%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : REL045-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 20:10:38 EDT 2022
% Result : Unsatisfiable 45.80s 46.18s
% Output : CNFRefutation 45.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : REL045-1 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.12 % Command : woody %s
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.34 % DateTime : Fri Jul 8 13:09:29 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.60/1.00 ********************************************************************************
% 0.60/1.00 * W A L D M E I S T E R \| \ / \|/ *
% 0.60/1.00 * |/ | \/ | *
% 0.60/1.00 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.60/1.00 * A. Jaeger and B. Loechner | | *
% 0.60/1.00 * <waldmeister@informatik.uni-kl.de> | *
% 0.60/1.00 ********************************************************************************
% 0.60/1.00
% 0.60/1.00
% 0.60/1.00 Goals:
% 0.60/1.00 ------
% 0.60/1.00
% 0.60/1.00 ( 1) join(sk1,composition(composition(sk1,converse(sk1)),sk1)) ?=? composition(composition(sk1,converse(sk1)),sk1)
% 0.60/1.00
% 0.60/1.00 Detected structure: Orkus
% 0.60/1.00 ********************************************************************************
% 0.60/1.00 ****************************** COMPLETION - PROOF ******************************
% 0.60/1.00 ********************************************************************************
% 0.60/1.00
% 45.80/46.18 joined goal: 1 join(sk1,composition(composition(sk1,converse(sk1)),sk1)) ?= composition(composition(sk1,converse(sk1)),sk1) to composition(sk1,composition(converse(sk1),sk1))
% 45.80/46.18 goal joined
% 45.80/46.18 % SZS status Unsatisfiable
% 45.80/46.18 #START OF PROOF
% 45.80/46.18 % SZS output start CNFRefutation
% 45.80/46.18 cnf('0.1.0.0',axiom,
% 45.80/46.18 ( X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))) ),
% 45.80/46.18 file('/tmp/WALDMEISTER_5833_n013')).
% 45.80/46.18 cnf('0.1.1.0',plain,
% 45.80/46.18 ( X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.1.0.0']),
% 45.80/46.18 [weight('<0,0,0,[0,0,0,1]>')]).
% 45.80/46.18 cnf('0.1.2.0',plain,
% 45.80/46.18 ( join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))) = X1 ),
% 45.80/46.18 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_1]).
% 45.80/46.18 cnf('0.2.0.0',axiom,
% 45.80/46.18 ( X1 = composition(X1,one) ),
% 45.80/46.18 file('/tmp/WALDMEISTER_5833_n013')).
% 45.80/46.18 cnf('0.2.1.0',plain,
% 45.80/46.18 ( X1 = composition(X1,one) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.2.0.0']),
% 45.80/46.18 [weight('<1,0,0,[0,0,0,2]>')]).
% 45.80/46.18 cnf('0.2.2.0',plain,
% 45.80/46.18 ( composition(X1,one) = X1 ),
% 45.80/46.18 inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_2]).
% 45.80/46.18 cnf('0.3.0.0',axiom,
% 45.80/46.18 ( X1 = converse(converse(X1)) ),
% 45.80/46.18 file('/tmp/WALDMEISTER_5833_n013')).
% 45.80/46.18 cnf('0.3.1.0',plain,
% 45.80/46.18 ( X1 = converse(converse(X1)) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.3.0.0']),
% 45.80/46.18 [weight('<2,0,0,[0,0,0,3]>')]).
% 45.80/46.18 cnf('0.3.2.0',plain,
% 45.80/46.18 ( converse(converse(X1)) = X1 ),
% 45.80/46.18 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_3]).
% 45.80/46.18 cnf('0.4.0.0',axiom,
% 45.80/46.18 ( join(X1,X2) = join(X2,X1) ),
% 45.80/46.18 file('/tmp/WALDMEISTER_5833_n013')).
% 45.80/46.18 cnf('0.4.1.0',plain,
% 45.80/46.18 ( join(X1,X2) = join(X2,X1) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.4.0.0']),
% 45.80/46.18 [weight('<3,0,0,[0,0,0,4]>')]).
% 45.80/46.18 cnf('0.4.2.0',plain,
% 45.80/46.18 ( join(X1,X2) = join(X2,X1) ),
% 45.80/46.18 inference(activate,[status(thm)],['0.4.1.0']),
% 45.80/46.18 [equation_1]).
% 45.80/46.18 cnf('0.5.0.0',axiom,
% 45.80/46.18 ( join(X1,join(X2,X3)) = join(join(X1,X2),X3) ),
% 45.80/46.18 file('/tmp/WALDMEISTER_5833_n013')).
% 45.80/46.18 cnf('0.5.1.0',plain,
% 45.80/46.18 ( join(X1,join(X2,X3)) = join(join(X1,X2),X3) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.5.0.0']),
% 45.80/46.18 [weight('<4,0,0,[0,0,0,5]>')]).
% 45.80/46.18 cnf('0.5.2.0',plain,
% 45.80/46.18 ( join(join(X1,X2),X3) = join(X1,join(X2,X3)) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.5.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_4]).
% 45.80/46.18 cnf('0.6.0.0',axiom,
% 45.80/46.18 ( join(X1,complement(X1)) = top ),
% 45.80/46.18 file('/tmp/WALDMEISTER_5833_n013')).
% 45.80/46.18 cnf('0.6.1.0',plain,
% 45.80/46.18 ( join(X1,complement(X1)) = top ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.6.0.0']),
% 45.80/46.18 [weight('<5,0,0,[0,0,0,6]>')]).
% 45.80/46.18 cnf('0.6.2.0',plain,
% 45.80/46.18 ( join(X1,complement(X1)) = top ),
% 45.80/46.18 inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 45.80/46.18 [u,rule_5]).
% 45.80/46.18 cnf('0.7.0.0',axiom,
% 45.80/46.18 ( join(composition(X1,X2),composition(X3,X2)) = composition(join(X1,X3),X2) ),
% 45.80/46.18 file('/tmp/WALDMEISTER_5833_n013')).
% 45.80/46.18 cnf('0.7.1.0',plain,
% 45.80/46.18 ( join(composition(X1,X2),composition(X3,X2)) = composition(join(X1,X3),X2) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.7.0.0']),
% 45.80/46.18 [weight('<6,0,0,[0,0,0,7]>')]).
% 45.80/46.18 cnf('0.7.2.0',plain,
% 45.80/46.18 ( join(composition(X1,X2),composition(X3,X2)) = composition(join(X1,X3),X2) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.7.1.0',theory(equality)]),
% 45.80/46.18 [u,rule_6]).
% 45.80/46.18 cnf('0.8.0.0',axiom,
% 45.80/46.18 ( join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2) ),
% 45.80/46.18 file('/tmp/WALDMEISTER_5833_n013')).
% 45.80/46.18 cnf('0.8.1.0',plain,
% 45.80/46.18 ( join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.8.0.0']),
% 45.80/46.18 [weight('<7,0,0,[0,0,0,8]>')]).
% 45.80/46.18 cnf('0.8.1.1',plain,
% 45.80/46.18 ( join(complement(X2),composition(converse(X1),complement(composition(X1,X2)))) = complement(X2) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.8.1.0','0.4.2.0',theory(equality)]),
% 45.80/46.18 [pos('L','L')]).
% 45.80/46.18 cnf('0.8.2.0',plain,
% 45.80/46.18 ( join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.8.1.1',theory(equality)]),
% 45.80/46.18 [u,rule_7]).
% 45.80/46.18 cnf('0.9.0.0',axiom,
% 45.80/46.18 ( join(converse(X1),converse(X2)) = converse(join(X1,X2)) ),
% 45.80/46.18 file('/tmp/WALDMEISTER_5833_n013')).
% 45.80/46.18 cnf('0.9.1.0',plain,
% 45.80/46.18 ( join(converse(X1),converse(X2)) = converse(join(X1,X2)) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.9.0.0']),
% 45.80/46.18 [weight('<8,0,0,[0,0,0,9]>')]).
% 45.80/46.18 cnf('0.9.2.0',plain,
% 45.80/46.18 ( join(converse(X1),converse(X2)) = converse(join(X1,X2)) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.9.1.0',theory(equality)]),
% 45.80/46.18 [u,rule_8]).
% 45.80/46.18 cnf('0.10.0.0',axiom,
% 45.80/46.18 ( complement(join(complement(X1),complement(X2))) = meet(X1,X2) ),
% 45.80/46.18 file('/tmp/WALDMEISTER_5833_n013')).
% 45.80/46.18 cnf('0.10.1.0',plain,
% 45.80/46.18 ( complement(join(complement(X1),complement(X2))) = meet(X1,X2) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.10.0.0']),
% 45.80/46.18 [weight('<9,0,0,[0,0,0,10]>')]).
% 45.80/46.18 cnf('0.10.2.0',plain,
% 45.80/46.18 ( complement(join(complement(X1),complement(X2))) = meet(X1,X2) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.10.1.0',theory(equality)]),
% 45.80/46.18 [u,rule_9]).
% 45.80/46.18 cnf('0.11.0.0',axiom,
% 45.80/46.18 ( composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3) ),
% 45.80/46.18 file('/tmp/WALDMEISTER_5833_n013')).
% 45.80/46.18 cnf('0.11.1.0',plain,
% 45.80/46.18 ( composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.11.0.0']),
% 45.80/46.18 [weight('<10,0,0,[0,0,0,11]>')]).
% 45.80/46.18 cnf('0.11.2.0',plain,
% 45.80/46.18 ( composition(composition(X1,X2),X3) = composition(X1,composition(X2,X3)) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.11.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_10]).
% 45.80/46.18 cnf('0.12.0.0',axiom,
% 45.80/46.18 ( composition(converse(X1),converse(X2)) = converse(composition(X2,X1)) ),
% 45.80/46.18 file('/tmp/WALDMEISTER_5833_n013')).
% 45.80/46.18 cnf('0.12.1.0',plain,
% 45.80/46.18 ( composition(converse(X1),converse(X2)) = converse(composition(X2,X1)) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.12.0.0']),
% 45.80/46.18 [weight('<11,0,0,[0,0,0,12]>')]).
% 45.80/46.18 cnf('0.12.2.0',plain,
% 45.80/46.18 ( composition(converse(X1),converse(X2)) = converse(composition(X2,X1)) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.12.1.0',theory(equality)]),
% 45.80/46.18 [u,rule_11]).
% 45.80/46.18 cnf('0.13.0.0',axiom,
% 45.80/46.18 ( meet(X1,complement(X1)) = zero ),
% 45.80/46.18 file('/tmp/WALDMEISTER_5833_n013')).
% 45.80/46.18 cnf('0.13.1.0',plain,
% 45.80/46.18 ( meet(X1,complement(X1)) = zero ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.13.0.0']),
% 45.80/46.18 [weight('<12,0,0,[0,0,0,13]>')]).
% 45.80/46.18 cnf('0.13.2.0',plain,
% 45.80/46.18 ( meet(X1,complement(X1)) = zero ),
% 45.80/46.18 inference(orient,[status(thm)],['0.13.1.0',theory(equality)]),
% 45.80/46.18 [u,rule_12]).
% 45.80/46.18 cnf('0.14.0.0',plain,
% 45.80/46.18 ( meet(X1,complement(X1)) = complement(top) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.10.2.0','0.6.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.14.1.0',plain,
% 45.80/46.18 ( meet(X1,complement(X1)) = complement(top) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.14.0.0']),
% 45.80/46.18 [weight('<34,10,6,[1,0,0,1]>')]).
% 45.80/46.18 cnf('0.14.1.1',plain,
% 45.80/46.18 ( zero = complement(top) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.14.1.0','0.13.2.0',theory(equality)]),
% 45.80/46.18 [pos('L','L')]).
% 45.80/46.18 cnf('0.14.2.0',plain,
% 45.80/46.18 ( complement(top) = zero ),
% 45.80/46.18 inference(orient,[status(thm)],['0.14.1.1',theory(equality)]),
% 45.80/46.18 [x,rule_13]).
% 45.80/46.18 cnf('0.17.0.0',plain,
% 45.80/46.18 ( meet(X1,X2) = complement(join(complement(X2),complement(X1))) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.10.2.0','0.4.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.17.0.1',plain,
% 45.80/46.18 ( meet(X1,X2) = meet(X2,X1) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.17.0.0','0.10.2.0',theory(equality)]),
% 45.80/46.18 [pos('R','L')]).
% 45.80/46.18 cnf('0.17.1.0',plain,
% 45.80/46.18 ( meet(X1,X2) = meet(X2,X1) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.17.0.1']),
% 45.80/46.18 [weight('<48,10,4,[1,0,0,1]>')]).
% 45.80/46.18 cnf('0.17.2.0',plain,
% 45.80/46.18 ( meet(X1,X2) = meet(X2,X1) ),
% 45.80/46.18 inference(activate,[status(thm)],['0.17.1.0']),
% 45.80/46.18 [equation_2]).
% 45.80/46.18 cnf('0.19.0.0',plain,
% 45.80/46.18 ( meet(top,X1) = complement(join(zero,complement(X1))) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.10.2.0','0.14.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1.1','L')]).
% 45.80/46.18 cnf('0.19.1.0',plain,
% 45.80/46.18 ( meet(top,X1) = complement(join(zero,complement(X1))) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.19.0.0']),
% 45.80/46.18 [weight('<53,14,10,[0,0,0,2]>')]).
% 45.80/46.18 cnf('0.19.2.0',plain,
% 45.80/46.18 ( complement(join(zero,complement(X1))) = meet(top,X1) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.19.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_17]).
% 45.80/46.18 cnf('0.24.0.0',plain,
% 45.80/46.18 ( converse(join(converse(X1),X2)) = join(X1,converse(X2)) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.9.2.0','0.3.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.24.1.0',plain,
% 45.80/46.18 ( converse(join(converse(X1),X2)) = join(X1,converse(X2)) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.24.0.0']),
% 45.80/46.18 [weight('<59,9,3,[1,0,0,1]>')]).
% 45.80/46.18 cnf('0.24.2.0',plain,
% 45.80/46.18 ( converse(join(converse(X1),X2)) = join(X1,converse(X2)) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.24.1.0',theory(equality)]),
% 45.80/46.18 [u,rule_22]).
% 45.80/46.18 cnf('0.25.0.0',plain,
% 45.80/46.18 ( converse(join(X1,converse(X2))) = join(converse(X1),X2) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.9.2.0','0.3.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2','L')]).
% 45.80/46.18 cnf('0.25.1.0',plain,
% 45.80/46.18 ( converse(join(X1,converse(X2))) = join(converse(X1),X2) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.25.0.0']),
% 45.80/46.18 [weight('<59,9,3,[1,0,0,3]>')]).
% 45.80/46.18 cnf('0.25.2.0',plain,
% 45.80/46.18 ( converse(join(X1,converse(X2))) = join(converse(X1),X2) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.25.1.0',theory(equality)]),
% 45.80/46.18 [u,rule_23]).
% 45.80/46.18 cnf('0.26.0.0',plain,
% 45.80/46.18 ( converse(composition(X1,converse(X2))) = composition(X2,converse(X1)) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.12.2.0','0.3.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.26.1.0',plain,
% 45.80/46.18 ( converse(composition(X1,converse(X2))) = composition(X2,converse(X1)) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.26.0.0']),
% 45.80/46.18 [weight('<59,12,3,[1,0,0,1]>')]).
% 45.80/46.18 cnf('0.26.2.0',plain,
% 45.80/46.18 ( converse(composition(X1,converse(X2))) = composition(X2,converse(X1)) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.26.1.0',theory(equality)]),
% 45.80/46.18 [u,rule_24]).
% 45.80/46.18 cnf('0.27.0.0',plain,
% 45.80/46.18 ( converse(composition(converse(X1),X2)) = composition(converse(X2),X1) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.12.2.0','0.3.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2','L')]).
% 45.80/46.18 cnf('0.27.1.0',plain,
% 45.80/46.18 ( converse(composition(converse(X1),X2)) = composition(converse(X2),X1) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.27.0.0']),
% 45.80/46.18 [weight('<59,12,3,[1,0,0,3]>')]).
% 45.80/46.18 cnf('0.27.2.0',plain,
% 45.80/46.18 ( converse(composition(converse(X1),X2)) = composition(converse(X2),X1) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.27.1.0',theory(equality)]),
% 45.80/46.18 [u,rule_25]).
% 45.80/46.18 cnf('0.28.0.0',plain,
% 45.80/46.18 ( composition(converse(one),X1) = converse(converse(X1)) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.27.2.0','0.2.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.28.0.1',plain,
% 45.80/46.18 ( composition(converse(one),X1) = X1 ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.28.0.0','0.3.2.0',theory(equality)]),
% 45.80/46.18 [pos('R','L')]).
% 45.80/46.18 cnf('0.28.1.0',plain,
% 45.80/46.18 ( composition(converse(one),X1) = X1 ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.28.0.1']),
% 45.80/46.18 [weight('<29,27,2,[1,0,0,1]>')]).
% 45.80/46.18 cnf('0.28.2.0',plain,
% 45.80/46.18 ( composition(converse(one),X1) = X1 ),
% 45.80/46.18 inference(orient,[status(thm)],['0.28.1.0',theory(equality)]),
% 45.80/46.18 [u,rule_26]).
% 45.80/46.18 cnf('0.29.0.0',plain,
% 45.80/46.18 ( one = converse(one) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.28.2.0','0.2.2.0',theory(equality)]),
% 45.80/46.18 [pos('L','L')]).
% 45.80/46.18 cnf('0.29.1.0',plain,
% 45.80/46.18 ( one = converse(one) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.29.0.0']),
% 45.80/46.18 [weight('<11,28,2,[1,0,0,0]>')]).
% 45.80/46.18 cnf('0.29.2.0',plain,
% 45.80/46.18 ( converse(one) = one ),
% 45.80/46.18 inference(orient,[status(thm)],['0.29.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_27]).
% 45.80/46.18 cnf('0.30.0.0',plain,
% 45.80/46.18 ( composition(converse(one),X1) = X1 ),
% 45.80/46.18 inference(interreduction_right,[status(thm)],['0.28.2.0'])).
% 45.80/46.18 cnf('0.30.0.1',plain,
% 45.80/46.18 ( composition(one,X1) = X1 ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.30.0.0','0.29.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.30.1.0',plain,
% 45.80/46.18 ( composition(one,X1) = X1 ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.30.0.1']),
% 45.80/46.18 [weight('<19,28,29,[0,0,0,0]>')]).
% 45.80/46.18 cnf('0.30.2.0',plain,
% 45.80/46.18 ( composition(one,X1) = X1 ),
% 45.80/46.18 inference(orient,[status(thm)],['0.30.1.0',theory(equality)]),
% 45.80/46.18 [u,rule_28]).
% 45.80/46.18 cnf('0.31.0.0',plain,
% 45.80/46.18 ( converse(join(one,X1)) = join(one,converse(X1)) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.9.2.0','0.29.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.31.1.0',plain,
% 45.80/46.18 ( converse(join(one,X1)) = join(one,converse(X1)) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.31.0.0']),
% 45.80/46.18 [weight('<44,29,9,[0,0,0,1]>')]).
% 45.80/46.18 cnf('0.31.2.0',plain,
% 45.80/46.18 ( converse(join(one,X1)) = join(one,converse(X1)) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.31.1.0',theory(equality)]),
% 45.80/46.18 [u,rule_29]).
% 45.80/46.18 cnf('0.33.0.0',plain,
% 45.80/46.18 ( complement(X1) = join(complement(X1),composition(converse(one),complement(X1))) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.8.2.0','0.30.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2.2.1','L')]).
% 45.80/46.18 cnf('0.33.0.1',plain,
% 45.80/46.18 ( complement(X1) = join(complement(X1),composition(one,complement(X1))) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.33.0.0','0.29.2.0',theory(equality)]),
% 45.80/46.18 [pos('R.2.1','L')]).
% 45.80/46.18 cnf('0.33.0.2',plain,
% 45.80/46.18 ( complement(X1) = join(complement(X1),complement(X1)) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.33.0.1','0.30.2.0',theory(equality)]),
% 45.80/46.18 [pos('R.2','L')]).
% 45.80/46.18 cnf('0.33.1.0',plain,
% 45.80/46.18 ( complement(X1) = join(complement(X1),complement(X1)) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.33.0.2']),
% 45.80/46.18 [weight('<47,30,8,[0,0,0,7]>')]).
% 45.80/46.18 cnf('0.33.2.0',plain,
% 45.80/46.18 ( join(complement(X1),complement(X1)) = complement(X1) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.33.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_31]).
% 45.80/46.18 cnf('0.34.0.0',plain,
% 45.80/46.18 ( complement(top) = join(zero,complement(top)) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.33.2.0','0.14.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.34.0.1',plain,
% 45.80/46.18 ( zero = join(zero,complement(top)) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.34.0.0','0.14.2.0',theory(equality)]),
% 45.80/46.18 [pos('L','L')]).
% 45.80/46.18 cnf('0.34.0.2',plain,
% 45.80/46.18 ( zero = join(zero,zero) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.34.0.1','0.14.2.0',theory(equality)]),
% 45.80/46.18 [pos('R.2','L')]).
% 45.80/46.18 cnf('0.34.1.0',plain,
% 45.80/46.18 ( zero = join(zero,zero) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.34.0.2']),
% 45.80/46.18 [weight('<19,33,14,[1,0,0,1]>')]).
% 45.80/46.18 cnf('0.34.2.0',plain,
% 45.80/46.18 ( join(zero,zero) = zero ),
% 45.80/46.18 inference(orient,[status(thm)],['0.34.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_32]).
% 45.80/46.18 cnf('0.37.0.0',plain,
% 45.80/46.18 ( meet(X1,X1) = complement(complement(X1)) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.10.2.0','0.33.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.37.1.0',plain,
% 45.80/46.18 ( meet(X1,X1) = complement(complement(X1)) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.37.0.0']),
% 45.80/46.18 [weight('<48,33,10,[0,0,0,1]>')]).
% 45.80/46.18 cnf('0.37.2.0',plain,
% 45.80/46.18 ( meet(X1,X1) = complement(complement(X1)) ),
% 45.80/46.18 inference(activate,[status(thm)],['0.37.1.0']),
% 45.80/46.18 [equation_3]).
% 45.80/46.18 cnf('0.38.0.0',plain,
% 45.80/46.18 ( join(zero,join(zero,X1)) = join(zero,X1) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.5.2.0','0.34.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.38.1.0',plain,
% 45.80/46.18 ( join(zero,join(zero,X1)) = join(zero,X1) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.38.0.0']),
% 45.80/46.18 [weight('<53,34,5,[0,0,0,1]>')]).
% 45.80/46.18 cnf('0.38.2.0',plain,
% 45.80/46.18 ( join(zero,join(zero,X1)) = join(zero,X1) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.38.1.0',theory(equality)]),
% 45.80/46.18 [u,rule_35]).
% 45.80/46.18 cnf('0.39.0.0',plain,
% 45.80/46.18 ( join(zero,X1) = join(zero,join(X1,zero)) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.38.2.0','0.4.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2','L')]).
% 45.80/46.18 cnf('0.39.1.0',plain,
% 45.80/46.18 ( join(zero,X1) = join(zero,join(X1,zero)) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.39.0.0']),
% 45.80/46.18 [weight('<53,38,4,[1,0,0,2]>')]).
% 45.80/46.18 cnf('0.39.2.0',plain,
% 45.80/46.18 ( join(zero,join(X1,zero)) = join(zero,X1) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.39.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_36]).
% 45.80/46.18 cnf('0.42.0.0',plain,
% 45.80/46.18 ( join(X1,converse(complement(converse(X1)))) = converse(top) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.24.2.0','0.6.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.42.1.0',plain,
% 45.80/46.18 ( join(X1,converse(complement(converse(X1)))) = converse(top) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.42.0.0']),
% 45.80/46.18 [weight('<62,24,6,[1,0,0,1]>')]).
% 45.80/46.18 cnf('0.42.2.0',plain,
% 45.80/46.18 ( join(X1,converse(complement(converse(X1)))) = converse(top) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.42.1.0',theory(equality)]),
% 45.80/46.18 [u,rule_39]).
% 45.80/46.18 cnf('0.45.0.0',plain,
% 45.80/46.18 ( composition(join(one,X1),X2) = join(X2,composition(X1,X2)) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.7.2.0','0.30.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.45.1.0',plain,
% 45.80/46.18 ( composition(join(one,X1),X2) = join(X2,composition(X1,X2)) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.45.0.0']),
% 45.80/46.18 [weight('<65,30,7,[0,0,0,1]>')]).
% 45.80/46.18 cnf('0.45.2.0',plain,
% 45.80/46.18 ( join(X1,composition(X2,X1)) = composition(join(one,X2),X1) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.45.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_42]).
% 45.80/46.18 cnf('0.46.0.0',plain,
% 45.80/46.18 ( join(X1,join(complement(X1),X2)) = join(top,X2) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.5.2.0','0.6.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.46.1.0',plain,
% 45.80/46.18 ( join(X1,join(complement(X1),X2)) = join(top,X2) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.46.0.0']),
% 45.80/46.18 [weight('<69,6,5,[0,0,0,1]>')]).
% 45.80/46.18 cnf('0.46.2.0',plain,
% 45.80/46.18 ( join(X1,join(complement(X1),X2)) = join(top,X2) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.46.1.0',theory(equality)]),
% 45.80/46.18 [u,rule_43]).
% 45.80/46.18 cnf('0.47.0.0',plain,
% 45.80/46.18 ( join(top,complement(X1)) = join(X1,complement(X1)) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.46.2.0','0.33.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2','L')]).
% 45.80/46.18 cnf('0.47.0.1',plain,
% 45.80/46.18 ( join(top,complement(X1)) = top ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.47.0.0','0.6.2.0',theory(equality)]),
% 45.80/46.18 [pos('R','L')]).
% 45.80/46.18 cnf('0.47.1.0',plain,
% 45.80/46.18 ( join(top,complement(X1)) = top ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.47.0.1']),
% 45.80/46.18 [weight('<29,46,33,[1,0,0,2]>')]).
% 45.80/46.18 cnf('0.47.2.0',plain,
% 45.80/46.18 ( join(top,complement(X1)) = top ),
% 45.80/46.18 inference(orient,[status(thm)],['0.47.1.0',theory(equality)]),
% 45.80/46.18 [u,rule_44]).
% 45.80/46.18 cnf('0.50.0.0',plain,
% 45.80/46.18 ( join(top,complement(complement(X1))) = join(X1,top) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.46.2.0','0.6.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2','L')]).
% 45.80/46.18 cnf('0.50.1.0',plain,
% 45.80/46.18 ( join(top,complement(complement(X1))) = join(X1,top) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.50.0.0']),
% 45.80/46.18 [weight('<53,46,6,[1,0,0,2]>')]).
% 45.80/46.18 cnf('0.50.1.1',plain,
% 45.80/46.18 ( top = join(X1,top) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.50.1.0','0.47.2.0',theory(equality)]),
% 45.80/46.18 [pos('L','L')]).
% 45.80/46.18 cnf('0.50.2.0',plain,
% 45.80/46.18 ( join(X1,top) = top ),
% 45.80/46.18 inference(orient,[status(thm)],['0.50.1.1',theory(equality)]),
% 45.80/46.18 [x,rule_47]).
% 45.80/46.18 cnf('0.51.0.0',plain,
% 45.80/46.18 ( top = join(top,X1) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.50.2.0','0.4.2.0',theory(equality)]),
% 45.80/46.18 [pos('L','L')]).
% 45.80/46.18 cnf('0.51.1.0',plain,
% 45.80/46.18 ( top = join(top,X1) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.51.0.0']),
% 45.80/46.18 [weight('<19,50,4,[1,0,0,0]>')]).
% 45.80/46.18 cnf('0.51.2.0',plain,
% 45.80/46.18 ( join(top,X1) = top ),
% 45.80/46.18 inference(orient,[status(thm)],['0.51.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_48]).
% 45.80/46.18 cnf('0.52.0.0',plain,
% 45.80/46.18 ( top = converse(top) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.51.2.0','0.42.2.0',theory(equality)]),
% 45.80/46.18 [pos('L','L')]).
% 45.80/46.18 cnf('0.52.1.0',plain,
% 45.80/46.18 ( top = converse(top) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.52.0.0']),
% 45.80/46.18 [weight('<11,51,42,[1,0,0,0]>')]).
% 45.80/46.18 cnf('0.52.2.0',plain,
% 45.80/46.18 ( converse(top) = top ),
% 45.80/46.18 inference(orient,[status(thm)],['0.52.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_49]).
% 45.80/46.18 cnf('0.54.0.0',plain,
% 45.80/46.18 ( top = composition(join(one,X1),top) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.51.2.0','0.45.2.0',theory(equality)]),
% 45.80/46.18 [pos('L','L')]).
% 45.80/46.18 cnf('0.54.1.0',plain,
% 45.80/46.18 ( top = composition(join(one,X1),top) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.54.0.0']),
% 45.80/46.18 [weight('<41,51,45,[1,0,0,0]>')]).
% 45.80/46.18 cnf('0.54.2.0',plain,
% 45.80/46.18 ( composition(join(one,X1),top) = top ),
% 45.80/46.18 inference(orient,[status(thm)],['0.54.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_51]).
% 45.80/46.18 cnf('0.55.0.0',plain,
% 45.80/46.18 ( top = composition(top,top) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.54.2.0','0.6.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.55.1.0',plain,
% 45.80/46.18 ( top = composition(top,top) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.55.0.0']),
% 45.80/46.18 [weight('<19,54,6,[1,0,0,1]>')]).
% 45.80/46.18 cnf('0.55.2.0',plain,
% 45.80/46.18 ( composition(top,top) = top ),
% 45.80/46.18 inference(orient,[status(thm)],['0.55.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_52]).
% 45.80/46.18 cnf('0.56.0.0',plain,
% 45.80/46.18 ( complement(top) = join(complement(top),composition(converse(top),complement(top))) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.8.2.0','0.55.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2.2.1','L')]).
% 45.80/46.18 cnf('0.56.0.1',plain,
% 45.80/46.18 ( zero = join(complement(top),composition(converse(top),complement(top))) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.56.0.0','0.14.2.0',theory(equality)]),
% 45.80/46.18 [pos('L','L')]).
% 45.80/46.18 cnf('0.56.0.2',plain,
% 45.80/46.18 ( zero = composition(join(one,converse(top)),complement(top)) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.56.0.1','0.45.2.0',theory(equality)]),
% 45.80/46.18 [pos('R','L')]).
% 45.80/46.18 cnf('0.56.0.3',plain,
% 45.80/46.18 ( zero = composition(join(one,top),complement(top)) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.56.0.2','0.52.2.0',theory(equality)]),
% 45.80/46.18 [pos('R.1.2','L')]).
% 45.80/46.18 cnf('0.56.0.4',plain,
% 45.80/46.18 ( zero = composition(top,complement(top)) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.56.0.3','0.50.2.0',theory(equality)]),
% 45.80/46.18 [pos('R.1','L')]).
% 45.80/46.18 cnf('0.56.0.5',plain,
% 45.80/46.18 ( zero = composition(top,zero) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.56.0.4','0.14.2.0',theory(equality)]),
% 45.80/46.18 [pos('R.2','L')]).
% 45.80/46.18 cnf('0.56.1.0',plain,
% 45.80/46.18 ( zero = composition(top,zero) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.56.0.5']),
% 45.80/46.18 [weight('<19,55,8,[0,0,0,7]>')]).
% 45.80/46.18 cnf('0.56.2.0',plain,
% 45.80/46.18 ( composition(top,zero) = zero ),
% 45.80/46.18 inference(orient,[status(thm)],['0.56.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_53]).
% 45.80/46.18 cnf('0.59.0.0',plain,
% 45.80/46.18 ( join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))) = X1 ),
% 45.80/46.18 inference(interreduction_right,[status(thm)],['0.1.2.0'])).
% 45.80/46.18 cnf('0.59.1.0',plain,
% 45.80/46.18 ( join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))) = X1 ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.59.0.0']),
% 45.80/46.18 [weight('<?,1,4,[0,0,0,0]>')]).
% 45.80/46.18 cnf('0.59.1.1',plain,
% 45.80/46.18 ( join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1 ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.59.1.0','0.4.2.0',theory(equality)]),
% 45.80/46.18 [pos('L','L')]).
% 45.80/46.18 cnf('0.59.1.2',plain,
% 45.80/46.18 ( join(complement(join(complement(X1),X2)),meet(X1,X2)) = X1 ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.59.1.1','0.10.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2','L')]).
% 45.80/46.18 cnf('0.59.1.3',plain,
% 45.80/46.18 ( join(meet(X1,X2),complement(join(complement(X1),X2))) = X1 ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.59.1.2','0.4.2.0',theory(equality)]),
% 45.80/46.18 [pos('L','L')]).
% 45.80/46.18 cnf('0.59.2.0',plain,
% 45.80/46.18 ( join(meet(X1,X2),complement(join(complement(X1),X2))) = X1 ),
% 45.80/46.18 inference(orient,[status(thm)],['0.59.1.3',theory(equality)]),
% 45.80/46.18 [u,rule_56]).
% 45.80/46.18 cnf('0.60.0.0',plain,
% 45.80/46.18 ( composition(join(top,X1),zero) = join(zero,composition(X1,zero)) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.7.2.0','0.56.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.60.0.1',plain,
% 45.80/46.18 ( composition(top,zero) = join(zero,composition(X1,zero)) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.60.0.0','0.51.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.60.0.2',plain,
% 45.80/46.18 ( zero = join(zero,composition(X1,zero)) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.60.0.1','0.56.2.0',theory(equality)]),
% 45.80/46.18 [pos('L','L')]).
% 45.80/46.18 cnf('0.60.0.3',plain,
% 45.80/46.18 ( zero = composition(join(one,X1),zero) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.60.0.2','0.45.2.0',theory(equality)]),
% 45.80/46.18 [pos('R','L')]).
% 45.80/46.18 cnf('0.60.1.0',plain,
% 45.80/46.18 ( zero = composition(join(one,X1),zero) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.60.0.3']),
% 45.80/46.18 [weight('<41,56,7,[0,0,0,1]>')]).
% 45.80/46.18 cnf('0.60.2.0',plain,
% 45.80/46.18 ( composition(join(one,X1),zero) = zero ),
% 45.80/46.18 inference(orient,[status(thm)],['0.60.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_57]).
% 45.80/46.18 cnf('0.61.0.0',plain,
% 45.80/46.18 ( X1 = join(zero,complement(join(complement(X1),complement(X1)))) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.59.2.0','0.13.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.61.0.1',plain,
% 45.80/46.18 ( X1 = join(zero,meet(X1,X1)) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.61.0.0','0.10.2.0',theory(equality)]),
% 45.80/46.18 [pos('R.2','L')]).
% 45.80/46.18 cnf('0.61.1.0',plain,
% 45.80/46.18 ( X1 = join(zero,meet(X1,X1)) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.61.0.1']),
% 45.80/46.18 [weight('<41,59,13,[1,0,0,1]>')]).
% 45.80/46.18 cnf('0.61.2.0',plain,
% 45.80/46.18 ( join(zero,meet(X1,X1)) = X1 ),
% 45.80/46.18 inference(orient,[status(thm)],['0.61.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_58]).
% 45.80/46.18 cnf('0.62.0.0',plain,
% 45.80/46.18 ( join(zero,meet(X1,X1)) = join(zero,X1) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.38.2.0','0.61.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2','L')]).
% 45.80/46.18 cnf('0.62.0.1',plain,
% 45.80/46.18 ( X1 = join(zero,X1) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.62.0.0','0.61.2.0',theory(equality)]),
% 45.80/46.18 [pos('L','L')]).
% 45.80/46.18 cnf('0.62.1.0',plain,
% 45.80/46.18 ( X1 = join(zero,X1) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.62.0.1']),
% 45.80/46.18 [weight('<19,61,38,[0,0,0,2]>')]).
% 45.80/46.18 cnf('0.62.2.0',plain,
% 45.80/46.18 ( join(zero,X1) = X1 ),
% 45.80/46.18 inference(orient,[status(thm)],['0.62.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_59]).
% 45.80/46.18 cnf('0.65.0.0',plain,
% 45.80/46.18 ( join(zero,join(X1,zero)) = join(zero,X1) ),
% 45.80/46.18 inference(interreduction_right,[status(thm)],['0.39.2.0'])).
% 45.80/46.18 cnf('0.65.0.1',plain,
% 45.80/46.18 ( join(X1,zero) = join(zero,X1) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.65.0.0','0.62.2.0',theory(equality)]),
% 45.80/46.18 [pos('L','L')]).
% 45.80/46.18 cnf('0.65.0.2',plain,
% 45.80/46.18 ( join(X1,zero) = X1 ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.65.0.1','0.62.2.0',theory(equality)]),
% 45.80/46.18 [pos('R','L')]).
% 45.80/46.18 cnf('0.65.1.0',plain,
% 45.80/46.18 ( join(X1,zero) = X1 ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.65.0.2']),
% 45.80/46.18 [weight('<19,39,62,[0,0,0,0]>')]).
% 45.80/46.18 cnf('0.65.2.0',plain,
% 45.80/46.18 ( join(X1,zero) = X1 ),
% 45.80/46.18 inference(orient,[status(thm)],['0.65.1.0',theory(equality)]),
% 45.80/46.18 [u,rule_62]).
% 45.80/46.18 cnf('0.66.0.0',plain,
% 45.80/46.18 ( join(zero,meet(X1,X1)) = X1 ),
% 45.80/46.18 inference(interreduction_right,[status(thm)],['0.61.2.0'])).
% 45.80/46.18 cnf('0.66.0.1',plain,
% 45.80/46.18 ( meet(X1,X1) = X1 ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.66.0.0','0.62.2.0',theory(equality)]),
% 45.80/46.18 [pos('L','L')]).
% 45.80/46.18 cnf('0.66.1.0',plain,
% 45.80/46.18 ( meet(X1,X1) = X1 ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.66.0.1']),
% 45.80/46.18 [weight('<19,61,62,[0,0,0,0]>')]).
% 45.80/46.18 cnf('0.66.2.0',plain,
% 45.80/46.18 ( meet(X1,X1) = X1 ),
% 45.80/46.18 inference(orient,[status(thm)],['0.66.1.0',theory(equality)]),
% 45.80/46.18 [u,rule_63]).
% 45.80/46.18 cnf('0.67.0.0',plain,
% 45.80/46.18 ( meet(X1,X1) = complement(complement(X1)) ),
% 45.80/46.18 inference(interreduction_right,[status(thm)],['0.37.2.0'])).
% 45.80/46.18 cnf('0.67.0.1',plain,
% 45.80/46.18 ( X1 = complement(complement(X1)) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.67.0.0','0.66.2.0',theory(equality)]),
% 45.80/46.18 [pos('L','L')]).
% 45.80/46.18 cnf('0.67.1.0',plain,
% 45.80/46.18 ( X1 = complement(complement(X1)) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.67.0.1']),
% 45.80/46.18 [weight('<19,37,66,[0,0,0,0]>')]).
% 45.80/46.18 cnf('0.67.2.0',plain,
% 45.80/46.18 ( complement(complement(X1)) = X1 ),
% 45.80/46.18 inference(orient,[status(thm)],['0.67.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_64]).
% 45.80/46.18 cnf('0.68.0.0',plain,
% 45.80/46.18 ( composition(X1,zero) = composition(join(one,X1),zero) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.62.2.0','0.45.2.0',theory(equality)]),
% 45.80/46.18 [pos('L','L')]).
% 45.80/46.18 cnf('0.68.0.1',plain,
% 45.80/46.18 ( composition(X1,zero) = zero ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.68.0.0','0.60.2.0',theory(equality)]),
% 45.80/46.18 [pos('R','L')]).
% 45.80/46.18 cnf('0.68.1.0',plain,
% 45.80/46.18 ( composition(X1,zero) = zero ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.68.0.1']),
% 45.80/46.18 [weight('<19,62,45,[1,0,0,0]>')]).
% 45.80/46.18 cnf('0.68.2.0',plain,
% 45.80/46.18 ( composition(X1,zero) = zero ),
% 45.80/46.18 inference(orient,[status(thm)],['0.68.1.0',theory(equality)]),
% 45.80/46.18 [u,rule_65]).
% 45.80/46.18 cnf('0.71.0.0',plain,
% 45.80/46.18 ( complement(complement(X1)) = join(X1,complement(complement(X1))) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.33.2.0','0.67.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.71.0.1',plain,
% 45.80/46.18 ( X1 = join(X1,complement(complement(X1))) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.71.0.0','0.67.2.0',theory(equality)]),
% 45.80/46.18 [pos('L','L')]).
% 45.80/46.18 cnf('0.71.0.2',plain,
% 45.80/46.18 ( X1 = join(X1,X1) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.71.0.1','0.67.2.0',theory(equality)]),
% 45.80/46.18 [pos('R.2','L')]).
% 45.80/46.18 cnf('0.71.1.0',plain,
% 45.80/46.18 ( X1 = join(X1,X1) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.71.0.2']),
% 45.80/46.18 [weight('<19,67,33,[0,0,0,1]>')]).
% 45.80/46.18 cnf('0.71.2.0',plain,
% 45.80/46.18 ( join(X1,X1) = X1 ),
% 45.80/46.18 inference(orient,[status(thm)],['0.71.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_68]).
% 45.80/46.18 cnf('0.72.0.0',plain,
% 45.80/46.18 ( complement(join(zero,complement(X1))) = meet(top,X1) ),
% 45.80/46.18 inference(interreduction_right,[status(thm)],['0.19.2.0'])).
% 45.80/46.18 cnf('0.72.0.1',plain,
% 45.80/46.18 ( complement(complement(X1)) = meet(top,X1) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.72.0.0','0.62.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.72.1.0',plain,
% 45.80/46.18 ( complement(complement(X1)) = meet(top,X1) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.72.0.1']),
% 45.80/46.18 [weight('<27,19,62,[0,0,0,0]>')]).
% 45.80/46.18 cnf('0.72.1.1',plain,
% 45.80/46.18 ( X1 = meet(top,X1) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.72.1.0','0.67.2.0',theory(equality)]),
% 45.80/46.18 [pos('L','L')]).
% 45.80/46.18 cnf('0.72.2.0',plain,
% 45.80/46.18 ( meet(top,X1) = X1 ),
% 45.80/46.18 inference(orient,[status(thm)],['0.72.1.1',theory(equality)]),
% 45.80/46.18 [x,rule_69]).
% 45.80/46.18 cnf('0.73.0.0',plain,
% 45.80/46.18 ( X1 = meet(X1,top) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.72.2.0','0.17.2.0',theory(equality)]),
% 45.80/46.18 [pos('L','L')]).
% 45.80/46.18 cnf('0.73.1.0',plain,
% 45.80/46.18 ( X1 = meet(X1,top) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.73.0.0']),
% 45.80/46.18 [weight('<19,72,17,[1,0,0,0]>')]).
% 45.80/46.18 cnf('0.73.2.0',plain,
% 45.80/46.18 ( meet(X1,top) = X1 ),
% 45.80/46.18 inference(orient,[status(thm)],['0.73.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_70]).
% 45.80/46.18 cnf('0.74.0.0',plain,
% 45.80/46.18 ( join(converse(zero),X1) = converse(converse(X1)) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.25.2.0','0.62.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.74.0.1',plain,
% 45.80/46.18 ( join(converse(zero),X1) = X1 ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.74.0.0','0.3.2.0',theory(equality)]),
% 45.80/46.18 [pos('R','L')]).
% 45.80/46.18 cnf('0.74.1.0',plain,
% 45.80/46.18 ( join(converse(zero),X1) = X1 ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.74.0.1']),
% 45.80/46.18 [weight('<29,62,25,[0,0,0,1]>')]).
% 45.80/46.18 cnf('0.74.2.0',plain,
% 45.80/46.18 ( join(converse(zero),X1) = X1 ),
% 45.80/46.18 inference(orient,[status(thm)],['0.74.1.0',theory(equality)]),
% 45.80/46.18 [u,rule_71]).
% 45.80/46.18 cnf('0.75.0.0',plain,
% 45.80/46.18 ( zero = converse(zero) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.74.2.0','0.65.2.0',theory(equality)]),
% 45.80/46.18 [pos('L','L')]).
% 45.80/46.18 cnf('0.75.1.0',plain,
% 45.80/46.18 ( zero = converse(zero) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.75.0.0']),
% 45.80/46.18 [weight('<11,74,65,[1,0,0,0]>')]).
% 45.80/46.18 cnf('0.75.2.0',plain,
% 45.80/46.18 ( converse(zero) = zero ),
% 45.80/46.18 inference(orient,[status(thm)],['0.75.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_72]).
% 45.80/46.18 cnf('0.78.0.0',plain,
% 45.80/46.18 ( converse(composition(X1,top)) = composition(top,converse(X1)) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.12.2.0','0.52.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.78.1.0',plain,
% 45.80/46.18 ( converse(composition(X1,top)) = composition(top,converse(X1)) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.78.0.0']),
% 45.80/46.18 [weight('<44,52,12,[0,0,0,1]>')]).
% 45.80/46.18 cnf('0.78.2.0',plain,
% 45.80/46.18 ( converse(composition(X1,top)) = composition(top,converse(X1)) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.78.1.0',theory(equality)]),
% 45.80/46.18 [u,rule_75]).
% 45.80/46.18 cnf('0.79.0.0',plain,
% 45.80/46.18 ( converse(composition(top,X1)) = composition(converse(X1),top) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.12.2.0','0.52.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2','L')]).
% 45.80/46.18 cnf('0.79.1.0',plain,
% 45.80/46.18 ( converse(composition(top,X1)) = composition(converse(X1),top) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.79.0.0']),
% 45.80/46.18 [weight('<44,52,12,[0,0,0,3]>')]).
% 45.80/46.18 cnf('0.79.2.0',plain,
% 45.80/46.18 ( converse(composition(top,X1)) = composition(converse(X1),top) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.79.1.0',theory(equality)]),
% 45.80/46.18 [u,rule_76]).
% 45.80/46.18 cnf('0.81.0.0',plain,
% 45.80/46.18 ( join(X1,join(X1,X2)) = join(X1,X2) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.5.2.0','0.71.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.81.1.0',plain,
% 45.80/46.18 ( join(X1,join(X1,X2)) = join(X1,X2) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.81.0.0']),
% 45.80/46.18 [weight('<53,71,5,[0,0,0,1]>')]).
% 45.80/46.18 cnf('0.81.2.0',plain,
% 45.80/46.18 ( join(X1,join(X1,X2)) = join(X1,X2) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.81.1.0',theory(equality)]),
% 45.80/46.18 [u,rule_78]).
% 45.80/46.18 cnf('0.82.0.0',plain,
% 45.80/46.18 ( join(meet(X1,X2),complement(join(complement(X1),X2))) = join(meet(X1,X2),X1) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.81.2.0','0.59.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2','L')]).
% 45.80/46.18 cnf('0.82.0.1',plain,
% 45.80/46.18 ( X1 = join(meet(X1,X2),X1) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.82.0.0','0.59.2.0',theory(equality)]),
% 45.80/46.18 [pos('L','L')]).
% 45.80/46.18 cnf('0.82.1.0',plain,
% 45.80/46.18 ( X1 = join(meet(X1,X2),X1) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.82.0.1']),
% 45.80/46.18 [weight('<41,81,59,[1,0,0,2]>')]).
% 45.80/46.18 cnf('0.82.1.1',plain,
% 45.80/46.18 ( X1 = join(X1,meet(X1,X2)) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.82.1.0','0.4.2.0',theory(equality)]),
% 45.80/46.18 [pos('R','L')]).
% 45.80/46.18 cnf('0.82.2.0',plain,
% 45.80/46.18 ( join(X1,meet(X1,X2)) = X1 ),
% 45.80/46.18 inference(orient,[status(thm)],['0.82.1.1',theory(equality)]),
% 45.80/46.18 [x,rule_79]).
% 45.80/46.18 cnf('0.83.0.0',plain,
% 45.80/46.18 ( X1 = join(X1,meet(X2,X1)) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.82.2.0','0.17.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2','L')]).
% 45.80/46.18 cnf('0.83.1.0',plain,
% 45.80/46.18 ( X1 = join(X1,meet(X2,X1)) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.83.0.0']),
% 45.80/46.18 [weight('<41,82,17,[1,0,0,2]>')]).
% 45.80/46.18 cnf('0.83.2.0',plain,
% 45.80/46.18 ( join(X1,meet(X2,X1)) = X1 ),
% 45.80/46.18 inference(orient,[status(thm)],['0.83.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_80]).
% 45.80/46.18 cnf('0.84.0.0',plain,
% 45.80/46.18 ( join(X1,X2) = join(X1,join(X2,X1)) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.81.2.0','0.4.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2','L')]).
% 45.80/46.18 cnf('0.84.1.0',plain,
% 45.80/46.18 ( join(X1,X2) = join(X1,join(X2,X1)) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.84.0.0']),
% 45.80/46.18 [weight('<53,81,4,[1,0,0,2]>')]).
% 45.80/46.18 cnf('0.84.2.0',plain,
% 45.80/46.18 ( join(X1,join(X2,X1)) = join(X1,X2) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.84.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_81]).
% 45.80/46.18 cnf('0.85.0.0',plain,
% 45.80/46.18 ( join(X1,converse(complement(converse(X1)))) = converse(top) ),
% 45.80/46.18 inference(interreduction_right,[status(thm)],['0.42.2.0'])).
% 45.80/46.18 cnf('0.85.0.1',plain,
% 45.80/46.18 ( join(X1,converse(complement(converse(X1)))) = top ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.85.0.0','0.52.2.0',theory(equality)]),
% 45.80/46.18 [pos('R','L')]).
% 45.80/46.18 cnf('0.85.1.0',plain,
% 45.80/46.18 ( join(X1,converse(complement(converse(X1)))) = top ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.85.0.1']),
% 45.80/46.18 [weight('<55,42,52,[0,0,0,0]>')]).
% 45.80/46.18 cnf('0.85.2.0',plain,
% 45.80/46.18 ( join(X1,converse(complement(converse(X1)))) = top ),
% 45.80/46.18 inference(orient,[status(thm)],['0.85.1.0',theory(equality)]),
% 45.80/46.18 [u,rule_82]).
% 45.80/46.18 cnf('0.86.0.0',plain,
% 45.80/46.18 ( join(X1,join(complement(X1),X2)) = join(top,X2) ),
% 45.80/46.18 inference(interreduction_right,[status(thm)],['0.46.2.0'])).
% 45.80/46.18 cnf('0.86.0.1',plain,
% 45.80/46.18 ( join(X1,join(complement(X1),X2)) = top ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.86.0.0','0.51.2.0',theory(equality)]),
% 45.80/46.18 [pos('R','L')]).
% 45.80/46.18 cnf('0.86.1.0',plain,
% 45.80/46.18 ( join(X1,join(complement(X1),X2)) = top ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.86.0.1']),
% 45.80/46.18 [weight('<55,46,51,[0,0,0,0]>')]).
% 45.80/46.18 cnf('0.86.2.0',plain,
% 45.80/46.18 ( join(X1,join(complement(X1),X2)) = top ),
% 45.80/46.18 inference(orient,[status(thm)],['0.86.1.0',theory(equality)]),
% 45.80/46.18 [u,rule_83]).
% 45.80/46.18 cnf('0.87.0.0',plain,
% 45.80/46.18 ( X1 = join(meet(X1,join(complement(complement(X1)),X2)),complement(top)) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.59.2.0','0.86.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2.1','L')]).
% 45.80/46.18 cnf('0.87.0.1',plain,
% 45.80/46.18 ( X1 = join(meet(X1,join(X1,X2)),complement(top)) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.87.0.0','0.67.2.0',theory(equality)]),
% 45.80/46.18 [pos('R.1.2.1','L')]).
% 45.80/46.18 cnf('0.87.0.2',plain,
% 45.80/46.18 ( X1 = join(meet(X1,join(X1,X2)),zero) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.87.0.1','0.14.2.0',theory(equality)]),
% 45.80/46.18 [pos('R.2','L')]).
% 45.80/46.18 cnf('0.87.0.3',plain,
% 45.80/46.18 ( X1 = meet(X1,join(X1,X2)) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.87.0.2','0.65.2.0',theory(equality)]),
% 45.80/46.18 [pos('R','L')]).
% 45.80/46.18 cnf('0.87.1.0',plain,
% 45.80/46.18 ( X1 = meet(X1,join(X1,X2)) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.87.0.3']),
% 45.80/46.18 [weight('<41,86,59,[0,0,0,5]>')]).
% 45.80/46.18 cnf('0.87.2.0',plain,
% 45.80/46.18 ( meet(X1,join(X1,X2)) = X1 ),
% 45.80/46.18 inference(orient,[status(thm)],['0.87.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_84]).
% 45.80/46.18 cnf('0.88.0.0',plain,
% 45.80/46.18 ( X1 = meet(X1,join(X2,X1)) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.87.2.0','0.4.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2','L')]).
% 45.80/46.18 cnf('0.88.1.0',plain,
% 45.80/46.18 ( X1 = meet(X1,join(X2,X1)) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.88.0.0']),
% 45.80/46.18 [weight('<41,87,4,[1,0,0,2]>')]).
% 45.80/46.18 cnf('0.88.2.0',plain,
% 45.80/46.18 ( meet(X1,join(X2,X1)) = X1 ),
% 45.80/46.18 inference(orient,[status(thm)],['0.88.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_85]).
% 45.80/46.18 cnf('0.90.0.0',plain,
% 45.80/46.18 ( meet(X1,X2) = meet(meet(X1,X2),X2) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.88.2.0','0.83.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2','L')]).
% 45.80/46.18 cnf('0.90.1.0',plain,
% 45.80/46.18 ( meet(X1,X2) = meet(meet(X1,X2),X2) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.90.0.0']),
% 45.80/46.18 [weight('<53,88,83,[1,0,0,2]>')]).
% 45.80/46.18 cnf('0.90.1.1',plain,
% 45.80/46.18 ( meet(X1,X2) = meet(X2,meet(X1,X2)) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.90.1.0','0.17.2.0',theory(equality)]),
% 45.80/46.18 [pos('R','L')]).
% 45.80/46.18 cnf('0.90.2.0',plain,
% 45.80/46.18 ( meet(X1,meet(X2,X1)) = meet(X2,X1) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.90.1.1',theory(equality)]),
% 45.80/46.18 [x,rule_87]).
% 45.80/46.18 cnf('0.98.0.0',plain,
% 45.80/46.18 ( join(join(complement(X1),X2),X1) = join(join(complement(X1),X2),top) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.84.2.0','0.86.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2','L')]).
% 45.80/46.18 cnf('0.98.0.1',plain,
% 45.80/46.18 ( join(complement(X1),join(X2,X1)) = join(join(complement(X1),X2),top) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.98.0.0','0.5.2.0',theory(equality)]),
% 45.80/46.18 [pos('L','L')]).
% 45.80/46.18 cnf('0.98.0.2',plain,
% 45.80/46.18 ( join(complement(X1),join(X2,X1)) = join(complement(X1),join(X2,top)) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.98.0.1','0.5.2.0',theory(equality)]),
% 45.80/46.18 [pos('R','L')]).
% 45.80/46.18 cnf('0.98.0.3',plain,
% 45.80/46.18 ( join(complement(X1),join(X2,X1)) = join(complement(X1),top) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.98.0.2','0.50.2.0',theory(equality)]),
% 45.80/46.18 [pos('R.2','L')]).
% 45.80/46.18 cnf('0.98.0.4',plain,
% 45.80/46.18 ( join(complement(X1),join(X2,X1)) = top ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.98.0.3','0.50.2.0',theory(equality)]),
% 45.80/46.18 [pos('R','L')]).
% 45.80/46.18 cnf('0.98.1.0',plain,
% 45.80/46.18 ( join(complement(X1),join(X2,X1)) = top ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.98.0.4']),
% 45.80/46.18 [weight('<55,86,84,[0,0,0,2]>')]).
% 45.80/46.18 cnf('0.98.2.0',plain,
% 45.80/46.18 ( join(complement(X1),join(X2,X1)) = top ),
% 45.80/46.18 inference(orient,[status(thm)],['0.98.1.0',theory(equality)]),
% 45.80/46.18 [u,rule_95]).
% 45.80/46.18 cnf('0.100.0.0',plain,
% 45.80/46.18 ( top = join(complement(meet(X1,X2)),X2) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.98.2.0','0.83.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2','L')]).
% 45.80/46.18 cnf('0.100.1.0',plain,
% 45.80/46.18 ( top = join(complement(meet(X1,X2)),X2) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.100.0.0']),
% 45.80/46.18 [weight('<55,98,83,[1,0,0,3]>')]).
% 45.80/46.18 cnf('0.100.1.1',plain,
% 45.80/46.18 ( top = join(X2,complement(meet(X1,X2))) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.100.1.0','0.4.2.0',theory(equality)]),
% 45.80/46.18 [pos('R','L')]).
% 45.80/46.18 cnf('0.100.2.0',plain,
% 45.80/46.18 ( join(X1,complement(meet(X2,X1))) = top ),
% 45.80/46.18 inference(orient,[status(thm)],['0.100.1.1',theory(equality)]),
% 45.80/46.18 [x,rule_97]).
% 45.80/46.18 cnf('0.102.0.0',plain,
% 45.80/46.18 ( meet(X1,meet(X2,complement(X1))) = complement(top) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.10.2.0','0.100.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.102.0.1',plain,
% 45.80/46.18 ( meet(X1,meet(X2,complement(X1))) = zero ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.102.0.0','0.14.2.0',theory(equality)]),
% 45.80/46.18 [pos('R','L')]).
% 45.80/46.18 cnf('0.102.1.0',plain,
% 45.80/46.18 ( meet(X1,meet(X2,complement(X1))) = zero ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.102.0.1']),
% 45.80/46.18 [weight('<55,100,10,[0,0,0,1]>')]).
% 45.80/46.18 cnf('0.102.2.0',plain,
% 45.80/46.18 ( meet(X1,meet(X2,complement(X1))) = zero ),
% 45.80/46.18 inference(orient,[status(thm)],['0.102.1.0',theory(equality)]),
% 45.80/46.18 [u,rule_99]).
% 45.80/46.18 cnf('0.104.0.0',plain,
% 45.80/46.18 ( zero = meet(complement(X1),meet(X2,X1)) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.102.2.0','0.67.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2.2','L')]).
% 45.80/46.18 cnf('0.104.1.0',plain,
% 45.80/46.18 ( zero = meet(complement(X1),meet(X2,X1)) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.104.0.0']),
% 45.80/46.18 [weight('<55,102,67,[1,0,0,4]>')]).
% 45.80/46.18 cnf('0.104.2.0',plain,
% 45.80/46.18 ( meet(complement(X1),meet(X2,X1)) = zero ),
% 45.80/46.18 inference(orient,[status(thm)],['0.104.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_101]).
% 45.80/46.18 cnf('0.106.0.0',plain,
% 45.80/46.18 ( zero = meet(complement(join(X1,X2)),X2) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.104.2.0','0.88.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2','L')]).
% 45.80/46.18 cnf('0.106.1.0',plain,
% 45.80/46.18 ( zero = meet(complement(join(X1,X2)),X2) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.106.0.0']),
% 45.80/46.18 [weight('<55,104,88,[1,0,0,3]>')]).
% 45.80/46.18 cnf('0.106.1.1',plain,
% 45.80/46.18 ( zero = meet(X2,complement(join(X1,X2))) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.106.1.0','0.17.2.0',theory(equality)]),
% 45.80/46.18 [pos('R','L')]).
% 45.80/46.18 cnf('0.106.2.0',plain,
% 45.80/46.18 ( meet(X1,complement(join(X2,X1))) = zero ),
% 45.80/46.18 inference(orient,[status(thm)],['0.106.1.1',theory(equality)]),
% 45.80/46.18 [x,rule_103]).
% 45.80/46.18 cnf('0.107.0.0',plain,
% 45.80/46.18 ( meet(complement(X1),X2) = complement(join(X1,complement(X2))) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.10.2.0','0.67.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1.1','L')]).
% 45.80/46.18 cnf('0.107.1.0',plain,
% 45.80/46.18 ( meet(complement(X1),X2) = complement(join(X1,complement(X2))) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.107.0.0']),
% 45.80/46.18 [weight('<59,67,10,[0,0,0,2]>')]).
% 45.80/46.18 cnf('0.107.2.0',plain,
% 45.80/46.18 ( complement(join(X1,complement(X2))) = meet(complement(X1),X2) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.107.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_104]).
% 45.80/46.18 cnf('0.108.0.0',plain,
% 45.80/46.18 ( meet(complement(X1),X2) = complement(join(complement(X2),X1)) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.107.2.0','0.4.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.108.1.0',plain,
% 45.80/46.18 ( meet(complement(X1),X2) = complement(join(complement(X2),X1)) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.108.0.0']),
% 45.80/46.18 [weight('<59,107,4,[1,0,0,1]>')]).
% 45.80/46.18 cnf('0.108.2.0',plain,
% 45.80/46.18 ( complement(join(complement(X1),X2)) = meet(complement(X2),X1) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.108.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_105]).
% 45.80/46.18 cnf('0.109.0.0',plain,
% 45.80/46.18 ( join(X1,complement(X2)) = complement(meet(complement(X1),X2)) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.67.2.0','0.107.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.109.1.0',plain,
% 45.80/46.18 ( join(X1,complement(X2)) = complement(meet(complement(X1),X2)) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.109.0.0']),
% 45.80/46.18 [weight('<59,107,67,[0,0,0,1]>')]).
% 45.80/46.18 cnf('0.109.2.0',plain,
% 45.80/46.18 ( complement(meet(complement(X1),X2)) = join(X1,complement(X2)) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.109.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_106]).
% 45.80/46.18 cnf('0.112.0.0',plain,
% 45.80/46.18 ( join(X1,complement(X2)) = complement(meet(X2,complement(X1))) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.109.2.0','0.17.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.112.1.0',plain,
% 45.80/46.18 ( join(X1,complement(X2)) = complement(meet(X2,complement(X1))) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.112.0.0']),
% 45.80/46.18 [weight('<59,109,17,[1,0,0,1]>')]).
% 45.80/46.18 cnf('0.112.2.0',plain,
% 45.80/46.18 ( complement(meet(X1,complement(X2))) = join(X2,complement(X1)) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.112.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_108]).
% 45.80/46.18 cnf('0.113.0.0',plain,
% 45.80/46.18 ( join(complement(X1),complement(X2)) = complement(meet(X1,X2)) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.109.2.0','0.67.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1.1','L')]).
% 45.80/46.18 cnf('0.113.1.0',plain,
% 45.80/46.18 ( join(complement(X1),complement(X2)) = complement(meet(X1,X2)) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.113.0.0']),
% 45.80/46.18 [weight('<59,109,67,[1,0,0,2]>')]).
% 45.80/46.18 cnf('0.113.2.0',plain,
% 45.80/46.18 ( join(complement(X1),complement(X2)) = complement(meet(X1,X2)) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.113.1.0',theory(equality)]),
% 45.80/46.18 [u,rule_109]).
% 45.80/46.18 cnf('0.120.0.0',plain,
% 45.80/46.18 ( X1 = meet(X1,composition(join(one,X2),X1)) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.87.2.0','0.45.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2','L')]).
% 45.80/46.18 cnf('0.120.1.0',plain,
% 45.80/46.18 ( X1 = meet(X1,composition(join(one,X2),X1)) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.120.0.0']),
% 45.80/46.18 [weight('<71,87,45,[1,0,0,2]>')]).
% 45.80/46.18 cnf('0.120.2.0',plain,
% 45.80/46.18 ( meet(X1,composition(join(one,X2),X1)) = X1 ),
% 45.80/46.18 inference(orient,[status(thm)],['0.120.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_116]).
% 45.80/46.18 cnf('0.121.0.0',plain,
% 45.80/46.18 ( X1 = meet(X1,composition(top,X1)) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.120.2.0','0.6.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2.1','L')]).
% 45.80/46.18 cnf('0.121.1.0',plain,
% 45.80/46.18 ( X1 = meet(X1,composition(top,X1)) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.121.0.0']),
% 45.80/46.18 [weight('<41,120,6,[1,0,0,3]>')]).
% 45.80/46.18 cnf('0.121.2.0',plain,
% 45.80/46.18 ( meet(X1,composition(top,X1)) = X1 ),
% 45.80/46.18 inference(orient,[status(thm)],['0.121.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_117]).
% 45.80/46.18 cnf('0.125.0.0',plain,
% 45.80/46.18 ( X1 = meet(X1,join(X2,join(X3,X1))) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.88.2.0','0.5.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2','L')]).
% 45.80/46.18 cnf('0.125.1.0',plain,
% 45.80/46.18 ( X1 = meet(X1,join(X2,join(X3,X1))) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.125.0.0']),
% 45.80/46.18 [weight('<71,88,5,[1,0,0,2]>')]).
% 45.80/46.18 cnf('0.125.2.0',plain,
% 45.80/46.18 ( meet(X1,join(X2,join(X3,X1))) = X1 ),
% 45.80/46.18 inference(orient,[status(thm)],['0.125.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_121]).
% 45.80/46.18 cnf('0.147.0.0',plain,
% 45.80/46.18 ( join(X1,join(meet(X1,X2),X3)) = join(X1,X3) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.5.2.0','0.82.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.147.1.0',plain,
% 45.80/46.18 ( join(X1,join(meet(X1,X2),X3)) = join(X1,X3) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.147.0.0']),
% 45.80/46.18 [weight('<87,82,5,[0,0,0,1]>')]).
% 45.80/46.18 cnf('0.147.2.0',plain,
% 45.80/46.18 ( join(X1,join(meet(X1,X2),X3)) = join(X1,X3) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.147.1.0',theory(equality)]),
% 45.80/46.18 [u,rule_143]).
% 45.80/46.18 cnf('0.152.0.0',plain,
% 45.80/46.18 ( join(X1,join(meet(X2,X1),X3)) = join(X1,X3) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.5.2.0','0.83.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.152.1.0',plain,
% 45.80/46.18 ( join(X1,join(meet(X2,X1),X3)) = join(X1,X3) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.152.0.0']),
% 45.80/46.18 [weight('<87,83,5,[0,0,0,1]>')]).
% 45.80/46.18 cnf('0.152.2.0',plain,
% 45.80/46.18 ( join(X1,join(meet(X2,X1),X3)) = join(X1,X3) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.152.1.0',theory(equality)]),
% 45.80/46.18 [u,rule_148]).
% 45.80/46.18 cnf('0.157.0.0',plain,
% 45.80/46.18 ( meet(X1,X2) = meet(meet(X1,X2),join(X3,X2)) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.125.2.0','0.83.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2.2','L')]).
% 45.80/46.18 cnf('0.157.1.0',plain,
% 45.80/46.18 ( meet(X1,X2) = meet(meet(X1,X2),join(X3,X2)) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.157.0.0']),
% 45.80/46.18 [weight('<87,125,83,[1,0,0,4]>')]).
% 45.80/46.18 cnf('0.157.2.0',plain,
% 45.80/46.18 ( meet(meet(X1,X2),join(X3,X2)) = meet(X1,X2) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.157.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_153]).
% 45.80/46.18 cnf('0.158.0.0',plain,
% 45.80/46.18 ( meet(X1,composition(top,X1)) = meet(X1,join(X2,composition(top,X1))) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.157.2.0','0.121.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.158.0.1',plain,
% 45.80/46.18 ( X1 = meet(X1,join(X2,composition(top,X1))) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.158.0.0','0.121.2.0',theory(equality)]),
% 45.80/46.18 [pos('L','L')]).
% 45.80/46.18 cnf('0.158.1.0',plain,
% 45.80/46.18 ( X1 = meet(X1,join(X2,composition(top,X1))) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.158.0.1']),
% 45.80/46.18 [weight('<71,157,121,[1,0,0,1]>')]).
% 45.80/46.18 cnf('0.158.2.0',plain,
% 45.80/46.18 ( meet(X1,join(X2,composition(top,X1))) = X1 ),
% 45.80/46.18 inference(orient,[status(thm)],['0.158.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_154]).
% 45.80/46.18 cnf('0.182.0.0',plain,
% 45.80/46.18 ( join(meet(X1,X2),complement(join(complement(X1),X2))) = X1 ),
% 45.80/46.18 inference(interreduction_right,[status(thm)],['0.59.2.0'])).
% 45.80/46.18 cnf('0.182.0.1',plain,
% 45.80/46.18 ( join(meet(X1,X2),meet(complement(X2),X1)) = X1 ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.182.0.0','0.108.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2','L')]).
% 45.80/46.18 cnf('0.182.1.0',plain,
% 45.80/46.18 ( join(meet(X1,X2),meet(complement(X2),X1)) = X1 ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.182.0.1']),
% 45.80/46.18 [weight('<89,59,108,[0,0,0,0]>')]).
% 45.80/46.18 cnf('0.182.2.0',plain,
% 45.80/46.18 ( join(meet(X1,X2),meet(complement(X2),X1)) = X1 ),
% 45.80/46.18 inference(orient,[status(thm)],['0.182.1.0',theory(equality)]),
% 45.80/46.18 [u,rule_177]).
% 45.80/46.18 cnf('0.183.0.0',plain,
% 45.80/46.18 ( join(X1,meet(complement(X1),X2)) = join(X1,X2) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.152.2.0','0.182.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2','L')]).
% 45.80/46.18 cnf('0.183.1.0',plain,
% 45.80/46.18 ( join(X1,meet(complement(X1),X2)) = join(X1,X2) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.183.0.0']),
% 45.80/46.18 [weight('<69,182,152,[0,0,0,2]>')]).
% 45.80/46.18 cnf('0.183.2.0',plain,
% 45.80/46.18 ( join(X1,meet(complement(X1),X2)) = join(X1,X2) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.183.1.0',theory(equality)]),
% 45.80/46.18 [u,rule_178]).
% 45.80/46.18 cnf('0.187.0.0',plain,
% 45.80/46.18 ( meet(complement(meet(complement(complement(X1)),X2)),X1) = complement(join(complement(X1),X2)) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.108.2.0','0.183.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.187.0.1',plain,
% 45.80/46.18 ( meet(join(complement(X1),complement(X2)),X1) = complement(join(complement(X1),X2)) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.187.0.0','0.109.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.187.0.2',plain,
% 45.80/46.18 ( meet(complement(meet(X1,X2)),X1) = complement(join(complement(X1),X2)) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.187.0.1','0.113.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.187.0.3',plain,
% 45.80/46.18 ( meet(complement(meet(X1,X2)),X1) = meet(complement(X2),X1) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.187.0.2','0.108.2.0',theory(equality)]),
% 45.80/46.18 [pos('R','L')]).
% 45.80/46.18 cnf('0.187.1.0',plain,
% 45.80/46.18 ( meet(complement(meet(X1,X2)),X1) = meet(complement(X2),X1) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.187.0.3']),
% 45.80/46.18 [weight('<76,183,108,[0,0,0,1]>')]).
% 45.80/46.18 cnf('0.187.1.1',plain,
% 45.80/46.18 ( meet(X1,complement(meet(X1,X2))) = meet(complement(X2),X1) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.187.1.0','0.17.2.0',theory(equality)]),
% 45.80/46.18 [pos('L','L')]).
% 45.80/46.18 cnf('0.187.2.0',plain,
% 45.80/46.18 ( meet(X1,complement(meet(X1,X2))) = meet(complement(X2),X1) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.187.1.1',theory(equality)]),
% 45.80/46.18 [u,rule_182]).
% 45.80/46.18 cnf('0.188.0.0',plain,
% 45.80/46.18 ( meet(complement(complement(X1)),X2) = meet(X2,join(X1,complement(X2))) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.187.2.0','0.112.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2','L')]).
% 45.80/46.18 cnf('0.188.0.1',plain,
% 45.80/46.18 ( meet(X1,X2) = meet(X2,join(X1,complement(X2))) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.188.0.0','0.67.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.188.1.0',plain,
% 45.80/46.18 ( meet(X1,X2) = meet(X2,join(X1,complement(X2))) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.188.0.1']),
% 45.80/46.18 [weight('<69,187,112,[1,0,0,2]>')]).
% 45.80/46.18 cnf('0.188.2.0',plain,
% 45.80/46.18 ( meet(X1,join(X2,complement(X1))) = meet(X2,X1) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.188.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_183]).
% 45.80/46.18 cnf('0.189.0.0',plain,
% 45.80/46.18 ( meet(X1,X2) = meet(X2,join(complement(X2),X1)) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.188.2.0','0.4.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2','L')]).
% 45.80/46.18 cnf('0.189.1.0',plain,
% 45.80/46.18 ( meet(X1,X2) = meet(X2,join(complement(X2),X1)) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.189.0.0']),
% 45.80/46.18 [weight('<69,188,4,[1,0,0,2]>')]).
% 45.80/46.18 cnf('0.189.2.0',plain,
% 45.80/46.18 ( meet(X1,join(complement(X1),X2)) = meet(X2,X1) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.189.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_184]).
% 45.80/46.18 cnf('0.190.0.0',plain,
% 45.80/46.18 ( meet(converse(complement(converse(complement(X1)))),X1) = meet(X1,top) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.189.2.0','0.85.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2','L')]).
% 45.80/46.18 cnf('0.190.0.1',plain,
% 45.80/46.18 ( meet(converse(complement(converse(complement(X1)))),X1) = X1 ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.190.0.0','0.73.2.0',theory(equality)]),
% 45.80/46.18 [pos('R','L')]).
% 45.80/46.18 cnf('0.190.1.0',plain,
% 45.80/46.18 ( meet(converse(complement(converse(complement(X1)))),X1) = X1 ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.190.0.1']),
% 45.80/46.18 [weight('<71,189,85,[1,0,0,2]>')]).
% 45.80/46.18 cnf('0.190.1.1',plain,
% 45.80/46.18 ( meet(X1,converse(complement(converse(complement(X1))))) = X1 ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.190.1.0','0.17.2.0',theory(equality)]),
% 45.80/46.18 [pos('L','L')]).
% 45.80/46.18 cnf('0.190.2.0',plain,
% 45.80/46.18 ( meet(X1,converse(complement(converse(complement(X1))))) = X1 ),
% 45.80/46.18 inference(orient,[status(thm)],['0.190.1.1',theory(equality)]),
% 45.80/46.18 [u,rule_185]).
% 45.80/46.18 cnf('0.191.0.0',plain,
% 45.80/46.18 ( join(X1,complement(converse(complement(converse(complement(complement(X1))))))) = complement(complement(X1)) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.109.2.0','0.190.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.191.0.1',plain,
% 45.80/46.18 ( join(X1,complement(converse(complement(converse(X1))))) = complement(complement(X1)) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.191.0.0','0.67.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2.1.1.1.1','L')]).
% 45.80/46.18 cnf('0.191.0.2',plain,
% 45.80/46.18 ( join(X1,complement(converse(complement(converse(X1))))) = X1 ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.191.0.1','0.67.2.0',theory(equality)]),
% 45.80/46.18 [pos('R','L')]).
% 45.80/46.18 cnf('0.191.1.0',plain,
% 45.80/46.18 ( join(X1,complement(converse(complement(converse(X1))))) = X1 ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.191.0.2']),
% 45.80/46.18 [weight('<71,190,109,[0,0,0,1]>')]).
% 45.80/46.18 cnf('0.191.2.0',plain,
% 45.80/46.18 ( join(X1,complement(converse(complement(converse(X1))))) = X1 ),
% 45.80/46.18 inference(orient,[status(thm)],['0.191.1.0',theory(equality)]),
% 45.80/46.18 [u,rule_186]).
% 45.80/46.18 cnf('0.203.0.0',plain,
% 45.80/46.18 ( join(X1,converse(complement(converse(complement(converse(converse(X1))))))) = converse(converse(X1)) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.24.2.0','0.191.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.203.0.1',plain,
% 45.80/46.18 ( join(X1,converse(complement(converse(complement(X1))))) = converse(converse(X1)) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.203.0.0','0.3.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2.1.1.1.1','L')]).
% 45.80/46.18 cnf('0.203.0.2',plain,
% 45.80/46.18 ( join(X1,converse(complement(converse(complement(X1))))) = X1 ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.203.0.1','0.3.2.0',theory(equality)]),
% 45.80/46.18 [pos('R','L')]).
% 45.80/46.18 cnf('0.203.1.0',plain,
% 45.80/46.18 ( join(X1,converse(complement(converse(complement(X1))))) = X1 ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.203.0.2']),
% 45.80/46.18 [weight('<71,191,24,[0,0,0,1]>')]).
% 45.80/46.18 cnf('0.203.2.0',plain,
% 45.80/46.18 ( join(X1,converse(complement(converse(complement(X1))))) = X1 ),
% 45.80/46.18 inference(orient,[status(thm)],['0.203.1.0',theory(equality)]),
% 45.80/46.18 [u,rule_198]).
% 45.80/46.18 cnf('0.206.0.0',plain,
% 45.80/46.18 ( meet(complement(converse(complement(converse(complement(complement(X1)))))),X1) = complement(complement(X1)) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.108.2.0','0.203.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.206.0.1',plain,
% 45.80/46.18 ( meet(complement(converse(complement(converse(X1)))),X1) = complement(complement(X1)) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.206.0.0','0.67.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1.1.1.1.1','L')]).
% 45.80/46.18 cnf('0.206.0.2',plain,
% 45.80/46.18 ( meet(complement(converse(complement(converse(X1)))),X1) = X1 ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.206.0.1','0.67.2.0',theory(equality)]),
% 45.80/46.18 [pos('R','L')]).
% 45.80/46.18 cnf('0.206.1.0',plain,
% 45.80/46.18 ( meet(complement(converse(complement(converse(X1)))),X1) = X1 ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.206.0.2']),
% 45.80/46.18 [weight('<71,203,108,[0,0,0,1]>')]).
% 45.80/46.18 cnf('0.206.1.1',plain,
% 45.80/46.18 ( meet(X1,complement(converse(complement(converse(X1))))) = X1 ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.206.1.0','0.17.2.0',theory(equality)]),
% 45.80/46.18 [pos('L','L')]).
% 45.80/46.18 cnf('0.206.2.0',plain,
% 45.80/46.18 ( meet(X1,complement(converse(complement(converse(X1))))) = X1 ),
% 45.80/46.18 inference(orient,[status(thm)],['0.206.1.1',theory(equality)]),
% 45.80/46.18 [u,rule_201]).
% 45.80/46.18 cnf('0.213.0.0',plain,
% 45.80/46.18 ( meet(X1,complement(X2)) = meet(complement(X2),join(X1,X2)) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.188.2.0','0.67.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2.2','L')]).
% 45.80/46.18 cnf('0.213.1.0',plain,
% 45.80/46.18 ( meet(X1,complement(X2)) = meet(complement(X2),join(X1,X2)) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.213.0.0']),
% 45.80/46.18 [weight('<76,188,67,[1,0,0,4]>')]).
% 45.80/46.18 cnf('0.213.2.0',plain,
% 45.80/46.18 ( meet(complement(X1),join(X2,X1)) = meet(X2,complement(X1)) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.213.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_208]).
% 45.80/46.18 cnf('0.214.0.0',plain,
% 45.80/46.18 ( meet(X1,complement(converse(complement(converse(X1))))) = meet(complement(converse(complement(converse(X1)))),top) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.213.2.0','0.85.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2','L')]).
% 45.80/46.18 cnf('0.214.0.1',plain,
% 45.80/46.18 ( X1 = meet(complement(converse(complement(converse(X1)))),top) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.214.0.0','0.206.2.0',theory(equality)]),
% 45.80/46.18 [pos('L','L')]).
% 45.80/46.18 cnf('0.214.0.2',plain,
% 45.80/46.18 ( X1 = complement(converse(complement(converse(X1)))) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.214.0.1','0.73.2.0',theory(equality)]),
% 45.80/46.18 [pos('R','L')]).
% 45.80/46.18 cnf('0.214.1.0',plain,
% 45.80/46.18 ( X1 = complement(converse(complement(converse(X1)))) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.214.0.2']),
% 45.80/46.18 [weight('<41,213,85,[1,0,0,3]>')]).
% 45.80/46.18 cnf('0.214.2.0',plain,
% 45.80/46.18 ( complement(converse(complement(converse(X1)))) = X1 ),
% 45.80/46.18 inference(orient,[status(thm)],['0.214.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_209]).
% 45.80/46.18 cnf('0.215.0.0',plain,
% 45.80/46.18 ( converse(X1) = complement(converse(complement(X1))) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.214.2.0','0.3.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1.1.1','L')]).
% 45.80/46.18 cnf('0.215.1.0',plain,
% 45.80/46.18 ( converse(X1) = complement(converse(complement(X1))) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.215.0.0']),
% 45.80/46.18 [weight('<34,214,3,[1,0,0,3]>')]).
% 45.80/46.18 cnf('0.215.2.0',plain,
% 45.80/46.18 ( complement(converse(complement(X1))) = converse(X1) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.215.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_210]).
% 45.80/46.18 cnf('0.216.0.0',plain,
% 45.80/46.18 ( converse(complement(X1)) = complement(converse(X1)) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.67.2.0','0.215.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.216.1.0',plain,
% 45.80/46.18 ( converse(complement(X1)) = complement(converse(X1)) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.216.0.0']),
% 45.80/46.18 [weight('<27,215,67,[0,0,0,1]>')]).
% 45.80/46.18 cnf('0.216.2.0',plain,
% 45.80/46.18 ( complement(converse(X1)) = converse(complement(X1)) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.216.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_211]).
% 45.80/46.18 cnf('0.218.0.0',plain,
% 45.80/46.18 ( converse(complement(composition(X1,top))) = complement(composition(top,converse(X1))) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.216.2.0','0.78.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.218.1.0',plain,
% 45.80/46.18 ( converse(complement(composition(X1,top))) = complement(composition(top,converse(X1))) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.218.0.0']),
% 45.80/46.18 [weight('<65,216,78,[1,0,0,1]>')]).
% 45.80/46.18 cnf('0.218.2.0',plain,
% 45.80/46.18 ( complement(composition(top,converse(X1))) = converse(complement(composition(X1,top))) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.218.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_213]).
% 45.80/46.18 cnf('0.219.0.0',plain,
% 45.80/46.18 ( converse(complement(composition(top,X1))) = complement(composition(converse(X1),top)) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.216.2.0','0.79.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.219.1.0',plain,
% 45.80/46.18 ( converse(complement(composition(top,X1))) = complement(composition(converse(X1),top)) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.219.0.0']),
% 45.80/46.18 [weight('<65,216,79,[1,0,0,1]>')]).
% 45.80/46.18 cnf('0.219.2.0',plain,
% 45.80/46.18 ( complement(composition(converse(X1),top)) = converse(complement(composition(top,X1))) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.219.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_214]).
% 45.80/46.18 cnf('0.225.0.0',plain,
% 45.80/46.18 ( complement(top) = join(complement(top),composition(converse(converse(X1)),converse(complement(composition(top,X1))))) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.8.2.0','0.219.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2.2','L')]).
% 45.80/46.18 cnf('0.225.0.1',plain,
% 45.80/46.18 ( zero = join(complement(top),composition(converse(converse(X1)),converse(complement(composition(top,X1))))) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.225.0.0','0.14.2.0',theory(equality)]),
% 45.80/46.18 [pos('L','L')]).
% 45.80/46.18 cnf('0.225.0.2',plain,
% 45.80/46.18 ( zero = join(zero,composition(converse(converse(X1)),converse(complement(composition(top,X1))))) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.225.0.1','0.14.2.0',theory(equality)]),
% 45.80/46.18 [pos('R.1','L')]).
% 45.80/46.18 cnf('0.225.0.3',plain,
% 45.80/46.18 ( zero = composition(converse(converse(X1)),converse(complement(composition(top,X1)))) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.225.0.2','0.62.2.0',theory(equality)]),
% 45.80/46.18 [pos('R','L')]).
% 45.80/46.18 cnf('0.225.0.4',plain,
% 45.80/46.18 ( zero = converse(composition(complement(composition(top,X1)),converse(X1))) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.225.0.3','0.12.2.0',theory(equality)]),
% 45.80/46.18 [pos('R','L')]).
% 45.80/46.18 cnf('0.225.0.5',plain,
% 45.80/46.18 ( zero = composition(X1,converse(complement(composition(top,X1)))) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.225.0.4','0.26.2.0',theory(equality)]),
% 45.80/46.18 [pos('R','L')]).
% 45.80/46.18 cnf('0.225.1.0',plain,
% 45.80/46.18 ( zero = composition(X1,converse(complement(composition(top,X1)))) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.225.0.5']),
% 45.80/46.18 [weight('<71,219,8,[0,0,0,6]>')]).
% 45.80/46.18 cnf('0.225.2.0',plain,
% 45.80/46.18 ( composition(X1,converse(complement(composition(top,X1)))) = zero ),
% 45.80/46.18 inference(orient,[status(thm)],['0.225.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_220]).
% 45.80/46.18 cnf('0.231.0.0',plain,
% 45.80/46.18 ( composition(converse(converse(complement(composition(top,converse(X1))))),X1) = converse(zero) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.27.2.0','0.225.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.231.0.1',plain,
% 45.80/46.18 ( composition(complement(composition(top,converse(X1))),X1) = converse(zero) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.231.0.0','0.3.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.231.0.2',plain,
% 45.80/46.18 ( composition(converse(complement(composition(X1,top))),X1) = converse(zero) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.231.0.1','0.218.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.231.0.3',plain,
% 45.80/46.18 ( composition(converse(complement(composition(X1,top))),X1) = zero ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.231.0.2','0.75.2.0',theory(equality)]),
% 45.80/46.18 [pos('R','L')]).
% 45.80/46.18 cnf('0.231.1.0',plain,
% 45.80/46.18 ( composition(converse(complement(composition(X1,top))),X1) = zero ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.231.0.3']),
% 45.80/46.18 [weight('<71,225,27,[0,0,0,1]>')]).
% 45.80/46.18 cnf('0.231.2.0',plain,
% 45.80/46.18 ( composition(converse(complement(composition(X1,top))),X1) = zero ),
% 45.80/46.18 inference(orient,[status(thm)],['0.231.1.0',theory(equality)]),
% 45.80/46.18 [u,rule_226]).
% 45.80/46.18 cnf('0.286.0.0',plain,
% 45.80/46.18 ( zero = meet(X1,complement(join(X2,join(X3,X1)))) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.106.2.0','0.5.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2.1','L')]).
% 45.80/46.18 cnf('0.286.1.0',plain,
% 45.80/46.18 ( zero = meet(X1,complement(join(X2,join(X3,X1)))) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.286.0.0']),
% 45.80/46.18 [weight('<89,106,5,[1,0,0,3]>')]).
% 45.80/46.18 cnf('0.286.2.0',plain,
% 45.80/46.18 ( meet(X1,complement(join(X2,join(X3,X1)))) = zero ),
% 45.80/46.18 inference(orient,[status(thm)],['0.286.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_281]).
% 45.80/46.18 cnf('0.314.0.0',plain,
% 45.80/46.18 ( complement(X1) = join(complement(X1),composition(X2,complement(composition(converse(X2),X1)))) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.8.2.0','0.3.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2.1','L')]).
% 45.80/46.18 cnf('0.314.1.0',plain,
% 45.80/46.18 ( complement(X1) = join(complement(X1),composition(X2,complement(composition(converse(X2),X1)))) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.314.0.0']),
% 45.80/46.18 [weight('<?,8,3,[1,0,0,4]>')]).
% 45.80/46.18 cnf('0.314.2.0',plain,
% 45.80/46.18 ( join(complement(X1),composition(X2,complement(composition(converse(X2),X1)))) = complement(X1) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.314.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_309]).
% 45.80/46.18 cnf('0.336.0.0',plain,
% 45.80/46.18 ( X1 = join(meet(X2,X1),meet(complement(X2),X1)) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.182.2.0','0.17.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.336.1.0',plain,
% 45.80/46.18 ( X1 = join(meet(X2,X1),meet(complement(X2),X1)) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.336.0.0']),
% 45.80/46.18 [weight('<89,182,17,[1,0,0,1]>')]).
% 45.80/46.18 cnf('0.336.2.0',plain,
% 45.80/46.18 ( join(meet(X1,X2),meet(complement(X1),X2)) = X2 ),
% 45.80/46.18 inference(orient,[status(thm)],['0.336.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_331]).
% 45.80/46.18 cnf('0.399.0.0',plain,
% 45.80/46.18 ( zero = meet(X1,meet(complement(join(X2,X1)),X3)) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.286.2.0','0.108.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2','L')]).
% 45.80/46.18 cnf('0.399.1.0',plain,
% 45.80/46.18 ( zero = meet(X1,meet(complement(join(X2,X1)),X3)) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.399.0.0']),
% 45.80/46.18 [weight('<89,286,108,[1,0,0,2]>')]).
% 45.80/46.18 cnf('0.399.2.0',plain,
% 45.80/46.18 ( meet(X1,meet(complement(join(X2,X1)),X3)) = zero ),
% 45.80/46.18 inference(orient,[status(thm)],['0.399.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_394]).
% 45.80/46.18 cnf('0.436.0.0',plain,
% 45.80/46.18 ( join(X1,converse(composition(X2,converse(X1)))) = converse(composition(join(one,X2),converse(X1))) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.24.2.0','0.45.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.436.0.1',plain,
% 45.80/46.18 ( join(X1,composition(X1,converse(X2))) = converse(composition(join(one,X2),converse(X1))) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.436.0.0','0.26.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2','L')]).
% 45.80/46.18 cnf('0.436.0.2',plain,
% 45.80/46.18 ( join(X1,composition(X1,converse(X2))) = composition(X1,converse(join(one,X2))) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.436.0.1','0.26.2.0',theory(equality)]),
% 45.80/46.18 [pos('R','L')]).
% 45.80/46.18 cnf('0.436.0.3',plain,
% 45.80/46.18 ( join(X1,composition(X1,converse(X2))) = composition(X1,join(one,converse(X2))) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.436.0.2','0.31.2.0',theory(equality)]),
% 45.80/46.18 [pos('R.2','L')]).
% 45.80/46.18 cnf('0.436.1.0',plain,
% 45.80/46.18 ( join(X1,composition(X1,converse(X2))) = composition(X1,join(one,converse(X2))) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.436.0.3']),
% 45.80/46.18 [weight('<90,45,24,[0,0,0,1]>')]).
% 45.80/46.18 cnf('0.436.2.0',plain,
% 45.80/46.18 ( join(X1,composition(X1,converse(X2))) = composition(X1,join(one,converse(X2))) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.436.1.0',theory(equality)]),
% 45.80/46.18 [u,rule_431]).
% 45.80/46.18 cnf('0.437.0.0',plain,
% 45.80/46.18 ( composition(X1,join(one,converse(converse(X2)))) = join(X1,composition(X1,X2)) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.436.2.0','0.3.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2.2','L')]).
% 45.80/46.18 cnf('0.437.0.1',plain,
% 45.80/46.18 ( composition(X1,join(one,X2)) = join(X1,composition(X1,X2)) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.437.0.0','0.3.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2.2','L')]).
% 45.80/46.18 cnf('0.437.1.0',plain,
% 45.80/46.18 ( composition(X1,join(one,X2)) = join(X1,composition(X1,X2)) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.437.0.1']),
% 45.80/46.18 [weight('<65,436,3,[1,0,0,4]>')]).
% 45.80/46.18 cnf('0.437.2.0',plain,
% 45.80/46.18 ( join(X1,composition(X1,X2)) = composition(X1,join(one,X2)) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.437.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_432]).
% 45.80/46.18 cnf('0.489.0.0',plain,
% 45.80/46.18 ( join(X1,composition(top,X2)) = join(X2,meet(complement(X2),join(X1,composition(top,X2)))) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.336.2.0','0.158.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.489.0.1',plain,
% 45.80/46.18 ( join(X1,composition(top,X2)) = join(X2,join(X1,composition(top,X2))) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.489.0.0','0.183.2.0',theory(equality)]),
% 45.80/46.18 [pos('R','L')]).
% 45.80/46.18 cnf('0.489.1.0',plain,
% 45.80/46.18 ( join(X1,composition(top,X2)) = join(X2,join(X1,composition(top,X2))) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.489.0.1']),
% 45.80/46.18 [weight('<103,336,158,[1,0,0,1]>')]).
% 45.80/46.18 cnf('0.489.2.0',plain,
% 45.80/46.18 ( join(X1,join(X2,composition(top,X1))) = join(X2,composition(top,X1)) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.489.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_484]).
% 45.80/46.18 cnf('0.494.0.0',plain,
% 45.80/46.18 ( join(X1,meet(complement(meet(X1,X2)),X3)) = join(X1,join(meet(X1,X2),X3)) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.147.2.0','0.183.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2','L')]).
% 45.80/46.18 cnf('0.494.0.1',plain,
% 45.80/46.18 ( join(X1,meet(complement(meet(X1,X2)),X3)) = join(X1,X3) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.494.0.0','0.147.2.0',theory(equality)]),
% 45.80/46.18 [pos('R','L')]).
% 45.80/46.18 cnf('0.494.1.0',plain,
% 45.80/46.18 ( join(X1,meet(complement(meet(X1,X2)),X3)) = join(X1,X3) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.494.0.1']),
% 45.80/46.18 [weight('<107,183,147,[0,0,0,2]>')]).
% 45.80/46.18 cnf('0.494.2.0',plain,
% 45.80/46.18 ( join(X1,meet(complement(meet(X1,X2)),X3)) = join(X1,X3) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.494.1.0',theory(equality)]),
% 45.80/46.18 [u,rule_489]).
% 45.80/46.18 cnf('0.502.0.0',plain,
% 45.80/46.18 ( join(X1,X2) = join(X1,meet(join(X3,complement(X1)),X2)) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.494.2.0','0.112.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2.1','L')]).
% 45.80/46.18 cnf('0.502.1.0',plain,
% 45.80/46.18 ( join(X1,X2) = join(X1,meet(join(X3,complement(X1)),X2)) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.502.0.0']),
% 45.80/46.18 [weight('<107,494,112,[1,0,0,3]>')]).
% 45.80/46.18 cnf('0.502.2.0',plain,
% 45.80/46.18 ( join(X1,meet(join(X2,complement(X1)),X3)) = join(X1,X3) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.502.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_497]).
% 45.80/46.18 cnf('0.503.0.0',plain,
% 45.80/46.18 ( meet(meet(join(X1,complement(complement(X2))),X3),X2) = meet(X2,join(complement(X2),X3)) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.189.2.0','0.502.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2','L')]).
% 45.80/46.18 cnf('0.503.0.1',plain,
% 45.80/46.18 ( meet(meet(join(X1,X2),X3),X2) = meet(X2,join(complement(X2),X3)) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.503.0.0','0.67.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1.1.2','L')]).
% 45.80/46.18 cnf('0.503.0.2',plain,
% 45.80/46.18 ( meet(meet(join(X1,X2),X3),X2) = meet(X3,X2) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.503.0.1','0.189.2.0',theory(equality)]),
% 45.80/46.18 [pos('R','L')]).
% 45.80/46.18 cnf('0.503.1.0',plain,
% 45.80/46.18 ( meet(meet(join(X1,X2),X3),X2) = meet(X3,X2) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.503.0.2']),
% 45.80/46.18 [weight('<87,502,189,[0,0,0,2]>')]).
% 45.80/46.18 cnf('0.503.1.1',plain,
% 45.80/46.18 ( meet(X2,meet(join(X1,X2),X3)) = meet(X3,X2) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.503.1.0','0.17.2.0',theory(equality)]),
% 45.80/46.18 [pos('L','L')]).
% 45.80/46.18 cnf('0.503.2.0',plain,
% 45.80/46.18 ( meet(X1,meet(join(X2,X1),X3)) = meet(X3,X1) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.503.1.1',theory(equality)]),
% 45.80/46.18 [u,rule_498]).
% 45.80/46.18 cnf('0.505.0.0',plain,
% 45.80/46.18 ( meet(X1,X2) = meet(X2,meet(X1,join(X3,X2))) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.503.2.0','0.17.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2','L')]).
% 45.80/46.18 cnf('0.505.1.0',plain,
% 45.80/46.18 ( meet(X1,X2) = meet(X2,meet(X1,join(X3,X2))) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.505.0.0']),
% 45.80/46.18 [weight('<87,503,17,[1,0,0,2]>')]).
% 45.80/46.18 cnf('0.505.2.0',plain,
% 45.80/46.18 ( meet(X1,meet(X2,join(X3,X1))) = meet(X2,X1) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.505.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_500]).
% 45.80/46.18 cnf('0.508.0.0',plain,
% 45.80/46.18 ( meet(X1,meet(X2,X3)) = meet(meet(X2,X3),meet(X3,X1)) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.503.2.0','0.83.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2.1','L')]).
% 45.80/46.18 cnf('0.508.1.0',plain,
% 45.80/46.18 ( meet(X1,meet(X2,X3)) = meet(meet(X2,X3),meet(X3,X1)) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.508.0.0']),
% 45.80/46.18 [weight('<103,503,83,[1,0,0,3]>')]).
% 45.80/46.18 cnf('0.508.2.0',plain,
% 45.80/46.18 ( meet(meet(X1,X2),meet(X2,X3)) = meet(X3,meet(X1,X2)) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.508.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_503]).
% 45.80/46.18 cnf('0.513.0.0',plain,
% 45.80/46.18 ( meet(X1,meet(X2,X3)) = meet(meet(X2,X3),meet(X1,X2)) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.505.2.0','0.82.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2.2','L')]).
% 45.80/46.18 cnf('0.513.1.0',plain,
% 45.80/46.18 ( meet(X1,meet(X2,X3)) = meet(meet(X2,X3),meet(X1,X2)) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.513.0.0']),
% 45.80/46.18 [weight('<103,505,82,[1,0,0,4]>')]).
% 45.80/46.18 cnf('0.513.2.0',plain,
% 45.80/46.18 ( meet(meet(X1,X2),meet(X3,X1)) = meet(X3,meet(X1,X2)) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.513.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_508]).
% 45.80/46.18 cnf('0.514.0.0',plain,
% 45.80/46.18 ( meet(X1,meet(X2,X3)) = meet(meet(X2,X3),meet(X1,X3)) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.505.2.0','0.83.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2.2','L')]).
% 45.80/46.18 cnf('0.514.1.0',plain,
% 45.80/46.18 ( meet(X1,meet(X2,X3)) = meet(meet(X2,X3),meet(X1,X3)) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.514.0.0']),
% 45.80/46.18 [weight('<103,505,83,[1,0,0,4]>')]).
% 45.80/46.18 cnf('0.514.2.0',plain,
% 45.80/46.18 ( meet(meet(X1,X2),meet(X3,X2)) = meet(X3,meet(X1,X2)) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.514.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_509]).
% 45.80/46.18 cnf('0.515.0.0',plain,
% 45.80/46.18 ( meet(X1,meet(X2,X3)) = meet(meet(X3,X1),meet(X2,X3)) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.508.2.0','0.17.2.0',theory(equality)]),
% 45.80/46.18 [pos('L','L')]).
% 45.80/46.18 cnf('0.515.1.0',plain,
% 45.80/46.18 ( meet(X1,meet(X2,X3)) = meet(meet(X3,X1),meet(X2,X3)) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.515.0.0']),
% 45.80/46.18 [weight('<103,508,17,[1,0,0,0]>')]).
% 45.80/46.18 cnf('0.515.1.1',plain,
% 45.80/46.18 ( meet(X1,meet(X2,X3)) = meet(X2,meet(X3,X1)) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.515.1.0','0.513.2.0',theory(equality)]),
% 45.80/46.18 [pos('R','L')]).
% 45.80/46.18 cnf('0.515.2.0',plain,
% 45.80/46.18 ( meet(X1,meet(X2,X3)) = meet(X2,meet(X3,X1)) ),
% 45.80/46.18 inference(activate,[status(thm)],['0.515.1.1']),
% 45.80/46.18 [equation_6]).
% 45.80/46.18 cnf('0.516.0.0',plain,
% 45.80/46.18 ( meet(X1,meet(X2,X3)) = meet(meet(X1,X2),X3) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.515.2.0','0.17.2.0',theory(equality)]),
% 45.80/46.18 [pos('L','L')]).
% 45.80/46.18 cnf('0.516.1.0',plain,
% 45.80/46.18 ( meet(X1,meet(X2,X3)) = meet(meet(X1,X2),X3) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.516.0.0']),
% 45.80/46.18 [weight('<65,515,17,[1,0,0,0]>')]).
% 45.80/46.18 cnf('0.516.2.0',plain,
% 45.80/46.18 ( meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.516.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_510]).
% 45.80/46.18 cnf('0.521.0.0',plain,
% 45.80/46.18 ( meet(meet(X1,X2),meet(X3,X2)) = meet(X3,meet(X1,X2)) ),
% 45.80/46.18 inference(interreduction_right,[status(thm)],['0.514.2.0'])).
% 45.80/46.18 cnf('0.521.1.0',plain,
% 45.80/46.18 ( meet(meet(X1,X2),meet(X3,X2)) = meet(X3,meet(X1,X2)) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.521.0.0']),
% 45.80/46.18 [weight('<103,514,515,[0,0,0,0]>')]).
% 45.80/46.18 cnf('0.521.1.1',plain,
% 45.80/46.18 ( meet(X1,meet(X2,meet(X3,X2))) = meet(X3,meet(X1,X2)) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.521.1.0','0.516.2.0',theory(equality)]),
% 45.80/46.18 [pos('L','L')]).
% 45.80/46.18 cnf('0.521.1.2',plain,
% 45.80/46.18 ( meet(X1,meet(X3,X2)) = meet(X3,meet(X1,X2)) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.521.1.1','0.90.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2','L')]).
% 45.80/46.18 cnf('0.521.2.0',plain,
% 45.80/46.18 ( meet(X1,meet(X2,X3)) = meet(X2,meet(X1,X3)) ),
% 45.80/46.18 inference(activate,[status(thm)],['0.521.1.2']),
% 45.80/46.18 [equation_8]).
% 45.80/46.18 cnf('0.671.0.0',plain,
% 45.80/46.18 ( composition(join(X1,converse(X2)),converse(X3)) = join(composition(X1,converse(X3)),converse(composition(X3,X2))) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.7.2.0','0.12.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2','L')]).
% 45.80/46.18 cnf('0.671.1.0',plain,
% 45.80/46.18 ( composition(join(X1,converse(X2)),converse(X3)) = join(composition(X1,converse(X3)),converse(composition(X3,X2))) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.671.0.0']),
% 45.80/46.18 [weight('<?,12,7,[0,0,0,4]>')]).
% 45.80/46.18 cnf('0.671.2.0',plain,
% 45.80/46.18 ( join(composition(X1,converse(X2)),converse(composition(X2,X3))) = composition(join(X1,converse(X3)),converse(X2)) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.671.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_663]).
% 45.80/46.18 cnf('0.714.0.0',plain,
% 45.80/46.18 ( composition(converse(X1),composition(converse(X2),X3)) = composition(converse(composition(X2,X1)),X3) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.11.2.0','0.12.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.714.1.0',plain,
% 45.80/46.18 ( composition(converse(X1),composition(converse(X2),X3)) = composition(converse(composition(X2,X1)),X3) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.714.0.0']),
% 45.80/46.18 [weight('<111,12,11,[0,0,0,1]>')]).
% 45.80/46.18 cnf('0.714.2.0',plain,
% 45.80/46.18 ( composition(converse(X1),composition(converse(X2),X3)) = composition(converse(composition(X2,X1)),X3) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.714.1.0',theory(equality)]),
% 45.80/46.18 [u,rule_706]).
% 45.80/46.18 cnf('0.721.0.0',plain,
% 45.80/46.18 ( converse(join(composition(X1,top),X2)) = join(composition(top,converse(X1)),converse(X2)) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.9.2.0','0.78.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.721.1.0',plain,
% 45.80/46.18 ( converse(join(composition(X1,top),X2)) = join(composition(top,converse(X1)),converse(X2)) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.721.0.0']),
% 45.80/46.18 [weight('<111,78,9,[0,0,0,1]>')]).
% 45.80/46.18 cnf('0.721.2.0',plain,
% 45.80/46.18 ( join(composition(top,converse(X1)),converse(X2)) = converse(join(composition(X1,top),X2)) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.721.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_713]).
% 45.80/46.18 cnf('0.855.0.0',plain,
% 45.80/46.18 ( converse(composition(join(converse(X1),X2),X3)) = composition(converse(X3),join(X1,converse(X2))) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.12.2.0','0.24.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2','L')]).
% 45.80/46.18 cnf('0.855.1.0',plain,
% 45.80/46.18 ( converse(composition(join(converse(X1),X2),X3)) = composition(converse(X3),join(X1,converse(X2))) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.855.0.0']),
% 45.80/46.18 [weight('<119,24,12,[0,0,0,3]>')]).
% 45.80/46.18 cnf('0.855.2.0',plain,
% 45.80/46.18 ( converse(composition(join(converse(X1),X2),X3)) = composition(converse(X3),join(X1,converse(X2))) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.855.1.0',theory(equality)]),
% 45.80/46.18 [u,rule_845]).
% 45.80/46.18 cnf('0.861.0.0',plain,
% 45.80/46.18 ( converse(join(composition(converse(X1),X2),X3)) = join(composition(converse(X2),X1),converse(X3)) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.9.2.0','0.27.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.861.1.0',plain,
% 45.80/46.18 ( converse(join(composition(converse(X1),X2),X3)) = join(composition(converse(X2),X1),converse(X3)) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.861.0.0']),
% 45.80/46.18 [weight('<119,27,9,[0,0,0,1]>')]).
% 45.80/46.18 cnf('0.861.2.0',plain,
% 45.80/46.18 ( converse(join(composition(converse(X1),X2),X3)) = join(composition(converse(X2),X1),converse(X3)) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.861.1.0',theory(equality)]),
% 45.80/46.18 [u,rule_851]).
% 45.80/46.18 cnf('0.862.0.0',plain,
% 45.80/46.18 ( join(composition(converse(converse(X1)),X2),converse(converse(composition(X1,X3)))) = converse(composition(join(converse(X2),converse(X3)),converse(X1))) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.861.2.0','0.671.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.862.0.1',plain,
% 45.80/46.18 ( join(composition(X1,X2),converse(converse(composition(X1,X3)))) = converse(composition(join(converse(X2),converse(X3)),converse(X1))) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.862.0.0','0.3.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1.1','L')]).
% 45.80/46.18 cnf('0.862.0.2',plain,
% 45.80/46.18 ( join(composition(X1,X2),composition(X1,X3)) = converse(composition(join(converse(X2),converse(X3)),converse(X1))) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.862.0.1','0.3.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2','L')]).
% 45.80/46.18 cnf('0.862.0.3',plain,
% 45.80/46.18 ( join(composition(X1,X2),composition(X1,X3)) = composition(converse(converse(X1)),join(X2,converse(converse(X3)))) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.862.0.2','0.855.2.0',theory(equality)]),
% 45.80/46.18 [pos('R','L')]).
% 45.80/46.18 cnf('0.862.0.4',plain,
% 45.80/46.18 ( join(composition(X1,X2),composition(X1,X3)) = composition(X1,join(X2,converse(converse(X3)))) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.862.0.3','0.3.2.0',theory(equality)]),
% 45.80/46.18 [pos('R.1','L')]).
% 45.80/46.18 cnf('0.862.0.5',plain,
% 45.80/46.18 ( join(composition(X1,X2),composition(X1,X3)) = composition(X1,join(X2,X3)) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.862.0.4','0.3.2.0',theory(equality)]),
% 45.80/46.18 [pos('R.2.2','L')]).
% 45.80/46.18 cnf('0.862.1.0',plain,
% 45.80/46.18 ( join(composition(X1,X2),composition(X1,X3)) = composition(X1,join(X2,X3)) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.862.0.5']),
% 45.80/46.18 [weight('<103,861,671,[1,0,0,1]>')]).
% 45.80/46.18 cnf('0.862.2.0',plain,
% 45.80/46.18 ( join(composition(X1,X2),composition(X1,X3)) = composition(X1,join(X2,X3)) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.862.1.0',theory(equality)]),
% 45.80/46.18 [u,rule_852]).
% 45.80/46.18 cnf('0.867.0.0',plain,
% 45.80/46.18 ( composition(join(one,composition(X1,X2)),X3) = join(X3,composition(X1,composition(X2,X3))) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.45.2.0','0.11.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2','L')]).
% 45.80/46.18 cnf('0.867.1.0',plain,
% 45.80/46.18 ( composition(join(one,composition(X1,X2)),X3) = join(X3,composition(X1,composition(X2,X3))) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.867.0.0']),
% 45.80/46.18 [weight('<119,45,11,[1,0,0,2]>')]).
% 45.80/46.18 cnf('0.867.2.0',plain,
% 45.80/46.18 ( join(X1,composition(X2,composition(X3,X1))) = composition(join(one,composition(X2,X3)),X1) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.867.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_857]).
% 45.80/46.18 cnf('0.961.0.0',plain,
% 45.80/46.18 ( composition(join(one,composition(X1,X2)),X1) = composition(X1,join(one,composition(X2,X1))) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.867.2.0','0.437.2.0',theory(equality)]),
% 45.80/46.18 [pos('L','L')]).
% 45.80/46.18 cnf('0.961.1.0',plain,
% 45.80/46.18 ( composition(join(one,composition(X1,X2)),X1) = composition(X1,join(one,composition(X2,X1))) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.961.0.0']),
% 45.80/46.18 [weight('<119,867,437,[1,0,0,0]>')]).
% 45.80/46.18 cnf('0.961.2.0',plain,
% 45.80/46.18 ( composition(join(one,composition(X1,X2)),X1) = composition(X1,join(one,composition(X2,X1))) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.961.1.0',theory(equality)]),
% 45.80/46.18 [u,rule_950]).
% 45.80/46.18 cnf('0.968.0.0',plain,
% 45.80/46.18 ( join(X1,join(meet(complement(X1),X2),X3)) = join(join(X1,X2),X3) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.5.2.0','0.183.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.968.0.1',plain,
% 45.80/46.18 ( join(X1,join(meet(complement(X1),X2),X3)) = join(X1,join(X2,X3)) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.968.0.0','0.5.2.0',theory(equality)]),
% 45.80/46.18 [pos('R','L')]).
% 45.80/46.18 cnf('0.968.1.0',plain,
% 45.80/46.18 ( join(X1,join(meet(complement(X1),X2),X3)) = join(X1,join(X2,X3)) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.968.0.1']),
% 45.80/46.18 [weight('<125,183,5,[0,0,0,1]>')]).
% 45.80/46.18 cnf('0.968.2.0',plain,
% 45.80/46.18 ( join(X1,join(meet(complement(X1),X2),X3)) = join(X1,join(X2,X3)) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.968.1.0',theory(equality)]),
% 45.80/46.18 [u,rule_956]).
% 45.80/46.18 cnf('0.969.0.0',plain,
% 45.80/46.18 ( meet(join(meet(complement(complement(X1)),X2),X3),X1) = meet(X1,join(complement(X1),join(X2,X3))) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.189.2.0','0.968.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2','L')]).
% 45.80/46.18 cnf('0.969.0.1',plain,
% 45.80/46.18 ( meet(join(meet(X1,X2),X3),X1) = meet(X1,join(complement(X1),join(X2,X3))) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.969.0.0','0.67.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1.1.1','L')]).
% 45.80/46.18 cnf('0.969.0.2',plain,
% 45.80/46.18 ( meet(join(meet(X1,X2),X3),X1) = meet(join(X2,X3),X1) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.969.0.1','0.189.2.0',theory(equality)]),
% 45.80/46.18 [pos('R','L')]).
% 45.80/46.18 cnf('0.969.1.0',plain,
% 45.80/46.18 ( meet(join(meet(X1,X2),X3),X1) = meet(join(X2,X3),X1) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.969.0.2']),
% 45.80/46.18 [weight('<103,968,189,[0,0,0,2]>')]).
% 45.80/46.18 cnf('0.969.1.1',plain,
% 45.80/46.18 ( meet(X1,join(meet(X1,X2),X3)) = meet(join(X2,X3),X1) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.969.1.0','0.17.2.0',theory(equality)]),
% 45.80/46.18 [pos('L','L')]).
% 45.80/46.18 cnf('0.969.2.0',plain,
% 45.80/46.18 ( meet(X1,join(meet(X1,X2),X3)) = meet(join(X2,X3),X1) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.969.1.1',theory(equality)]),
% 45.80/46.18 [u,rule_957]).
% 45.80/46.18 cnf('0.971.0.0',plain,
% 45.80/46.18 ( meet(join(X1,X2),X3) = meet(X3,join(meet(X1,X3),X2)) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.969.2.0','0.17.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2.1','L')]).
% 45.80/46.18 cnf('0.971.1.0',plain,
% 45.80/46.18 ( meet(join(X1,X2),X3) = meet(X3,join(meet(X1,X3),X2)) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.971.0.0']),
% 45.80/46.18 [weight('<103,969,0,[1,0,0,3]>')]).
% 45.80/46.18 cnf('0.971.2.0',plain,
% 45.80/46.18 ( meet(X1,join(meet(X2,X1),X3)) = meet(join(X2,X3),X1) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.971.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_959]).
% 45.80/46.18 cnf('0.1005.0.0',plain,
% 45.80/46.18 ( join(X1,X2) = meet(join(X1,X2),join(X1,join(X2,X3))) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.87.2.0','0.5.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2','L')]).
% 45.80/46.18 cnf('0.1005.1.0',plain,
% 45.80/46.18 ( join(X1,X2) = meet(join(X1,X2),join(X1,join(X2,X3))) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.1005.0.0']),
% 45.80/46.18 [weight('<129,87,5,[1,0,0,2]>')]).
% 45.80/46.18 cnf('0.1005.2.0',plain,
% 45.80/46.18 ( meet(join(X1,X2),join(X1,join(X2,X3))) = join(X1,X2) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.1005.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_993]).
% 45.80/46.18 cnf('0.1121.0.0',plain,
% 45.80/46.18 ( composition(join(converse(complement(composition(X1,top))),X2),X1) = join(zero,composition(X2,X1)) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.7.2.0','0.231.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.1121.0.1',plain,
% 45.80/46.18 ( composition(join(converse(complement(composition(X1,top))),X2),X1) = composition(X2,X1) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.1121.0.0','0.62.2.0',theory(equality)]),
% 45.80/46.18 [pos('R','L')]).
% 45.80/46.18 cnf('0.1121.1.0',plain,
% 45.80/46.18 ( composition(join(converse(complement(composition(X1,top))),X2),X1) = composition(X2,X1) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.1121.0.1']),
% 45.80/46.18 [weight('<129,231,7,[0,0,0,1]>')]).
% 45.80/46.18 cnf('0.1121.2.0',plain,
% 45.80/46.18 ( composition(join(converse(complement(composition(X1,top))),X2),X1) = composition(X2,X1) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.1121.1.0',theory(equality)]),
% 45.80/46.18 [u,rule_1109]).
% 45.80/46.18 cnf('0.1126.0.0',plain,
% 45.80/46.18 ( composition(join(complement(converse(complement(composition(X1,top)))),X2),X1) = composition(top,X1) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.1121.2.0','0.86.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.1126.0.1',plain,
% 45.80/46.18 ( composition(join(converse(complement(complement(composition(X1,top)))),X2),X1) = composition(top,X1) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.1126.0.0','0.216.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1.1','L')]).
% 45.80/46.18 cnf('0.1126.0.2',plain,
% 45.80/46.18 ( composition(join(converse(composition(X1,top)),X2),X1) = composition(top,X1) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.1126.0.1','0.67.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1.1.1','L')]).
% 45.80/46.18 cnf('0.1126.0.3',plain,
% 45.80/46.18 ( composition(join(composition(top,converse(X1)),X2),X1) = composition(top,X1) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.1126.0.2','0.78.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1.1','L')]).
% 45.80/46.18 cnf('0.1126.1.0',plain,
% 45.80/46.18 ( composition(join(composition(top,converse(X1)),X2),X1) = composition(top,X1) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.1126.0.3']),
% 45.80/46.18 [weight('<107,1121,86,[1,0,0,1]>')]).
% 45.80/46.18 cnf('0.1126.2.0',plain,
% 45.80/46.18 ( composition(join(composition(top,converse(X1)),X2),X1) = composition(top,X1) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.1126.1.0',theory(equality)]),
% 45.80/46.18 [u,rule_1114]).
% 45.80/46.18 cnf('0.1135.0.0',plain,
% 45.80/46.18 ( composition(top,X1) = composition(converse(join(composition(X1,top),X2)),X1) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.1126.2.0','0.721.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.1135.1.0',plain,
% 45.80/46.18 ( composition(top,X1) = composition(converse(join(composition(X1,top),X2)),X1) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.1135.0.0']),
% 45.80/46.18 [weight('<107,1126,721,[1,0,0,1]>')]).
% 45.80/46.18 cnf('0.1135.2.0',plain,
% 45.80/46.18 ( composition(converse(join(composition(X1,top),X2)),X1) = composition(top,X1) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.1135.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_1123]).
% 45.80/46.18 cnf('0.1143.0.0',plain,
% 45.80/46.18 ( composition(top,X1) = composition(converse(composition(join(X1,X2),top)),X1) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.1135.2.0','0.7.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1.1','L')]).
% 45.80/46.18 cnf('0.1143.0.1',plain,
% 45.80/46.18 ( composition(top,X1) = composition(composition(top,converse(join(X1,X2))),X1) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.1143.0.0','0.78.2.0',theory(equality)]),
% 45.80/46.18 [pos('R.1','L')]).
% 45.80/46.18 cnf('0.1143.0.2',plain,
% 45.80/46.18 ( composition(top,X1) = composition(top,composition(converse(join(X1,X2)),X1)) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.1143.0.1','0.11.2.0',theory(equality)]),
% 45.80/46.18 [pos('R','L')]).
% 45.80/46.18 cnf('0.1143.1.0',plain,
% 45.80/46.18 ( composition(top,X1) = composition(top,composition(converse(join(X1,X2)),X1)) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.1143.0.2']),
% 45.80/46.18 [weight('<107,1135,7,[1,0,0,2]>')]).
% 45.80/46.18 cnf('0.1143.2.0',plain,
% 45.80/46.18 ( composition(top,composition(converse(join(X1,X2)),X1)) = composition(top,X1) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.1143.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_1131]).
% 45.80/46.18 cnf('0.1205.0.0',plain,
% 45.80/46.18 ( composition(top,meet(X1,X2)) = composition(top,composition(converse(X1),meet(X1,X2))) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.1143.2.0','0.182.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2.1.1','L')]).
% 45.80/46.18 cnf('0.1205.1.0',plain,
% 45.80/46.18 ( composition(top,meet(X1,X2)) = composition(top,composition(converse(X1),meet(X1,X2))) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.1205.0.0']),
% 45.80/46.18 [weight('<125,1143,182,[1,0,0,4]>')]).
% 45.80/46.18 cnf('0.1205.2.0',plain,
% 45.80/46.18 ( composition(top,composition(converse(X1),meet(X1,X2))) = composition(top,meet(X1,X2)) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.1205.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_1192]).
% 45.80/46.18 cnf('0.1326.0.0',plain,
% 45.80/46.18 ( composition(X1,X2) = meet(composition(X1,X2),composition(X1,join(X3,X2))) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.88.2.0','0.862.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2','L')]).
% 45.80/46.18 cnf('0.1326.1.0',plain,
% 45.80/46.18 ( composition(X1,X2) = meet(composition(X1,X2),composition(X1,join(X3,X2))) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.1326.0.0']),
% 45.80/46.18 [weight('<129,862,88,[0,0,0,2]>')]).
% 45.80/46.18 cnf('0.1326.2.0',plain,
% 45.80/46.18 ( meet(composition(X1,X2),composition(X1,join(X3,X2))) = composition(X1,X2) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.1326.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_1313]).
% 45.80/46.18 cnf('0.1349.0.0',plain,
% 45.80/46.18 ( join(X1,X2) = meet(join(X1,X2),join(X2,composition(top,X1))) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.1005.2.0','0.489.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2','L')]).
% 45.80/46.18 cnf('0.1349.1.0',plain,
% 45.80/46.18 ( join(X1,X2) = meet(join(X1,X2),join(X2,composition(top,X1))) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.1349.0.0']),
% 45.80/46.18 [weight('<129,1005,489,[1,0,0,4]>')]).
% 45.80/46.18 cnf('0.1349.2.0',plain,
% 45.80/46.18 ( meet(join(X1,X2),join(X2,composition(top,X1))) = join(X1,X2) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.1349.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_1336]).
% 45.80/46.18 cnf('0.2766.0.0',plain,
% 45.80/46.18 ( join(meet(X1,X2),meet(complement(X2),X1)) = meet(X1,join(meet(complement(X2),X1),composition(top,meet(X1,X2)))) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.1349.2.0','0.182.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.1','L')]).
% 45.80/46.18 cnf('0.2766.0.1',plain,
% 45.80/46.18 ( X1 = meet(X1,join(meet(complement(X2),X1),composition(top,meet(X1,X2)))) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.2766.0.0','0.182.2.0',theory(equality)]),
% 45.80/46.18 [pos('L','L')]).
% 45.80/46.18 cnf('0.2766.0.2',plain,
% 45.80/46.18 ( X1 = meet(join(complement(X2),composition(top,meet(X1,X2))),X1) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.2766.0.1','0.971.2.0',theory(equality)]),
% 45.80/46.18 [pos('R','L')]).
% 45.80/46.18 cnf('0.2766.1.0',plain,
% 45.80/46.18 ( X1 = meet(join(complement(X2),composition(top,meet(X1,X2))),X1) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.2766.0.2']),
% 45.80/46.18 [weight('<131,1349,182,[1,0,0,1]>')]).
% 45.80/46.18 cnf('0.2766.1.1',plain,
% 45.80/46.18 ( X1 = meet(X1,join(complement(X2),composition(top,meet(X1,X2)))) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.2766.1.0','0.17.2.0',theory(equality)]),
% 45.80/46.18 [pos('R','L')]).
% 45.80/46.18 cnf('0.2766.2.0',plain,
% 45.80/46.18 ( meet(X1,join(complement(X2),composition(top,meet(X1,X2)))) = X1 ),
% 45.80/46.18 inference(orient,[status(thm)],['0.2766.1.1',theory(equality)]),
% 45.80/46.18 [x,rule_2746]).
% 45.80/46.18 cnf('0.4541.0.0',plain,
% 45.80/46.18 ( composition(X1,meet(X2,X3)) = meet(composition(X1,meet(X2,X3)),composition(X1,X2)) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.1326.2.0','0.82.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2.2','L')]).
% 45.80/46.18 cnf('0.4541.1.0',plain,
% 45.80/46.18 ( composition(X1,meet(X2,X3)) = meet(composition(X1,meet(X2,X3)),composition(X1,X2)) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.4541.0.0']),
% 45.80/46.18 [weight('<149,1326,82,[1,0,0,6]>')]).
% 45.80/46.18 cnf('0.4541.1.1',plain,
% 45.80/46.18 ( composition(X1,meet(X2,X3)) = meet(composition(X1,X2),composition(X1,meet(X2,X3))) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.4541.1.0','0.17.2.0',theory(equality)]),
% 45.80/46.18 [pos('R','L')]).
% 45.80/46.18 cnf('0.4541.2.0',plain,
% 45.80/46.18 ( meet(composition(X1,X2),composition(X1,meet(X2,X3))) = composition(X1,meet(X2,X3)) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.4541.1.1',theory(equality)]),
% 45.80/46.18 [x,rule_4515]).
% 45.80/46.18 cnf('0.4546.0.0',plain,
% 45.80/46.18 ( composition(X1,meet(X2,X3)) = meet(composition(X1,meet(X2,X3)),composition(X1,X3)) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.1326.2.0','0.83.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2.2','L')]).
% 45.80/46.18 cnf('0.4546.1.0',plain,
% 45.80/46.18 ( composition(X1,meet(X2,X3)) = meet(composition(X1,meet(X2,X3)),composition(X1,X3)) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.4546.0.0']),
% 45.80/46.18 [weight('<149,1326,83,[1,0,0,6]>')]).
% 45.80/46.18 cnf('0.4546.1.1',plain,
% 45.80/46.18 ( composition(X1,meet(X2,X3)) = meet(composition(X1,X3),composition(X1,meet(X2,X3))) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.4546.1.0','0.17.2.0',theory(equality)]),
% 45.80/46.18 [pos('R','L')]).
% 45.80/46.18 cnf('0.4546.2.0',plain,
% 45.80/46.18 ( meet(composition(X1,X2),composition(X1,meet(X3,X2))) = composition(X1,meet(X3,X2)) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.4546.1.1',theory(equality)]),
% 45.80/46.18 [x,rule_4520]).
% 45.80/46.18 cnf('0.6380.0.0',plain,
% 45.80/46.18 ( zero = meet(composition(X1,complement(composition(converse(X1),X2))),meet(complement(complement(X2)),X3)) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.399.2.0','0.314.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2.1.1','L')]).
% 45.80/46.18 cnf('0.6380.0.1',plain,
% 45.80/46.18 ( zero = meet(composition(X1,complement(composition(converse(X1),X2))),meet(X2,X3)) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.6380.0.0','0.67.2.0',theory(equality)]),
% 45.80/46.18 [pos('R.2.1','L')]).
% 45.80/46.18 cnf('0.6380.1.0',plain,
% 45.80/46.18 ( zero = meet(composition(X1,complement(composition(converse(X1),X2))),meet(X2,X3)) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.6380.0.1']),
% 45.80/46.18 [weight('<155,399,314,[1,0,0,4]>')]).
% 45.80/46.18 cnf('0.6380.1.1',plain,
% 45.80/46.18 ( zero = meet(X2,meet(composition(X1,complement(composition(converse(X1),X2))),X3)) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.6380.1.0','0.521.2.0',theory(equality)]),
% 45.80/46.18 [pos('R','L')]).
% 45.80/46.18 cnf('0.6380.2.0',plain,
% 45.80/46.18 ( meet(X1,meet(composition(X2,complement(composition(converse(X2),X1))),X3)) = zero ),
% 45.80/46.18 inference(orient,[status(thm)],['0.6380.1.1',theory(equality)]),
% 45.80/46.18 [x,rule_6324]).
% 45.80/46.18 cnf('0.9372.0.0',plain,
% 45.80/46.18 ( zero = meet(X1,composition(X2,meet(complement(composition(converse(X2),X1)),X3))) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.6380.2.0','0.4541.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2','L')]).
% 45.80/46.18 cnf('0.9372.1.0',plain,
% 45.80/46.18 ( zero = meet(X1,composition(X2,meet(complement(composition(converse(X2),X1)),X3))) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.9372.0.0']),
% 45.80/46.18 [weight('<155,6380,4541,[1,0,0,2]>')]).
% 45.80/46.18 cnf('0.9372.2.0',plain,
% 45.80/46.18 ( meet(X1,composition(X2,meet(complement(composition(converse(X2),X1)),X3))) = zero ),
% 45.80/46.18 inference(orient,[status(thm)],['0.9372.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_9314]).
% 45.80/46.18 cnf('0.10150.0.0',plain,
% 45.80/46.18 ( zero = composition(X1,meet(complement(composition(converse(X1),composition(X1,X2))),X2)) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.9372.2.0','0.4546.2.0',theory(equality)]),
% 45.80/46.18 [pos('L','L')]).
% 45.80/46.18 cnf('0.10150.1.0',plain,
% 45.80/46.18 ( zero = composition(X1,meet(complement(composition(converse(X1),composition(X1,X2))),X2)) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.10150.0.0']),
% 45.80/46.18 [weight('<155,9372,4546,[1,0,0,0]>')]).
% 45.80/46.18 cnf('0.10150.1.1',plain,
% 45.80/46.18 ( zero = composition(X1,meet(X2,complement(composition(converse(X1),composition(X1,X2))))) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.10150.1.0','0.17.2.0',theory(equality)]),
% 45.80/46.18 [pos('R.2','L')]).
% 45.80/46.18 cnf('0.10150.2.0',plain,
% 45.80/46.18 ( composition(X1,meet(X2,complement(composition(converse(X1),composition(X1,X2))))) = zero ),
% 45.80/46.18 inference(orient,[status(thm)],['0.10150.1.1',theory(equality)]),
% 45.80/46.18 [x,rule_10092]).
% 45.80/46.18 cnf('0.10499.0.0',plain,
% 45.80/46.18 ( composition(top,meet(X1,complement(composition(converse(converse(X1)),composition(converse(X1),X1))))) = composition(top,zero) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.1205.2.0','0.10150.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2','L')]).
% 45.80/46.18 cnf('0.10499.0.1',plain,
% 45.80/46.18 ( composition(top,meet(X1,complement(composition(converse(composition(X1,converse(X1))),X1)))) = composition(top,zero) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.10499.0.0','0.714.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2.2.1','L')]).
% 45.80/46.18 cnf('0.10499.0.2',plain,
% 45.80/46.18 ( composition(top,meet(X1,complement(composition(composition(X1,converse(X1)),X1)))) = composition(top,zero) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.10499.0.1','0.26.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2.2.1.1','L')]).
% 45.80/46.18 cnf('0.10499.0.3',plain,
% 45.80/46.18 ( composition(top,meet(X1,complement(composition(X1,composition(converse(X1),X1))))) = composition(top,zero) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.10499.0.2','0.11.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2.2.1','L')]).
% 45.80/46.18 cnf('0.10499.0.4',plain,
% 45.80/46.18 ( composition(top,meet(X1,complement(composition(X1,composition(converse(X1),X1))))) = zero ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.10499.0.3','0.68.2.0',theory(equality)]),
% 45.80/46.18 [pos('R','L')]).
% 45.80/46.18 cnf('0.10499.1.0',plain,
% 45.80/46.18 ( composition(top,meet(X1,complement(composition(X1,composition(converse(X1),X1))))) = zero ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.10499.0.4']),
% 45.80/46.18 [weight('<155,10150,1205,[0,0,0,2]>')]).
% 45.80/46.18 cnf('0.10499.2.0',plain,
% 45.80/46.18 ( composition(top,meet(X1,complement(composition(X1,composition(converse(X1),X1))))) = zero ),
% 45.80/46.18 inference(orient,[status(thm)],['0.10499.1.0',theory(equality)]),
% 45.80/46.18 [u,rule_10441]).
% 45.80/46.18 cnf('0.10500.0.0',plain,
% 45.80/46.18 ( X1 = meet(X1,join(complement(complement(composition(X1,composition(converse(X1),X1)))),zero)) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.2766.2.0','0.10499.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2.2','L')]).
% 45.80/46.18 cnf('0.10500.0.1',plain,
% 45.80/46.18 ( X1 = meet(X1,complement(complement(composition(X1,composition(converse(X1),X1))))) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.10500.0.0','0.65.2.0',theory(equality)]),
% 45.80/46.18 [pos('R.2','L')]).
% 45.80/46.18 cnf('0.10500.0.2',plain,
% 45.80/46.18 ( X1 = meet(X1,composition(X1,composition(converse(X1),X1))) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.10500.0.1','0.67.2.0',theory(equality)]),
% 45.80/46.18 [pos('R.2','L')]).
% 45.80/46.18 cnf('0.10500.1.0',plain,
% 45.80/46.18 ( X1 = meet(X1,composition(X1,composition(converse(X1),X1))) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.10500.0.2']),
% 45.80/46.18 [weight('<89,10499,2766,[0,0,0,5]>')]).
% 45.80/46.18 cnf('0.10500.2.0',plain,
% 45.80/46.18 ( meet(X1,composition(X1,composition(converse(X1),X1))) = X1 ),
% 45.80/46.18 inference(orient,[status(thm)],['0.10500.1.0',theory(equality)]),
% 45.80/46.18 [x,rule_10442]).
% 45.80/46.18 cnf('0.10504.0.0',plain,
% 45.80/46.18 ( composition(X1,composition(converse(X1),X1)) = join(composition(X1,composition(converse(X1),X1)),X1) ),
% 45.80/46.18 inference(cp,[status(thm)],['0.83.2.0','0.10500.2.0',theory(equality)]),
% 45.80/46.18 [pos('L.2','L')]).
% 45.80/46.18 cnf('0.10504.1.0',plain,
% 45.80/46.18 ( composition(X1,composition(converse(X1),X1)) = join(composition(X1,composition(converse(X1),X1)),X1) ),
% 45.80/46.18 inference(weigh,[status(thm)],['0.10504.0.0']),
% 45.80/46.18 [weight('<134,10500,83,[0,0,0,2]>')]).
% 45.80/46.18 cnf('0.10504.1.1',plain,
% 45.80/46.18 ( composition(X1,composition(converse(X1),X1)) = join(X1,composition(X1,composition(converse(X1),X1))) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.10504.1.0','0.4.2.0',theory(equality)]),
% 45.80/46.18 [pos('R','L')]).
% 45.80/46.18 cnf('0.10504.1.2',plain,
% 45.80/46.18 ( composition(X1,composition(converse(X1),X1)) = composition(join(one,composition(X1,converse(X1))),X1) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.10504.1.1','0.867.2.0',theory(equality)]),
% 45.80/46.18 [pos('R','L')]).
% 45.80/46.18 cnf('0.10504.1.3',plain,
% 45.80/46.18 ( composition(X1,composition(converse(X1),X1)) = composition(X1,join(one,composition(converse(X1),X1))) ),
% 45.80/46.18 inference(reduction,[status(thm)],['0.10504.1.2','0.961.2.0',theory(equality)]),
% 45.80/46.18 [pos('R','L')]).
% 45.80/46.18 cnf('0.10504.2.0',plain,
% 45.80/46.18 ( composition(X1,join(one,composition(converse(X1),X1))) = composition(X1,composition(converse(X1),X1)) ),
% 45.80/46.18 inference(orient,[status(thm)],['0.10504.1.3',theory(equality)]),
% 45.80/46.18 [x,rule_10446]).
% 45.80/46.18 cnf('1.0.0.0',conjecture,
% 45.80/46.18 ( join(sk1,composition(composition(sk1,converse(sk1)),sk1)) = composition(composition(sk1,converse(sk1)),sk1) ),
% 45.80/46.18 file('/tmp/WALDMEISTER_5833_n013',conjecture_1)).
% 45.80/46.18 cnf('1.0.0.1',plain,
% 45.80/46.18 ( join(sk1,composition(composition(sk1,converse(sk1)),sk1)) = composition(sk1,composition(converse(sk1),sk1)) ),
% 45.80/46.18 inference(reduction,[status(thm)],['1.0.0.0','0.11.2.0',theory(equality)]),
% 45.80/46.18 [pos('R','L')]).
% 45.80/46.18 cnf('1.0.0.2',plain,
% 45.80/46.18 ( composition(join(one,composition(sk1,converse(sk1))),sk1) = composition(sk1,composition(converse(sk1),sk1)) ),
% 45.80/46.18 inference(reduction,[status(thm)],['1.0.0.1','0.45.2.0',theory(equality)]),
% 45.80/46.18 [pos('L','L')]).
% 45.80/46.18 cnf('1.0.0.3',plain,
% 45.80/46.18 ( composition(sk1,join(one,composition(converse(sk1),sk1))) = composition(sk1,composition(converse(sk1),sk1)) ),
% 45.80/46.18 inference(reduction,[status(thm)],['1.0.0.2','0.961.2.0',theory(equality)]),
% 45.80/46.18 [pos('L','L')]).
% 45.80/46.18 cnf('1.0.0.4',plain,
% 45.80/46.18 ( composition(sk1,composition(converse(sk1),sk1)) = composition(sk1,composition(converse(sk1),sk1)) ),
% 45.80/46.18 inference(reduction,[status(thm)],['1.0.0.3','0.10504.2.0',theory(equality)]),
% 45.80/46.18 [pos('L','L')]).
% 45.80/46.18 cnf('1.0.0.5',plain,
% 45.80/46.18 ( $true ),
% 45.80/46.18 inference(trivial,[status(thm)],['1.0.0.4',theory(equality)]),
% 45.80/46.18 [conjecture_1]).
% 45.80/46.18
% 45.80/46.18 Proved Goals:
% 45.80/46.18 No. 1: join(sk1,composition(composition(sk1,converse(sk1)),sk1)) ?= composition(composition(sk1,converse(sk1)),sk1) joined, current: composition(sk1,composition(converse(sk1),sk1)) = composition(sk1,composition(converse(sk1),sk1))
% 45.80/46.18 1 goal was specified, which was proved.
% 45.80/46.18 % SZS output end CNFRefutation
% 45.80/46.18 #END OF PROOF
% 45.80/46.18
% 45.80/46.18 Problem WALDMEISTER_5833_n013
% 45.80/46.18 CPs.gen 18319099
% 45.80/46.18 CPs.reexp 0
% 45.80/46.18 Select 702667
% 45.80/46.18 R 10446
% 45.80/46.18 E 58
% 45.80/46.18 vsize 15.5M
% 45.80/46.18 rss 10.9M
% 45.80/46.18 process.time 45.182s
% 45.80/46.18 wallclock.time 45.179s
% 45.80/46.18 status S
% 45.80/46.18
% 45.80/46.18
% 45.80/46.18 Waldmeister states: Goal proved.
% 45.80/46.18 % SZS status Unsatisfiable
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