top) = join(converse(A),converse(complement(A))),
inference(paramod,[status(thm)],[c_17,c_12]) ).
cnf(c_40,plain,
join(converse(A),converse(complement(A))) = converse(top),
inference(copy,[status(thm)],[c_1756]) ).
cnf(c_1757,plain,
join(zero,composition(converse(A),complement(composition(A,top)))) = complement(top),
inference(paramod,[status(thm)],[c_19,c_15]) ).
cnf(c_43,plain,
join(zero,composition(converse(A),complement(composition(A,top)))) = zero,
inference(paramod,[status(thm)],[c_19,c_1757]) ).
cnf(c_1758,plain,
join(one,A) = join(one,join(sk1,A)),
inference(paramod,[status(thm)],[c_21,c_3]) ).
cnf(c_45,plain,
join(one,join(sk1,A)) = join(one,A),
inference(copy,[status(thm)],[c_1758]) ).
cnf(c_1759,plain,
composition(one,A) = join(composition(one,A),composition(sk1,A)),
inference(paramod,[status(thm)],[c_21,c_10]) ).
cnf(c_47,plain,
join(composition(one,A),composition(sk1,A)) = composition(one,A),
inference(copy,[status(thm)],[c_1759]) ).
cnf(c_1760,plain,
converse(one) = join(converse(one),converse(sk1)),
inference(paramod,[status(thm)],[c_21,c_12]) ).
cnf(c_48,plain,
join(converse(one),converse(sk1)) = converse(one),
inference(copy,[status(thm)],[c_1760]) ).
cnf(c_1761,plain,
A = join(complement(join(complement(A),complement(B))),complement(join(B,complement(A)))),
inference(paramod,[status(thm)],[c_26,c_1]) ).
cnf(c_51,plain,
join(complement(join(complement(A),complement(B))),complement(join(B,complement(A)))) = A,
inference(copy,[status(thm)],[c_1761]) ).
cnf(c_1762,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_30]) ).
cnf(c_61,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_11,c_1762]) ).
cnf(c_1763,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_61,c_9]) ).
cnf(c_63,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_1763]) ).
cnf(c_67,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_61,c_15]) ).
cnf(c_68,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_63,c_61]) ).
cnf(c_1764,plain,
join(one,converse(sk1)) = converse(one),
inference(paramod,[status(thm)],[c_63,c_48]) ).
cnf(c_69,plain,
join(one,converse(sk1)) = one,
inference(paramod,[status(thm)],[c_63,c_1764]) ).
cnf(c_1765,plain,
join(A,composition(sk1,A)) = composition(one,A),
inference(paramod,[status(thm)],[c_68,c_47]) ).
cnf(c_70,plain,
join(A,composition(sk1,A)) = A,
inference(paramod,[status(thm)],[c_68,c_1765]) ).
cnf(c_71,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_68,c_67]) ).
cnf(c_72,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_71,c_38]) ).
cnf(c_1766,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_17,c_27]) ).
cnf(c_1767,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_1,c_1766]) ).
cnf(c_1768,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_19,c_1767]) ).
cnf(c_75,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_1,c_1768]) ).
cnf(c_76,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_75,c_37]) ).
cnf(c_77,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_76,c_75]) ).
cnf(c_78,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_76,c_72]) ).
cnf(c_79,plain,
complement(join(A,A)) = complement(A),
inference(paramod,[status(thm)],[c_78,c_77]) ).
cnf(c_81,plain,
composition(converse(A),complement(composition(A,top))) = zero,
inference(paramod,[status(thm)],[c_78,c_43]) ).
cnf(c_1769,plain,
join(converse(complement(top)),converse(complement(join(complement(A),complement(complement(complement(A))))))) = converse(A),
inference(paramod,[status(thm)],[c_17,c_29]) ).
cnf(c_1770,plain,
join(converse(zero),converse(complement(join(complement(A),complement(complement(complement(A))))))) = converse(A),
inference(paramod,[status(thm)],[c_19,c_1769]) ).
cnf(c_1771,plain,
join(converse(zero),converse(complement(join(complement(A),complement(A))))) = converse(A),
inference(paramod,[status(thm)],[c_76,c_1770]) ).
cnf(c_1772,plain,
join(converse(zero),converse(complement(complement(A)))) = converse(A),
inference(paramod,[status(thm)],[c_71,c_1771]) ).
cnf(c_83,plain,
join(converse(zero),converse(A)) = converse(A),
inference(paramod,[status(thm)],[c_76,c_1772]) ).
cnf(c_1773,plain,
A = join(A,zero),
inference(paramod,[status(thm)],[c_78,c_1]) ).
cnf(c_86,plain,
join(A,zero) = A,
inference(copy,[status(thm)],[c_1773]) ).
cnf(c_1774,plain,
composition(one,A) = join(composition(one,A),composition(converse(sk1),A)),
inference(paramod,[status(thm)],[c_69,c_10]) ).
cnf(c_1775,plain,
A = join(composition(one,A),composition(converse(sk1),A)),
inference(paramod,[status(thm)],[c_68,c_1774]) ).
cnf(c_1776,plain,
A = join(A,composition(converse(sk1),A)),
inference(paramod,[status(thm)],[c_68,c_1775]) ).
cnf(c_95,plain,
join(A,composition(converse(sk1),A)) = A,
inference(copy,[status(thm)],[c_1776]) ).
cnf(c_1777,plain,
join(complement(join(A,B)),complement(join(complement(complement(A)),complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_76,c_5]) ).
cnf(c_117,plain,
join(complement(join(A,B)),complement(join(A,complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_76,c_1777]) ).
cnf(c_1778,plain,
join(complement(join(A,B)),complement(join(complement(complement(B)),complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_76,c_26]) ).
cnf(c_119,plain,
join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_76,c_1778]) ).
cnf(c_122,plain,
join(complement(one),composition(converse(complement(A)),A)) = complement(one),
inference(paramod,[status(thm)],[c_76,c_32]) ).
cnf(c_1779,plain,
join(join(A,A),complement(A)) = top,
inference(paramod,[status(thm)],[c_79,c_17]) ).
cnf(c_1780,plain,
join(A,join(A,complement(A))) = top,
inference(paramod,[status(thm)],[c_3,c_1779]) ).
cnf(c_125,plain,
join(A,top) = top,
inference(paramod,[status(thm)],[c_17,c_1780]) ).
cnf(c_1781,plain,
complement(complement(A)) = join(A,A),
inference(paramod,[status(thm)],[c_79,c_76]) ).
cnf(c_1782,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_76,c_1781]) ).
cnf(c_126,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_1782]) ).
cnf(c_1783,plain,
top = join(top,A),
inference(paramod,[status(thm)],[c_125,c_1]) ).
cnf(c_128,plain,
join(top,A) = top,
inference(copy,[status(thm)],[c_1783]) ).
cnf(c_1784,plain,
composition(top,A) = join(composition(B,A),composition(top,A)),
inference(paramod,[status(thm)],[c_125,c_10]) ).
cnf(c_129,plain,
join(composition(A,B),composition(top,B)) = composition(top,B),
inference(copy,[status(thm)],[c_1784]) ).
cnf(c_1785,plain,
converse(top) = join(converse(A),converse(top)),
inference(paramod,[status(thm)],[c_125,c_12]) ).
cnf(c_130,plain,
join(converse(A),converse(top)) = converse(top),
inference(copy,[status(thm)],[c_1785]) ).
cnf(c_131,plain,
join(A,join(complement(A),B)) = top,
inference(paramod,[status(thm)],[c_128,c_35]) ).
cnf(c_1786,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_126,c_3]) ).
cnf(c_132,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_1786]) ).
cnf(c_1787,plain,
join(converse(zero),composition(converse(complement(composition(A,top))),A)) = converse(complement(top)),
inference(paramod,[status(thm)],[c_19,c_34]) ).
cnf(c_137,plain,
join(converse(zero),composition(converse(complement(composition(A,top))),A)) = converse(zero),
inference(paramod,[status(thm)],[c_19,c_1787]) ).
cnf(c_1788,plain,
join(converse(zero),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_83]) ).
cnf(c_145,plain,
join(converse(zero),A) = A,
inference(paramod,[status(thm)],[c_11,c_1788]) ).
cnf(c_147,plain,
composition(converse(complement(composition(A,top))),A) = converse(zero),
inference(paramod,[status(thm)],[c_145,c_137]) ).
cnf(c_1789,plain,
zero = converse(zero),
inference(paramod,[status(thm)],[c_145,c_86]) ).
cnf(c_151,plain,
converse(zero) = zero,
inference(copy,[status(thm)],[c_1789]) ).
cnf(c_152,plain,
composition(converse(complement(composition(A,top))),A) = zero,
inference(paramod,[status(thm)],[c_151,c_147]) ).
cnf(c_1790,plain,
join(A,composition(top,B)) = join(composition(C,B),join(A,composition(complement(C),B))),
inference(paramod,[status(thm)],[c_39,c_25]) ).
cnf(c_166,plain,
join(composition(A,B),join(C,composition(complement(A),B))) = join(C,composition(top,B)),
inference(copy,[status(thm)],[c_1790]) ).
cnf(c_171,plain,
join(A,converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_11,c_130]) ).
cnf(c_174,plain,
converse(top) = top,
inference(paramod,[status(thm)],[c_171,c_128]) ).
cnf(c_179,plain,
join(converse(A),converse(complement(A))) = top,
inference(paramod,[status(thm)],[c_174,c_40]) ).
cnf(c_1791,plain,
join(one,top) = join(one,complement(sk1)),
inference(paramod,[status(thm)],[c_17,c_45]) ).
cnf(c_1792,plain,
top = join(one,complement(sk1)),
inference(paramod,[status(thm)],[c_125,c_1791]) ).
cnf(c_188,plain,
join(one,complement(sk1)) = top,
inference(copy,[status(thm)],[c_1792]) ).
cnf(c_1793,plain,
converse(A) = join(converse(A),converse(composition(converse(sk1),A))),
inference(paramod,[status(thm)],[c_95,c_12]) ).
cnf(c_1794,plain,
converse(A) = join(converse(A),composition(converse(A),converse(converse(sk1)))),
inference(paramod,[status(thm)],[c_13,c_1793]) ).
cnf(c_1795,plain,
converse(A) = join(converse(A),composition(converse(A),sk1)),
inference(paramod,[status(thm)],[c_11,c_1794]) ).
cnf(c_210,plain,
join(converse(A),composition(converse(A),sk1)) = converse(A),
inference(copy,[status(thm)],[c_1795]) ).
cnf(c_1796,plain,
join(complement(join(complement(sk1),complement(one))),complement(top)) = sk1,
inference(paramod,[status(thm)],[c_188,c_51]) ).
cnf(c_1797,plain,
join(complement(join(complement(one),complement(sk1))),complement(top)) = sk1,
inference(paramod,[status(thm)],[c_1,c_1796]) ).
cnf(c_1798,plain,
join(complement(join(complement(one),complement(sk1))),zero) = sk1,
inference(paramod,[status(thm)],[c_19,c_1797]) ).
cnf(c_1799,plain,
join(zero,complement(join(complement(one),complement(sk1)))) = sk1,
inference(paramod,[status(thm)],[c_1,c_1798]) ).
cnf(c_217,plain,
complement(join(complement(one),complement(sk1))) = sk1,
inference(paramod,[status(thm)],[c_78,c_1799]) ).
cnf(c_229,plain,
join(A,converse(complement(converse(A)))) = top,
inference(paramod,[status(thm)],[c_11,c_179]) ).
cnf(c_232,plain,
join(one,converse(complement(one))) = top,
inference(paramod,[status(thm)],[c_63,c_179]) ).
cnf(c_1800,plain,
complement(sk1) = join(complement(one),complement(sk1)),
inference(paramod,[status(thm)],[c_217,c_76]) ).
cnf(c_244,plain,
join(complement(one),complement(sk1)) = complement(sk1),
inference(copy,[status(thm)],[c_1800]) ).
cnf(c_253,plain,
composition(top,complement(composition(top,top))) = zero,
inference(paramod,[status(thm)],[c_174,c_81]) ).
cnf(c_1801,plain,
composition(join(top,A),complement(composition(top,top))) = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_253,c_10]) ).
cnf(c_1802,plain,
composition(top,complement(composition(top,top))) = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_128,c_1801]) ).
cnf(c_1803,plain,
zero = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_253,c_1802]) ).
cnf(c_1804,plain,
zero = composition(A,complement(composition(top,top))),
inference(paramod,[status(thm)],[c_78,c_1803]) ).
cnf(c_268,plain,
composition(A,complement(composition(top,top))) = zero,
inference(copy,[status(thm)],[c_1804]) ).
cnf(c_1805,plain,
zero = complement(composition(top,top)),
inference(paramod,[status(thm)],[c_268,c_68]) ).
cnf(c_272,plain,
complement(composition(top,top)) = zero,
inference(copy,[status(thm)],[c_1805]) ).
cnf(c_1806,plain,
join(composition(top,top),zero) = top,
inference(paramod,[status(thm)],[c_272,c_17]) ).
cnf(c_1807,plain,
join(zero,composition(top,top)) = top,
inference(paramod,[status(thm)],[c_1,c_1806]) ).
cnf(c_278,plain,
composition(top,top) = top,
inference(paramod,[status(thm)],[c_78,c_1807]) ).
cnf(c_1808,plain,
composition(top,A) = composition(top,composition(top,A)),
inference(paramod,[status(thm)],[c_278,c_8]) ).
cnf(c_287,plain,
composition(top,composition(top,A)) = composition(top,A),
inference(copy,[status(thm)],[c_1808]) ).
cnf(c_295,plain,
join(A,composition(top,A)) = composition(top,A),
inference(paramod,[status(thm)],[c_68,c_129]) ).
cnf(c_1809,plain,
join(complement(composition(top,A)),composition(converse(top),complement(composition(top,A)))) = complement(composition(top,A)),
inference(paramod,[status(thm)],[c_287,c_15]) ).
cnf(c_1810,plain,
join(complement(composition(top,A)),composition(top,complement(composition(top,A)))) = complement(composition(top,A)),
inference(paramod,[status(thm)],[c_174,c_1809]) ).
cnf(c_342,plain,
composition(top,complement(composition(top,A))) = complement(composition(top,A)),
inference(paramod,[status(thm)],[c_295,c_1810]) ).
cnf(c_379,plain,
join(A,composition(top,complement(A))) = top,
inference(paramod,[status(thm)],[c_295,c_131]) ).
cnf(c_385,plain,
join(complement(A),composition(top,A)) = top,
inference(paramod,[status(thm)],[c_76,c_379]) ).
cnf(c_1811,plain,
converse(top) = join(converse(complement(A)),converse(composition(top,A))),
inference(paramod,[status(thm)],[c_385,c_12]) ).
cnf(c_1812,plain,
top = join(converse(complement(A)),converse(composition(top,A))),
inference(paramod,[status(thm)],[c_174,c_1811]) ).
cnf(c_1813,plain,
top = join(converse(complement(A)),composition(converse(A),converse(top))),
inference(paramod,[status(thm)],[c_13,c_1812]) ).
cnf(c_1814,plain,
top = join(converse(complement(A)),composition(converse(A),top)),
inference(paramod,[status(thm)],[c_174,c_1813]) ).
cnf(c_1815,plain,
top = join(composition(converse(A),top),converse(complement(A))),
inference(paramod,[status(thm)],[c_1,c_1814]) ).
cnf(c_391,plain,
join(composition(converse(A),top),converse(complement(A))) = top,
inference(copy,[status(thm)],[c_1815]) ).
cnf(c_1816,plain,
join(A,composition(converse(converse(A)),sk1)) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_210]) ).
cnf(c_1817,plain,
join(A,composition(A,sk1)) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_1816]) ).
cnf(c_437,plain,
join(A,composition(A,sk1)) = A,
inference(paramod,[status(thm)],[c_11,c_1817]) ).
cnf(c_487,plain,
join(composition(A,top),converse(complement(converse(A)))) = top,
inference(paramod,[status(thm)],[c_11,c_391]) ).
cnf(c_1818,plain,
join(complement(join(A,B)),complement(A)) = join(complement(join(A,B)),complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_117,c_132]) ).
cnf(c_1819,plain,
join(complement(A),complement(join(A,B))) = join(complement(join(A,B)),complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_1,c_1818]) ).
cnf(c_505,plain,
join(complement(A),complement(join(A,B))) = complement(A),
inference(paramod,[status(thm)],[c_117,c_1819]) ).
cnf(c_521,plain,
join(complement(A),complement(join(B,A))) = complement(A),
inference(paramod,[status(thm)],[c_1,c_505]) ).
cnf(c_1820,plain,
join(A,complement(join(B,complement(A)))) = complement(complement(A)),
inference(paramod,[status(thm)],[c_76,c_521]) ).
cnf(c_542,plain,
join(A,complement(join(B,complement(A)))) = A,
inference(paramod,[status(thm)],[c_76,c_1820]) ).
cnf(c_1821,plain,
join(complement(top),complement(join(converse(complement(one)),complement(one)))) = complement(converse(complement(one))),
inference(paramod,[status(thm)],[c_232,c_119]) ).
cnf(c_1822,plain,
join(zero,complement(join(converse(complement(one)),complement(one)))) = complement(converse(complement(one))),
inference(paramod,[status(thm)],[c_19,c_1821]) ).
cnf(c_1823,plain,
join(zero,complement(join(complement(one),converse(complement(one))))) = complement(converse(complement(one))),
inference(paramod,[status(thm)],[c_1,c_1822]) ).
cnf(c_589,plain,
complement(join(complement(one),converse(complement(one)))) = complement(converse(complement(one))),
inference(paramod,[status(thm)],[c_78,c_1823]) ).
cnf(c_1824,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_117,c_119]) ).
cnf(c_1825,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_76,c_1824]) ).
cnf(c_1826,plain,
join(A,complement(join(complement(join(A,complement(B))),join(A,B)))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_76,c_1825]) ).
cnf(c_1827,plain,
join(A,complement(join(join(A,B),complement(join(A,complement(B)))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_1,c_1826]) ).
cnf(c_1828,plain,
join(A,complement(join(A,join(B,complement(join(A,complement(B))))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_3,c_1827]) ).
cnf(c_1829,plain,
join(A,complement(join(A,B))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_542,c_1828]) ).
cnf(c_600,plain,
join(A,complement(join(A,B))) = join(A,complement(B)),
inference(paramod,[status(thm)],[c_76,c_1829]) ).
cnf(c_1830,plain,
join(zero,composition(complement(converse(complement(composition(A,top)))),A)) = composition(top,A),
inference(paramod,[status(thm)],[c_152,c_39]) ).
cnf(c_612,plain,
composition(complement(converse(complement(composition(A,top)))),A) = composition(top,A),
inference(paramod,[status(thm)],[c_78,c_1830]) ).
cnf(c_678,plain,
join(complement(one),converse(complement(one))) = complement(one),
inference(paramod,[status(thm)],[c_9,c_122]) ).
cnf(c_1831,plain,
complement(complement(one)) = complement(converse(complement(one))),
inference(paramod,[status(thm)],[c_678,c_589]) ).
cnf(c_1832,plain,
one = complement(converse(complement(one))),
inference(paramod,[status(thm)],[c_76,c_1831]) ).
cnf(c_682,plain,
complement(converse(complement(one))) = one,
inference(copy,[status(thm)],[c_1832]) ).
cnf(c_1833,plain,
complement(one) = converse(complement(one)),
inference(paramod,[status(thm)],[c_682,c_76]) ).
cnf(c_690,plain,
converse(complement(one)) = complement(one),
inference(copy,[status(thm)],[c_1833]) ).
cnf(c_791,plain,
join(A,complement(join(B,A))) = join(A,complement(B)),
inference(paramod,[status(thm)],[c_1,c_600]) ).
cnf(c_1834,plain,
join(composition(A,sk1),complement(A)) = join(complement(A),composition(top,sk1)),
inference(paramod,[status(thm)],[c_437,c_166]) ).
cnf(c_1835,plain,
join(complement(A),composition(A,sk1)) = join(complement(A),composition(top,sk1)),
inference(paramod,[status(thm)],[c_1,c_1834]) ).
cnf(c_833,plain,
join(complement(A),composition(top,sk1)) = join(complement(A),composition(A,sk1)),
inference(copy,[status(thm)],[c_1835]) ).
cnf(c_1836,plain,
join(converse(complement(A)),complement(top)) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_179,c_791]) ).
cnf(c_1837,plain,
join(converse(complement(A)),zero) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_19,c_1836]) ).
cnf(c_1838,plain,
join(zero,converse(complement(A))) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_1,c_1837]) ).
cnf(c_1839,plain,
converse(complement(A)) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_78,c_1838]) ).
cnf(c_1840,plain,
converse(complement(A)) = join(complement(converse(A)),converse(complement(A))),
inference(paramod,[status(thm)],[c_1,c_1839]) ).
cnf(c_859,plain,
join(complement(converse(A)),converse(complement(A))) = converse(complement(A)),
inference(copy,[status(thm)],[c_1840]) ).
cnf(c_1841,plain,
join(converse(complement(converse(A))),complement(top)) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_229,c_791]) ).
cnf(c_1842,plain,
join(converse(complement(converse(A))),zero) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_19,c_1841]) ).
cnf(c_1843,plain,
join(zero,converse(complement(converse(A)))) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_1,c_1842]) ).
cnf(c_1844,plain,
converse(complement(converse(A))) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_78,c_1843]) ).
cnf(c_1845,plain,
converse(complement(converse(A))) = join(complement(A),converse(complement(converse(A)))),
inference(paramod,[status(thm)],[c_1,c_1844]) ).
cnf(c_862,plain,
join(complement(A),converse(complement(converse(A)))) = converse(complement(converse(A))),
inference(copy,[status(thm)],[c_1845]) ).
cnf(c_1846,plain,
join(complement(one),composition(top,sk1)) = join(complement(one),sk1),
inference(paramod,[status(thm)],[c_68,c_833]) ).
cnf(c_905,plain,
join(complement(one),composition(top,sk1)) = join(sk1,complement(one)),
inference(paramod,[status(thm)],[c_1,c_1846]) ).
cnf(c_1847,plain,
join(complement(one),complement(join(sk1,complement(one)))) = join(complement(one),complement(composition(top,sk1))),
inference(paramod,[status(thm)],[c_905,c_600]) ).
cnf(c_1848,plain,
join(complement(one),complement(sk1)) = join(complement(one),complement(composition(top,sk1))),
inference(paramod,[status(thm)],[c_791,c_1847]) ).
cnf(c_1849,plain,
complement(sk1) = join(complement(one),complement(composition(top,sk1))),
inference(paramod,[status(thm)],[c_244,c_1848]) ).
cnf(c_942,plain,
join(complement(one),complement(composition(top,sk1))) = complement(sk1),
inference(copy,[status(thm)],[c_1849]) ).
cnf(c_1850,plain,
converse(complement(sk1)) = join(converse(complement(one)),converse(complement(composition(top,sk1)))),
inference(paramod,[status(thm)],[c_942,c_12]) ).
cnf(c_1851,plain,
converse(complement(sk1)) = join(complement(one),converse(complement(composition(top,sk1)))),
inference(paramod,[status(thm)],[c_690,c_1850]) ).
cnf(c_946,plain,
join(complement(one),converse(complement(composition(top,sk1)))) = converse(complement(sk1)),
inference(copy,[status(thm)],[c_1851]) ).
cnf(c_1852,plain,
join(A,complement(sk1)) = join(complement(one),join(A,complement(composition(top,sk1)))),
inference(paramod,[status(thm)],[c_942,c_25]) ).
cnf(c_947,plain,
join(complement(one),join(A,complement(composition(top,sk1)))) = join(A,complement(sk1)),
inference(copy,[status(thm)],[c_1852]) ).
cnf(c_1853,plain,
converse(converse(complement(A))) = join(converse(complement(converse(A))),converse(converse(complement(A)))),
inference(paramod,[status(thm)],[c_859,c_12]) ).
cnf(c_1854,plain,
complement(A) = join(converse(complement(converse(A))),converse(converse(complement(A)))),
inference(paramod,[status(thm)],[c_11,c_1853]) ).
cnf(c_1855,plain,
complement(A) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_11,c_1854]) ).
cnf(c_1856,plain,
complement(A) = join(complement(A),converse(complement(converse(A)))),
inference(paramod,[status(thm)],[c_1,c_1855]) ).
cnf(c_1857,plain,
complement(A) = converse(complement(converse(A))),
inference(paramod,[status(thm)],[c_862,c_1856]) ).
cnf(c_952,plain,
converse(complement(converse(A))) = complement(A),
inference(copy,[status(thm)],[c_1857]) ).
cnf(c_1858,plain,
join(composition(A,top),complement(A)) = top,
inference(paramod,[status(thm)],[c_952,c_487]) ).
cnf(c_958,plain,
join(complement(A),composition(A,top)) = top,
inference(paramod,[status(thm)],[c_1,c_1858]) ).
cnf(c_1859,plain,
join(complement(A),complement(top)) = join(complement(A),complement(composition(A,top))),
inference(paramod,[status(thm)],[c_958,c_600]) ).
cnf(c_1860,plain,
join(complement(A),zero) = join(complement(A),complement(composition(A,top))),
inference(paramod,[status(thm)],[c_19,c_1859]) ).
cnf(c_1861,plain,
join(zero,complement(A)) = join(complement(A),complement(composition(A,top))),
inference(paramod,[status(thm)],[c_1,c_1860]) ).
cnf(c_1862,plain,
complement(A) = join(complement(A),complement(composition(A,top))),
inference(paramod,[status(thm)],[c_78,c_1861]) ).
cnf(c_980,plain,
join(complement(A),complement(composition(A,top))) = complement(A),
inference(copy,[status(thm)],[c_1862]) ).
cnf(c_982,plain,
converse(complement(A)) = complement(converse(A)),
inference(paramod,[status(thm)],[c_952,c_11]) ).
cnf(c_1863,plain,
join(complement(one),complement(converse(composition(top,sk1)))) = converse(complement(sk1)),
inference(paramod,[status(thm)],[c_982,c_946]) ).
cnf(c_1864,plain,
join(complement(one),complement(composition(converse(sk1),converse(top)))) = converse(complement(sk1)),
inference(paramod,[status(thm)],[c_13,c_1863]) ).
cnf(c_1865,plain,
join(complement(one),complement(composition(converse(sk1),top))) = converse(complement(sk1)),
inference(paramod,[status(thm)],[c_174,c_1864]) ).
cnf(c_1003,plain,
join(complement(one),complement(composition(converse(sk1),top))) = complement(converse(sk1)),
inference(paramod,[status(thm)],[c_982,c_1865]) ).
cnf(c_1866,plain,
composition(complement(complement(converse(composition(A,top)))),A) = composition(top,A),
inference(paramod,[status(thm)],[c_982,c_612]) ).
cnf(c_1867,plain,
composition(complement(complement(composition(converse(top),converse(A)))),A) = composition(top,A),
inference(paramod,[status(thm)],[c_13,c_1866]) ).
cnf(c_1868,plain,
composition(complement(complement(composition(top,converse(A)))),A) = composition(top,A),
inference(paramod,[status(thm)],[c_174,c_1867]) ).
cnf(c_1869,plain,
composition(composition(top,converse(A)),A) = composition(top,A),
inference(paramod,[status(thm)],[c_76,c_1868]) ).
cnf(c_1021,plain,
composition(top,composition(converse(A),A)) = composition(top,A),
inference(paramod,[status(thm)],[c_8,c_1869]) ).
cnf(c_1870,plain,
converse(composition(top,A)) = composition(converse(composition(converse(A),A)),converse(top)),
inference(paramod,[status(thm)],[c_1021,c_13]) ).
cnf(c_1871,plain,
composition(converse(A),converse(top)) = composition(converse(composition(converse(A),A)),converse(top)),
inference(paramod,[status(thm)],[c_13,c_1870]) ).
cnf(c_1872,plain,
composition(converse(A),top) = composition(converse(composition(converse(A),A)),converse(top)),
inference(paramod,[status(thm)],[c_174,c_1871]) ).
cnf(c_1873,plain,
composition(converse(A),top) = composition(composition(converse(A),converse(converse(A))),converse(top)),
inference(paramod,[status(thm)],[c_13,c_1872]) ).
cnf(c_1874,plain,
composition(converse(A),top) = composition(composition(converse(A),A),converse(top)),
inference(paramod,[status(thm)],[c_11,c_1873]) ).
cnf(c_1875,plain,
composition(converse(A),top) = composition(composition(converse(A),A),top),
inference(paramod,[status(thm)],[c_174,c_1874]) ).
cnf(c_1876,plain,
composition(converse(A),top) = composition(converse(A),composition(A,top)),
inference(paramod,[status(thm)],[c_8,c_1875]) ).
cnf(c_1345,plain,
composition(converse(A),composition(A,top)) = composition(converse(A),top),
inference(copy,[status(thm)],[c_1876]) ).
cnf(c_1877,plain,
composition(A,composition(converse(A),top)) = composition(converse(converse(A)),top),
inference(paramod,[status(thm)],[c_11,c_1345]) ).
cnf(c_1351,plain,
composition(A,composition(converse(A),top)) = composition(A,top),
inference(paramod,[status(thm)],[c_11,c_1877]) ).
cnf(c_1352,plain,
join(composition(sk1,top),composition(converse(sk1),top)) = composition(sk1,top),
inference(paramod,[status(thm)],[c_1345,c_95]) ).
cnf(c_1878,plain,
join(composition(converse(sk1),top),composition(sk1,top)) = composition(converse(sk1),top),
inference(paramod,[status(thm)],[c_1351,c_70]) ).
cnf(c_1879,plain,
join(composition(sk1,top),composition(converse(sk1),top)) = composition(converse(sk1),top),
inference(paramod,[status(thm)],[c_1,c_1878]) ).
cnf(c_1880,plain,
composition(sk1,top) = composition(converse(sk1),top),
inference(paramod,[status(thm)],[c_1352,c_1879]) ).
cnf(c_1673,plain,
composition(converse(sk1),top) = composition(sk1,top),
inference(copy,[status(thm)],[c_1880]) ).
cnf(c_1881,plain,
join(complement(one),complement(composition(sk1,top))) = complement(converse(sk1)),
inference(paramod,[status(thm)],[c_1673,c_1003]) ).
cnf(c_1686,plain,
complement(converse(sk1)) = join(complement(one),complement(composition(sk1,top))),
inference(copy,[status(thm)],[c_1881]) ).
cnf(c_1882,plain,
converse(composition(sk1,top)) = composition(converse(top),converse(converse(sk1))),
inference(paramod,[status(thm)],[c_1673,c_13]) ).
cnf(c_1883,plain,
composition(converse(top),converse(sk1)) = composition(converse(top),converse(converse(sk1))),
inference(paramod,[status(thm)],[c_13,c_1882]) ).
cnf(c_1884,plain,
composition(top,converse(sk1)) = composition(converse(top),converse(converse(sk1))),
inference(paramod,[status(thm)],[c_174,c_1883]) ).
cnf(c_1885,plain,
composition(top,converse(sk1)) = composition(top,converse(converse(sk1))),
inference(paramod,[status(thm)],[c_174,c_1884]) ).
cnf(c_1693,plain,
composition(top,converse(sk1)) = composition(top,sk1),
inference(paramod,[status(thm)],[c_11,c_1885]) ).
cnf(c_1886,plain,
join(complement(converse(sk1)),composition(converse(top),complement(composition(top,sk1)))) = complement(converse(sk1)),
inference(paramod,[status(thm)],[c_1693,c_15]) ).
cnf(c_1887,plain,
join(join(complement(one),complement(composition(sk1,top))),composition(converse(top),complement(composition(top,sk1)))) = complement(converse(sk1)),
inference(paramod,[status(thm)],[c_1686,c_1886]) ).
cnf(c_1888,plain,
join(join(complement(one),complement(composition(sk1,top))),composition(top,complement(composition(top,sk1)))) = complement(converse(sk1)),
inference(paramod,[status(thm)],[c_174,c_1887]) ).
cnf(c_1889,plain,
join(join(complement(one),complement(composition(sk1,top))),complement(composition(top,sk1))) = complement(converse(sk1)),
inference(paramod,[status(thm)],[c_342,c_1888]) ).
cnf(c_1890,plain,
join(complement(one),join(complement(composition(sk1,top)),complement(composition(top,sk1)))) = complement(converse(sk1)),
inference(paramod,[status(thm)],[c_3,c_1889]) ).
cnf(c_1891,plain,
join(complement(composition(sk1,top)),complement(sk1)) = complement(converse(sk1)),
inference(paramod,[status(thm)],[c_947,c_1890]) ).
cnf(c_1892,plain,
join(complement(sk1),complement(composition(sk1,top))) = complement(converse(sk1)),
inference(paramod,[status(thm)],[c_1,c_1891]) ).
cnf(c_1893,plain,
complement(sk1) = complement(converse(sk1)),
inference(paramod,[status(thm)],[c_980,c_1892]) ).
cnf(c_1894,plain,
complement(sk1) = join(complement(one),complement(composition(sk1,top))),
inference(paramod,[status(thm)],[c_1686,c_1893]) ).
cnf(c_1709,plain,
join(complement(one),complement(composition(sk1,top))) = complement(sk1),
inference(copy,[status(thm)],[c_1894]) ).
cnf(c_1720,plain,
complement(converse(sk1)) = complement(sk1),
inference(paramod,[status(thm)],[c_1709,c_1686]) ).
cnf(c_1895,plain,
complement(complement(sk1)) = converse(sk1),
inference(paramod,[status(thm)],[c_1720,c_76]) ).
cnf(c_1896,plain,
sk1 = converse(sk1),
inference(paramod,[status(thm)],[c_76,c_1895]) ).
cnf(c_1727,plain,
converse(sk1) = sk1,
inference(copy,[status(thm)],[c_1896]) ).
cnf(c_1897,plain,
( join(sk1,converse(sk1)) != sk1
| join(sk1,sk1) != converse(sk1) ),
inference(paramod,[status(thm)],[c_1727,c_23]) ).
cnf(c_1898,plain,
( join(sk1,converse(sk1)) != sk1
| sk1 != converse(sk1) ),
inference(paramod,[status(thm)],[c_126,c_1897]) ).
cnf(c_1899,plain,
( join(sk1,converse(sk1)) != sk1
| sk1 != sk1 ),
inference(paramod,[status(thm)],[c_1727,c_1898]) ).
cnf(c_1900,plain,
( join(sk1,sk1) != sk1
| sk1 != sk1 ),
inference(paramod,[status(thm)],[c_1727,c_1899]) ).
cnf(c_1901,plain,
( sk1 != sk1
| sk1 != sk1 ),
inference(paramod,[status(thm)],[c_126,c_1900]) ).
cnf(c_1902,plain,
sk1 != sk1,
inference(copy,[status(thm)],[c_1901]) ).
cnf(c_1741,plain,
$false,
inference(copy,[status(thm)],[c_1902]) ).
%------------------------------------------------------------------------------
%----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
% 0.10/0.37 % Computer : n015.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 05:35:28 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 3244810 was started by sandbox2 on n015,
% 0.10/0.38 % Sat Sep 26 05:35:28 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 6.86/1.37
% 6.86/1.37 % SZS status Unsatisfiable for theBenchmark
% 6.86/1.37
% 6.86/1.37 % Proof 1 at 0.61 (+ 0.24) seconds.
% 6.86/1.37 % Length of proof is 127.
% 6.86/1.37 % Level of proof is 27.
% 6.86/1.37 % Maximum clause weight is 30.000.
% 6.86/1.37 % Given clauses 298.
% 6.86/1.37
% 6.86/1.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------