%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL030-1 : 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 : n006.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 08:24:59 AM UTC 2026
% Result : Unsatisfiable 44.00s 12.01s
% Output : CNFRefutation 44.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 89
% Number of leaves : 15
% Syntax : Number of formulae : 385 ( 385 unt; 0 def)
% Number of atoms : 385 ( 384 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 15 ( 15 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 432 ( 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_10198,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_10198]) ).
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_10199,plain,
zero = complement(join(complement(A),complement(complement(A)))),
inference(paramod,[status(thm)],[c_6,c_18]) ).
cnf(c_10200,plain,
zero = complement(top),
inference(paramod,[status(thm)],[c_17,c_10199]) ).
cnf(c_19,plain,
complement(top) = zero,
inference(copy,[status(thm)],[c_10200]) ).
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_15,axiom,
meet(composition(sk1,sk2),complement(sk3)) != meet(composition(sk1,sk2),complement(composition(sk1,sk3))),
file('theBenchmark.p',goals_15) ).
cnf(c_22,plain,
meet(composition(sk1,sk2),complement(sk3)) != meet(composition(sk1,sk2),complement(composition(sk1,sk3))),
inference(clausify,[status(thm)],[goals_15]) ).
cnf(c_10201,plain,
complement(join(complement(composition(sk1,sk2)),complement(complement(sk3)))) != meet(composition(sk1,sk2),complement(composition(sk1,sk3))),
inference(paramod,[status(thm)],[c_6,c_22]) ).
cnf(c_10202,plain,
complement(join(complement(complement(sk3)),complement(composition(sk1,sk2)))) != meet(composition(sk1,sk2),complement(composition(sk1,sk3))),
inference(paramod,[status(thm)],[c_1,c_10201]) ).
cnf(c_10203,plain,
complement(join(complement(complement(sk3)),complement(composition(sk1,sk2)))) != complement(join(complement(composition(sk1,sk2)),complement(complement(composition(sk1,sk3))))),
inference(paramod,[status(thm)],[c_6,c_10202]) ).
cnf(c_23,plain,
complement(join(complement(composition(sk1,sk2)),complement(complement(composition(sk1,sk3))))) != complement(join(complement(complement(sk3)),complement(composition(sk1,sk2)))),
inference(copy,[status(thm)],[c_10203]) ).
cnf(c_10204,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_10204]) ).
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_10205,plain,
join(A,B) = join(complement(join(complement(A),C)),join(complement(join(complement(A),complement(C))),B)),
inference(paramod,[status(thm)],[c_5,c_3]) ).
cnf(c_28,plain,
join(complement(join(complement(A),B)),join(complement(join(complement(A),complement(B))),C)) = join(A,C),
inference(copy,[status(thm)],[c_10205]) ).
cnf(c_10206,plain,
join(complement(join(complement(join(complement(A),B)),join(complement(A),complement(B)))),complement(A)) = join(complement(A),B),
inference(paramod,[status(thm)],[c_5,c_5]) ).
cnf(c_10207,plain,
join(complement(join(join(complement(A),complement(B)),complement(join(complement(A),B)))),complement(A)) = join(complement(A),B),
inference(paramod,[status(thm)],[c_1,c_10206]) ).
cnf(c_10208,plain,
join(complement(join(complement(A),join(complement(B),complement(join(complement(A),B))))),complement(A)) = join(complement(A),B),
inference(paramod,[status(thm)],[c_3,c_10207]) ).
cnf(c_30,plain,
join(complement(A),complement(join(complement(A),join(complement(B),complement(join(complement(A),B)))))) = join(complement(A),B),
inference(paramod,[status(thm)],[c_1,c_10208]) ).
cnf(c_10209,plain,
converse(A) = composition(converse(one),converse(A)),
inference(paramod,[status(thm)],[c_9,c_13]) ).
cnf(c_34,plain,
composition(converse(one),converse(A)) = converse(A),
inference(copy,[status(thm)],[c_10209]) ).
cnf(c_10210,plain,
join(complement(A),B) = join(complement(A),join(composition(converse(C),complement(composition(C,A))),B)),
inference(paramod,[status(thm)],[c_15,c_3]) ).
cnf(c_36,plain,
join(complement(A),join(composition(converse(B),complement(composition(B,A))),C)) = join(complement(A),C),
inference(copy,[status(thm)],[c_10210]) ).
cnf(c_42,plain,
join(complement(A),composition(B,complement(composition(converse(B),A)))) = complement(A),
inference(paramod,[status(thm)],[c_11,c_15]) ).
cnf(c_10211,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_10212,plain,
converse(complement(A)) = join(converse(complement(A)),composition(converse(complement(composition(B,A))),converse(converse(B)))),
inference(paramod,[status(thm)],[c_13,c_10211]) ).
cnf(c_10213,plain,
converse(complement(A)) = join(converse(complement(A)),composition(converse(complement(composition(B,A))),B)),
inference(paramod,[status(thm)],[c_11,c_10212]) ).
cnf(c_43,plain,
join(converse(complement(A)),composition(converse(complement(composition(B,A))),B)) = converse(complement(A)),
inference(copy,[status(thm)],[c_10213]) ).
cnf(c_10214,plain,
join(top,A) = join(B,join(complement(B),A)),
inference(paramod,[status(thm)],[c_17,c_3]) ).
cnf(c_44,plain,
join(A,join(complement(A),B)) = join(top,B),
inference(copy,[status(thm)],[c_10214]) ).
cnf(c_10215,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_17,c_5]) ).
cnf(c_46,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_19,c_10215]) ).
cnf(c_10216,plain,
composition(top,A) = join(composition(B,A),composition(complement(B),A)),
inference(paramod,[status(thm)],[c_17,c_10]) ).
cnf(c_48,plain,
join(composition(A,B),composition(complement(A),B)) = composition(top,B),
inference(copy,[status(thm)],[c_10216]) ).
cnf(c_10217,plain,
converse(top) = join(converse(A),converse(complement(A))),
inference(paramod,[status(thm)],[c_17,c_12]) ).
cnf(c_49,plain,
join(converse(A),converse(complement(A))) = converse(top),
inference(copy,[status(thm)],[c_10217]) ).
cnf(c_10218,plain,
join(one,A) = join(one,join(sk1,A)),
inference(paramod,[status(thm)],[c_21,c_3]) ).
cnf(c_54,plain,
join(one,join(sk1,A)) = join(one,A),
inference(copy,[status(thm)],[c_10218]) ).
cnf(c_10219,plain,
composition(one,A) = join(composition(one,A),composition(sk1,A)),
inference(paramod,[status(thm)],[c_21,c_10]) ).
cnf(c_56,plain,
join(composition(one,A),composition(sk1,A)) = composition(one,A),
inference(copy,[status(thm)],[c_10219]) ).
cnf(c_10220,plain,
converse(one) = join(converse(one),converse(sk1)),
inference(paramod,[status(thm)],[c_21,c_12]) ).
cnf(c_57,plain,
join(converse(one),converse(sk1)) = converse(one),
inference(copy,[status(thm)],[c_10220]) ).
cnf(c_10221,plain,
join(A,B) = join(complement(join(complement(B),C)),join(A,complement(join(complement(B),complement(C))))),
inference(paramod,[status(thm)],[c_5,c_25]) ).
cnf(c_59,plain,
join(complement(join(complement(A),B)),join(C,complement(join(complement(A),complement(B))))) = join(C,A),
inference(copy,[status(thm)],[c_10221]) ).
cnf(c_10222,plain,
A = join(complement(join(complement(A),complement(B))),complement(join(B,complement(A)))),
inference(paramod,[status(thm)],[c_26,c_1]) ).
cnf(c_63,plain,
join(complement(join(complement(A),complement(B))),complement(join(B,complement(A)))) = A,
inference(copy,[status(thm)],[c_10222]) ).
cnf(c_10223,plain,
join(A,B) = join(complement(join(C,complement(A))),join(complement(join(complement(A),complement(C))),B)),
inference(paramod,[status(thm)],[c_26,c_3]) ).
cnf(c_65,plain,
join(complement(join(A,complement(B))),join(complement(join(complement(B),complement(A))),C)) = join(B,C),
inference(copy,[status(thm)],[c_10223]) ).
cnf(c_10224,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_17,c_27]) ).
cnf(c_10225,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_1,c_10224]) ).
cnf(c_10226,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_19,c_10225]) ).
cnf(c_82,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_1,c_10226]) ).
cnf(c_10227,plain,
join(complement(join(complement(join(complement(A),complement(B))),join(complement(B),A))),complement(B)) = join(complement(A),complement(B)),
inference(paramod,[status(thm)],[c_27,c_27]) ).
cnf(c_10228,plain,
join(complement(join(join(complement(B),A),complement(join(complement(A),complement(B))))),complement(B)) = join(complement(A),complement(B)),
inference(paramod,[status(thm)],[c_1,c_10227]) ).
cnf(c_10229,plain,
join(complement(join(complement(B),join(A,complement(join(complement(A),complement(B)))))),complement(B)) = join(complement(A),complement(B)),
inference(paramod,[status(thm)],[c_3,c_10228]) ).
cnf(c_87,plain,
join(complement(A),complement(join(complement(A),join(B,complement(join(complement(B),complement(A))))))) = join(complement(B),complement(A)),
inference(paramod,[status(thm)],[c_1,c_10229]) ).
cnf(c_88,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_82,c_46]) ).
cnf(c_89,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_88,c_82]) ).
cnf(c_10230,plain,
complement(join(complement(composition(sk1,sk2)),composition(sk1,sk3))) != complement(join(complement(complement(sk3)),complement(composition(sk1,sk2)))),
inference(paramod,[status(thm)],[c_88,c_23]) ).
cnf(c_91,plain,
complement(join(complement(composition(sk1,sk2)),composition(sk1,sk3))) != complement(join(sk3,complement(composition(sk1,sk2)))),
inference(paramod,[status(thm)],[c_88,c_10230]) ).
cnf(c_10231,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_34]) ).
cnf(c_98,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_11,c_10231]) ).
cnf(c_10232,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_98,c_9]) ).
cnf(c_100,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_10232]) ).
cnf(c_104,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_98,c_15]) ).
cnf(c_105,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_100,c_98]) ).
cnf(c_10233,plain,
join(one,converse(sk1)) = converse(one),
inference(paramod,[status(thm)],[c_100,c_57]) ).
cnf(c_106,plain,
join(one,converse(sk1)) = one,
inference(paramod,[status(thm)],[c_100,c_10233]) ).
cnf(c_10234,plain,
join(A,composition(sk1,A)) = composition(one,A),
inference(paramod,[status(thm)],[c_105,c_56]) ).
cnf(c_107,plain,
join(A,composition(sk1,A)) = A,
inference(paramod,[status(thm)],[c_105,c_10234]) ).
cnf(c_108,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_105,c_104]) ).
cnf(c_10235,plain,
composition(one,A) = join(composition(one,A),composition(converse(sk1),A)),
inference(paramod,[status(thm)],[c_106,c_10]) ).
cnf(c_10236,plain,
A = join(composition(one,A),composition(converse(sk1),A)),
inference(paramod,[status(thm)],[c_105,c_10235]) ).
cnf(c_10237,plain,
A = join(A,composition(converse(sk1),A)),
inference(paramod,[status(thm)],[c_105,c_10236]) ).
cnf(c_110,plain,
join(A,composition(converse(sk1),A)) = A,
inference(copy,[status(thm)],[c_10237]) ).
cnf(c_10238,plain,
join(complement(join(complement(A),B)),B) = join(A,complement(join(complement(B),complement(complement(A))))),
inference(paramod,[status(thm)],[c_26,c_28]) ).
cnf(c_10239,plain,
join(B,complement(join(complement(A),B))) = join(A,complement(join(complement(B),complement(complement(A))))),
inference(paramod,[status(thm)],[c_1,c_10238]) ).
cnf(c_128,plain,
join(A,complement(join(complement(B),A))) = join(B,complement(join(complement(A),B))),
inference(paramod,[status(thm)],[c_88,c_10239]) ).
cnf(c_10240,plain,
join(A,join(complement(B),C)) = join(complement(B),join(A,complement(join(complement(B),join(complement(C),complement(join(complement(B),C))))))),
inference(paramod,[status(thm)],[c_30,c_25]) ).
cnf(c_141,plain,
join(complement(A),join(B,complement(join(complement(A),join(complement(C),complement(join(complement(A),C))))))) = join(B,join(complement(A),C)),
inference(copy,[status(thm)],[c_10240]) ).
cnf(c_10241,plain,
join(complement(join(complement(A),B)),complement(join(complement(join(complement(A),join(complement(B),complement(join(complement(A),B))))),complement(complement(A))))) = join(complement(A),join(complement(B),complement(join(complement(A),B)))),
inference(paramod,[status(thm)],[c_30,c_26]) ).
cnf(c_10242,plain,
join(complement(join(complement(A),B)),complement(join(complement(join(complement(A),join(complement(B),complement(join(complement(A),B))))),A))) = join(complement(A),join(complement(B),complement(join(complement(A),B)))),
inference(paramod,[status(thm)],[c_88,c_10241]) ).
cnf(c_143,plain,
join(complement(join(complement(A),B)),complement(join(A,complement(join(complement(A),join(complement(B),complement(join(complement(A),B)))))))) = join(complement(A),join(complement(B),complement(join(complement(A),B)))),
inference(paramod,[status(thm)],[c_1,c_10242]) ).
cnf(c_10243,plain,
join(complement(join(complement(A),B)),complement(join(complement(join(complement(A),B)),join(complement(join(complement(join(complement(A),complement(B))),C)),complement(join(A,C)))))) = join(complement(join(complement(A),B)),join(complement(join(complement(A),complement(B))),C)),
inference(paramod,[status(thm)],[c_28,c_30]) ).
cnf(c_10244,plain,
join(complement(join(complement(A),B)),complement(join(complement(join(complement(A),B)),join(complement(join(A,C)),complement(join(complement(join(complement(A),complement(B))),C)))))) = join(complement(join(complement(A),B)),join(complement(join(complement(A),complement(B))),C)),
inference(paramod,[status(thm)],[c_1,c_10243]) ).
cnf(c_149,plain,
join(complement(join(complement(A),B)),complement(join(complement(join(complement(A),B)),join(complement(join(A,C)),complement(join(complement(join(complement(A),complement(B))),C)))))) = join(A,C),
inference(paramod,[status(thm)],[c_28,c_10244]) ).
cnf(c_10245,plain,
converse(A) = join(converse(A),converse(composition(sk1,A))),
inference(paramod,[status(thm)],[c_107,c_12]) ).
cnf(c_10246,plain,
converse(A) = join(converse(A),composition(converse(A),converse(sk1))),
inference(paramod,[status(thm)],[c_13,c_10245]) ).
cnf(c_167,plain,
join(converse(A),composition(converse(A),converse(sk1))) = converse(A),
inference(copy,[status(thm)],[c_10246]) ).
cnf(c_10247,plain,
join(A,B) = join(B,join(A,composition(sk1,B))),
inference(paramod,[status(thm)],[c_107,c_25]) ).
cnf(c_168,plain,
join(A,join(B,composition(sk1,A))) = join(B,A),
inference(copy,[status(thm)],[c_10247]) ).
cnf(c_10248,plain,
join(complement(complement(A)),complement(join(complement(A),complement(complement(A))))) = A,
inference(paramod,[status(thm)],[c_108,c_5]) ).
cnf(c_10249,plain,
join(A,complement(join(complement(A),complement(complement(A))))) = A,
inference(paramod,[status(thm)],[c_88,c_10248]) ).
cnf(c_10250,plain,
join(A,complement(join(complement(A),A))) = A,
inference(paramod,[status(thm)],[c_88,c_10249]) ).
cnf(c_10251,plain,
join(A,complement(join(A,complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_10250]) ).
cnf(c_10252,plain,
join(A,complement(top)) = A,
inference(paramod,[status(thm)],[c_17,c_10251]) ).
cnf(c_178,plain,
join(A,zero) = A,
inference(paramod,[status(thm)],[c_19,c_10252]) ).
cnf(c_10253,plain,
join(complement(join(complement(A),A)),complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_108,c_5]) ).
cnf(c_10254,plain,
join(complement(join(A,complement(A))),complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_1,c_10253]) ).
cnf(c_10255,plain,
join(complement(top),complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_17,c_10254]) ).
cnf(c_10256,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_19,c_10255]) ).
cnf(c_179,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_88,c_10256]) ).
cnf(c_10257,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(A,complement(join(complement(A),complement(B)))),
inference(paramod,[status(thm)],[c_108,c_28]) ).
cnf(c_10258,plain,
A = join(A,complement(join(complement(A),complement(B)))),
inference(paramod,[status(thm)],[c_5,c_10257]) ).
cnf(c_182,plain,
join(A,complement(join(complement(A),complement(B)))) = A,
inference(copy,[status(thm)],[c_10258]) ).
cnf(c_191,plain,
complement(join(A,A)) = complement(A),
inference(paramod,[status(thm)],[c_179,c_89]) ).
cnf(c_194,plain,
join(complement(A),complement(join(complement(A),B))) = join(complement(B),complement(A)),
inference(paramod,[status(thm)],[c_182,c_87]) ).
cnf(c_10259,plain,
join(complement(join(complement(join(A,C)),complement(join(complement(join(complement(A),complement(B))),C)))),complement(join(complement(A),B))) = join(A,C),
inference(paramod,[status(thm)],[c_194,c_149]) ).
cnf(c_196,plain,
join(complement(join(complement(A),B)),complement(join(complement(join(A,C)),complement(join(complement(join(complement(A),complement(B))),C))))) = join(A,C),
inference(paramod,[status(thm)],[c_1,c_10259]) ).
cnf(c_10260,plain,
converse(A) = join(converse(A),converse(zero)),
inference(paramod,[status(thm)],[c_178,c_12]) ).
cnf(c_204,plain,
join(converse(A),converse(zero)) = converse(A),
inference(copy,[status(thm)],[c_10260]) ).
cnf(c_209,plain,
complement(zero) = top,
inference(paramod,[status(thm)],[c_179,c_17]) ).
cnf(c_10261,plain,
join(complement(A),composition(converse(B),complement(composition(B,A)))) = join(complement(A),composition(sk1,composition(converse(B),complement(composition(B,A))))),
inference(paramod,[status(thm)],[c_107,c_36]) ).
cnf(c_10262,plain,
complement(A) = join(complement(A),composition(sk1,composition(converse(B),complement(composition(B,A))))),
inference(paramod,[status(thm)],[c_15,c_10261]) ).
cnf(c_246,plain,
join(complement(A),composition(sk1,composition(converse(B),complement(composition(B,A))))) = complement(A),
inference(copy,[status(thm)],[c_10262]) ).
cnf(c_10263,plain,
join(complement(join(complement(A),B)),complement(join(complement(join(A,A)),complement(B)))) = join(A,A),
inference(paramod,[status(thm)],[c_191,c_5]) ).
cnf(c_10264,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(A,A),
inference(paramod,[status(thm)],[c_191,c_10263]) ).
cnf(c_10265,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_5,c_10264]) ).
cnf(c_257,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_10265]) ).
cnf(c_10266,plain,
join(complement(join(complement(A),B)),join(complement(join(complement(A),complement(B))),A)) = A,
inference(paramod,[status(thm)],[c_257,c_28]) ).
cnf(c_10267,plain,
join(complement(join(complement(A),B)),join(A,complement(join(complement(A),complement(B))))) = A,
inference(paramod,[status(thm)],[c_1,c_10266]) ).
cnf(c_10268,plain,
join(complement(join(complement(A),B)),A) = A,
inference(paramod,[status(thm)],[c_182,c_10267]) ).
cnf(c_261,plain,
join(A,complement(join(complement(A),B))) = A,
inference(paramod,[status(thm)],[c_1,c_10268]) ).
cnf(c_10269,plain,
join(complement(join(complement(A),B)),complement(A)) = join(complement(A),join(complement(B),complement(join(complement(A),B)))),
inference(paramod,[status(thm)],[c_261,c_143]) ).
cnf(c_10270,plain,
join(complement(A),complement(join(complement(A),B))) = join(complement(A),join(complement(B),complement(join(complement(A),B)))),
inference(paramod,[status(thm)],[c_1,c_10269]) ).
cnf(c_10271,plain,
join(complement(B),complement(A)) = join(complement(A),join(complement(B),complement(join(complement(A),B)))),
inference(paramod,[status(thm)],[c_194,c_10270]) ).
cnf(c_263,plain,
join(complement(A),join(complement(B),complement(join(complement(A),B)))) = join(complement(B),complement(A)),
inference(copy,[status(thm)],[c_10271]) ).
cnf(c_266,plain,
join(complement(A),join(B,complement(join(complement(C),complement(A))))) = join(B,join(complement(A),C)),
inference(paramod,[status(thm)],[c_263,c_141]) ).
cnf(c_10272,plain,
join(A,converse(zero)) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_204]) ).
cnf(c_269,plain,
join(A,converse(zero)) = A,
inference(paramod,[status(thm)],[c_11,c_10272]) ).
cnf(c_10273,plain,
zero = converse(zero),
inference(paramod,[status(thm)],[c_269,c_179]) ).
cnf(c_275,plain,
converse(zero) = zero,
inference(copy,[status(thm)],[c_10273]) ).
cnf(c_10274,plain,
join(complement(join(A,B)),complement(join(complement(complement(A)),complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_88,c_5]) ).
cnf(c_330,plain,
join(complement(join(A,B)),complement(join(A,complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_88,c_10274]) ).
cnf(c_10275,plain,
join(zero,composition(A,complement(composition(converse(A),top)))) = complement(top),
inference(paramod,[status(thm)],[c_19,c_42]) ).
cnf(c_10276,plain,
composition(A,complement(composition(converse(A),top))) = complement(top),
inference(paramod,[status(thm)],[c_179,c_10275]) ).
cnf(c_368,plain,
composition(A,complement(composition(converse(A),top))) = zero,
inference(paramod,[status(thm)],[c_19,c_10276]) ).
cnf(c_10277,plain,
join(converse(zero),composition(converse(complement(composition(A,top))),A)) = converse(complement(top)),
inference(paramod,[status(thm)],[c_19,c_43]) ).
cnf(c_10278,plain,
join(zero,composition(converse(complement(composition(A,top))),A)) = converse(complement(top)),
inference(paramod,[status(thm)],[c_275,c_10277]) ).
cnf(c_10279,plain,
composition(converse(complement(composition(A,top))),A) = converse(complement(top)),
inference(paramod,[status(thm)],[c_179,c_10278]) ).
cnf(c_10280,plain,
composition(converse(complement(composition(A,top))),A) = converse(zero),
inference(paramod,[status(thm)],[c_19,c_10279]) ).
cnf(c_375,plain,
composition(converse(complement(composition(A,top))),A) = zero,
inference(paramod,[status(thm)],[c_275,c_10280]) ).
cnf(c_10281,plain,
converse(A) = join(converse(A),converse(composition(converse(sk1),A))),
inference(paramod,[status(thm)],[c_110,c_12]) ).
cnf(c_10282,plain,
converse(A) = join(converse(A),composition(converse(A),converse(converse(sk1)))),
inference(paramod,[status(thm)],[c_13,c_10281]) ).
cnf(c_10283,plain,
converse(A) = join(converse(A),composition(converse(A),sk1)),
inference(paramod,[status(thm)],[c_11,c_10282]) ).
cnf(c_389,plain,
join(converse(A),composition(converse(A),sk1)) = converse(A),
inference(copy,[status(thm)],[c_10283]) ).
cnf(c_10284,plain,
join(A,complement(A)) = join(top,complement(A)),
inference(paramod,[status(thm)],[c_257,c_44]) ).
cnf(c_10285,plain,
top = join(top,complement(A)),
inference(paramod,[status(thm)],[c_17,c_10284]) ).
cnf(c_412,plain,
join(top,complement(A)) = top,
inference(copy,[status(thm)],[c_10285]) ).
cnf(c_10286,plain,
join(A,join(complement(A),top)) = top,
inference(paramod,[status(thm)],[c_257,c_44]) ).
cnf(c_10287,plain,
join(A,join(top,complement(A))) = top,
inference(paramod,[status(thm)],[c_1,c_10286]) ).
cnf(c_413,plain,
join(A,top) = top,
inference(paramod,[status(thm)],[c_412,c_10287]) ).
cnf(c_438,plain,
join(A,composition(complement(one),A)) = composition(top,A),
inference(paramod,[status(thm)],[c_105,c_48]) ).
cnf(c_10288,plain,
top = join(top,A),
inference(paramod,[status(thm)],[c_413,c_1]) ).
cnf(c_443,plain,
join(top,A) = top,
inference(copy,[status(thm)],[c_10288]) ).
cnf(c_10289,plain,
converse(top) = join(converse(A),converse(top)),
inference(paramod,[status(thm)],[c_413,c_12]) ).
cnf(c_445,plain,
join(converse(A),converse(top)) = converse(top),
inference(copy,[status(thm)],[c_10289]) ).
cnf(c_460,plain,
join(A,converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_11,c_445]) ).
cnf(c_463,plain,
converse(top) = top,
inference(paramod,[status(thm)],[c_460,c_443]) ).
cnf(c_472,plain,
join(converse(A),converse(complement(A))) = top,
inference(paramod,[status(thm)],[c_463,c_49]) ).
cnf(c_10290,plain,
join(one,top) = join(one,complement(sk1)),
inference(paramod,[status(thm)],[c_17,c_54]) ).
cnf(c_10291,plain,
top = join(one,complement(sk1)),
inference(paramod,[status(thm)],[c_413,c_10290]) ).
cnf(c_479,plain,
join(one,complement(sk1)) = top,
inference(copy,[status(thm)],[c_10291]) ).
cnf(c_10292,plain,
join(complement(join(zero,A)),join(B,complement(join(complement(top),complement(A))))) = join(B,top),
inference(paramod,[status(thm)],[c_19,c_59]) ).
cnf(c_10293,plain,
join(complement(A),join(B,complement(join(complement(top),complement(A))))) = join(B,top),
inference(paramod,[status(thm)],[c_179,c_10292]) ).
cnf(c_10294,plain,
join(complement(A),join(B,complement(join(zero,complement(A))))) = join(B,top),
inference(paramod,[status(thm)],[c_19,c_10293]) ).
cnf(c_10295,plain,
join(complement(A),join(B,complement(complement(A)))) = join(B,top),
inference(paramod,[status(thm)],[c_179,c_10294]) ).
cnf(c_10296,plain,
join(complement(A),join(B,A)) = join(B,top),
inference(paramod,[status(thm)],[c_88,c_10295]) ).
cnf(c_544,plain,
join(complement(A),join(B,A)) = top,
inference(paramod,[status(thm)],[c_413,c_10296]) ).
cnf(c_10297,plain,
join(complement(join(complement(sk1),complement(one))),complement(top)) = sk1,
inference(paramod,[status(thm)],[c_479,c_63]) ).
cnf(c_10298,plain,
join(complement(join(complement(one),complement(sk1))),complement(top)) = sk1,
inference(paramod,[status(thm)],[c_1,c_10297]) ).
cnf(c_10299,plain,
join(complement(join(complement(one),complement(sk1))),zero) = sk1,
inference(paramod,[status(thm)],[c_19,c_10298]) ).
cnf(c_10300,plain,
join(zero,complement(join(complement(one),complement(sk1)))) = sk1,
inference(paramod,[status(thm)],[c_1,c_10299]) ).
cnf(c_588,plain,
complement(join(complement(one),complement(sk1))) = sk1,
inference(paramod,[status(thm)],[c_179,c_10300]) ).
cnf(c_10301,plain,
join(complement(join(A,complement(B))),join(complement(join(complement(B),complement(A))),B)) = B,
inference(paramod,[status(thm)],[c_257,c_65]) ).
cnf(c_10302,plain,
join(complement(join(A,complement(B))),join(B,complement(join(complement(B),complement(A))))) = B,
inference(paramod,[status(thm)],[c_1,c_10301]) ).
cnf(c_10303,plain,
join(complement(join(A,complement(B))),B) = B,
inference(paramod,[status(thm)],[c_261,c_10302]) ).
cnf(c_601,plain,
join(A,complement(join(B,complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_10303]) ).
cnf(c_623,plain,
join(one,converse(complement(one))) = top,
inference(paramod,[status(thm)],[c_100,c_472]) ).
cnf(c_10304,plain,
complement(sk1) = join(complement(one),complement(sk1)),
inference(paramod,[status(thm)],[c_588,c_88]) ).
cnf(c_685,plain,
join(complement(one),complement(sk1)) = complement(sk1),
inference(copy,[status(thm)],[c_10304]) ).
cnf(c_10305,plain,
join(A,composition(converse(converse(A)),sk1)) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_389]) ).
cnf(c_10306,plain,
join(A,composition(A,sk1)) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_10305]) ).
cnf(c_764,plain,
join(A,composition(A,sk1)) = A,
inference(paramod,[status(thm)],[c_11,c_10306]) ).
cnf(c_10307,plain,
join(A,B) = join(A,join(composition(A,sk1),B)),
inference(paramod,[status(thm)],[c_764,c_3]) ).
cnf(c_769,plain,
join(A,join(composition(A,sk1),B)) = join(A,B),
inference(copy,[status(thm)],[c_10307]) ).
cnf(c_10308,plain,
join(complement(composition(A,sk1)),A) = top,
inference(paramod,[status(thm)],[c_764,c_544]) ).
cnf(c_775,plain,
join(A,complement(composition(A,sk1))) = top,
inference(paramod,[status(thm)],[c_1,c_10308]) ).
cnf(c_10309,plain,
converse(composition(top,A)) = join(converse(A),converse(composition(complement(one),A))),
inference(paramod,[status(thm)],[c_438,c_12]) ).
cnf(c_10310,plain,
composition(converse(A),converse(top)) = join(converse(A),converse(composition(complement(one),A))),
inference(paramod,[status(thm)],[c_13,c_10309]) ).
cnf(c_10311,plain,
composition(converse(A),top) = join(converse(A),converse(composition(complement(one),A))),
inference(paramod,[status(thm)],[c_463,c_10310]) ).
cnf(c_10312,plain,
composition(converse(A),top) = join(converse(A),composition(converse(A),converse(complement(one)))),
inference(paramod,[status(thm)],[c_13,c_10311]) ).
cnf(c_821,plain,
join(converse(A),composition(converse(A),converse(complement(one)))) = composition(converse(A),top),
inference(copy,[status(thm)],[c_10312]) ).
cnf(c_10313,plain,
join(A,composition(converse(converse(A)),converse(sk1))) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_167]) ).
cnf(c_10314,plain,
join(A,composition(A,converse(sk1))) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_10313]) ).
cnf(c_906,plain,
join(A,composition(A,converse(sk1))) = A,
inference(paramod,[status(thm)],[c_11,c_10314]) ).
cnf(c_10315,plain,
join(complement(composition(A,converse(sk1))),A) = top,
inference(paramod,[status(thm)],[c_906,c_544]) ).
cnf(c_1068,plain,
join(A,complement(composition(A,converse(sk1)))) = top,
inference(paramod,[status(thm)],[c_1,c_10315]) ).
cnf(c_10316,plain,
join(complement(A),join(composition(converse(B),complement(composition(B,A))),complement(join(complement(C),complement(A))))) = join(C,complement(join(complement(complement(A)),C))),
inference(paramod,[status(thm)],[c_128,c_36]) ).
cnf(c_10317,plain,
join(composition(converse(B),complement(composition(B,A))),join(complement(A),C)) = join(C,complement(join(complement(complement(A)),C))),
inference(paramod,[status(thm)],[c_266,c_10316]) ).
cnf(c_10318,plain,
join(complement(A),join(composition(converse(B),complement(composition(B,A))),C)) = join(C,complement(join(complement(complement(A)),C))),
inference(paramod,[status(thm)],[c_25,c_10317]) ).
cnf(c_10319,plain,
join(complement(A),C) = join(C,complement(join(complement(complement(A)),C))),
inference(paramod,[status(thm)],[c_36,c_10318]) ).
cnf(c_10320,plain,
join(complement(A),C) = join(C,complement(join(A,C))),
inference(paramod,[status(thm)],[c_88,c_10319]) ).
cnf(c_1179,plain,
join(A,complement(join(B,A))) = join(complement(B),A),
inference(copy,[status(thm)],[c_10320]) ).
cnf(c_1243,plain,
join(A,complement(join(A,B))) = join(complement(B),A),
inference(paramod,[status(thm)],[c_1,c_1179]) ).
cnf(c_10321,plain,
join(converse(complement(A)),complement(top)) = join(complement(converse(A)),converse(complement(A))),
inference(paramod,[status(thm)],[c_472,c_1179]) ).
cnf(c_10322,plain,
join(converse(complement(A)),zero) = join(complement(converse(A)),converse(complement(A))),
inference(paramod,[status(thm)],[c_19,c_10321]) ).
cnf(c_10323,plain,
join(zero,converse(complement(A))) = join(complement(converse(A)),converse(complement(A))),
inference(paramod,[status(thm)],[c_1,c_10322]) ).
cnf(c_10324,plain,
converse(complement(A)) = join(complement(converse(A)),converse(complement(A))),
inference(paramod,[status(thm)],[c_179,c_10323]) ).
cnf(c_1257,plain,
join(complement(converse(A)),converse(complement(A))) = converse(complement(A)),
inference(copy,[status(thm)],[c_10324]) ).
cnf(c_10325,plain,
join(converse(complement(one)),complement(top)) = join(complement(one),converse(complement(one))),
inference(paramod,[status(thm)],[c_623,c_1179]) ).
cnf(c_10326,plain,
join(converse(complement(one)),zero) = join(complement(one),converse(complement(one))),
inference(paramod,[status(thm)],[c_19,c_10325]) ).
cnf(c_10327,plain,
join(zero,converse(complement(one))) = join(complement(one),converse(complement(one))),
inference(paramod,[status(thm)],[c_1,c_10326]) ).
cnf(c_10328,plain,
converse(complement(one)) = join(complement(one),converse(complement(one))),
inference(paramod,[status(thm)],[c_179,c_10327]) ).
cnf(c_1258,plain,
join(complement(one),converse(complement(one))) = converse(complement(one)),
inference(copy,[status(thm)],[c_10328]) ).
cnf(c_10329,plain,
join(complement(composition(A,sk1)),complement(top)) = join(complement(A),complement(composition(A,sk1))),
inference(paramod,[status(thm)],[c_775,c_1179]) ).
cnf(c_10330,plain,
join(complement(composition(A,sk1)),zero) = join(complement(A),complement(composition(A,sk1))),
inference(paramod,[status(thm)],[c_19,c_10329]) ).
cnf(c_10331,plain,
join(zero,complement(composition(A,sk1))) = join(complement(A),complement(composition(A,sk1))),
inference(paramod,[status(thm)],[c_1,c_10330]) ).
cnf(c_10332,plain,
complement(composition(A,sk1)) = join(complement(A),complement(composition(A,sk1))),
inference(paramod,[status(thm)],[c_179,c_10331]) ).
cnf(c_1262,plain,
join(complement(A),complement(composition(A,sk1))) = complement(composition(A,sk1)),
inference(copy,[status(thm)],[c_10332]) ).
cnf(c_10333,plain,
converse(converse(complement(one))) = join(converse(complement(one)),converse(converse(complement(one)))),
inference(paramod,[status(thm)],[c_1258,c_12]) ).
cnf(c_10334,plain,
complement(one) = join(converse(complement(one)),converse(converse(complement(one)))),
inference(paramod,[status(thm)],[c_11,c_10333]) ).
cnf(c_10335,plain,
complement(one) = join(converse(complement(one)),complement(one)),
inference(paramod,[status(thm)],[c_11,c_10334]) ).
cnf(c_10336,plain,
complement(one) = join(complement(one),converse(complement(one))),
inference(paramod,[status(thm)],[c_1,c_10335]) ).
cnf(c_10337,plain,
complement(one) = converse(complement(one)),
inference(paramod,[status(thm)],[c_1258,c_10336]) ).
cnf(c_1470,plain,
converse(complement(one)) = complement(one),
inference(copy,[status(thm)],[c_10337]) ).
cnf(c_1478,plain,
join(converse(A),composition(converse(A),complement(one))) = composition(converse(A),top),
inference(paramod,[status(thm)],[c_1470,c_821]) ).
cnf(c_10338,plain,
join(composition(A,B),complement(composition(top,B))) = join(complement(composition(complement(A),B)),composition(A,B)),
inference(paramod,[status(thm)],[c_48,c_1243]) ).
cnf(c_10339,plain,
join(composition(A,B),complement(composition(top,B))) = join(composition(A,B),complement(composition(complement(A),B))),
inference(paramod,[status(thm)],[c_1,c_10338]) ).
cnf(c_1686,plain,
join(composition(A,B),complement(composition(complement(A),B))) = join(composition(A,B),complement(composition(top,B))),
inference(copy,[status(thm)],[c_10339]) ).
cnf(c_1863,plain,
join(complement(A),converse(complement(converse(A)))) = converse(complement(converse(A))),
inference(paramod,[status(thm)],[c_11,c_1257]) ).
cnf(c_10340,plain,
converse(converse(complement(A))) = join(converse(complement(converse(A))),converse(converse(complement(A)))),
inference(paramod,[status(thm)],[c_1257,c_12]) ).
cnf(c_10341,plain,
complement(A) = join(converse(complement(converse(A))),converse(converse(complement(A)))),
inference(paramod,[status(thm)],[c_11,c_10340]) ).
cnf(c_10342,plain,
complement(A) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_11,c_10341]) ).
cnf(c_10343,plain,
complement(A) = join(complement(A),converse(complement(converse(A)))),
inference(paramod,[status(thm)],[c_1,c_10342]) ).
cnf(c_10344,plain,
complement(A) = converse(complement(converse(A))),
inference(paramod,[status(thm)],[c_1863,c_10343]) ).
cnf(c_1864,plain,
converse(complement(converse(A))) = complement(A),
inference(copy,[status(thm)],[c_10344]) ).
cnf(c_1875,plain,
converse(complement(A)) = complement(converse(A)),
inference(paramod,[status(thm)],[c_1864,c_11]) ).
cnf(c_10345,plain,
composition(complement(converse(composition(A,top))),A) = zero,
inference(paramod,[status(thm)],[c_1875,c_375]) ).
cnf(c_10346,plain,
composition(complement(composition(converse(top),converse(A))),A) = zero,
inference(paramod,[status(thm)],[c_13,c_10345]) ).
cnf(c_1924,plain,
composition(complement(composition(top,converse(A))),A) = zero,
inference(paramod,[status(thm)],[c_463,c_10346]) ).
cnf(c_10347,plain,
join(complement(join(complement(complement(A)),B)),complement(join(complement(complement(composition(A,sk1))),complement(join(complement(join(complement(complement(A)),complement(B))),complement(composition(A,sk1))))))) = join(complement(A),complement(composition(A,sk1))),
inference(paramod,[status(thm)],[c_1262,c_196]) ).
cnf(c_10348,plain,
join(complement(join(A,B)),complement(join(complement(complement(composition(A,sk1))),complement(join(complement(join(complement(complement(A)),complement(B))),complement(composition(A,sk1))))))) = join(complement(A),complement(composition(A,sk1))),
inference(paramod,[status(thm)],[c_88,c_10347]) ).
cnf(c_10349,plain,
join(complement(join(A,B)),complement(join(composition(A,sk1),complement(join(complement(join(complement(complement(A)),complement(B))),complement(composition(A,sk1))))))) = join(complement(A),complement(composition(A,sk1))),
inference(paramod,[status(thm)],[c_88,c_10348]) ).
cnf(c_10350,plain,
join(complement(join(A,B)),complement(join(composition(A,sk1),complement(join(complement(join(A,complement(B))),complement(composition(A,sk1))))))) = join(complement(A),complement(composition(A,sk1))),
inference(paramod,[status(thm)],[c_88,c_10349]) ).
cnf(c_10351,plain,
join(complement(join(A,B)),complement(composition(A,sk1))) = join(complement(A),complement(composition(A,sk1))),
inference(paramod,[status(thm)],[c_601,c_10350]) ).
cnf(c_2257,plain,
join(complement(join(A,B)),complement(composition(A,sk1))) = complement(composition(A,sk1)),
inference(paramod,[status(thm)],[c_1262,c_10351]) ).
cnf(c_10352,plain,
join(A,composition(converse(converse(A)),complement(one))) = composition(converse(converse(A)),top),
inference(paramod,[status(thm)],[c_11,c_1478]) ).
cnf(c_10353,plain,
join(A,composition(A,complement(one))) = composition(converse(converse(A)),top),
inference(paramod,[status(thm)],[c_11,c_10352]) ).
cnf(c_2659,plain,
join(A,composition(A,complement(one))) = composition(A,top),
inference(paramod,[status(thm)],[c_11,c_10353]) ).
cnf(c_2690,plain,
join(complement(one),composition(sk1,top)) = join(sk1,complement(one)),
inference(paramod,[status(thm)],[c_2659,c_168]) ).
cnf(c_10354,plain,
join(complement(one),complement(join(sk1,complement(one)))) = join(complement(composition(sk1,top)),complement(one)),
inference(paramod,[status(thm)],[c_2690,c_1243]) ).
cnf(c_10355,plain,
join(complement(sk1),complement(one)) = join(complement(composition(sk1,top)),complement(one)),
inference(paramod,[status(thm)],[c_1179,c_10354]) ).
cnf(c_10356,plain,
join(complement(one),complement(sk1)) = join(complement(composition(sk1,top)),complement(one)),
inference(paramod,[status(thm)],[c_1,c_10355]) ).
cnf(c_10357,plain,
complement(sk1) = join(complement(composition(sk1,top)),complement(one)),
inference(paramod,[status(thm)],[c_685,c_10356]) ).
cnf(c_10358,plain,
complement(sk1) = join(complement(one),complement(composition(sk1,top))),
inference(paramod,[status(thm)],[c_1,c_10357]) ).
cnf(c_2716,plain,
join(complement(one),complement(composition(sk1,top))) = complement(sk1),
inference(copy,[status(thm)],[c_10358]) ).
cnf(c_10359,plain,
converse(complement(sk1)) = join(converse(complement(one)),converse(complement(composition(sk1,top)))),
inference(paramod,[status(thm)],[c_2716,c_12]) ).
cnf(c_10360,plain,
complement(converse(sk1)) = join(converse(complement(one)),converse(complement(composition(sk1,top)))),
inference(paramod,[status(thm)],[c_1875,c_10359]) ).
cnf(c_10361,plain,
complement(converse(sk1)) = join(complement(converse(one)),converse(complement(composition(sk1,top)))),
inference(paramod,[status(thm)],[c_1875,c_10360]) ).
cnf(c_10362,plain,
complement(converse(sk1)) = join(complement(one),converse(complement(composition(sk1,top)))),
inference(paramod,[status(thm)],[c_100,c_10361]) ).
cnf(c_10363,plain,
complement(converse(sk1)) = join(complement(one),complement(converse(composition(sk1,top)))),
inference(paramod,[status(thm)],[c_1875,c_10362]) ).
cnf(c_10364,plain,
complement(converse(sk1)) = join(complement(one),complement(composition(converse(top),converse(sk1)))),
inference(paramod,[status(thm)],[c_13,c_10363]) ).
cnf(c_10365,plain,
complement(converse(sk1)) = join(complement(one),complement(composition(top,converse(sk1)))),
inference(paramod,[status(thm)],[c_463,c_10364]) ).
cnf(c_2723,plain,
join(complement(one),complement(composition(top,converse(sk1)))) = complement(converse(sk1)),
inference(copy,[status(thm)],[c_10365]) ).
cnf(c_10366,plain,
converse(zero) = composition(converse(complement(composition(converse(A),top))),converse(A)),
inference(paramod,[status(thm)],[c_368,c_13]) ).
cnf(c_10367,plain,
zero = composition(converse(complement(composition(converse(A),top))),converse(A)),
inference(paramod,[status(thm)],[c_275,c_10366]) ).
cnf(c_10368,plain,
zero = composition(complement(converse(composition(converse(A),top))),converse(A)),
inference(paramod,[status(thm)],[c_1875,c_10367]) ).
cnf(c_10369,plain,
zero = composition(complement(composition(converse(top),converse(converse(A)))),converse(A)),
inference(paramod,[status(thm)],[c_13,c_10368]) ).
cnf(c_10370,plain,
zero = composition(complement(composition(top,converse(converse(A)))),converse(A)),
inference(paramod,[status(thm)],[c_463,c_10369]) ).
cnf(c_10371,plain,
zero = composition(complement(composition(top,A)),converse(A)),
inference(paramod,[status(thm)],[c_11,c_10370]) ).
cnf(c_2870,plain,
composition(complement(composition(top,A)),converse(A)) = zero,
inference(copy,[status(thm)],[c_10371]) ).
cnf(c_10372,plain,
join(zero,composition(complement(complement(composition(top,A))),converse(A))) = composition(top,converse(A)),
inference(paramod,[status(thm)],[c_2870,c_48]) ).
cnf(c_10373,plain,
join(zero,composition(composition(top,A),converse(A))) = composition(top,converse(A)),
inference(paramod,[status(thm)],[c_88,c_10372]) ).
cnf(c_10374,plain,
join(zero,composition(top,composition(A,converse(A)))) = composition(top,converse(A)),
inference(paramod,[status(thm)],[c_8,c_10373]) ).
cnf(c_2925,plain,
composition(top,composition(A,converse(A))) = composition(top,converse(A)),
inference(paramod,[status(thm)],[c_179,c_10374]) ).
cnf(c_10375,plain,
join(zero,composition(complement(complement(composition(top,converse(A)))),A)) = composition(top,A),
inference(paramod,[status(thm)],[c_1924,c_48]) ).
cnf(c_10376,plain,
join(zero,composition(composition(top,converse(A)),A)) = composition(top,A),
inference(paramod,[status(thm)],[c_88,c_10375]) ).
cnf(c_10377,plain,
join(zero,composition(top,composition(converse(A),A))) = composition(top,A),
inference(paramod,[status(thm)],[c_8,c_10376]) ).
cnf(c_3361,plain,
composition(top,composition(converse(A),A)) = composition(top,A),
inference(paramod,[status(thm)],[c_179,c_10377]) ).
cnf(c_10378,plain,
join(complement(complement(composition(A,sk1))),complement(composition(complement(A),sk1))) = complement(composition(complement(A),sk1)),
inference(paramod,[status(thm)],[c_1262,c_2257]) ).
cnf(c_10379,plain,
join(composition(A,sk1),complement(composition(complement(A),sk1))) = complement(composition(complement(A),sk1)),
inference(paramod,[status(thm)],[c_88,c_10378]) ).
cnf(c_10380,plain,
join(composition(A,sk1),complement(composition(top,sk1))) = complement(composition(complement(A),sk1)),
inference(paramod,[status(thm)],[c_1686,c_10379]) ).
cnf(c_3728,plain,
complement(composition(complement(A),sk1)) = join(composition(A,sk1),complement(composition(top,sk1))),
inference(copy,[status(thm)],[c_10380]) ).
cnf(c_10381,plain,
join(complement(complement(A)),complement(composition(complement(A),sk1))) = complement(composition(complement(A),sk1)),
inference(paramod,[status(thm)],[c_246,c_2257]) ).
cnf(c_10382,plain,
join(A,complement(composition(complement(A),sk1))) = complement(composition(complement(A),sk1)),
inference(paramod,[status(thm)],[c_88,c_10381]) ).
cnf(c_10383,plain,
join(A,join(composition(A,sk1),complement(composition(top,sk1)))) = complement(composition(complement(A),sk1)),
inference(paramod,[status(thm)],[c_3728,c_10382]) ).
cnf(c_10384,plain,
join(A,complement(composition(top,sk1))) = complement(composition(complement(A),sk1)),
inference(paramod,[status(thm)],[c_769,c_10383]) ).
cnf(c_10385,plain,
join(A,complement(composition(top,sk1))) = join(composition(A,sk1),complement(composition(top,sk1))),
inference(paramod,[status(thm)],[c_3728,c_10384]) ).
cnf(c_3733,plain,
join(composition(A,sk1),complement(composition(top,sk1))) = join(A,complement(composition(top,sk1))),
inference(copy,[status(thm)],[c_10385]) ).
cnf(c_3750,plain,
complement(composition(complement(A),sk1)) = join(A,complement(composition(top,sk1))),
inference(paramod,[status(thm)],[c_3733,c_3728]) ).
cnf(c_3766,plain,
complement(composition(A,sk1)) = join(complement(A),complement(composition(top,sk1))),
inference(paramod,[status(thm)],[c_88,c_3750]) ).
cnf(c_10386,plain,
complement(zero) = join(composition(top,converse(sk1)),complement(composition(top,sk1))),
inference(paramod,[status(thm)],[c_1924,c_3750]) ).
cnf(c_10387,plain,
top = join(composition(top,converse(sk1)),complement(composition(top,sk1))),
inference(paramod,[status(thm)],[c_209,c_10386]) ).
cnf(c_10388,plain,
top = join(complement(composition(top,sk1)),composition(top,converse(sk1))),
inference(paramod,[status(thm)],[c_1,c_10387]) ).
cnf(c_3778,plain,
join(complement(composition(top,sk1)),composition(top,converse(sk1))) = top,
inference(copy,[status(thm)],[c_10388]) ).
cnf(c_10389,plain,
join(composition(top,converse(sk1)),complement(top)) = join(complement(complement(composition(top,sk1))),composition(top,converse(sk1))),
inference(paramod,[status(thm)],[c_3778,c_1179]) ).
cnf(c_10390,plain,
join(composition(top,converse(sk1)),zero) = join(complement(complement(composition(top,sk1))),composition(top,converse(sk1))),
inference(paramod,[status(thm)],[c_19,c_10389]) ).
cnf(c_10391,plain,
join(zero,composition(top,converse(sk1))) = join(complement(complement(composition(top,sk1))),composition(top,converse(sk1))),
inference(paramod,[status(thm)],[c_1,c_10390]) ).
cnf(c_10392,plain,
composition(top,converse(sk1)) = join(complement(complement(composition(top,sk1))),composition(top,converse(sk1))),
inference(paramod,[status(thm)],[c_179,c_10391]) ).
cnf(c_10393,plain,
composition(top,converse(sk1)) = join(composition(top,sk1),composition(top,converse(sk1))),
inference(paramod,[status(thm)],[c_88,c_10392]) ).
cnf(c_4071,plain,
join(composition(top,sk1),composition(top,converse(sk1))) = composition(top,converse(sk1)),
inference(copy,[status(thm)],[c_10393]) ).
cnf(c_10394,plain,
converse(complement(composition(A,sk1))) = join(converse(complement(A)),converse(complement(composition(top,sk1)))),
inference(paramod,[status(thm)],[c_3766,c_12]) ).
cnf(c_10395,plain,
complement(converse(composition(A,sk1))) = join(converse(complement(A)),converse(complement(composition(top,sk1)))),
inference(paramod,[status(thm)],[c_1875,c_10394]) ).
cnf(c_10396,plain,
complement(composition(converse(sk1),converse(A))) = join(converse(complement(A)),converse(complement(composition(top,sk1)))),
inference(paramod,[status(thm)],[c_13,c_10395]) ).
cnf(c_10397,plain,
complement(composition(converse(sk1),converse(A))) = join(complement(converse(A)),converse(complement(composition(top,sk1)))),
inference(paramod,[status(thm)],[c_1875,c_10396]) ).
cnf(c_10398,plain,
complement(composition(converse(sk1),converse(A))) = join(complement(converse(A)),complement(converse(composition(top,sk1)))),
inference(paramod,[status(thm)],[c_1875,c_10397]) ).
cnf(c_10399,plain,
complement(composition(converse(sk1),converse(A))) = join(complement(converse(A)),complement(composition(converse(sk1),converse(top)))),
inference(paramod,[status(thm)],[c_13,c_10398]) ).
cnf(c_4082,plain,
complement(composition(converse(sk1),converse(A))) = join(complement(converse(A)),complement(composition(converse(sk1),top))),
inference(paramod,[status(thm)],[c_463,c_10399]) ).
cnf(c_10400,plain,
complement(sk1) = join(complement(one),complement(composition(top,sk1))),
inference(paramod,[status(thm)],[c_105,c_3766]) ).
cnf(c_4086,plain,
join(complement(one),complement(composition(top,sk1))) = complement(sk1),
inference(copy,[status(thm)],[c_10400]) ).
cnf(c_10401,plain,
join(complement(A),complement(complement(composition(A,sk1)))) = join(complement(complement(composition(top,sk1))),complement(A)),
inference(paramod,[status(thm)],[c_3766,c_1243]) ).
cnf(c_10402,plain,
join(complement(A),composition(A,sk1)) = join(complement(complement(composition(top,sk1))),complement(A)),
inference(paramod,[status(thm)],[c_88,c_10401]) ).
cnf(c_10403,plain,
join(complement(A),composition(A,sk1)) = join(composition(top,sk1),complement(A)),
inference(paramod,[status(thm)],[c_88,c_10402]) ).
cnf(c_4108,plain,
join(composition(top,sk1),complement(A)) = join(complement(A),composition(A,sk1)),
inference(copy,[status(thm)],[c_10403]) ).
cnf(c_10404,plain,
join(complement(composition(composition(top,sk1),converse(sk1))),composition(composition(composition(top,sk1),converse(sk1)),sk1)) = top,
inference(paramod,[status(thm)],[c_4108,c_1068]) ).
cnf(c_10405,plain,
join(complement(composition(top,composition(sk1,converse(sk1)))),composition(composition(composition(top,sk1),converse(sk1)),sk1)) = top,
inference(paramod,[status(thm)],[c_8,c_10404]) ).
cnf(c_10406,plain,
join(complement(composition(top,converse(sk1))),composition(composition(composition(top,sk1),converse(sk1)),sk1)) = top,
inference(paramod,[status(thm)],[c_2925,c_10405]) ).
cnf(c_10407,plain,
join(complement(composition(top,converse(sk1))),composition(composition(top,composition(sk1,converse(sk1))),sk1)) = top,
inference(paramod,[status(thm)],[c_8,c_10406]) ).
cnf(c_10408,plain,
join(complement(composition(top,converse(sk1))),composition(composition(top,converse(sk1)),sk1)) = top,
inference(paramod,[status(thm)],[c_2925,c_10407]) ).
cnf(c_10409,plain,
join(complement(composition(top,converse(sk1))),composition(top,composition(converse(sk1),sk1))) = top,
inference(paramod,[status(thm)],[c_8,c_10408]) ).
cnf(c_10410,plain,
join(complement(composition(top,converse(sk1))),composition(top,sk1)) = top,
inference(paramod,[status(thm)],[c_3361,c_10409]) ).
cnf(c_4182,plain,
join(composition(top,sk1),complement(composition(top,converse(sk1)))) = top,
inference(paramod,[status(thm)],[c_1,c_10410]) ).
cnf(c_10411,plain,
join(complement(composition(top,converse(sk1))),complement(join(composition(top,sk1),complement(composition(top,converse(sk1)))))) = complement(composition(top,sk1)),
inference(paramod,[status(thm)],[c_4071,c_330]) ).
cnf(c_10412,plain,
join(complement(composition(top,converse(sk1))),complement(top)) = complement(composition(top,sk1)),
inference(paramod,[status(thm)],[c_4182,c_10411]) ).
cnf(c_10413,plain,
join(complement(composition(top,converse(sk1))),zero) = complement(composition(top,sk1)),
inference(paramod,[status(thm)],[c_19,c_10412]) ).
cnf(c_10414,plain,
join(zero,complement(composition(top,converse(sk1)))) = complement(composition(top,sk1)),
inference(paramod,[status(thm)],[c_1,c_10413]) ).
cnf(c_4377,plain,
complement(composition(top,converse(sk1))) = complement(composition(top,sk1)),
inference(paramod,[status(thm)],[c_179,c_10414]) ).
cnf(c_10415,plain,
join(complement(one),complement(composition(top,sk1))) = complement(converse(sk1)),
inference(paramod,[status(thm)],[c_4377,c_2723]) ).
cnf(c_10416,plain,
complement(sk1) = complement(converse(sk1)),
inference(paramod,[status(thm)],[c_4086,c_10415]) ).
cnf(c_4388,plain,
complement(converse(sk1)) = complement(sk1),
inference(copy,[status(thm)],[c_10416]) ).
cnf(c_10417,plain,
complement(complement(sk1)) = converse(sk1),
inference(paramod,[status(thm)],[c_4388,c_88]) ).
cnf(c_10418,plain,
sk1 = converse(sk1),
inference(paramod,[status(thm)],[c_88,c_10417]) ).
cnf(c_4438,plain,
converse(sk1) = sk1,
inference(copy,[status(thm)],[c_10418]) ).
cnf(c_10419,plain,
complement(composition(sk1,converse(A))) = join(complement(converse(A)),complement(composition(converse(sk1),top))),
inference(paramod,[status(thm)],[c_4438,c_4082]) ).
cnf(c_10420,plain,
complement(composition(sk1,converse(A))) = join(complement(converse(A)),complement(composition(sk1,top))),
inference(paramod,[status(thm)],[c_4438,c_10419]) ).
cnf(c_4475,plain,
complement(composition(sk1,converse(A))) = join(complement(composition(sk1,top)),complement(converse(A))),
inference(paramod,[status(thm)],[c_1,c_10420]) ).
cnf(c_10421,plain,
complement(composition(sk1,A)) = join(complement(composition(sk1,top)),complement(converse(converse(A)))),
inference(paramod,[status(thm)],[c_11,c_4475]) ).
cnf(c_6418,plain,
complement(composition(sk1,A)) = join(complement(composition(sk1,top)),complement(A)),
inference(paramod,[status(thm)],[c_11,c_10421]) ).
cnf(c_10422,plain,
complement(join(join(complement(composition(sk1,top)),complement(sk2)),composition(sk1,sk3))) != complement(join(sk3,complement(composition(sk1,sk2)))),
inference(paramod,[status(thm)],[c_6418,c_91]) ).
cnf(c_10423,plain,
complement(join(join(complement(sk2),complement(composition(sk1,top))),composition(sk1,sk3))) != complement(join(sk3,complement(composition(sk1,sk2)))),
inference(paramod,[status(thm)],[c_1,c_10422]) ).
cnf(c_6489,plain,
complement(join(complement(sk2),join(complement(composition(sk1,top)),composition(sk1,sk3)))) != complement(join(sk3,complement(composition(sk1,sk2)))),
inference(paramod,[status(thm)],[c_3,c_10423]) ).
cnf(c_10424,plain,
join(complement(composition(sk1,top)),complement(complement(composition(sk1,A)))) = join(complement(complement(A)),complement(composition(sk1,top))),
inference(paramod,[status(thm)],[c_6418,c_1243]) ).
cnf(c_10425,plain,
join(complement(composition(sk1,top)),composition(sk1,A)) = join(complement(complement(A)),complement(composition(sk1,top))),
inference(paramod,[status(thm)],[c_88,c_10424]) ).
cnf(c_6517,plain,
join(complement(composition(sk1,top)),composition(sk1,A)) = join(A,complement(composition(sk1,top))),
inference(paramod,[status(thm)],[c_88,c_10425]) ).
cnf(c_10426,plain,
complement(join(complement(sk2),join(complement(composition(sk1,top)),composition(sk1,sk3)))) != complement(join(sk3,join(complement(composition(sk1,top)),complement(sk2)))),
inference(paramod,[status(thm)],[c_6418,c_6489]) ).
cnf(c_6987,plain,
complement(join(complement(sk2),join(complement(composition(sk1,top)),composition(sk1,sk3)))) != complement(join(sk3,join(complement(sk2),complement(composition(sk1,top))))),
inference(paramod,[status(thm)],[c_1,c_10426]) ).
cnf(c_10427,plain,
complement(join(complement(sk2),join(sk3,complement(composition(sk1,top))))) != complement(join(sk3,join(complement(sk2),complement(composition(sk1,top))))),
inference(paramod,[status(thm)],[c_6517,c_6987]) ).
cnf(c_10428,plain,
complement(join(sk3,join(complement(sk2),complement(composition(sk1,top))))) != complement(join(sk3,join(complement(sk2),complement(composition(sk1,top))))),
inference(paramod,[status(thm)],[c_25,c_10427]) ).
cnf(c_10197,plain,
$false,
inference(copy,[status(thm)],[c_10428]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : REL030-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/5.66 % Computer : n006.cluster.edu
% 0.19/5.66 % Model : x86_64 x86_64
% 0.19/5.66 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/5.66 % Memory : 8046.5625MB
% 0.19/5.66 % OS : Linux 6.8.0-71-generic
% 0.19/5.67 % CPULimit : 300
% 0.19/5.67 % WCLimit : 300
% 0.19/5.67 % DateTime : Sat Sep 26 05:34:18 UTC 2026
% 0.19/5.67 % CPUTime :
% 0.19/5.67 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/5.67 % Process 473314 was started by sandbox2 on n006,
% 0.19/5.67 % Sat Sep 26 05:34:18 2026
% 0.19/5.67 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/5.67
% 0.19/5.67 % From the command line: assign(max_seconds, 300).
% 44.00/12.01
% 44.00/12.01 % SZS status Unsatisfiable for theBenchmark
% 44.00/12.01
% 44.00/12.01 % Proof 1 at 4.84 (+ 1.04) seconds.
% 44.00/12.01 % Length of proof is 139.
% 44.00/12.01 % Level of proof is 29.
% 44.00/12.01 % Maximum clause weight is 93.000.
% 44.00/12.01 % Given clauses 469.
% 44.00/12.01
% 44.00/12.01 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------