%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL029-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 08:24:57 AM UTC 2026
% Result : Unsatisfiable 110.33s 28.91s
% Output : CNFRefutation 110.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 137
% Number of leaves : 19
% Syntax : Number of formulae : 643 ( 643 unt; 0 def)
% Number of atoms : 643 ( 642 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 35 ( 35 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 11 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 585 ( 29 sgn 34 !; 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_11354,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_11354]) ).
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_11355,plain,
zero = complement(join(complement(A),complement(complement(A)))),
inference(paramod,[status(thm)],[c_6,c_18]) ).
cnf(c_11356,plain,
zero = complement(top),
inference(paramod,[status(thm)],[c_17,c_11355]) ).
cnf(c_19,plain,
complement(top) = zero,
inference(copy,[status(thm)],[c_11356]) ).
fof(dedekind_law_14,axiom,
! [VAR_0,VAR_1,VAR_2] : join(meet(composition(VAR_0,VAR_1),VAR_2),composition(meet(VAR_0,composition(VAR_2,converse(VAR_1))),meet(VAR_1,composition(converse(VAR_0),VAR_2)))) = composition(meet(VAR_0,composition(VAR_2,converse(VAR_1))),meet(VAR_1,composition(converse(VAR_0),VAR_2))),
file('theBenchmark.p',dedekind_law_14) ).
cnf(c_20,plain,
join(meet(composition(A,B),C),composition(meet(A,composition(C,converse(B))),meet(B,composition(converse(A),C)))) = composition(meet(A,composition(C,converse(B))),meet(B,composition(converse(A),C))),
inference(clausify,[status(thm)],[dedekind_law_14]) ).
cnf(c_11357,plain,
join(complement(join(complement(composition(A,B)),complement(C))),composition(meet(A,composition(C,converse(B))),meet(B,composition(converse(A),C)))) = composition(meet(A,composition(C,converse(B))),meet(B,composition(converse(A),C))),
inference(paramod,[status(thm)],[c_6,c_20]) ).
cnf(c_11358,plain,
join(complement(join(complement(composition(A,B)),complement(C))),composition(complement(join(complement(A),complement(composition(C,converse(B))))),meet(B,composition(converse(A),C)))) = composition(meet(A,composition(C,converse(B))),meet(B,composition(converse(A),C))),
inference(paramod,[status(thm)],[c_6,c_11357]) ).
cnf(c_11359,plain,
join(complement(join(complement(composition(A,B)),complement(C))),composition(complement(join(complement(A),complement(composition(C,converse(B))))),complement(join(complement(B),complement(composition(converse(A),C)))))) = composition(meet(A,composition(C,converse(B))),meet(B,composition(converse(A),C))),
inference(paramod,[status(thm)],[c_6,c_11358]) ).
cnf(c_11360,plain,
join(complement(join(complement(composition(A,B)),complement(C))),composition(complement(join(complement(A),complement(composition(C,converse(B))))),complement(join(complement(B),complement(composition(converse(A),C)))))) = composition(complement(join(complement(A),complement(composition(C,converse(B))))),meet(B,composition(converse(A),C))),
inference(paramod,[status(thm)],[c_6,c_11359]) ).
cnf(c_21,plain,
join(complement(join(complement(composition(A,B)),complement(C))),composition(complement(join(complement(A),complement(composition(C,converse(B))))),complement(join(complement(B),complement(composition(converse(A),C)))))) = composition(complement(join(complement(A),complement(composition(C,converse(B))))),complement(join(complement(B),complement(composition(converse(A),C))))),
inference(paramod,[status(thm)],[c_6,c_11360]) ).
fof(modular_law_1_15,axiom,
! [VAR_0,VAR_1,VAR_2] : join(meet(composition(VAR_0,VAR_1),VAR_2),meet(composition(VAR_0,meet(VAR_1,composition(converse(VAR_0),VAR_2))),VAR_2)) = meet(composition(VAR_0,meet(VAR_1,composition(converse(VAR_0),VAR_2))),VAR_2),
file('theBenchmark.p',modular_law_1_15) ).
cnf(c_22,plain,
join(meet(composition(A,B),C),meet(composition(A,meet(B,composition(converse(A),C))),C)) = meet(composition(A,meet(B,composition(converse(A),C))),C),
inference(clausify,[status(thm)],[modular_law_1_15]) ).
cnf(c_11361,plain,
join(complement(join(complement(composition(A,B)),complement(C))),meet(composition(A,meet(B,composition(converse(A),C))),C)) = meet(composition(A,meet(B,composition(converse(A),C))),C),
inference(paramod,[status(thm)],[c_6,c_22]) ).
cnf(c_11362,plain,
join(complement(join(complement(composition(A,B)),complement(C))),meet(composition(A,complement(join(complement(B),complement(composition(converse(A),C))))),C)) = meet(composition(A,meet(B,composition(converse(A),C))),C),
inference(paramod,[status(thm)],[c_6,c_11361]) ).
cnf(c_11363,plain,
join(complement(join(complement(composition(A,B)),complement(C))),complement(join(complement(composition(A,complement(join(complement(B),complement(composition(converse(A),C)))))),complement(C)))) = meet(composition(A,meet(B,composition(converse(A),C))),C),
inference(paramod,[status(thm)],[c_6,c_11362]) ).
cnf(c_11364,plain,
join(complement(join(complement(composition(A,B)),complement(C))),complement(join(complement(C),complement(composition(A,complement(join(complement(B),complement(composition(converse(A),C))))))))) = meet(composition(A,meet(B,composition(converse(A),C))),C),
inference(paramod,[status(thm)],[c_1,c_11363]) ).
cnf(c_11365,plain,
join(complement(join(complement(composition(A,B)),complement(C))),complement(join(complement(C),complement(composition(A,complement(join(complement(B),complement(composition(converse(A),C))))))))) = meet(composition(A,complement(join(complement(B),complement(composition(converse(A),C))))),C),
inference(paramod,[status(thm)],[c_6,c_11364]) ).
cnf(c_11366,plain,
join(complement(join(complement(composition(A,B)),complement(C))),complement(join(complement(C),complement(composition(A,complement(join(complement(B),complement(composition(converse(A),C))))))))) = complement(join(complement(composition(A,complement(join(complement(B),complement(composition(converse(A),C)))))),complement(C))),
inference(paramod,[status(thm)],[c_6,c_11365]) ).
cnf(c_23,plain,
join(complement(join(complement(composition(A,B)),complement(C))),complement(join(complement(C),complement(composition(A,complement(join(complement(B),complement(composition(converse(A),C))))))))) = complement(join(complement(C),complement(composition(A,complement(join(complement(B),complement(composition(converse(A),C)))))))),
inference(paramod,[status(thm)],[c_1,c_11366]) ).
fof(modular_law_2_16,axiom,
! [VAR_0,VAR_1,VAR_2] : join(meet(composition(VAR_0,VAR_1),VAR_2),meet(composition(meet(VAR_0,composition(VAR_2,converse(VAR_1))),VAR_1),VAR_2)) = meet(composition(meet(VAR_0,composition(VAR_2,converse(VAR_1))),VAR_1),VAR_2),
file('theBenchmark.p',modular_law_2_16) ).
cnf(c_24,plain,
join(meet(composition(A,B),C),meet(composition(meet(A,composition(C,converse(B))),B),C)) = meet(composition(meet(A,composition(C,converse(B))),B),C),
inference(clausify,[status(thm)],[modular_law_2_16]) ).
cnf(c_11367,plain,
join(complement(join(complement(composition(A,B)),complement(C))),meet(composition(meet(A,composition(C,converse(B))),B),C)) = meet(composition(meet(A,composition(C,converse(B))),B),C),
inference(paramod,[status(thm)],[c_6,c_24]) ).
cnf(c_11368,plain,
join(complement(join(complement(composition(A,B)),complement(C))),meet(composition(complement(join(complement(A),complement(composition(C,converse(B))))),B),C)) = meet(composition(meet(A,composition(C,converse(B))),B),C),
inference(paramod,[status(thm)],[c_6,c_11367]) ).
cnf(c_11369,plain,
join(complement(join(complement(composition(A,B)),complement(C))),complement(join(complement(composition(complement(join(complement(A),complement(composition(C,converse(B))))),B)),complement(C)))) = meet(composition(meet(A,composition(C,converse(B))),B),C),
inference(paramod,[status(thm)],[c_6,c_11368]) ).
cnf(c_11370,plain,
join(complement(join(complement(composition(A,B)),complement(C))),complement(join(complement(C),complement(composition(complement(join(complement(A),complement(composition(C,converse(B))))),B))))) = meet(composition(meet(A,composition(C,converse(B))),B),C),
inference(paramod,[status(thm)],[c_1,c_11369]) ).
cnf(c_11371,plain,
join(complement(join(complement(composition(A,B)),complement(C))),complement(join(complement(C),complement(composition(complement(join(complement(A),complement(composition(C,converse(B))))),B))))) = meet(composition(complement(join(complement(A),complement(composition(C,converse(B))))),B),C),
inference(paramod,[status(thm)],[c_6,c_11370]) ).
cnf(c_11372,plain,
join(complement(join(complement(composition(A,B)),complement(C))),complement(join(complement(C),complement(composition(complement(join(complement(A),complement(composition(C,converse(B))))),B))))) = complement(join(complement(composition(complement(join(complement(A),complement(composition(C,converse(B))))),B)),complement(C))),
inference(paramod,[status(thm)],[c_6,c_11371]) ).
cnf(c_25,plain,
join(complement(join(complement(composition(A,B)),complement(C))),complement(join(complement(C),complement(composition(complement(join(complement(A),complement(composition(C,converse(B))))),B))))) = complement(join(complement(C),complement(composition(complement(join(complement(A),complement(composition(C,converse(B))))),B)))),
inference(paramod,[status(thm)],[c_1,c_11372]) ).
fof(goals_17,axiom,
join(sk1,one) = one,
file('theBenchmark.p',goals_17) ).
cnf(c_26,plain,
join(sk1,one) = one,
inference(clausify,[status(thm)],[goals_17]) ).
cnf(c_27,plain,
join(one,sk1) = one,
inference(paramod,[status(thm)],[c_1,c_26]) ).
fof(goals_18,axiom,
join(sk2,one) = one,
file('theBenchmark.p',goals_18) ).
cnf(c_28,plain,
join(sk2,one) = one,
inference(clausify,[status(thm)],[goals_18]) ).
cnf(c_29,plain,
join(one,sk2) = one,
inference(paramod,[status(thm)],[c_1,c_28]) ).
fof(goals_19,axiom,
tuple(join(meet(composition(sk1,sk3),composition(sk2,sk3)),composition(meet(sk1,sk2),sk3)),join(composition(meet(sk1,sk2),sk3),meet(composition(sk1,sk3),composition(sk2,sk3)))) != tuple(composition(meet(sk1,sk2),sk3),meet(composition(sk1,sk3),composition(sk2,sk3))),
file('theBenchmark.p',goals_19) ).
cnf(c_30,plain,
tuple(join(meet(composition(sk1,sk3),composition(sk2,sk3)),composition(meet(sk1,sk2),sk3)),join(composition(meet(sk1,sk2),sk3),meet(composition(sk1,sk3),composition(sk2,sk3)))) != tuple(composition(meet(sk1,sk2),sk3),meet(composition(sk1,sk3),composition(sk2,sk3))),
inference(clausify,[status(thm)],[goals_19]) ).
cnf(c_11373,plain,
tuple(join(complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3)))),composition(meet(sk1,sk2),sk3)),join(composition(meet(sk1,sk2),sk3),meet(composition(sk1,sk3),composition(sk2,sk3)))) != tuple(composition(meet(sk1,sk2),sk3),meet(composition(sk1,sk3),composition(sk2,sk3))),
inference(paramod,[status(thm)],[c_6,c_30]) ).
cnf(c_11374,plain,
tuple(join(complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3)))),composition(complement(join(complement(sk1),complement(sk2))),sk3)),join(composition(meet(sk1,sk2),sk3),meet(composition(sk1,sk3),composition(sk2,sk3)))) != tuple(composition(meet(sk1,sk2),sk3),meet(composition(sk1,sk3),composition(sk2,sk3))),
inference(paramod,[status(thm)],[c_6,c_11373]) ).
cnf(c_11375,plain,
tuple(join(complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3)))),composition(complement(join(complement(sk1),complement(sk2))),sk3)),join(composition(complement(join(complement(sk1),complement(sk2))),sk3),meet(composition(sk1,sk3),composition(sk2,sk3)))) != tuple(composition(meet(sk1,sk2),sk3),meet(composition(sk1,sk3),composition(sk2,sk3))),
inference(paramod,[status(thm)],[c_6,c_11374]) ).
cnf(c_11376,plain,
tuple(join(complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3)))),composition(complement(join(complement(sk1),complement(sk2))),sk3)),join(composition(complement(join(complement(sk1),complement(sk2))),sk3),complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3)))))) != tuple(composition(meet(sk1,sk2),sk3),meet(composition(sk1,sk3),composition(sk2,sk3))),
inference(paramod,[status(thm)],[c_6,c_11375]) ).
cnf(c_11377,plain,
tuple(join(complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3)))),composition(complement(join(complement(sk1),complement(sk2))),sk3)),join(complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3)))),composition(complement(join(complement(sk1),complement(sk2))),sk3))) != tuple(composition(meet(sk1,sk2),sk3),meet(composition(sk1,sk3),composition(sk2,sk3))),
inference(paramod,[status(thm)],[c_1,c_11376]) ).
cnf(c_11378,plain,
tuple(join(complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3)))),composition(complement(join(complement(sk1),complement(sk2))),sk3)),join(complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3)))),composition(complement(join(complement(sk1),complement(sk2))),sk3))) != tuple(composition(complement(join(complement(sk1),complement(sk2))),sk3),meet(composition(sk1,sk3),composition(sk2,sk3))),
inference(paramod,[status(thm)],[c_6,c_11377]) ).
cnf(c_31,plain,
tuple(join(complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3)))),composition(complement(join(complement(sk1),complement(sk2))),sk3)),join(complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3)))),composition(complement(join(complement(sk1),complement(sk2))),sk3))) != tuple(composition(complement(join(complement(sk1),complement(sk2))),sk3),complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3))))),
inference(paramod,[status(thm)],[c_6,c_11378]) ).
cnf(c_11379,plain,
join(join(A,B),C) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_33,plain,
join(A,join(B,C)) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_3,c_11379]) ).
cnf(c_34,plain,
join(complement(join(A,complement(B))),complement(join(complement(B),complement(A)))) = B,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_35,plain,
join(complement(join(complement(A),B)),complement(join(complement(B),complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_11380,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_36,plain,
join(complement(join(complement(A),B)),join(complement(join(complement(A),complement(B))),C)) = join(A,C),
inference(copy,[status(thm)],[c_11380]) ).
cnf(c_11381,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_11382,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_11381]) ).
cnf(c_11383,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_11382]) ).
cnf(c_38,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_11383]) ).
cnf(c_11384,plain,
composition(A,B) = join(composition(complement(join(complement(A),C)),B),composition(complement(join(complement(A),complement(C))),B)),
inference(paramod,[status(thm)],[c_5,c_10]) ).
cnf(c_40,plain,
join(composition(complement(join(complement(A),B)),C),composition(complement(join(complement(A),complement(B))),C)) = composition(A,C),
inference(copy,[status(thm)],[c_11384]) ).
cnf(c_11385,plain,
converse(A) = composition(converse(one),converse(A)),
inference(paramod,[status(thm)],[c_9,c_13]) ).
cnf(c_42,plain,
composition(converse(one),converse(A)) = converse(A),
inference(copy,[status(thm)],[c_11385]) ).
cnf(c_11386,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_44,plain,
join(complement(A),join(composition(converse(B),complement(composition(B,A))),C)) = join(complement(A),C),
inference(copy,[status(thm)],[c_11386]) ).
cnf(c_11387,plain,
join(top,A) = join(B,join(complement(B),A)),
inference(paramod,[status(thm)],[c_17,c_3]) ).
cnf(c_52,plain,
join(A,join(complement(A),B)) = join(top,B),
inference(copy,[status(thm)],[c_11387]) ).
cnf(c_11388,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_17,c_5]) ).
cnf(c_54,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_19,c_11388]) ).
cnf(c_11389,plain,
join(complement(join(complement(A),complement(A))),complement(top)) = A,
inference(paramod,[status(thm)],[c_17,c_5]) ).
cnf(c_11390,plain,
join(complement(join(complement(A),complement(A))),zero) = A,
inference(paramod,[status(thm)],[c_19,c_11389]) ).
cnf(c_55,plain,
join(zero,complement(join(complement(A),complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_11390]) ).
cnf(c_11391,plain,
composition(top,A) = join(composition(B,A),composition(complement(B),A)),
inference(paramod,[status(thm)],[c_17,c_10]) ).
cnf(c_56,plain,
join(composition(A,B),composition(complement(A),B)) = composition(top,B),
inference(copy,[status(thm)],[c_11391]) ).
cnf(c_11392,plain,
converse(top) = join(converse(A),converse(complement(A))),
inference(paramod,[status(thm)],[c_17,c_12]) ).
cnf(c_57,plain,
join(converse(A),converse(complement(A))) = converse(top),
inference(copy,[status(thm)],[c_11392]) ).
cnf(c_62,plain,
join(complement(join(complement(A),complement(composition(B,C)))),composition(complement(join(complement(B),complement(composition(A,converse(C))))),complement(join(complement(C),complement(composition(converse(B),A)))))) = composition(complement(join(complement(B),complement(composition(A,converse(C))))),complement(join(complement(C),complement(composition(converse(B),A))))),
inference(paramod,[status(thm)],[c_1,c_21]) ).
cnf(c_65,plain,
join(complement(join(complement(A),complement(B))),composition(complement(join(complement(A),complement(composition(B,converse(one))))),complement(join(complement(one),complement(composition(converse(A),B)))))) = composition(complement(join(complement(A),complement(composition(B,converse(one))))),complement(join(complement(one),complement(composition(converse(A),B))))),
inference(paramod,[status(thm)],[c_9,c_21]) ).
cnf(c_11393,plain,
join(complement(join(complement(composition(converse(A),B)),complement(C))),composition(complement(join(complement(converse(A)),complement(composition(C,converse(B))))),complement(join(complement(B),complement(composition(A,C)))))) = composition(complement(join(complement(converse(A)),complement(composition(C,converse(B))))),complement(join(complement(B),complement(composition(converse(converse(A)),C))))),
inference(paramod,[status(thm)],[c_11,c_21]) ).
cnf(c_68,plain,
join(complement(join(complement(composition(converse(A),B)),complement(C))),composition(complement(join(complement(converse(A)),complement(composition(C,converse(B))))),complement(join(complement(B),complement(composition(A,C)))))) = composition(complement(join(complement(converse(A)),complement(composition(C,converse(B))))),complement(join(complement(B),complement(composition(A,C))))),
inference(paramod,[status(thm)],[c_11,c_11393]) ).
cnf(c_11394,plain,
join(complement(join(complement(composition(converse(A),B)),complement(C))),complement(join(complement(C),complement(composition(converse(A),complement(join(complement(B),complement(composition(A,C))))))))) = complement(join(complement(C),complement(composition(converse(A),complement(join(complement(B),complement(composition(converse(converse(A)),C)))))))),
inference(paramod,[status(thm)],[c_11,c_23]) ).
cnf(c_78,plain,
join(complement(join(complement(composition(converse(A),B)),complement(C))),complement(join(complement(C),complement(composition(converse(A),complement(join(complement(B),complement(composition(A,C))))))))) = complement(join(complement(C),complement(composition(converse(A),complement(join(complement(B),complement(composition(A,C)))))))),
inference(paramod,[status(thm)],[c_11,c_11394]) ).
cnf(c_11395,plain,
join(one,A) = join(one,join(sk1,A)),
inference(paramod,[status(thm)],[c_27,c_3]) ).
cnf(c_87,plain,
join(one,join(sk1,A)) = join(one,A),
inference(copy,[status(thm)],[c_11395]) ).
cnf(c_11396,plain,
composition(one,A) = join(composition(one,A),composition(sk1,A)),
inference(paramod,[status(thm)],[c_27,c_10]) ).
cnf(c_89,plain,
join(composition(one,A),composition(sk1,A)) = composition(one,A),
inference(copy,[status(thm)],[c_11396]) ).
cnf(c_11397,plain,
converse(one) = join(converse(one),converse(sk1)),
inference(paramod,[status(thm)],[c_27,c_12]) ).
cnf(c_90,plain,
join(converse(one),converse(sk1)) = converse(one),
inference(copy,[status(thm)],[c_11397]) ).
cnf(c_11398,plain,
join(one,A) = join(one,join(sk2,A)),
inference(paramod,[status(thm)],[c_29,c_3]) ).
cnf(c_91,plain,
join(one,join(sk2,A)) = join(one,A),
inference(copy,[status(thm)],[c_11398]) ).
cnf(c_11399,plain,
join(join(A,one),sk2) = join(A,one),
inference(paramod,[status(thm)],[c_29,c_3]) ).
cnf(c_92,plain,
join(sk2,join(A,one)) = join(A,one),
inference(paramod,[status(thm)],[c_1,c_11399]) ).
cnf(c_11400,plain,
composition(one,A) = join(composition(one,A),composition(sk2,A)),
inference(paramod,[status(thm)],[c_29,c_10]) ).
cnf(c_93,plain,
join(composition(one,A),composition(sk2,A)) = composition(one,A),
inference(copy,[status(thm)],[c_11400]) ).
cnf(c_11401,plain,
converse(one) = join(converse(one),converse(sk2)),
inference(paramod,[status(thm)],[c_29,c_12]) ).
cnf(c_94,plain,
join(converse(one),converse(sk2)) = converse(one),
inference(copy,[status(thm)],[c_11401]) ).
cnf(c_11402,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_33]) ).
cnf(c_96,plain,
join(complement(join(complement(A),B)),join(C,complement(join(complement(A),complement(B))))) = join(C,A),
inference(copy,[status(thm)],[c_11402]) ).
cnf(c_11403,plain,
A = join(complement(join(complement(A),complement(B))),complement(join(B,complement(A)))),
inference(paramod,[status(thm)],[c_34,c_1]) ).
cnf(c_101,plain,
join(complement(join(complement(A),complement(B))),complement(join(B,complement(A)))) = A,
inference(copy,[status(thm)],[c_11403]) ).
cnf(c_102,plain,
join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B,
inference(paramod,[status(thm)],[c_1,c_34]) ).
cnf(c_104,plain,
join(complement(join(A,join(B,complement(C)))),complement(join(complement(C),complement(join(A,B))))) = C,
inference(paramod,[status(thm)],[c_3,c_34]) ).
cnf(c_11404,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_42]) ).
cnf(c_119,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_11,c_11404]) ).
cnf(c_11405,plain,
join(complement(join(complement(composition(A,B)),complement(converse(one)))),complement(join(complement(converse(one)),complement(composition(complement(join(complement(A),complement(converse(B)))),B))))) = complement(join(complement(converse(one)),complement(composition(complement(join(complement(A),complement(composition(converse(one),converse(B))))),B)))),
inference(paramod,[status(thm)],[c_42,c_25]) ).
cnf(c_127,plain,
join(complement(join(complement(composition(A,B)),complement(converse(one)))),complement(join(complement(converse(one)),complement(composition(complement(join(complement(A),complement(converse(B)))),B))))) = complement(join(complement(converse(one)),complement(composition(complement(join(complement(A),complement(converse(B)))),B)))),
inference(paramod,[status(thm)],[c_119,c_11405]) ).
cnf(c_11406,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_119,c_9]) ).
cnf(c_128,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_11406]) ).
cnf(c_132,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_119,c_15]) ).
cnf(c_11407,plain,
join(complement(join(complement(A),complement(B))),complement(join(complement(B),complement(composition(complement(join(complement(converse(one)),complement(composition(B,converse(A))))),A))))) = complement(join(complement(B),complement(composition(complement(join(complement(converse(one)),complement(composition(B,converse(A))))),A)))),
inference(paramod,[status(thm)],[c_119,c_25]) ).
cnf(c_11408,plain,
join(complement(join(complement(A),complement(B))),complement(join(complement(B),complement(composition(complement(join(complement(one),complement(composition(B,converse(A))))),A))))) = complement(join(complement(B),complement(composition(complement(join(complement(converse(one)),complement(composition(B,converse(A))))),A)))),
inference(paramod,[status(thm)],[c_128,c_11407]) ).
cnf(c_140,plain,
join(complement(join(complement(A),complement(B))),complement(join(complement(B),complement(composition(complement(join(complement(one),complement(composition(B,converse(A))))),A))))) = complement(join(complement(B),complement(composition(complement(join(complement(one),complement(composition(B,converse(A))))),A)))),
inference(paramod,[status(thm)],[c_128,c_11408]) ).
cnf(c_11409,plain,
join(complement(join(complement(composition(A,B)),complement(one))),complement(join(complement(converse(one)),complement(composition(complement(join(complement(A),complement(converse(B)))),B))))) = complement(join(complement(converse(one)),complement(composition(complement(join(complement(A),complement(converse(B)))),B)))),
inference(paramod,[status(thm)],[c_128,c_127]) ).
cnf(c_11410,plain,
join(complement(join(complement(one),complement(composition(A,B)))),complement(join(complement(converse(one)),complement(composition(complement(join(complement(A),complement(converse(B)))),B))))) = complement(join(complement(converse(one)),complement(composition(complement(join(complement(A),complement(converse(B)))),B)))),
inference(paramod,[status(thm)],[c_1,c_11409]) ).
cnf(c_11411,plain,
join(complement(join(complement(one),complement(composition(A,B)))),complement(join(complement(one),complement(composition(complement(join(complement(A),complement(converse(B)))),B))))) = complement(join(complement(converse(one)),complement(composition(complement(join(complement(A),complement(converse(B)))),B)))),
inference(paramod,[status(thm)],[c_128,c_11410]) ).
cnf(c_142,plain,
join(complement(join(complement(one),complement(composition(A,B)))),complement(join(complement(one),complement(composition(complement(join(complement(A),complement(converse(B)))),B))))) = complement(join(complement(one),complement(composition(complement(join(complement(A),complement(converse(B)))),B)))),
inference(paramod,[status(thm)],[c_128,c_11411]) ).
cnf(c_146,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_128,c_119]) ).
cnf(c_11412,plain,
join(one,converse(sk2)) = converse(one),
inference(paramod,[status(thm)],[c_128,c_94]) ).
cnf(c_147,plain,
join(one,converse(sk2)) = one,
inference(paramod,[status(thm)],[c_128,c_11412]) ).
cnf(c_11413,plain,
join(one,converse(sk1)) = converse(one),
inference(paramod,[status(thm)],[c_128,c_90]) ).
cnf(c_148,plain,
join(one,converse(sk1)) = one,
inference(paramod,[status(thm)],[c_128,c_11413]) ).
cnf(c_11414,plain,
join(complement(join(complement(A),complement(B))),composition(complement(join(complement(A),complement(composition(B,one)))),complement(join(complement(one),complement(composition(converse(A),B)))))) = composition(complement(join(complement(A),complement(composition(B,converse(one))))),complement(join(complement(one),complement(composition(converse(A),B))))),
inference(paramod,[status(thm)],[c_128,c_65]) ).
cnf(c_11415,plain,
join(complement(join(complement(A),complement(B))),composition(complement(join(complement(A),complement(B))),complement(join(complement(one),complement(composition(converse(A),B)))))) = composition(complement(join(complement(A),complement(composition(B,converse(one))))),complement(join(complement(one),complement(composition(converse(A),B))))),
inference(paramod,[status(thm)],[c_9,c_11414]) ).
cnf(c_11416,plain,
join(complement(join(complement(A),complement(B))),composition(complement(join(complement(A),complement(B))),complement(join(complement(one),complement(composition(converse(A),B)))))) = composition(complement(join(complement(A),complement(composition(B,one)))),complement(join(complement(one),complement(composition(converse(A),B))))),
inference(paramod,[status(thm)],[c_128,c_11415]) ).
cnf(c_150,plain,
join(complement(join(complement(A),complement(B))),composition(complement(join(complement(A),complement(B))),complement(join(complement(one),complement(composition(converse(A),B)))))) = composition(complement(join(complement(A),complement(B))),complement(join(complement(one),complement(composition(converse(A),B))))),
inference(paramod,[status(thm)],[c_9,c_11416]) ).
cnf(c_11417,plain,
join(A,composition(sk2,A)) = composition(one,A),
inference(paramod,[status(thm)],[c_146,c_93]) ).
cnf(c_151,plain,
join(A,composition(sk2,A)) = A,
inference(paramod,[status(thm)],[c_146,c_11417]) ).
cnf(c_11418,plain,
join(A,composition(sk1,A)) = composition(one,A),
inference(paramod,[status(thm)],[c_146,c_89]) ).
cnf(c_152,plain,
join(A,composition(sk1,A)) = A,
inference(paramod,[status(thm)],[c_146,c_11418]) ).
cnf(c_155,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_146,c_132]) ).
cnf(c_156,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_155,c_55]) ).
cnf(c_11419,plain,
composition(one,A) = join(composition(one,A),composition(converse(sk2),A)),
inference(paramod,[status(thm)],[c_147,c_10]) ).
cnf(c_11420,plain,
A = join(composition(one,A),composition(converse(sk2),A)),
inference(paramod,[status(thm)],[c_146,c_11419]) ).
cnf(c_11421,plain,
A = join(A,composition(converse(sk2),A)),
inference(paramod,[status(thm)],[c_146,c_11420]) ).
cnf(c_158,plain,
join(A,composition(converse(sk2),A)) = A,
inference(copy,[status(thm)],[c_11421]) ).
cnf(c_11422,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_17,c_35]) ).
cnf(c_11423,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_1,c_11422]) ).
cnf(c_11424,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_19,c_11423]) ).
cnf(c_167,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_1,c_11424]) ).
cnf(c_11425,plain,
join(complement(join(complement(join(complement(A),complement(B))),join(B,complement(A)))),complement(A)) = join(complement(A),complement(B)),
inference(paramod,[status(thm)],[c_34,c_35]) ).
cnf(c_11426,plain,
join(complement(join(join(B,complement(A)),complement(join(complement(A),complement(B))))),complement(A)) = join(complement(A),complement(B)),
inference(paramod,[status(thm)],[c_1,c_11425]) ).
cnf(c_11427,plain,
join(complement(join(B,join(complement(A),complement(join(complement(A),complement(B)))))),complement(A)) = join(complement(A),complement(B)),
inference(paramod,[status(thm)],[c_3,c_11426]) ).
cnf(c_171,plain,
join(complement(A),complement(join(B,join(complement(A),complement(join(complement(A),complement(B))))))) = join(complement(A),complement(B)),
inference(paramod,[status(thm)],[c_1,c_11427]) ).
cnf(c_11428,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_35,c_35]) ).
cnf(c_11429,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_11428]) ).
cnf(c_11430,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_11429]) ).
cnf(c_172,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_11430]) ).
cnf(c_173,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_167,c_54]) ).
cnf(c_174,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_173,c_167]) ).
cnf(c_175,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_173,c_156]) ).
cnf(c_178,plain,
complement(join(A,A)) = complement(A),
inference(paramod,[status(thm)],[c_175,c_174]) ).
cnf(c_11431,plain,
join(complement(join(complement(A),B)),B) = join(A,complement(join(complement(B),complement(complement(A))))),
inference(paramod,[status(thm)],[c_34,c_36]) ).
cnf(c_11432,plain,
join(B,complement(join(complement(A),B))) = join(A,complement(join(complement(B),complement(complement(A))))),
inference(paramod,[status(thm)],[c_1,c_11431]) ).
cnf(c_205,plain,
join(A,complement(join(complement(B),A))) = join(B,complement(join(complement(A),B))),
inference(paramod,[status(thm)],[c_173,c_11432]) ).
cnf(c_214,plain,
complement(zero) = top,
inference(paramod,[status(thm)],[c_175,c_17]) ).
cnf(c_11433,plain,
composition(one,A) = join(composition(one,A),composition(converse(sk1),A)),
inference(paramod,[status(thm)],[c_148,c_10]) ).
cnf(c_11434,plain,
A = join(composition(one,A),composition(converse(sk1),A)),
inference(paramod,[status(thm)],[c_146,c_11433]) ).
cnf(c_11435,plain,
A = join(A,composition(converse(sk1),A)),
inference(paramod,[status(thm)],[c_146,c_11434]) ).
cnf(c_229,plain,
join(A,composition(converse(sk1),A)) = A,
inference(copy,[status(thm)],[c_11435]) ).
cnf(c_11436,plain,
converse(A) = join(converse(A),converse(composition(sk2,A))),
inference(paramod,[status(thm)],[c_151,c_12]) ).
cnf(c_11437,plain,
converse(A) = join(converse(A),composition(converse(A),converse(sk2))),
inference(paramod,[status(thm)],[c_13,c_11436]) ).
cnf(c_234,plain,
join(converse(A),composition(converse(A),converse(sk2))) = converse(A),
inference(copy,[status(thm)],[c_11437]) ).
cnf(c_11438,plain,
join(A,B) = join(B,join(A,composition(sk2,B))),
inference(paramod,[status(thm)],[c_151,c_33]) ).
cnf(c_235,plain,
join(A,join(B,composition(sk2,A))) = join(B,A),
inference(copy,[status(thm)],[c_11438]) ).
cnf(c_11439,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_36,c_38]) ).
cnf(c_11440,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_11439]) ).
cnf(c_257,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_36,c_11440]) ).
cnf(c_11441,plain,
join(top,complement(join(complement(zero),join(complement(A),complement(join(complement(zero),A)))))) = join(complement(zero),A),
inference(paramod,[status(thm)],[c_214,c_38]) ).
cnf(c_11442,plain,
join(top,complement(join(top,join(complement(A),complement(join(complement(zero),A)))))) = join(complement(zero),A),
inference(paramod,[status(thm)],[c_214,c_11441]) ).
cnf(c_11443,plain,
join(top,complement(join(top,join(complement(A),complement(join(top,A)))))) = join(complement(zero),A),
inference(paramod,[status(thm)],[c_214,c_11442]) ).
cnf(c_258,plain,
join(top,complement(join(top,join(complement(A),complement(join(top,A)))))) = join(top,A),
inference(paramod,[status(thm)],[c_214,c_11443]) ).
cnf(c_266,plain,
join(composition(complement(join(A,join(complement(B),C))),D),composition(complement(join(complement(B),complement(join(A,C)))),D)) = composition(B,D),
inference(paramod,[status(thm)],[c_33,c_40]) ).
cnf(c_11444,plain,
converse(A) = join(converse(A),converse(composition(sk1,A))),
inference(paramod,[status(thm)],[c_152,c_12]) ).
cnf(c_11445,plain,
converse(A) = join(converse(A),composition(converse(A),converse(sk1))),
inference(paramod,[status(thm)],[c_13,c_11444]) ).
cnf(c_276,plain,
join(converse(A),composition(converse(A),converse(sk1))) = converse(A),
inference(copy,[status(thm)],[c_11445]) ).
cnf(c_11446,plain,
join(complement(join(complement(A),B)),complement(join(complement(join(A,A)),complement(B)))) = join(A,A),
inference(paramod,[status(thm)],[c_178,c_5]) ).
cnf(c_11447,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(A,A),
inference(paramod,[status(thm)],[c_178,c_11446]) ).
cnf(c_11448,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_5,c_11447]) ).
cnf(c_289,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_11448]) ).
cnf(c_11449,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_289,c_3]) ).
cnf(c_290,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_11449]) ).
cnf(c_11450,plain,
join(join(A,B),B) = join(A,B),
inference(paramod,[status(thm)],[c_289,c_3]) ).
cnf(c_292,plain,
join(A,join(B,A)) = join(B,A),
inference(paramod,[status(thm)],[c_1,c_11450]) ).
cnf(c_11451,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_289,c_36]) ).
cnf(c_11452,plain,
A = join(A,complement(join(complement(A),complement(B)))),
inference(paramod,[status(thm)],[c_5,c_11451]) ).
cnf(c_293,plain,
join(A,complement(join(complement(A),complement(B)))) = A,
inference(copy,[status(thm)],[c_11452]) ).
cnf(c_11453,plain,
join(complement(join(complement(A),B)),join(complement(join(complement(A),complement(B))),A)) = A,
inference(paramod,[status(thm)],[c_289,c_36]) ).
cnf(c_11454,plain,
join(complement(join(complement(A),B)),join(A,complement(join(complement(A),complement(B))))) = A,
inference(paramod,[status(thm)],[c_1,c_11453]) ).
cnf(c_11455,plain,
join(complement(join(complement(A),B)),A) = A,
inference(paramod,[status(thm)],[c_293,c_11454]) ).
cnf(c_294,plain,
join(A,complement(join(complement(A),B))) = A,
inference(paramod,[status(thm)],[c_1,c_11455]) ).
cnf(c_299,plain,
join(complement(A),complement(join(complement(A),B))) = join(complement(B),complement(A)),
inference(paramod,[status(thm)],[c_294,c_172]) ).
cnf(c_11456,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_299,c_257]) ).
cnf(c_302,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_11456]) ).
cnf(c_11457,plain,
join(complement(A),complement(join(B,join(complement(complement(B)),complement(A))))) = join(complement(A),complement(B)),
inference(paramod,[status(thm)],[c_299,c_171]) ).
cnf(c_11458,plain,
join(complement(A),complement(join(B,join(B,complement(A))))) = join(complement(A),complement(B)),
inference(paramod,[status(thm)],[c_173,c_11457]) ).
cnf(c_305,plain,
join(complement(A),complement(join(B,complement(A)))) = join(complement(A),complement(B)),
inference(paramod,[status(thm)],[c_290,c_11458]) ).
cnf(c_11459,plain,
join(complement(A),composition(converse(B),complement(composition(B,A)))) = join(complement(A),composition(sk2,composition(converse(B),complement(composition(B,A))))),
inference(paramod,[status(thm)],[c_151,c_44]) ).
cnf(c_11460,plain,
complement(A) = join(complement(A),composition(sk2,composition(converse(B),complement(composition(B,A))))),
inference(paramod,[status(thm)],[c_15,c_11459]) ).
cnf(c_394,plain,
join(complement(A),composition(sk2,composition(converse(B),complement(composition(B,A))))) = complement(A),
inference(copy,[status(thm)],[c_11460]) ).
cnf(c_11461,plain,
converse(A) = join(converse(A),converse(composition(converse(sk2),A))),
inference(paramod,[status(thm)],[c_158,c_12]) ).
cnf(c_11462,plain,
converse(A) = join(converse(A),composition(converse(A),converse(converse(sk2)))),
inference(paramod,[status(thm)],[c_13,c_11461]) ).
cnf(c_11463,plain,
converse(A) = join(converse(A),composition(converse(A),sk2)),
inference(paramod,[status(thm)],[c_11,c_11462]) ).
cnf(c_431,plain,
join(converse(A),composition(converse(A),sk2)) = converse(A),
inference(copy,[status(thm)],[c_11463]) ).
cnf(c_11464,plain,
converse(A) = join(converse(A),converse(composition(converse(sk1),A))),
inference(paramod,[status(thm)],[c_229,c_12]) ).
cnf(c_11465,plain,
converse(A) = join(converse(A),composition(converse(A),converse(converse(sk1)))),
inference(paramod,[status(thm)],[c_13,c_11464]) ).
cnf(c_11466,plain,
converse(A) = join(converse(A),composition(converse(A),sk1)),
inference(paramod,[status(thm)],[c_11,c_11465]) ).
cnf(c_478,plain,
join(converse(A),composition(converse(A),sk1)) = converse(A),
inference(copy,[status(thm)],[c_11466]) ).
cnf(c_502,plain,
join(A,converse(complement(converse(A)))) = converse(top),
inference(paramod,[status(thm)],[c_11,c_57]) ).
cnf(c_11467,plain,
join(one,top) = join(one,complement(sk1)),
inference(paramod,[status(thm)],[c_17,c_87]) ).
cnf(c_534,plain,
join(one,complement(sk1)) = join(one,top),
inference(copy,[status(thm)],[c_11467]) ).
cnf(c_11468,plain,
join(one,sk1) = join(one,composition(sk2,sk1)),
inference(paramod,[status(thm)],[c_151,c_87]) ).
cnf(c_11469,plain,
one = join(one,composition(sk2,sk1)),
inference(paramod,[status(thm)],[c_27,c_11468]) ).
cnf(c_537,plain,
join(one,composition(sk2,sk1)) = one,
inference(copy,[status(thm)],[c_11469]) ).
cnf(c_11470,plain,
join(A,complement(A)) = join(top,complement(A)),
inference(paramod,[status(thm)],[c_289,c_52]) ).
cnf(c_11471,plain,
top = join(top,complement(A)),
inference(paramod,[status(thm)],[c_17,c_11470]) ).
cnf(c_577,plain,
join(top,complement(A)) = top,
inference(copy,[status(thm)],[c_11471]) ).
cnf(c_11472,plain,
join(A,join(complement(A),top)) = top,
inference(paramod,[status(thm)],[c_289,c_52]) ).
cnf(c_11473,plain,
join(A,join(top,complement(A))) = top,
inference(paramod,[status(thm)],[c_1,c_11472]) ).
cnf(c_578,plain,
join(A,top) = top,
inference(paramod,[status(thm)],[c_577,c_11473]) ).
cnf(c_11474,plain,
top = join(top,A),
inference(paramod,[status(thm)],[c_577,c_258]) ).
cnf(c_592,plain,
join(top,A) = top,
inference(copy,[status(thm)],[c_11474]) ).
cnf(c_595,plain,
join(one,complement(sk1)) = top,
inference(paramod,[status(thm)],[c_578,c_534]) ).
cnf(c_11475,plain,
converse(top) = join(converse(A),converse(top)),
inference(paramod,[status(thm)],[c_578,c_12]) ).
cnf(c_606,plain,
join(converse(A),converse(top)) = converse(top),
inference(copy,[status(thm)],[c_11475]) ).
cnf(c_11476,plain,
composition(top,A) = join(composition(one,A),composition(complement(sk1),A)),
inference(paramod,[status(thm)],[c_595,c_10]) ).
cnf(c_11477,plain,
composition(top,A) = join(A,composition(complement(sk1),A)),
inference(paramod,[status(thm)],[c_146,c_11476]) ).
cnf(c_610,plain,
join(A,composition(complement(sk1),A)) = composition(top,A),
inference(copy,[status(thm)],[c_11477]) ).
cnf(c_615,plain,
join(A,converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_11,c_606]) ).
cnf(c_620,plain,
converse(top) = top,
inference(paramod,[status(thm)],[c_615,c_592]) ).
cnf(c_632,plain,
join(A,converse(complement(converse(A)))) = top,
inference(paramod,[status(thm)],[c_620,c_502]) ).
cnf(c_640,plain,
join(converse(A),converse(complement(A))) = top,
inference(paramod,[status(thm)],[c_620,c_57]) ).
cnf(c_11478,plain,
join(one,top) = join(one,complement(sk2)),
inference(paramod,[status(thm)],[c_17,c_91]) ).
cnf(c_11479,plain,
top = join(one,complement(sk2)),
inference(paramod,[status(thm)],[c_578,c_11478]) ).
cnf(c_798,plain,
join(one,complement(sk2)) = top,
inference(copy,[status(thm)],[c_11479]) ).
cnf(c_11480,plain,
join(one,sk2) = join(one,composition(sk1,sk2)),
inference(paramod,[status(thm)],[c_152,c_91]) ).
cnf(c_11481,plain,
one = join(one,composition(sk1,sk2)),
inference(paramod,[status(thm)],[c_29,c_11480]) ).
cnf(c_801,plain,
join(one,composition(sk1,sk2)) = one,
inference(copy,[status(thm)],[c_11481]) ).
cnf(c_11482,plain,
join(A,composition(converse(converse(A)),sk2)) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_431]) ).
cnf(c_11483,plain,
join(A,composition(A,sk2)) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_11482]) ).
cnf(c_938,plain,
join(A,composition(A,sk2)) = A,
inference(paramod,[status(thm)],[c_11,c_11483]) ).
cnf(c_11484,plain,
join(A,B) = join(A,join(composition(A,sk2),B)),
inference(paramod,[status(thm)],[c_938,c_3]) ).
cnf(c_942,plain,
join(A,join(composition(A,sk2),B)) = join(A,B),
inference(copy,[status(thm)],[c_11484]) ).
cnf(c_11485,plain,
join(A,composition(converse(converse(A)),sk1)) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_478]) ).
cnf(c_11486,plain,
join(A,composition(A,sk1)) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_11485]) ).
cnf(c_965,plain,
join(A,composition(A,sk1)) = A,
inference(paramod,[status(thm)],[c_11,c_11486]) ).
cnf(c_11487,plain,
converse(composition(top,A)) = join(converse(A),converse(composition(complement(sk1),A))),
inference(paramod,[status(thm)],[c_610,c_12]) ).
cnf(c_11488,plain,
composition(converse(A),converse(top)) = join(converse(A),converse(composition(complement(sk1),A))),
inference(paramod,[status(thm)],[c_13,c_11487]) ).
cnf(c_11489,plain,
composition(converse(A),top) = join(converse(A),converse(composition(complement(sk1),A))),
inference(paramod,[status(thm)],[c_620,c_11488]) ).
cnf(c_11490,plain,
composition(converse(A),top) = join(converse(A),composition(converse(A),converse(complement(sk1)))),
inference(paramod,[status(thm)],[c_13,c_11489]) ).
cnf(c_977,plain,
join(converse(A),composition(converse(A),converse(complement(sk1)))) = composition(converse(A),top),
inference(copy,[status(thm)],[c_11490]) ).
cnf(c_11491,plain,
join(complement(join(zero,A)),join(B,complement(join(complement(top),complement(A))))) = join(B,top),
inference(paramod,[status(thm)],[c_19,c_96]) ).
cnf(c_11492,plain,
join(complement(A),join(B,complement(join(complement(top),complement(A))))) = join(B,top),
inference(paramod,[status(thm)],[c_175,c_11491]) ).
cnf(c_11493,plain,
join(complement(A),join(B,complement(join(zero,complement(A))))) = join(B,top),
inference(paramod,[status(thm)],[c_19,c_11492]) ).
cnf(c_11494,plain,
join(complement(A),join(B,complement(complement(A)))) = join(B,top),
inference(paramod,[status(thm)],[c_175,c_11493]) ).
cnf(c_11495,plain,
join(complement(A),join(B,A)) = join(B,top),
inference(paramod,[status(thm)],[c_173,c_11494]) ).
cnf(c_1039,plain,
join(complement(A),join(B,A)) = top,
inference(paramod,[status(thm)],[c_578,c_11495]) ).
cnf(c_11496,plain,
join(complement(converse(sk2)),one) = top,
inference(paramod,[status(thm)],[c_147,c_1039]) ).
cnf(c_1067,plain,
join(one,complement(converse(sk2))) = top,
inference(paramod,[status(thm)],[c_1,c_11496]) ).
cnf(c_11497,plain,
join(complement(converse(sk1)),one) = top,
inference(paramod,[status(thm)],[c_148,c_1039]) ).
cnf(c_1068,plain,
join(one,complement(converse(sk1))) = top,
inference(paramod,[status(thm)],[c_1,c_11497]) ).
cnf(c_11498,plain,
join(complement(composition(sk1,sk2)),one) = top,
inference(paramod,[status(thm)],[c_801,c_1039]) ).
cnf(c_1087,plain,
join(one,complement(composition(sk1,sk2))) = top,
inference(paramod,[status(thm)],[c_1,c_11498]) ).
cnf(c_11499,plain,
join(complement(composition(A,sk2)),A) = top,
inference(paramod,[status(thm)],[c_938,c_1039]) ).
cnf(c_1095,plain,
join(A,complement(composition(A,sk2))) = top,
inference(paramod,[status(thm)],[c_1,c_11499]) ).
cnf(c_11500,plain,
join(complement(composition(A,sk1)),A) = top,
inference(paramod,[status(thm)],[c_965,c_1039]) ).
cnf(c_1096,plain,
join(A,complement(composition(A,sk1))) = top,
inference(paramod,[status(thm)],[c_1,c_11500]) ).
cnf(c_11501,plain,
join(complement(join(A,complement(B))),complement(join(B,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_173,c_101]) ).
cnf(c_1133,plain,
join(complement(join(A,complement(B))),complement(join(B,A))) = complement(A),
inference(paramod,[status(thm)],[c_173,c_11501]) ).
cnf(c_11502,plain,
join(complement(join(complement(sk1),complement(one))),complement(top)) = sk1,
inference(paramod,[status(thm)],[c_595,c_101]) ).
cnf(c_11503,plain,
join(complement(join(complement(one),complement(sk1))),complement(top)) = sk1,
inference(paramod,[status(thm)],[c_1,c_11502]) ).
cnf(c_11504,plain,
join(complement(join(complement(one),complement(sk1))),zero) = sk1,
inference(paramod,[status(thm)],[c_19,c_11503]) ).
cnf(c_11505,plain,
join(zero,complement(join(complement(one),complement(sk1)))) = sk1,
inference(paramod,[status(thm)],[c_1,c_11504]) ).
cnf(c_1134,plain,
complement(join(complement(one),complement(sk1))) = sk1,
inference(paramod,[status(thm)],[c_175,c_11505]) ).
cnf(c_11506,plain,
join(complement(join(complement(sk2),complement(one))),complement(top)) = sk2,
inference(paramod,[status(thm)],[c_798,c_101]) ).
cnf(c_11507,plain,
join(complement(join(complement(one),complement(sk2))),complement(top)) = sk2,
inference(paramod,[status(thm)],[c_1,c_11506]) ).
cnf(c_11508,plain,
join(complement(join(complement(one),complement(sk2))),zero) = sk2,
inference(paramod,[status(thm)],[c_19,c_11507]) ).
cnf(c_11509,plain,
join(zero,complement(join(complement(one),complement(sk2)))) = sk2,
inference(paramod,[status(thm)],[c_1,c_11508]) ).
cnf(c_1135,plain,
complement(join(complement(one),complement(sk2))) = sk2,
inference(paramod,[status(thm)],[c_175,c_11509]) ).
cnf(c_11510,plain,
join(complement(join(A,complement(B))),B) = join(complement(join(complement(B),complement(A))),complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_101,c_292]) ).
cnf(c_11511,plain,
join(B,complement(join(A,complement(B)))) = join(complement(join(complement(B),complement(A))),complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_1,c_11510]) ).
cnf(c_11512,plain,
join(B,complement(join(A,complement(B)))) = complement(complement(B)),
inference(paramod,[status(thm)],[c_1133,c_11511]) ).
cnf(c_1136,plain,
join(A,complement(join(B,complement(A)))) = A,
inference(paramod,[status(thm)],[c_173,c_11512]) ).
cnf(c_11513,plain,
join(complement(join(complement(converse(sk2)),complement(one))),complement(top)) = converse(sk2),
inference(paramod,[status(thm)],[c_1067,c_101]) ).
cnf(c_11514,plain,
join(complement(join(complement(one),complement(converse(sk2)))),complement(top)) = converse(sk2),
inference(paramod,[status(thm)],[c_1,c_11513]) ).
cnf(c_11515,plain,
join(complement(join(complement(one),complement(converse(sk2)))),zero) = converse(sk2),
inference(paramod,[status(thm)],[c_19,c_11514]) ).
cnf(c_11516,plain,
join(zero,complement(join(complement(one),complement(converse(sk2))))) = converse(sk2),
inference(paramod,[status(thm)],[c_1,c_11515]) ).
cnf(c_1138,plain,
complement(join(complement(one),complement(converse(sk2)))) = converse(sk2),
inference(paramod,[status(thm)],[c_175,c_11516]) ).
cnf(c_11517,plain,
join(complement(join(complement(converse(sk1)),complement(one))),complement(top)) = converse(sk1),
inference(paramod,[status(thm)],[c_1068,c_101]) ).
cnf(c_11518,plain,
join(complement(join(complement(one),complement(converse(sk1)))),complement(top)) = converse(sk1),
inference(paramod,[status(thm)],[c_1,c_11517]) ).
cnf(c_11519,plain,
join(complement(join(complement(one),complement(converse(sk1)))),zero) = converse(sk1),
inference(paramod,[status(thm)],[c_19,c_11518]) ).
cnf(c_11520,plain,
join(zero,complement(join(complement(one),complement(converse(sk1))))) = converse(sk1),
inference(paramod,[status(thm)],[c_1,c_11519]) ).
cnf(c_1139,plain,
complement(join(complement(one),complement(converse(sk1)))) = converse(sk1),
inference(paramod,[status(thm)],[c_175,c_11520]) ).
cnf(c_11521,plain,
join(complement(top),complement(join(complement(A),complement(composition(A,sk2))))) = composition(A,sk2),
inference(paramod,[status(thm)],[c_1095,c_102]) ).
cnf(c_11522,plain,
join(zero,complement(join(complement(A),complement(composition(A,sk2))))) = composition(A,sk2),
inference(paramod,[status(thm)],[c_19,c_11521]) ).
cnf(c_1188,plain,
complement(join(complement(A),complement(composition(A,sk2)))) = composition(A,sk2),
inference(paramod,[status(thm)],[c_175,c_11522]) ).
cnf(c_11523,plain,
join(complement(top),complement(join(complement(A),complement(composition(A,sk1))))) = composition(A,sk1),
inference(paramod,[status(thm)],[c_1096,c_102]) ).
cnf(c_11524,plain,
join(zero,complement(join(complement(A),complement(composition(A,sk1))))) = composition(A,sk1),
inference(paramod,[status(thm)],[c_19,c_11523]) ).
cnf(c_1190,plain,
complement(join(complement(A),complement(composition(A,sk1)))) = composition(A,sk1),
inference(paramod,[status(thm)],[c_175,c_11524]) ).
cnf(c_11525,plain,
complement(sk1) = join(complement(one),complement(sk1)),
inference(paramod,[status(thm)],[c_1134,c_173]) ).
cnf(c_1248,plain,
join(complement(one),complement(sk1)) = complement(sk1),
inference(copy,[status(thm)],[c_11525]) ).
cnf(c_11526,plain,
join(complement(sk1),A) = join(complement(one),join(complement(sk1),A)),
inference(paramod,[status(thm)],[c_1248,c_3]) ).
cnf(c_1254,plain,
join(complement(one),join(complement(sk1),A)) = join(complement(sk1),A),
inference(copy,[status(thm)],[c_11526]) ).
cnf(c_11527,plain,
complement(sk2) = join(complement(one),complement(sk2)),
inference(paramod,[status(thm)],[c_1135,c_173]) ).
cnf(c_1259,plain,
join(complement(one),complement(sk2)) = complement(sk2),
inference(copy,[status(thm)],[c_11527]) ).
cnf(c_11528,plain,
join(complement(sk2),A) = join(complement(one),join(complement(sk2),A)),
inference(paramod,[status(thm)],[c_1259,c_3]) ).
cnf(c_1265,plain,
join(complement(one),join(complement(sk2),A)) = join(complement(sk2),A),
inference(copy,[status(thm)],[c_11528]) ).
cnf(c_11529,plain,
join(complement(join(A,top)),complement(join(complement(composition(sk1,sk2)),complement(join(A,one))))) = composition(sk1,sk2),
inference(paramod,[status(thm)],[c_1087,c_104]) ).
cnf(c_11530,plain,
join(complement(top),complement(join(complement(composition(sk1,sk2)),complement(join(A,one))))) = composition(sk1,sk2),
inference(paramod,[status(thm)],[c_578,c_11529]) ).
cnf(c_11531,plain,
join(zero,complement(join(complement(composition(sk1,sk2)),complement(join(A,one))))) = composition(sk1,sk2),
inference(paramod,[status(thm)],[c_19,c_11530]) ).
cnf(c_1291,plain,
complement(join(complement(composition(sk1,sk2)),complement(join(A,one)))) = composition(sk1,sk2),
inference(paramod,[status(thm)],[c_175,c_11531]) ).
cnf(c_11532,plain,
join(A,composition(converse(converse(A)),converse(sk2))) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_234]) ).
cnf(c_11533,plain,
join(A,composition(A,converse(sk2))) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_11532]) ).
cnf(c_1343,plain,
join(A,composition(A,converse(sk2))) = A,
inference(paramod,[status(thm)],[c_11,c_11533]) ).
cnf(c_11534,plain,
join(A,composition(converse(converse(A)),converse(sk1))) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_276]) ).
cnf(c_11535,plain,
join(A,composition(A,converse(sk1))) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_11534]) ).
cnf(c_1396,plain,
join(A,composition(A,converse(sk1))) = A,
inference(paramod,[status(thm)],[c_11,c_11535]) ).
cnf(c_11536,plain,
join(complement(complement(sk1)),composition(complement(join(complement(one),complement(sk1))),complement(join(complement(one),complement(composition(converse(one),sk1)))))) = composition(complement(join(complement(one),complement(sk1))),complement(join(complement(one),complement(composition(converse(one),sk1))))),
inference(paramod,[status(thm)],[c_1248,c_150]) ).
cnf(c_11537,plain,
join(sk1,composition(complement(join(complement(one),complement(sk1))),complement(join(complement(one),complement(composition(converse(one),sk1)))))) = composition(complement(join(complement(one),complement(sk1))),complement(join(complement(one),complement(composition(converse(one),sk1))))),
inference(paramod,[status(thm)],[c_173,c_11536]) ).
cnf(c_11538,plain,
join(sk1,composition(complement(complement(sk1)),complement(join(complement(one),complement(composition(converse(one),sk1)))))) = composition(complement(join(complement(one),complement(sk1))),complement(join(complement(one),complement(composition(converse(one),sk1))))),
inference(paramod,[status(thm)],[c_1248,c_11537]) ).
cnf(c_11539,plain,
join(sk1,composition(sk1,complement(join(complement(one),complement(composition(converse(one),sk1)))))) = composition(complement(join(complement(one),complement(sk1))),complement(join(complement(one),complement(composition(converse(one),sk1))))),
inference(paramod,[status(thm)],[c_173,c_11538]) ).
cnf(c_11540,plain,
join(sk1,composition(sk1,complement(join(complement(one),complement(composition(one,sk1)))))) = composition(complement(join(complement(one),complement(sk1))),complement(join(complement(one),complement(composition(converse(one),sk1))))),
inference(paramod,[status(thm)],[c_128,c_11539]) ).
cnf(c_11541,plain,
join(sk1,composition(sk1,complement(join(complement(one),complement(sk1))))) = composition(complement(join(complement(one),complement(sk1))),complement(join(complement(one),complement(composition(converse(one),sk1))))),
inference(paramod,[status(thm)],[c_146,c_11540]) ).
cnf(c_11542,plain,
join(sk1,composition(sk1,complement(complement(sk1)))) = composition(complement(join(complement(one),complement(sk1))),complement(join(complement(one),complement(composition(converse(one),sk1))))),
inference(paramod,[status(thm)],[c_1248,c_11541]) ).
cnf(c_11543,plain,
join(sk1,composition(sk1,sk1)) = composition(complement(join(complement(one),complement(sk1))),complement(join(complement(one),complement(composition(converse(one),sk1))))),
inference(paramod,[status(thm)],[c_173,c_11542]) ).
cnf(c_11544,plain,
sk1 = composition(complement(join(complement(one),complement(sk1))),complement(join(complement(one),complement(composition(converse(one),sk1))))),
inference(paramod,[status(thm)],[c_965,c_11543]) ).
cnf(c_11545,plain,
sk1 = composition(complement(complement(sk1)),complement(join(complement(one),complement(composition(converse(one),sk1))))),
inference(paramod,[status(thm)],[c_1248,c_11544]) ).
cnf(c_11546,plain,
sk1 = composition(sk1,complement(join(complement(one),complement(composition(converse(one),sk1))))),
inference(paramod,[status(thm)],[c_173,c_11545]) ).
cnf(c_11547,plain,
sk1 = composition(sk1,complement(join(complement(one),complement(composition(one,sk1))))),
inference(paramod,[status(thm)],[c_128,c_11546]) ).
cnf(c_11548,plain,
sk1 = composition(sk1,complement(join(complement(one),complement(sk1)))),
inference(paramod,[status(thm)],[c_146,c_11547]) ).
cnf(c_11549,plain,
sk1 = composition(sk1,complement(complement(sk1))),
inference(paramod,[status(thm)],[c_1248,c_11548]) ).
cnf(c_11550,plain,
sk1 = composition(sk1,sk1),
inference(paramod,[status(thm)],[c_173,c_11549]) ).
cnf(c_1513,plain,
composition(sk1,sk1) = sk1,
inference(copy,[status(thm)],[c_11550]) ).
cnf(c_11551,plain,
join(complement(complement(sk2)),composition(complement(join(complement(one),complement(sk2))),complement(join(complement(one),complement(composition(converse(one),sk2)))))) = composition(complement(join(complement(one),complement(sk2))),complement(join(complement(one),complement(composition(converse(one),sk2))))),
inference(paramod,[status(thm)],[c_1259,c_150]) ).
cnf(c_11552,plain,
join(sk2,composition(complement(join(complement(one),complement(sk2))),complement(join(complement(one),complement(composition(converse(one),sk2)))))) = composition(complement(join(complement(one),complement(sk2))),complement(join(complement(one),complement(composition(converse(one),sk2))))),
inference(paramod,[status(thm)],[c_173,c_11551]) ).
cnf(c_11553,plain,
join(sk2,composition(complement(complement(sk2)),complement(join(complement(one),complement(composition(converse(one),sk2)))))) = composition(complement(join(complement(one),complement(sk2))),complement(join(complement(one),complement(composition(converse(one),sk2))))),
inference(paramod,[status(thm)],[c_1259,c_11552]) ).
cnf(c_11554,plain,
join(sk2,composition(sk2,complement(join(complement(one),complement(composition(converse(one),sk2)))))) = composition(complement(join(complement(one),complement(sk2))),complement(join(complement(one),complement(composition(converse(one),sk2))))),
inference(paramod,[status(thm)],[c_173,c_11553]) ).
cnf(c_11555,plain,
join(sk2,composition(sk2,complement(join(complement(one),complement(composition(one,sk2)))))) = composition(complement(join(complement(one),complement(sk2))),complement(join(complement(one),complement(composition(converse(one),sk2))))),
inference(paramod,[status(thm)],[c_128,c_11554]) ).
cnf(c_11556,plain,
join(sk2,composition(sk2,complement(join(complement(one),complement(sk2))))) = composition(complement(join(complement(one),complement(sk2))),complement(join(complement(one),complement(composition(converse(one),sk2))))),
inference(paramod,[status(thm)],[c_146,c_11555]) ).
cnf(c_11557,plain,
join(sk2,composition(sk2,complement(complement(sk2)))) = composition(complement(join(complement(one),complement(sk2))),complement(join(complement(one),complement(composition(converse(one),sk2))))),
inference(paramod,[status(thm)],[c_1259,c_11556]) ).
cnf(c_11558,plain,
join(sk2,composition(sk2,sk2)) = composition(complement(join(complement(one),complement(sk2))),complement(join(complement(one),complement(composition(converse(one),sk2))))),
inference(paramod,[status(thm)],[c_173,c_11557]) ).
cnf(c_11559,plain,
sk2 = composition(complement(join(complement(one),complement(sk2))),complement(join(complement(one),complement(composition(converse(one),sk2))))),
inference(paramod,[status(thm)],[c_938,c_11558]) ).
cnf(c_11560,plain,
sk2 = composition(complement(complement(sk2)),complement(join(complement(one),complement(composition(converse(one),sk2))))),
inference(paramod,[status(thm)],[c_1259,c_11559]) ).
cnf(c_11561,plain,
sk2 = composition(sk2,complement(join(complement(one),complement(composition(converse(one),sk2))))),
inference(paramod,[status(thm)],[c_173,c_11560]) ).
cnf(c_11562,plain,
sk2 = composition(sk2,complement(join(complement(one),complement(composition(one,sk2))))),
inference(paramod,[status(thm)],[c_128,c_11561]) ).
cnf(c_11563,plain,
sk2 = composition(sk2,complement(join(complement(one),complement(sk2)))),
inference(paramod,[status(thm)],[c_146,c_11562]) ).
cnf(c_11564,plain,
sk2 = composition(sk2,complement(complement(sk2))),
inference(paramod,[status(thm)],[c_1259,c_11563]) ).
cnf(c_11565,plain,
sk2 = composition(sk2,sk2),
inference(paramod,[status(thm)],[c_173,c_11564]) ).
cnf(c_1514,plain,
composition(sk2,sk2) = sk2,
inference(copy,[status(thm)],[c_11565]) ).
cnf(c_11566,plain,
converse(sk1) = composition(converse(sk1),converse(sk1)),
inference(paramod,[status(thm)],[c_1513,c_13]) ).
cnf(c_1525,plain,
composition(converse(sk1),converse(sk1)) = converse(sk1),
inference(copy,[status(thm)],[c_11566]) ).
cnf(c_11567,plain,
composition(sk2,A) = composition(sk2,composition(sk2,A)),
inference(paramod,[status(thm)],[c_1514,c_8]) ).
cnf(c_1543,plain,
composition(sk2,composition(sk2,A)) = composition(sk2,A),
inference(copy,[status(thm)],[c_11567]) ).
cnf(c_11568,plain,
converse(sk2) = composition(converse(sk2),converse(sk2)),
inference(paramod,[status(thm)],[c_1514,c_13]) ).
cnf(c_1544,plain,
composition(converse(sk2),converse(sk2)) = converse(sk2),
inference(copy,[status(thm)],[c_11568]) ).
cnf(c_11569,plain,
join(complement(join(complement(sk1),complement(converse(sk1)))),complement(join(complement(converse(sk1)),complement(composition(complement(join(complement(one),complement(converse(sk1)))),sk1))))) = complement(join(complement(converse(sk1)),complement(composition(complement(join(complement(one),complement(composition(converse(sk1),converse(sk1))))),sk1)))),
inference(paramod,[status(thm)],[c_1525,c_140]) ).
cnf(c_11570,plain,
join(complement(join(complement(sk1),complement(converse(sk1)))),complement(join(complement(converse(sk1)),complement(composition(converse(sk1),sk1))))) = complement(join(complement(converse(sk1)),complement(composition(complement(join(complement(one),complement(composition(converse(sk1),converse(sk1))))),sk1)))),
inference(paramod,[status(thm)],[c_1139,c_11569]) ).
cnf(c_11571,plain,
join(complement(join(complement(sk1),complement(converse(sk1)))),composition(converse(sk1),sk1)) = complement(join(complement(converse(sk1)),complement(composition(complement(join(complement(one),complement(composition(converse(sk1),converse(sk1))))),sk1)))),
inference(paramod,[status(thm)],[c_1190,c_11570]) ).
cnf(c_11572,plain,
join(complement(join(complement(sk1),complement(converse(sk1)))),composition(converse(sk1),sk1)) = complement(join(complement(converse(sk1)),complement(composition(complement(join(complement(one),complement(converse(sk1)))),sk1)))),
inference(paramod,[status(thm)],[c_1525,c_11571]) ).
cnf(c_11573,plain,
join(complement(join(complement(sk1),complement(converse(sk1)))),composition(converse(sk1),sk1)) = complement(join(complement(converse(sk1)),complement(composition(converse(sk1),sk1)))),
inference(paramod,[status(thm)],[c_1139,c_11572]) ).
cnf(c_1585,plain,
join(complement(join(complement(sk1),complement(converse(sk1)))),composition(converse(sk1),sk1)) = composition(converse(sk1),sk1),
inference(paramod,[status(thm)],[c_1190,c_11573]) ).
cnf(c_11574,plain,
join(complement(join(complement(one),complement(converse(sk1)))),complement(join(complement(one),complement(composition(complement(join(complement(converse(sk1)),complement(converse(converse(sk1))))),converse(sk1)))))) = complement(join(complement(one),complement(composition(complement(join(complement(converse(sk1)),complement(converse(converse(sk1))))),converse(sk1))))),
inference(paramod,[status(thm)],[c_1525,c_142]) ).
cnf(c_11575,plain,
join(converse(sk1),complement(join(complement(one),complement(composition(complement(join(complement(converse(sk1)),complement(converse(converse(sk1))))),converse(sk1)))))) = complement(join(complement(one),complement(composition(complement(join(complement(converse(sk1)),complement(converse(converse(sk1))))),converse(sk1))))),
inference(paramod,[status(thm)],[c_1139,c_11574]) ).
cnf(c_11576,plain,
join(converse(sk1),complement(join(complement(one),complement(composition(complement(join(complement(converse(sk1)),complement(sk1))),converse(sk1)))))) = complement(join(complement(one),complement(composition(complement(join(complement(converse(sk1)),complement(converse(converse(sk1))))),converse(sk1))))),
inference(paramod,[status(thm)],[c_11,c_11575]) ).
cnf(c_11577,plain,
join(converse(sk1),complement(join(complement(one),complement(composition(complement(join(complement(sk1),complement(converse(sk1)))),converse(sk1)))))) = complement(join(complement(one),complement(composition(complement(join(complement(converse(sk1)),complement(converse(converse(sk1))))),converse(sk1))))),
inference(paramod,[status(thm)],[c_1,c_11576]) ).
cnf(c_11578,plain,
join(converse(sk1),complement(join(complement(one),complement(composition(complement(join(complement(sk1),complement(converse(sk1)))),converse(sk1)))))) = complement(join(complement(one),complement(composition(complement(join(complement(converse(sk1)),complement(sk1))),converse(sk1))))),
inference(paramod,[status(thm)],[c_11,c_11577]) ).
cnf(c_1586,plain,
join(converse(sk1),complement(join(complement(one),complement(composition(complement(join(complement(sk1),complement(converse(sk1)))),converse(sk1)))))) = complement(join(complement(one),complement(composition(complement(join(complement(sk1),complement(converse(sk1)))),converse(sk1))))),
inference(paramod,[status(thm)],[c_1,c_11578]) ).
cnf(c_11579,plain,
join(complement(join(complement(sk1),complement(converse(sk1)))),composition(complement(join(complement(sk1),complement(converse(sk1)))),complement(join(complement(one),complement(converse(sk1)))))) = composition(complement(join(complement(sk1),complement(converse(sk1)))),complement(join(complement(one),complement(composition(converse(sk1),converse(sk1)))))),
inference(paramod,[status(thm)],[c_1525,c_150]) ).
cnf(c_11580,plain,
join(complement(join(complement(sk1),complement(converse(sk1)))),composition(complement(join(complement(sk1),complement(converse(sk1)))),converse(sk1))) = composition(complement(join(complement(sk1),complement(converse(sk1)))),complement(join(complement(one),complement(composition(converse(sk1),converse(sk1)))))),
inference(paramod,[status(thm)],[c_1139,c_11579]) ).
cnf(c_11581,plain,
complement(join(complement(sk1),complement(converse(sk1)))) = composition(complement(join(complement(sk1),complement(converse(sk1)))),complement(join(complement(one),complement(composition(converse(sk1),converse(sk1)))))),
inference(paramod,[status(thm)],[c_1396,c_11580]) ).
cnf(c_11582,plain,
complement(join(complement(sk1),complement(converse(sk1)))) = composition(complement(join(complement(sk1),complement(converse(sk1)))),complement(join(complement(one),complement(converse(sk1))))),
inference(paramod,[status(thm)],[c_1525,c_11581]) ).
cnf(c_11583,plain,
complement(join(complement(sk1),complement(converse(sk1)))) = composition(complement(join(complement(sk1),complement(converse(sk1)))),converse(sk1)),
inference(paramod,[status(thm)],[c_1139,c_11582]) ).
cnf(c_1588,plain,
composition(complement(join(complement(sk1),complement(converse(sk1)))),converse(sk1)) = complement(join(complement(sk1),complement(converse(sk1)))),
inference(copy,[status(thm)],[c_11583]) ).
cnf(c_11584,plain,
join(converse(sk1),complement(join(complement(one),complement(complement(join(complement(sk1),complement(converse(sk1)))))))) = complement(join(complement(one),complement(composition(complement(join(complement(sk1),complement(converse(sk1)))),converse(sk1))))),
inference(paramod,[status(thm)],[c_1588,c_1586]) ).
cnf(c_11585,plain,
join(converse(sk1),complement(join(complement(one),join(complement(sk1),complement(converse(sk1)))))) = complement(join(complement(one),complement(composition(complement(join(complement(sk1),complement(converse(sk1)))),converse(sk1))))),
inference(paramod,[status(thm)],[c_173,c_11584]) ).
cnf(c_11586,plain,
join(converse(sk1),complement(join(complement(sk1),complement(converse(sk1))))) = complement(join(complement(one),complement(composition(complement(join(complement(sk1),complement(converse(sk1)))),converse(sk1))))),
inference(paramod,[status(thm)],[c_1254,c_11585]) ).
cnf(c_11587,plain,
converse(sk1) = complement(join(complement(one),complement(composition(complement(join(complement(sk1),complement(converse(sk1)))),converse(sk1))))),
inference(paramod,[status(thm)],[c_1136,c_11586]) ).
cnf(c_11588,plain,
converse(sk1) = complement(join(complement(one),complement(complement(join(complement(sk1),complement(converse(sk1))))))),
inference(paramod,[status(thm)],[c_1588,c_11587]) ).
cnf(c_11589,plain,
converse(sk1) = complement(join(complement(one),join(complement(sk1),complement(converse(sk1))))),
inference(paramod,[status(thm)],[c_173,c_11588]) ).
cnf(c_11590,plain,
converse(sk1) = complement(join(complement(sk1),complement(converse(sk1)))),
inference(paramod,[status(thm)],[c_1254,c_11589]) ).
cnf(c_1590,plain,
complement(join(complement(sk1),complement(converse(sk1)))) = converse(sk1),
inference(copy,[status(thm)],[c_11590]) ).
cnf(c_11591,plain,
join(converse(sk1),composition(converse(sk1),sk1)) = composition(converse(sk1),sk1),
inference(paramod,[status(thm)],[c_1590,c_1585]) ).
cnf(c_11592,plain,
converse(sk1) = composition(converse(sk1),sk1),
inference(paramod,[status(thm)],[c_965,c_11591]) ).
cnf(c_1591,plain,
composition(converse(sk1),sk1) = converse(sk1),
inference(copy,[status(thm)],[c_11592]) ).
cnf(c_11593,plain,
converse(converse(sk1)) = composition(converse(sk1),converse(converse(sk1))),
inference(paramod,[status(thm)],[c_1591,c_13]) ).
cnf(c_11594,plain,
sk1 = composition(converse(sk1),converse(converse(sk1))),
inference(paramod,[status(thm)],[c_11,c_11593]) ).
cnf(c_11595,plain,
sk1 = composition(converse(sk1),sk1),
inference(paramod,[status(thm)],[c_11,c_11594]) ).
cnf(c_11596,plain,
sk1 = converse(sk1),
inference(paramod,[status(thm)],[c_1591,c_11595]) ).
cnf(c_1595,plain,
converse(sk1) = sk1,
inference(copy,[status(thm)],[c_11596]) ).
cnf(c_1631,plain,
join(sk1,converse(complement(sk1))) = top,
inference(paramod,[status(thm)],[c_1595,c_640]) ).
cnf(c_11597,plain,
join(complement(join(complement(sk2),complement(converse(sk2)))),complement(join(complement(converse(sk2)),complement(composition(complement(join(complement(one),complement(converse(sk2)))),sk2))))) = complement(join(complement(converse(sk2)),complement(composition(complement(join(complement(one),complement(composition(converse(sk2),converse(sk2))))),sk2)))),
inference(paramod,[status(thm)],[c_1544,c_140]) ).
cnf(c_11598,plain,
join(complement(join(complement(sk2),complement(converse(sk2)))),complement(join(complement(converse(sk2)),complement(composition(converse(sk2),sk2))))) = complement(join(complement(converse(sk2)),complement(composition(complement(join(complement(one),complement(composition(converse(sk2),converse(sk2))))),sk2)))),
inference(paramod,[status(thm)],[c_1138,c_11597]) ).
cnf(c_11599,plain,
join(complement(join(complement(sk2),complement(converse(sk2)))),composition(converse(sk2),sk2)) = complement(join(complement(converse(sk2)),complement(composition(complement(join(complement(one),complement(composition(converse(sk2),converse(sk2))))),sk2)))),
inference(paramod,[status(thm)],[c_1188,c_11598]) ).
cnf(c_11600,plain,
join(complement(join(complement(sk2),complement(converse(sk2)))),composition(converse(sk2),sk2)) = complement(join(complement(converse(sk2)),complement(composition(complement(join(complement(one),complement(converse(sk2)))),sk2)))),
inference(paramod,[status(thm)],[c_1544,c_11599]) ).
cnf(c_11601,plain,
join(complement(join(complement(sk2),complement(converse(sk2)))),composition(converse(sk2),sk2)) = complement(join(complement(converse(sk2)),complement(composition(converse(sk2),sk2)))),
inference(paramod,[status(thm)],[c_1138,c_11600]) ).
cnf(c_1672,plain,
join(complement(join(complement(sk2),complement(converse(sk2)))),composition(converse(sk2),sk2)) = composition(converse(sk2),sk2),
inference(paramod,[status(thm)],[c_1188,c_11601]) ).
cnf(c_11602,plain,
join(complement(join(complement(one),complement(converse(sk2)))),complement(join(complement(one),complement(composition(complement(join(complement(converse(sk2)),complement(converse(converse(sk2))))),converse(sk2)))))) = complement(join(complement(one),complement(composition(complement(join(complement(converse(sk2)),complement(converse(converse(sk2))))),converse(sk2))))),
inference(paramod,[status(thm)],[c_1544,c_142]) ).
cnf(c_11603,plain,
join(converse(sk2),complement(join(complement(one),complement(composition(complement(join(complement(converse(sk2)),complement(converse(converse(sk2))))),converse(sk2)))))) = complement(join(complement(one),complement(composition(complement(join(complement(converse(sk2)),complement(converse(converse(sk2))))),converse(sk2))))),
inference(paramod,[status(thm)],[c_1138,c_11602]) ).
cnf(c_11604,plain,
join(converse(sk2),complement(join(complement(one),complement(composition(complement(join(complement(converse(sk2)),complement(sk2))),converse(sk2)))))) = complement(join(complement(one),complement(composition(complement(join(complement(converse(sk2)),complement(converse(converse(sk2))))),converse(sk2))))),
inference(paramod,[status(thm)],[c_11,c_11603]) ).
cnf(c_11605,plain,
join(converse(sk2),complement(join(complement(one),complement(composition(complement(join(complement(sk2),complement(converse(sk2)))),converse(sk2)))))) = complement(join(complement(one),complement(composition(complement(join(complement(converse(sk2)),complement(converse(converse(sk2))))),converse(sk2))))),
inference(paramod,[status(thm)],[c_1,c_11604]) ).
cnf(c_11606,plain,
join(converse(sk2),complement(join(complement(one),complement(composition(complement(join(complement(sk2),complement(converse(sk2)))),converse(sk2)))))) = complement(join(complement(one),complement(composition(complement(join(complement(converse(sk2)),complement(sk2))),converse(sk2))))),
inference(paramod,[status(thm)],[c_11,c_11605]) ).
cnf(c_1673,plain,
join(converse(sk2),complement(join(complement(one),complement(composition(complement(join(complement(sk2),complement(converse(sk2)))),converse(sk2)))))) = complement(join(complement(one),complement(composition(complement(join(complement(sk2),complement(converse(sk2)))),converse(sk2))))),
inference(paramod,[status(thm)],[c_1,c_11606]) ).
cnf(c_11607,plain,
join(complement(join(complement(sk2),complement(converse(sk2)))),composition(complement(join(complement(sk2),complement(converse(sk2)))),complement(join(complement(one),complement(converse(sk2)))))) = composition(complement(join(complement(sk2),complement(converse(sk2)))),complement(join(complement(one),complement(composition(converse(sk2),converse(sk2)))))),
inference(paramod,[status(thm)],[c_1544,c_150]) ).
cnf(c_11608,plain,
join(complement(join(complement(sk2),complement(converse(sk2)))),composition(complement(join(complement(sk2),complement(converse(sk2)))),converse(sk2))) = composition(complement(join(complement(sk2),complement(converse(sk2)))),complement(join(complement(one),complement(composition(converse(sk2),converse(sk2)))))),
inference(paramod,[status(thm)],[c_1138,c_11607]) ).
cnf(c_11609,plain,
complement(join(complement(sk2),complement(converse(sk2)))) = composition(complement(join(complement(sk2),complement(converse(sk2)))),complement(join(complement(one),complement(composition(converse(sk2),converse(sk2)))))),
inference(paramod,[status(thm)],[c_1343,c_11608]) ).
cnf(c_11610,plain,
complement(join(complement(sk2),complement(converse(sk2)))) = composition(complement(join(complement(sk2),complement(converse(sk2)))),complement(join(complement(one),complement(converse(sk2))))),
inference(paramod,[status(thm)],[c_1544,c_11609]) ).
cnf(c_11611,plain,
complement(join(complement(sk2),complement(converse(sk2)))) = composition(complement(join(complement(sk2),complement(converse(sk2)))),converse(sk2)),
inference(paramod,[status(thm)],[c_1138,c_11610]) ).
cnf(c_1675,plain,
composition(complement(join(complement(sk2),complement(converse(sk2)))),converse(sk2)) = complement(join(complement(sk2),complement(converse(sk2)))),
inference(copy,[status(thm)],[c_11611]) ).
cnf(c_11612,plain,
join(converse(sk2),complement(join(complement(one),complement(complement(join(complement(sk2),complement(converse(sk2)))))))) = complement(join(complement(one),complement(composition(complement(join(complement(sk2),complement(converse(sk2)))),converse(sk2))))),
inference(paramod,[status(thm)],[c_1675,c_1673]) ).
cnf(c_11613,plain,
join(converse(sk2),complement(join(complement(one),join(complement(sk2),complement(converse(sk2)))))) = complement(join(complement(one),complement(composition(complement(join(complement(sk2),complement(converse(sk2)))),converse(sk2))))),
inference(paramod,[status(thm)],[c_173,c_11612]) ).
cnf(c_11614,plain,
join(converse(sk2),complement(join(complement(sk2),complement(converse(sk2))))) = complement(join(complement(one),complement(composition(complement(join(complement(sk2),complement(converse(sk2)))),converse(sk2))))),
inference(paramod,[status(thm)],[c_1265,c_11613]) ).
cnf(c_11615,plain,
converse(sk2) = complement(join(complement(one),complement(composition(complement(join(complement(sk2),complement(converse(sk2)))),converse(sk2))))),
inference(paramod,[status(thm)],[c_1136,c_11614]) ).
cnf(c_11616,plain,
converse(sk2) = complement(join(complement(one),complement(complement(join(complement(sk2),complement(converse(sk2))))))),
inference(paramod,[status(thm)],[c_1675,c_11615]) ).
cnf(c_11617,plain,
converse(sk2) = complement(join(complement(one),join(complement(sk2),complement(converse(sk2))))),
inference(paramod,[status(thm)],[c_173,c_11616]) ).
cnf(c_11618,plain,
converse(sk2) = complement(join(complement(sk2),complement(converse(sk2)))),
inference(paramod,[status(thm)],[c_1265,c_11617]) ).
cnf(c_1677,plain,
complement(join(complement(sk2),complement(converse(sk2)))) = converse(sk2),
inference(copy,[status(thm)],[c_11618]) ).
cnf(c_11619,plain,
join(converse(sk2),composition(converse(sk2),sk2)) = composition(converse(sk2),sk2),
inference(paramod,[status(thm)],[c_1677,c_1672]) ).
cnf(c_11620,plain,
converse(sk2) = composition(converse(sk2),sk2),
inference(paramod,[status(thm)],[c_938,c_11619]) ).
cnf(c_1678,plain,
composition(converse(sk2),sk2) = converse(sk2),
inference(copy,[status(thm)],[c_11620]) ).
cnf(c_11621,plain,
converse(converse(sk2)) = composition(converse(sk2),converse(converse(sk2))),
inference(paramod,[status(thm)],[c_1678,c_13]) ).
cnf(c_11622,plain,
sk2 = composition(converse(sk2),converse(converse(sk2))),
inference(paramod,[status(thm)],[c_11,c_11621]) ).
cnf(c_11623,plain,
sk2 = composition(converse(sk2),sk2),
inference(paramod,[status(thm)],[c_11,c_11622]) ).
cnf(c_11624,plain,
sk2 = converse(sk2),
inference(paramod,[status(thm)],[c_1678,c_11623]) ).
cnf(c_1701,plain,
converse(sk2) = sk2,
inference(copy,[status(thm)],[c_11624]) ).
cnf(c_2005,plain,
join(complement(A),complement(join(A,B))) = complement(A),
inference(paramod,[status(thm)],[c_173,c_294]) ).
cnf(c_2021,plain,
join(complement(A),complement(join(B,A))) = complement(A),
inference(paramod,[status(thm)],[c_1,c_2005]) ).
cnf(c_2031,plain,
join(complement(sk2),complement(join(A,one))) = complement(sk2),
inference(paramod,[status(thm)],[c_92,c_2005]) ).
cnf(c_11625,plain,
join(complement(composition(sk2,A)),complement(A)) = complement(composition(sk2,A)),
inference(paramod,[status(thm)],[c_151,c_2021]) ).
cnf(c_2043,plain,
join(complement(A),complement(composition(sk2,A))) = complement(composition(sk2,A)),
inference(paramod,[status(thm)],[c_1,c_11625]) ).
cnf(c_11626,plain,
join(complement(composition(sk1,A)),complement(A)) = complement(composition(sk1,A)),
inference(paramod,[status(thm)],[c_152,c_2021]) ).
cnf(c_2044,plain,
join(complement(A),complement(composition(sk1,A))) = complement(composition(sk1,A)),
inference(paramod,[status(thm)],[c_1,c_11626]) ).
cnf(c_11627,plain,
join(complement(composition(sk2,sk1)),complement(one)) = complement(composition(sk2,sk1)),
inference(paramod,[status(thm)],[c_537,c_2021]) ).
cnf(c_2052,plain,
join(complement(one),complement(composition(sk2,sk1))) = complement(composition(sk2,sk1)),
inference(paramod,[status(thm)],[c_1,c_11627]) ).
cnf(c_11628,plain,
join(complement(composition(sk1,sk2)),complement(one)) = complement(composition(sk1,sk2)),
inference(paramod,[status(thm)],[c_801,c_2021]) ).
cnf(c_2056,plain,
join(complement(one),complement(composition(sk1,sk2))) = complement(composition(sk1,sk2)),
inference(paramod,[status(thm)],[c_1,c_11628]) ).
cnf(c_11629,plain,
join(complement(composition(A,sk2)),complement(A)) = complement(composition(A,sk2)),
inference(paramod,[status(thm)],[c_938,c_2021]) ).
cnf(c_2060,plain,
join(complement(A),complement(composition(A,sk2))) = complement(composition(A,sk2)),
inference(paramod,[status(thm)],[c_1,c_11629]) ).
cnf(c_11630,plain,
join(complement(composition(sk1,A)),B) = join(complement(A),join(complement(composition(sk1,A)),B)),
inference(paramod,[status(thm)],[c_2044,c_3]) ).
cnf(c_2172,plain,
join(complement(A),join(complement(composition(sk1,A)),B)) = join(complement(composition(sk1,A)),B),
inference(copy,[status(thm)],[c_11630]) ).
cnf(c_11631,plain,
join(complement(complement(composition(sk2,sk1))),composition(complement(join(complement(sk2),complement(composition(one,converse(sk1))))),complement(join(complement(sk1),complement(composition(converse(sk2),one)))))) = composition(complement(join(complement(sk2),complement(composition(one,converse(sk1))))),complement(join(complement(sk1),complement(composition(converse(sk2),one))))),
inference(paramod,[status(thm)],[c_2052,c_62]) ).
cnf(c_11632,plain,
join(composition(sk2,sk1),composition(complement(join(complement(sk2),complement(composition(one,converse(sk1))))),complement(join(complement(sk1),complement(composition(converse(sk2),one)))))) = composition(complement(join(complement(sk2),complement(composition(one,converse(sk1))))),complement(join(complement(sk1),complement(composition(converse(sk2),one))))),
inference(paramod,[status(thm)],[c_173,c_11631]) ).
cnf(c_11633,plain,
join(composition(sk2,sk1),composition(complement(join(complement(sk2),complement(composition(one,sk1)))),complement(join(complement(sk1),complement(composition(converse(sk2),one)))))) = composition(complement(join(complement(sk2),complement(composition(one,converse(sk1))))),complement(join(complement(sk1),complement(composition(converse(sk2),one))))),
inference(paramod,[status(thm)],[c_1595,c_11632]) ).
cnf(c_11634,plain,
join(composition(sk2,sk1),composition(complement(join(complement(sk2),complement(sk1))),complement(join(complement(sk1),complement(composition(converse(sk2),one)))))) = composition(complement(join(complement(sk2),complement(composition(one,converse(sk1))))),complement(join(complement(sk1),complement(composition(converse(sk2),one))))),
inference(paramod,[status(thm)],[c_146,c_11633]) ).
cnf(c_11635,plain,
join(composition(sk2,sk1),composition(complement(join(complement(sk1),complement(sk2))),complement(join(complement(sk1),complement(composition(converse(sk2),one)))))) = composition(complement(join(complement(sk2),complement(composition(one,converse(sk1))))),complement(join(complement(sk1),complement(composition(converse(sk2),one))))),
inference(paramod,[status(thm)],[c_1,c_11634]) ).
cnf(c_11636,plain,
join(composition(sk2,sk1),composition(complement(join(complement(sk1),complement(sk2))),complement(join(complement(sk1),complement(composition(sk2,one)))))) = composition(complement(join(complement(sk2),complement(composition(one,converse(sk1))))),complement(join(complement(sk1),complement(composition(converse(sk2),one))))),
inference(paramod,[status(thm)],[c_1701,c_11635]) ).
cnf(c_11637,plain,
join(composition(sk2,sk1),composition(complement(join(complement(sk1),complement(sk2))),complement(join(complement(sk1),complement(sk2))))) = composition(complement(join(complement(sk2),complement(composition(one,converse(sk1))))),complement(join(complement(sk1),complement(composition(converse(sk2),one))))),
inference(paramod,[status(thm)],[c_9,c_11636]) ).
cnf(c_11638,plain,
join(composition(sk2,sk1),composition(complement(join(complement(sk1),complement(sk2))),complement(join(complement(sk1),complement(sk2))))) = composition(complement(join(complement(sk2),complement(composition(one,sk1)))),complement(join(complement(sk1),complement(composition(converse(sk2),one))))),
inference(paramod,[status(thm)],[c_1595,c_11637]) ).
cnf(c_11639,plain,
join(composition(sk2,sk1),composition(complement(join(complement(sk1),complement(sk2))),complement(join(complement(sk1),complement(sk2))))) = composition(complement(join(complement(sk2),complement(sk1))),complement(join(complement(sk1),complement(composition(converse(sk2),one))))),
inference(paramod,[status(thm)],[c_146,c_11638]) ).
cnf(c_11640,plain,
join(composition(sk2,sk1),composition(complement(join(complement(sk1),complement(sk2))),complement(join(complement(sk1),complement(sk2))))) = composition(complement(join(complement(sk1),complement(sk2))),complement(join(complement(sk1),complement(composition(converse(sk2),one))))),
inference(paramod,[status(thm)],[c_1,c_11639]) ).
cnf(c_11641,plain,
join(composition(sk2,sk1),composition(complement(join(complement(sk1),complement(sk2))),complement(join(complement(sk1),complement(sk2))))) = composition(complement(join(complement(sk1),complement(sk2))),complement(join(complement(sk1),complement(composition(sk2,one))))),
inference(paramod,[status(thm)],[c_1701,c_11640]) ).
cnf(c_2190,plain,
join(composition(sk2,sk1),composition(complement(join(complement(sk1),complement(sk2))),complement(join(complement(sk1),complement(sk2))))) = composition(complement(join(complement(sk1),complement(sk2))),complement(join(complement(sk1),complement(sk2)))),
inference(paramod,[status(thm)],[c_9,c_11641]) ).
cnf(c_11642,plain,
join(complement(join(complement(composition(converse(sk2),one)),complement(sk1))),complement(join(complement(sk1),complement(composition(converse(sk2),complement(complement(composition(sk2,sk1)))))))) = complement(join(complement(sk1),complement(composition(converse(sk2),complement(join(complement(one),complement(composition(sk2,sk1)))))))),
inference(paramod,[status(thm)],[c_2052,c_78]) ).
cnf(c_11643,plain,
join(complement(join(complement(composition(sk2,one)),complement(sk1))),complement(join(complement(sk1),complement(composition(converse(sk2),complement(complement(composition(sk2,sk1)))))))) = complement(join(complement(sk1),complement(composition(converse(sk2),complement(join(complement(one),complement(composition(sk2,sk1)))))))),
inference(paramod,[status(thm)],[c_1701,c_11642]) ).
cnf(c_11644,plain,
join(complement(join(complement(sk2),complement(sk1))),complement(join(complement(sk1),complement(composition(converse(sk2),complement(complement(composition(sk2,sk1)))))))) = complement(join(complement(sk1),complement(composition(converse(sk2),complement(join(complement(one),complement(composition(sk2,sk1)))))))),
inference(paramod,[status(thm)],[c_9,c_11643]) ).
cnf(c_11645,plain,
join(complement(join(complement(sk1),complement(sk2))),complement(join(complement(sk1),complement(composition(converse(sk2),complement(complement(composition(sk2,sk1)))))))) = complement(join(complement(sk1),complement(composition(converse(sk2),complement(join(complement(one),complement(composition(sk2,sk1)))))))),
inference(paramod,[status(thm)],[c_1,c_11644]) ).
cnf(c_11646,plain,
join(complement(join(complement(sk1),complement(sk2))),complement(join(complement(sk1),complement(composition(sk2,complement(complement(composition(sk2,sk1)))))))) = complement(join(complement(sk1),complement(composition(converse(sk2),complement(join(complement(one),complement(composition(sk2,sk1)))))))),
inference(paramod,[status(thm)],[c_1701,c_11645]) ).
cnf(c_11647,plain,
join(complement(join(complement(sk1),complement(sk2))),complement(join(complement(sk1),complement(composition(sk2,composition(sk2,sk1)))))) = complement(join(complement(sk1),complement(composition(converse(sk2),complement(join(complement(one),complement(composition(sk2,sk1)))))))),
inference(paramod,[status(thm)],[c_173,c_11646]) ).
cnf(c_11648,plain,
join(complement(join(complement(sk1),complement(sk2))),complement(join(complement(sk1),complement(composition(sk2,sk1))))) = complement(join(complement(sk1),complement(composition(converse(sk2),complement(join(complement(one),complement(composition(sk2,sk1)))))))),
inference(paramod,[status(thm)],[c_1543,c_11647]) ).
cnf(c_11649,plain,
join(complement(join(complement(sk1),complement(sk2))),complement(complement(composition(sk2,sk1)))) = complement(join(complement(sk1),complement(composition(converse(sk2),complement(join(complement(one),complement(composition(sk2,sk1)))))))),
inference(paramod,[status(thm)],[c_2043,c_11648]) ).
cnf(c_11650,plain,
join(complement(join(complement(sk1),complement(sk2))),composition(sk2,sk1)) = complement(join(complement(sk1),complement(composition(converse(sk2),complement(join(complement(one),complement(composition(sk2,sk1)))))))),
inference(paramod,[status(thm)],[c_173,c_11649]) ).
cnf(c_11651,plain,
join(complement(join(complement(sk1),complement(sk2))),composition(sk2,sk1)) = complement(join(complement(sk1),complement(composition(sk2,complement(join(complement(one),complement(composition(sk2,sk1)))))))),
inference(paramod,[status(thm)],[c_1701,c_11650]) ).
cnf(c_11652,plain,
join(complement(join(complement(sk1),complement(sk2))),composition(sk2,sk1)) = complement(join(complement(sk1),complement(composition(sk2,complement(complement(composition(sk2,sk1))))))),
inference(paramod,[status(thm)],[c_2052,c_11651]) ).
cnf(c_11653,plain,
join(complement(join(complement(sk1),complement(sk2))),composition(sk2,sk1)) = complement(join(complement(sk1),complement(composition(sk2,composition(sk2,sk1))))),
inference(paramod,[status(thm)],[c_173,c_11652]) ).
cnf(c_11654,plain,
join(complement(join(complement(sk1),complement(sk2))),composition(sk2,sk1)) = complement(join(complement(sk1),complement(composition(sk2,sk1)))),
inference(paramod,[status(thm)],[c_1543,c_11653]) ).
cnf(c_11655,plain,
join(complement(join(complement(sk1),complement(sk2))),composition(sk2,sk1)) = complement(complement(composition(sk2,sk1))),
inference(paramod,[status(thm)],[c_2043,c_11654]) ).
cnf(c_2194,plain,
join(complement(join(complement(sk1),complement(sk2))),composition(sk2,sk1)) = composition(sk2,sk1),
inference(paramod,[status(thm)],[c_173,c_11655]) ).
cnf(c_11656,plain,
join(complement(join(complement(composition(converse(sk1),one)),complement(sk2))),composition(complement(join(complement(converse(sk1)),complement(composition(sk2,converse(one))))),complement(complement(composition(sk1,sk2))))) = composition(complement(join(complement(converse(sk1)),complement(composition(sk2,converse(one))))),complement(join(complement(one),complement(composition(sk1,sk2))))),
inference(paramod,[status(thm)],[c_2056,c_68]) ).
cnf(c_11657,plain,
join(complement(join(complement(composition(sk1,one)),complement(sk2))),composition(complement(join(complement(converse(sk1)),complement(composition(sk2,converse(one))))),complement(complement(composition(sk1,sk2))))) = composition(complement(join(complement(converse(sk1)),complement(composition(sk2,converse(one))))),complement(join(complement(one),complement(composition(sk1,sk2))))),
inference(paramod,[status(thm)],[c_1595,c_11656]) ).
cnf(c_11658,plain,
join(complement(join(complement(sk1),complement(sk2))),composition(complement(join(complement(converse(sk1)),complement(composition(sk2,converse(one))))),complement(complement(composition(sk1,sk2))))) = composition(complement(join(complement(converse(sk1)),complement(composition(sk2,converse(one))))),complement(join(complement(one),complement(composition(sk1,sk2))))),
inference(paramod,[status(thm)],[c_9,c_11657]) ).
cnf(c_11659,plain,
join(complement(join(complement(sk1),complement(sk2))),composition(complement(join(complement(sk1),complement(composition(sk2,converse(one))))),complement(complement(composition(sk1,sk2))))) = composition(complement(join(complement(converse(sk1)),complement(composition(sk2,converse(one))))),complement(join(complement(one),complement(composition(sk1,sk2))))),
inference(paramod,[status(thm)],[c_1595,c_11658]) ).
cnf(c_11660,plain,
join(complement(join(complement(sk1),complement(sk2))),composition(complement(join(complement(sk1),complement(composition(sk2,one)))),complement(complement(composition(sk1,sk2))))) = composition(complement(join(complement(converse(sk1)),complement(composition(sk2,converse(one))))),complement(join(complement(one),complement(composition(sk1,sk2))))),
inference(paramod,[status(thm)],[c_128,c_11659]) ).
cnf(c_11661,plain,
join(complement(join(complement(sk1),complement(sk2))),composition(complement(join(complement(sk1),complement(sk2))),complement(complement(composition(sk1,sk2))))) = composition(complement(join(complement(converse(sk1)),complement(composition(sk2,converse(one))))),complement(join(complement(one),complement(composition(sk1,sk2))))),
inference(paramod,[status(thm)],[c_9,c_11660]) ).
cnf(c_11662,plain,
join(complement(join(complement(sk1),complement(sk2))),composition(complement(join(complement(sk1),complement(sk2))),composition(sk1,sk2))) = composition(complement(join(complement(converse(sk1)),complement(composition(sk2,converse(one))))),complement(join(complement(one),complement(composition(sk1,sk2))))),
inference(paramod,[status(thm)],[c_173,c_11661]) ).
cnf(c_11663,plain,
join(complement(join(complement(sk1),complement(sk2))),composition(complement(join(complement(sk1),complement(sk2))),composition(sk1,sk2))) = composition(complement(join(complement(sk1),complement(composition(sk2,converse(one))))),complement(join(complement(one),complement(composition(sk1,sk2))))),
inference(paramod,[status(thm)],[c_1595,c_11662]) ).
cnf(c_11664,plain,
join(complement(join(complement(sk1),complement(sk2))),composition(complement(join(complement(sk1),complement(sk2))),composition(sk1,sk2))) = composition(complement(join(complement(sk1),complement(composition(sk2,one)))),complement(join(complement(one),complement(composition(sk1,sk2))))),
inference(paramod,[status(thm)],[c_128,c_11663]) ).
cnf(c_11665,plain,
join(complement(join(complement(sk1),complement(sk2))),composition(complement(join(complement(sk1),complement(sk2))),composition(sk1,sk2))) = composition(complement(join(complement(sk1),complement(sk2))),complement(join(complement(one),complement(composition(sk1,sk2))))),
inference(paramod,[status(thm)],[c_9,c_11664]) ).
cnf(c_11666,plain,
join(complement(join(complement(sk1),complement(sk2))),composition(complement(join(complement(sk1),complement(sk2))),composition(sk1,sk2))) = composition(complement(join(complement(sk1),complement(sk2))),complement(complement(composition(sk1,sk2)))),
inference(paramod,[status(thm)],[c_2056,c_11665]) ).
cnf(c_2203,plain,
join(complement(join(complement(sk1),complement(sk2))),composition(complement(join(complement(sk1),complement(sk2))),composition(sk1,sk2))) = composition(complement(join(complement(sk1),complement(sk2))),composition(sk1,sk2)),
inference(paramod,[status(thm)],[c_173,c_11666]) ).
cnf(c_11667,plain,
join(A,complement(join(B,A))) = join(complement(B),complement(join(complement(A),complement(B)))),
inference(paramod,[status(thm)],[c_173,c_205]) ).
cnf(c_11668,plain,
join(A,complement(join(B,A))) = join(complement(B),complement(complement(A))),
inference(paramod,[status(thm)],[c_305,c_11667]) ).
cnf(c_2781,plain,
join(A,complement(join(B,A))) = join(complement(B),A),
inference(paramod,[status(thm)],[c_173,c_11668]) ).
cnf(c_2854,plain,
join(A,complement(join(A,B))) = join(complement(B),A),
inference(paramod,[status(thm)],[c_1,c_2781]) ).
cnf(c_11669,plain,
composition(join(complement(A),B),C) = join(composition(B,C),composition(complement(join(A,B)),C)),
inference(paramod,[status(thm)],[c_2781,c_10]) ).
cnf(c_11670,plain,
join(composition(complement(A),C),composition(B,C)) = join(composition(B,C),composition(complement(join(A,B)),C)),
inference(paramod,[status(thm)],[c_10,c_11669]) ).
cnf(c_2858,plain,
join(composition(A,B),composition(complement(join(C,A)),B)) = join(composition(complement(C),B),composition(A,B)),
inference(copy,[status(thm)],[c_11670]) ).
cnf(c_11671,plain,
join(converse(complement(A)),complement(top)) = join(complement(converse(A)),converse(complement(A))),
inference(paramod,[status(thm)],[c_640,c_2781]) ).
cnf(c_11672,plain,
join(converse(complement(A)),zero) = join(complement(converse(A)),converse(complement(A))),
inference(paramod,[status(thm)],[c_19,c_11671]) ).
cnf(c_11673,plain,
join(zero,converse(complement(A))) = join(complement(converse(A)),converse(complement(A))),
inference(paramod,[status(thm)],[c_1,c_11672]) ).
cnf(c_11674,plain,
converse(complement(A)) = join(complement(converse(A)),converse(complement(A))),
inference(paramod,[status(thm)],[c_175,c_11673]) ).
cnf(c_2867,plain,
join(complement(converse(A)),converse(complement(A))) = converse(complement(A)),
inference(copy,[status(thm)],[c_11674]) ).
cnf(c_11675,plain,
join(converse(complement(sk1)),complement(top)) = join(complement(sk1),converse(complement(sk1))),
inference(paramod,[status(thm)],[c_1631,c_2781]) ).
cnf(c_11676,plain,
join(converse(complement(sk1)),zero) = join(complement(sk1),converse(complement(sk1))),
inference(paramod,[status(thm)],[c_19,c_11675]) ).
cnf(c_11677,plain,
join(zero,converse(complement(sk1))) = join(complement(sk1),converse(complement(sk1))),
inference(paramod,[status(thm)],[c_1,c_11676]) ).
cnf(c_11678,plain,
converse(complement(sk1)) = join(complement(sk1),converse(complement(sk1))),
inference(paramod,[status(thm)],[c_175,c_11677]) ).
cnf(c_2895,plain,
join(complement(sk1),converse(complement(sk1))) = converse(complement(sk1)),
inference(copy,[status(thm)],[c_11678]) ).
cnf(c_11679,plain,
join(converse(complement(converse(A))),complement(top)) = join(complement(A),converse(complement(converse(A)))),
inference(paramod,[status(thm)],[c_632,c_2781]) ).
cnf(c_11680,plain,
join(converse(complement(converse(A))),zero) = join(complement(A),converse(complement(converse(A)))),
inference(paramod,[status(thm)],[c_19,c_11679]) ).
cnf(c_11681,plain,
join(zero,converse(complement(converse(A)))) = join(complement(A),converse(complement(converse(A)))),
inference(paramod,[status(thm)],[c_1,c_11680]) ).
cnf(c_11682,plain,
converse(complement(converse(A))) = join(complement(A),converse(complement(converse(A)))),
inference(paramod,[status(thm)],[c_175,c_11681]) ).
cnf(c_2901,plain,
join(complement(A),converse(complement(converse(A)))) = converse(complement(converse(A))),
inference(copy,[status(thm)],[c_11682]) ).
cnf(c_11683,plain,
converse(converse(complement(sk1))) = join(converse(complement(sk1)),converse(converse(complement(sk1)))),
inference(paramod,[status(thm)],[c_2895,c_12]) ).
cnf(c_11684,plain,
complement(sk1) = join(converse(complement(sk1)),converse(converse(complement(sk1)))),
inference(paramod,[status(thm)],[c_11,c_11683]) ).
cnf(c_11685,plain,
complement(sk1) = join(converse(complement(sk1)),complement(sk1)),
inference(paramod,[status(thm)],[c_11,c_11684]) ).
cnf(c_11686,plain,
complement(sk1) = join(complement(sk1),converse(complement(sk1))),
inference(paramod,[status(thm)],[c_1,c_11685]) ).
cnf(c_11687,plain,
complement(sk1) = converse(complement(sk1)),
inference(paramod,[status(thm)],[c_2895,c_11686]) ).
cnf(c_3201,plain,
converse(complement(sk1)) = complement(sk1),
inference(copy,[status(thm)],[c_11687]) ).
cnf(c_3224,plain,
join(converse(A),composition(converse(A),complement(sk1))) = composition(converse(A),top),
inference(paramod,[status(thm)],[c_3201,c_977]) ).
cnf(c_11688,plain,
join(composition(A,B),complement(composition(top,B))) = join(complement(composition(complement(A),B)),composition(A,B)),
inference(paramod,[status(thm)],[c_56,c_2854]) ).
cnf(c_11689,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_11688]) ).
cnf(c_3489,plain,
join(composition(A,B),complement(composition(complement(A),B))) = join(composition(A,B),complement(composition(top,B))),
inference(copy,[status(thm)],[c_11689]) ).
cnf(c_11690,plain,
converse(converse(complement(A))) = join(converse(complement(converse(A))),converse(converse(complement(A)))),
inference(paramod,[status(thm)],[c_2867,c_12]) ).
cnf(c_11691,plain,
complement(A) = join(converse(complement(converse(A))),converse(converse(complement(A)))),
inference(paramod,[status(thm)],[c_11,c_11690]) ).
cnf(c_11692,plain,
complement(A) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_11,c_11691]) ).
cnf(c_11693,plain,
complement(A) = join(complement(A),converse(complement(converse(A)))),
inference(paramod,[status(thm)],[c_1,c_11692]) ).
cnf(c_11694,plain,
complement(A) = converse(complement(converse(A))),
inference(paramod,[status(thm)],[c_2901,c_11693]) ).
cnf(c_3540,plain,
converse(complement(converse(A))) = complement(A),
inference(copy,[status(thm)],[c_11694]) ).
cnf(c_3549,plain,
converse(complement(A)) = complement(converse(A)),
inference(paramod,[status(thm)],[c_3540,c_11]) ).
cnf(c_11695,plain,
join(composition(complement(join(A,complement(sk2))),B),composition(complement(join(complement(one),complement(join(A,complement(sk2))))),B)) = composition(one,B),
inference(paramod,[status(thm)],[c_1259,c_266]) ).
cnf(c_11696,plain,
join(composition(complement(complement(one)),B),composition(complement(join(A,complement(sk2))),B)) = composition(one,B),
inference(paramod,[status(thm)],[c_2858,c_11695]) ).
cnf(c_11697,plain,
join(composition(one,B),composition(complement(join(A,complement(sk2))),B)) = composition(one,B),
inference(paramod,[status(thm)],[c_173,c_11696]) ).
cnf(c_11698,plain,
join(B,composition(complement(join(A,complement(sk2))),B)) = composition(one,B),
inference(paramod,[status(thm)],[c_146,c_11697]) ).
cnf(c_3899,plain,
join(A,composition(complement(join(B,complement(sk2))),A)) = A,
inference(paramod,[status(thm)],[c_146,c_11698]) ).
cnf(c_11699,plain,
join(complement(join(complement(complement(A)),B)),complement(join(complement(complement(composition(A,sk2))),complement(join(complement(join(complement(complement(A)),complement(B))),complement(composition(A,sk2))))))) = join(complement(A),complement(composition(A,sk2))),
inference(paramod,[status(thm)],[c_2060,c_302]) ).
cnf(c_11700,plain,
join(complement(join(A,B)),complement(join(complement(complement(composition(A,sk2))),complement(join(complement(join(complement(complement(A)),complement(B))),complement(composition(A,sk2))))))) = join(complement(A),complement(composition(A,sk2))),
inference(paramod,[status(thm)],[c_173,c_11699]) ).
cnf(c_11701,plain,
join(complement(join(A,B)),complement(join(composition(A,sk2),complement(join(complement(join(complement(complement(A)),complement(B))),complement(composition(A,sk2))))))) = join(complement(A),complement(composition(A,sk2))),
inference(paramod,[status(thm)],[c_173,c_11700]) ).
cnf(c_11702,plain,
join(complement(join(A,B)),complement(join(composition(A,sk2),complement(join(complement(join(A,complement(B))),complement(composition(A,sk2))))))) = join(complement(A),complement(composition(A,sk2))),
inference(paramod,[status(thm)],[c_173,c_11701]) ).
cnf(c_11703,plain,
join(complement(join(A,B)),complement(composition(A,sk2))) = join(complement(A),complement(composition(A,sk2))),
inference(paramod,[status(thm)],[c_1136,c_11702]) ).
cnf(c_4459,plain,
join(complement(join(A,B)),complement(composition(A,sk2))) = complement(composition(A,sk2)),
inference(paramod,[status(thm)],[c_2060,c_11703]) ).
cnf(c_11704,plain,
join(A,composition(converse(converse(A)),complement(sk1))) = composition(converse(converse(A)),top),
inference(paramod,[status(thm)],[c_11,c_3224]) ).
cnf(c_11705,plain,
join(A,composition(A,complement(sk1))) = composition(converse(converse(A)),top),
inference(paramod,[status(thm)],[c_11,c_11704]) ).
cnf(c_5086,plain,
join(A,composition(A,complement(sk1))) = composition(A,top),
inference(paramod,[status(thm)],[c_11,c_11705]) ).
cnf(c_5114,plain,
join(complement(sk1),composition(sk2,top)) = join(sk2,complement(sk1)),
inference(paramod,[status(thm)],[c_5086,c_235]) ).
cnf(c_11706,plain,
converse(join(sk2,complement(sk1))) = join(converse(complement(sk1)),converse(composition(sk2,top))),
inference(paramod,[status(thm)],[c_5114,c_12]) ).
cnf(c_11707,plain,
join(converse(sk2),converse(complement(sk1))) = join(converse(complement(sk1)),converse(composition(sk2,top))),
inference(paramod,[status(thm)],[c_12,c_11706]) ).
cnf(c_11708,plain,
join(sk2,converse(complement(sk1))) = join(converse(complement(sk1)),converse(composition(sk2,top))),
inference(paramod,[status(thm)],[c_1701,c_11707]) ).
cnf(c_11709,plain,
join(sk2,complement(converse(sk1))) = join(converse(complement(sk1)),converse(composition(sk2,top))),
inference(paramod,[status(thm)],[c_3549,c_11708]) ).
cnf(c_11710,plain,
join(sk2,complement(sk1)) = join(converse(complement(sk1)),converse(composition(sk2,top))),
inference(paramod,[status(thm)],[c_1595,c_11709]) ).
cnf(c_11711,plain,
join(sk2,complement(sk1)) = join(complement(converse(sk1)),converse(composition(sk2,top))),
inference(paramod,[status(thm)],[c_3549,c_11710]) ).
cnf(c_11712,plain,
join(sk2,complement(sk1)) = join(complement(sk1),converse(composition(sk2,top))),
inference(paramod,[status(thm)],[c_1595,c_11711]) ).
cnf(c_11713,plain,
join(sk2,complement(sk1)) = join(complement(sk1),composition(converse(top),converse(sk2))),
inference(paramod,[status(thm)],[c_13,c_11712]) ).
cnf(c_11714,plain,
join(sk2,complement(sk1)) = join(complement(sk1),composition(top,converse(sk2))),
inference(paramod,[status(thm)],[c_620,c_11713]) ).
cnf(c_11715,plain,
join(sk2,complement(sk1)) = join(complement(sk1),composition(top,sk2)),
inference(paramod,[status(thm)],[c_1701,c_11714]) ).
cnf(c_5155,plain,
join(complement(sk1),composition(top,sk2)) = join(sk2,complement(sk1)),
inference(copy,[status(thm)],[c_11715]) ).
cnf(c_11716,plain,
join(complement(sk1),complement(join(sk2,complement(sk1)))) = join(complement(composition(top,sk2)),complement(sk1)),
inference(paramod,[status(thm)],[c_5155,c_2854]) ).
cnf(c_11717,plain,
join(complement(sk2),complement(sk1)) = join(complement(composition(top,sk2)),complement(sk1)),
inference(paramod,[status(thm)],[c_2781,c_11716]) ).
cnf(c_11718,plain,
join(complement(sk1),complement(sk2)) = join(complement(composition(top,sk2)),complement(sk1)),
inference(paramod,[status(thm)],[c_1,c_11717]) ).
cnf(c_11719,plain,
join(complement(sk1),complement(sk2)) = join(complement(sk1),complement(composition(top,sk2))),
inference(paramod,[status(thm)],[c_1,c_11718]) ).
cnf(c_5180,plain,
join(complement(sk1),complement(composition(top,sk2))) = join(complement(sk1),complement(sk2)),
inference(copy,[status(thm)],[c_11719]) ).
cnf(c_11720,plain,
join(complement(complement(composition(A,sk2))),complement(composition(complement(A),sk2))) = complement(composition(complement(A),sk2)),
inference(paramod,[status(thm)],[c_2060,c_4459]) ).
cnf(c_11721,plain,
join(composition(A,sk2),complement(composition(complement(A),sk2))) = complement(composition(complement(A),sk2)),
inference(paramod,[status(thm)],[c_173,c_11720]) ).
cnf(c_11722,plain,
join(composition(A,sk2),complement(composition(top,sk2))) = complement(composition(complement(A),sk2)),
inference(paramod,[status(thm)],[c_3489,c_11721]) ).
cnf(c_7023,plain,
complement(composition(complement(A),sk2)) = join(composition(A,sk2),complement(composition(top,sk2))),
inference(copy,[status(thm)],[c_11722]) ).
cnf(c_11723,plain,
join(complement(complement(A)),complement(composition(complement(A),sk2))) = complement(composition(complement(A),sk2)),
inference(paramod,[status(thm)],[c_394,c_4459]) ).
cnf(c_11724,plain,
join(A,complement(composition(complement(A),sk2))) = complement(composition(complement(A),sk2)),
inference(paramod,[status(thm)],[c_173,c_11723]) ).
cnf(c_11725,plain,
join(A,join(composition(A,sk2),complement(composition(top,sk2)))) = complement(composition(complement(A),sk2)),
inference(paramod,[status(thm)],[c_7023,c_11724]) ).
cnf(c_11726,plain,
join(A,complement(composition(top,sk2))) = complement(composition(complement(A),sk2)),
inference(paramod,[status(thm)],[c_942,c_11725]) ).
cnf(c_11727,plain,
join(A,complement(composition(top,sk2))) = join(composition(A,sk2),complement(composition(top,sk2))),
inference(paramod,[status(thm)],[c_7023,c_11726]) ).
cnf(c_7040,plain,
join(composition(A,sk2),complement(composition(top,sk2))) = join(A,complement(composition(top,sk2))),
inference(copy,[status(thm)],[c_11727]) ).
cnf(c_7066,plain,
complement(composition(complement(A),sk2)) = join(A,complement(composition(top,sk2))),
inference(paramod,[status(thm)],[c_7040,c_7023]) ).
cnf(c_7083,plain,
complement(composition(A,sk2)) = join(complement(A),complement(composition(top,sk2))),
inference(paramod,[status(thm)],[c_173,c_7066]) ).
cnf(c_11728,plain,
complement(composition(complement(complement(sk1)),sk2)) = join(complement(sk1),complement(sk2)),
inference(paramod,[status(thm)],[c_5180,c_7066]) ).
cnf(c_7101,plain,
complement(composition(sk1,sk2)) = join(complement(sk1),complement(sk2)),
inference(paramod,[status(thm)],[c_173,c_11728]) ).
cnf(c_11729,plain,
complement(join(join(complement(sk1),complement(sk2)),complement(join(A,one)))) = composition(sk1,sk2),
inference(paramod,[status(thm)],[c_7101,c_1291]) ).
cnf(c_11730,plain,
complement(join(complement(sk1),join(complement(sk2),complement(join(A,one))))) = composition(sk1,sk2),
inference(paramod,[status(thm)],[c_3,c_11729]) ).
cnf(c_11731,plain,
complement(join(complement(sk1),complement(sk2))) = composition(sk1,sk2),
inference(paramod,[status(thm)],[c_2031,c_11730]) ).
cnf(c_7151,plain,
composition(sk1,sk2) = complement(join(complement(sk1),complement(sk2))),
inference(copy,[status(thm)],[c_11731]) ).
cnf(c_11732,plain,
join(complement(join(complement(sk1),complement(sk2))),composition(complement(join(complement(sk1),complement(sk2))),complement(join(complement(sk1),complement(sk2))))) = composition(complement(join(complement(sk1),complement(sk2))),composition(sk1,sk2)),
inference(paramod,[status(thm)],[c_7151,c_2203]) ).
cnf(c_11733,plain,
complement(join(complement(sk1),complement(sk2))) = composition(complement(join(complement(sk1),complement(sk2))),composition(sk1,sk2)),
inference(paramod,[status(thm)],[c_3899,c_11732]) ).
cnf(c_11734,plain,
complement(join(complement(sk1),complement(sk2))) = composition(complement(join(complement(sk1),complement(sk2))),complement(join(complement(sk1),complement(sk2)))),
inference(paramod,[status(thm)],[c_7151,c_11733]) ).
cnf(c_7182,plain,
composition(complement(join(complement(sk1),complement(sk2))),complement(join(complement(sk1),complement(sk2)))) = complement(join(complement(sk1),complement(sk2))),
inference(copy,[status(thm)],[c_11734]) ).
cnf(c_11735,plain,
join(composition(sk2,sk1),complement(join(complement(sk1),complement(sk2)))) = composition(complement(join(complement(sk1),complement(sk2))),complement(join(complement(sk1),complement(sk2)))),
inference(paramod,[status(thm)],[c_7182,c_2190]) ).
cnf(c_11736,plain,
join(complement(join(complement(sk1),complement(sk2))),composition(sk2,sk1)) = composition(complement(join(complement(sk1),complement(sk2))),complement(join(complement(sk1),complement(sk2)))),
inference(paramod,[status(thm)],[c_1,c_11735]) ).
cnf(c_11737,plain,
composition(sk2,sk1) = composition(complement(join(complement(sk1),complement(sk2))),complement(join(complement(sk1),complement(sk2)))),
inference(paramod,[status(thm)],[c_2194,c_11736]) ).
cnf(c_7184,plain,
composition(sk2,sk1) = complement(join(complement(sk1),complement(sk2))),
inference(paramod,[status(thm)],[c_7182,c_11737]) ).
cnf(c_7195,plain,
composition(complement(join(complement(sk1),complement(sk2))),A) = composition(sk1,composition(sk2,A)),
inference(paramod,[status(thm)],[c_7151,c_8]) ).
cnf(c_11738,plain,
tuple(join(complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3)))),composition(sk1,composition(sk2,sk3))),join(complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3)))),composition(complement(join(complement(sk1),complement(sk2))),sk3))) != tuple(composition(complement(join(complement(sk1),complement(sk2))),sk3),complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3))))),
inference(paramod,[status(thm)],[c_7195,c_31]) ).
cnf(c_11739,plain,
tuple(join(complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3)))),composition(sk1,composition(sk2,sk3))),join(complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3)))),composition(sk1,composition(sk2,sk3)))) != tuple(composition(complement(join(complement(sk1),complement(sk2))),sk3),complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3))))),
inference(paramod,[status(thm)],[c_7195,c_11738]) ).
cnf(c_7217,plain,
tuple(join(complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3)))),composition(sk1,composition(sk2,sk3))),join(complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3)))),composition(sk1,composition(sk2,sk3)))) != tuple(composition(sk1,composition(sk2,sk3)),complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3))))),
inference(paramod,[status(thm)],[c_7195,c_11739]) ).
cnf(c_11740,plain,
composition(complement(join(complement(sk1),complement(sk2))),A) = composition(sk2,composition(sk1,A)),
inference(paramod,[status(thm)],[c_7184,c_8]) ).
cnf(c_11741,plain,
composition(sk1,composition(sk2,A)) = composition(sk2,composition(sk1,A)),
inference(paramod,[status(thm)],[c_7195,c_11740]) ).
cnf(c_7218,plain,
composition(sk2,composition(sk1,A)) = composition(sk1,composition(sk2,A)),
inference(copy,[status(thm)],[c_11741]) ).
cnf(c_11742,plain,
converse(complement(composition(A,sk2))) = join(converse(complement(A)),converse(complement(composition(top,sk2)))),
inference(paramod,[status(thm)],[c_7083,c_12]) ).
cnf(c_11743,plain,
complement(converse(composition(A,sk2))) = join(converse(complement(A)),converse(complement(composition(top,sk2)))),
inference(paramod,[status(thm)],[c_3549,c_11742]) ).
cnf(c_11744,plain,
complement(composition(converse(sk2),converse(A))) = join(converse(complement(A)),converse(complement(composition(top,sk2)))),
inference(paramod,[status(thm)],[c_13,c_11743]) ).
cnf(c_11745,plain,
complement(composition(sk2,converse(A))) = join(converse(complement(A)),converse(complement(composition(top,sk2)))),
inference(paramod,[status(thm)],[c_1701,c_11744]) ).
cnf(c_11746,plain,
complement(composition(sk2,converse(A))) = join(complement(converse(A)),converse(complement(composition(top,sk2)))),
inference(paramod,[status(thm)],[c_3549,c_11745]) ).
cnf(c_11747,plain,
complement(composition(sk2,converse(A))) = join(complement(converse(A)),complement(converse(composition(top,sk2)))),
inference(paramod,[status(thm)],[c_3549,c_11746]) ).
cnf(c_11748,plain,
complement(composition(sk2,converse(A))) = join(complement(converse(A)),complement(composition(converse(sk2),converse(top)))),
inference(paramod,[status(thm)],[c_13,c_11747]) ).
cnf(c_11749,plain,
complement(composition(sk2,converse(A))) = join(complement(converse(A)),complement(composition(sk2,converse(top)))),
inference(paramod,[status(thm)],[c_1701,c_11748]) ).
cnf(c_11750,plain,
complement(composition(sk2,converse(A))) = join(complement(converse(A)),complement(composition(sk2,top))),
inference(paramod,[status(thm)],[c_620,c_11749]) ).
cnf(c_7285,plain,
complement(composition(sk2,converse(A))) = join(complement(composition(sk2,top)),complement(converse(A))),
inference(paramod,[status(thm)],[c_1,c_11750]) ).
cnf(c_11751,plain,
complement(composition(sk2,A)) = join(complement(composition(sk2,top)),complement(converse(converse(A)))),
inference(paramod,[status(thm)],[c_11,c_7285]) ).
cnf(c_10104,plain,
complement(composition(sk2,A)) = join(complement(composition(sk2,top)),complement(A)),
inference(paramod,[status(thm)],[c_11,c_11751]) ).
cnf(c_10154,plain,
complement(composition(sk2,A)) = join(complement(A),complement(composition(sk2,top))),
inference(paramod,[status(thm)],[c_10104,c_1]) ).
cnf(c_11752,plain,
tuple(join(complement(join(complement(composition(sk1,sk3)),join(complement(composition(sk2,top)),complement(sk3)))),composition(sk1,composition(sk2,sk3))),join(complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3)))),composition(sk1,composition(sk2,sk3)))) != tuple(composition(sk1,composition(sk2,sk3)),complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3))))),
inference(paramod,[status(thm)],[c_10104,c_7217]) ).
cnf(c_11753,plain,
tuple(join(complement(join(complement(composition(sk1,sk3)),join(complement(sk3),complement(composition(sk2,top))))),composition(sk1,composition(sk2,sk3))),join(complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3)))),composition(sk1,composition(sk2,sk3)))) != tuple(composition(sk1,composition(sk2,sk3)),complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3))))),
inference(paramod,[status(thm)],[c_1,c_11752]) ).
cnf(c_11754,plain,
tuple(join(complement(join(complement(sk3),join(complement(composition(sk1,sk3)),complement(composition(sk2,top))))),composition(sk1,composition(sk2,sk3))),join(complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3)))),composition(sk1,composition(sk2,sk3)))) != tuple(composition(sk1,composition(sk2,sk3)),complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3))))),
inference(paramod,[status(thm)],[c_33,c_11753]) ).
cnf(c_10292,plain,
tuple(join(complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,top)))),composition(sk1,composition(sk2,sk3))),join(complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3)))),composition(sk1,composition(sk2,sk3)))) != tuple(composition(sk1,composition(sk2,sk3)),complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3))))),
inference(paramod,[status(thm)],[c_2172,c_11754]) ).
cnf(c_11755,plain,
tuple(join(complement(complement(composition(sk2,composition(sk1,sk3)))),composition(sk1,composition(sk2,sk3))),join(complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3)))),composition(sk1,composition(sk2,sk3)))) != tuple(composition(sk1,composition(sk2,sk3)),complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3))))),
inference(paramod,[status(thm)],[c_10154,c_10292]) ).
cnf(c_11756,plain,
tuple(join(complement(complement(composition(sk1,composition(sk2,sk3)))),composition(sk1,composition(sk2,sk3))),join(complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3)))),composition(sk1,composition(sk2,sk3)))) != tuple(composition(sk1,composition(sk2,sk3)),complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3))))),
inference(paramod,[status(thm)],[c_7218,c_11755]) ).
cnf(c_11757,plain,
tuple(join(composition(sk1,composition(sk2,sk3)),composition(sk1,composition(sk2,sk3))),join(complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3)))),composition(sk1,composition(sk2,sk3)))) != tuple(composition(sk1,composition(sk2,sk3)),complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3))))),
inference(paramod,[status(thm)],[c_173,c_11756]) ).
cnf(c_10704,plain,
tuple(composition(sk1,composition(sk2,sk3)),join(complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3)))),composition(sk1,composition(sk2,sk3)))) != tuple(composition(sk1,composition(sk2,sk3)),complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3))))),
inference(paramod,[status(thm)],[c_289,c_11757]) ).
cnf(c_11758,plain,
tuple(composition(sk1,composition(sk2,sk3)),join(complement(join(complement(composition(sk1,sk3)),join(complement(composition(sk2,top)),complement(sk3)))),composition(sk1,composition(sk2,sk3)))) != tuple(composition(sk1,composition(sk2,sk3)),complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3))))),
inference(paramod,[status(thm)],[c_10104,c_10704]) ).
cnf(c_11759,plain,
tuple(composition(sk1,composition(sk2,sk3)),join(complement(join(complement(composition(sk1,sk3)),join(complement(sk3),complement(composition(sk2,top))))),composition(sk1,composition(sk2,sk3)))) != tuple(composition(sk1,composition(sk2,sk3)),complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3))))),
inference(paramod,[status(thm)],[c_1,c_11758]) ).
cnf(c_11760,plain,
tuple(composition(sk1,composition(sk2,sk3)),join(complement(join(complement(sk3),join(complement(composition(sk1,sk3)),complement(composition(sk2,top))))),composition(sk1,composition(sk2,sk3)))) != tuple(composition(sk1,composition(sk2,sk3)),complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3))))),
inference(paramod,[status(thm)],[c_33,c_11759]) ).
cnf(c_10705,plain,
tuple(composition(sk1,composition(sk2,sk3)),join(complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,top)))),composition(sk1,composition(sk2,sk3)))) != tuple(composition(sk1,composition(sk2,sk3)),complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3))))),
inference(paramod,[status(thm)],[c_2172,c_11760]) ).
cnf(c_11761,plain,
tuple(composition(sk1,composition(sk2,sk3)),join(complement(complement(composition(sk2,composition(sk1,sk3)))),composition(sk1,composition(sk2,sk3)))) != tuple(composition(sk1,composition(sk2,sk3)),complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3))))),
inference(paramod,[status(thm)],[c_10154,c_10705]) ).
cnf(c_11762,plain,
tuple(composition(sk1,composition(sk2,sk3)),join(complement(complement(composition(sk1,composition(sk2,sk3)))),composition(sk1,composition(sk2,sk3)))) != tuple(composition(sk1,composition(sk2,sk3)),complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3))))),
inference(paramod,[status(thm)],[c_7218,c_11761]) ).
cnf(c_11763,plain,
tuple(composition(sk1,composition(sk2,sk3)),join(composition(sk1,composition(sk2,sk3)),composition(sk1,composition(sk2,sk3)))) != tuple(composition(sk1,composition(sk2,sk3)),complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3))))),
inference(paramod,[status(thm)],[c_173,c_11762]) ).
cnf(c_10708,plain,
tuple(composition(sk1,composition(sk2,sk3)),composition(sk1,composition(sk2,sk3))) != tuple(composition(sk1,composition(sk2,sk3)),complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3))))),
inference(paramod,[status(thm)],[c_289,c_11763]) ).
cnf(c_11764,plain,
tuple(composition(sk1,composition(sk2,sk3)),composition(sk1,composition(sk2,sk3))) != tuple(composition(sk1,composition(sk2,sk3)),complement(join(complement(composition(sk1,sk3)),join(complement(composition(sk2,top)),complement(sk3))))),
inference(paramod,[status(thm)],[c_10104,c_10708]) ).
cnf(c_11765,plain,
tuple(composition(sk1,composition(sk2,sk3)),composition(sk1,composition(sk2,sk3))) != tuple(composition(sk1,composition(sk2,sk3)),complement(join(complement(composition(sk1,sk3)),join(complement(sk3),complement(composition(sk2,top)))))),
inference(paramod,[status(thm)],[c_1,c_11764]) ).
cnf(c_11766,plain,
tuple(composition(sk1,composition(sk2,sk3)),composition(sk1,composition(sk2,sk3))) != tuple(composition(sk1,composition(sk2,sk3)),complement(join(complement(sk3),join(complement(composition(sk1,sk3)),complement(composition(sk2,top)))))),
inference(paramod,[status(thm)],[c_33,c_11765]) ).
cnf(c_10709,plain,
tuple(composition(sk1,composition(sk2,sk3)),composition(sk1,composition(sk2,sk3))) != tuple(composition(sk1,composition(sk2,sk3)),complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,top))))),
inference(paramod,[status(thm)],[c_2172,c_11766]) ).
cnf(c_11767,plain,
tuple(composition(sk1,composition(sk2,sk3)),composition(sk1,composition(sk2,sk3))) != tuple(composition(sk1,composition(sk2,sk3)),complement(complement(composition(sk2,composition(sk1,sk3))))),
inference(paramod,[status(thm)],[c_10154,c_10709]) ).
cnf(c_11768,plain,
tuple(composition(sk1,composition(sk2,sk3)),composition(sk1,composition(sk2,sk3))) != tuple(composition(sk1,composition(sk2,sk3)),complement(complement(composition(sk1,composition(sk2,sk3))))),
inference(paramod,[status(thm)],[c_7218,c_11767]) ).
cnf(c_11769,plain,
tuple(composition(sk1,composition(sk2,sk3)),composition(sk1,composition(sk2,sk3))) != tuple(composition(sk1,composition(sk2,sk3)),composition(sk1,composition(sk2,sk3))),
inference(paramod,[status(thm)],[c_173,c_11768]) ).
cnf(c_11353,plain,
$false,
inference(copy,[status(thm)],[c_11769]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : REL029-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.41 % Computer : n016.cluster.edu
% 0.10/0.41 % Model : x86_64 x86_64
% 0.10/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.41 % Memory : 8046.5625MB
% 0.10/0.41 % OS : Linux 6.8.0-71-generic
% 0.10/0.41 % CPULimit : 300
% 0.10/0.41 % WCLimit : 300
% 0.10/0.41 % DateTime : Sat Sep 26 05:38:14 UTC 2026
% 0.10/0.41 % CPUTime :
% 0.10/0.41 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.41 % Process 94518 was started by sandbox on n016,
% 0.10/0.41 % Sat Sep 26 05:38:14 2026
% 0.10/0.41 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.42
% 0.10/0.42 % From the command line: assign(max_seconds, 300).
% 110.33/28.91
% 110.33/28.91 % given #500 (W,wt=34): 5316 join(complement(composition(sk1,top)),composition(top,complement(sk1))) = composition(top,complement(sk1)). [para(5138(a,1),2781(a,1,2,1)),rewrite([19(6),1(6),175(6)]),flip(a)].
% 110.33/28.91
% 110.33/28.91 % SZS status Unsatisfiable for theBenchmark
% 110.33/28.91
% 110.33/28.91 % Proof 1 at 2.60 (+ 0.51) seconds.
% 110.33/28.91 % Length of proof is 208.
% 110.33/28.91 % Level of proof is 38.
% 110.33/28.91 % Maximum clause weight is 100.000.
% 110.33/28.91 % Given clauses 587.
% 110.33/28.91
% 110.33/28.91 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------